Method and system for predicting chemical reaction pathways

Abstract

A computer-aided method for determining a reaction pathway may include: (a) providing instructions for reactants and products or at least one of drive coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting the reactants and products or at least one of drive coordinates; (c) using a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) determining a reliability index in the conformational coordinates; and optionally (e) evaluating first-principles energy or first-principles force in the conformational coordinates.

Description

Technical Field

[0001] Cross-reference This application claims the priority of U.S. Provisional Application No. 63 / 496,668, filed on April 17, 2023, the content of which is incorporated herein by reference for all purposes.

Background Art

[0002] Chemical reactions are an essential process in creating molecules and substances. Therefore, predicting chemical reactions has important value in the discovery process of new molecules and substances in a wide range of industries such as pharmaceuticals, advanced materials, and energy industries. Computational chemistry is an established tool for predicting chemical reaction pathways.

[0003] The situations in which researchers attempt to predict chemical reactions are diverse. As a first example, researchers may want to know whether the molecules (reactants) they possess can cause a chemical reaction, and if so, what reaction pathways those molecules will follow and / or what products will be obtained as a result of the chemical reaction. As a second example, researchers may already know the products as well as the molecules (reactants) that cause the chemical reaction, but may want to know the characteristics of the potential energy surface that defines the reaction, such as the reaction pathway and / or the activation barrier.

[0004] In either example, the above computational methods can generate intermediate molecular geometries that start from reactants and lead to the geometric structures of potential products.

Summary of the Invention

[0005] Numerous methods exist for determining intermediate molecular geometry in chemical reactions and tracking molecular trajectories. However, such calculations can be computationally expensive and / or inaccurate. Accuracy is particularly important near transition states. Density functional theory (DFT) is one such method, but in some cases DFT may not work, and more accurate theoretical levels such as bond clusters may be employed. However, performing high-precision calculations such as bond clusters can be computationally expensive. As another example, classical force field models, such as ReaxFF, can describe bond formation and breakage at the classical force field level, but their applicability may be limited by the force field parameters.

[0006] This disclosure provides a method and system for studying chemical reaction pathways to overcome at least one of the drawbacks identified above.

[0007] This disclosure provides a computational chemistry platform that can accurately and efficiently predict chemical reaction pathways by flexibly switching energy and force solvers between quantum chemical methods or other chemical potential methods such as DFT, CCSD(T), iFCI, QM / MM, DMET, ONIOM, and force-field-based potential, and ML models trained at the quantum chemical or chemical potential level, depending on the reliability of the inference provided by the machine learning (ML) model. The platform continues to use the ML model for a structure if the ML inference for that structure along the reaction pathway is deemed reliable. However, if the platform indicates that the ML inference is unreliable, it may switch to quantum chemical methods to solve the target structure. In this way, the present invention improves both accuracy and efficiency.

[0008] As another example of improved accuracy and efficiency, results obtained from quantum chemical calculations can be stored in the platform's database as training datasets to improve ML models. This allows the platform to reduce the number of times it uses quantum chemical methods to solve for target structures and continuously improve ML models to predict chemical reactions more quickly and accurately.

[0009] In one embodiment, the Disclosure provides a computer-aided method for determining a reaction pathway. The method may include: (a) providing instructions for reactants and at least one of products or driving coordinates; (b) providing a set of coordinates, the set of coordinates being on an energy plane connecting the reactants and at least one of the products or driving coordinates; (c) evaluating the energy or force at the coordinates of the set of coordinates using a trained model; (d) determining that a confidence index at the coordinates is less than a threshold confidence value; (e) evaluating the energy or force at the coordinates being at least in part on quantum chemical calculations corresponding to a training dataset of the trained model; and (f) outputting a set of energy or force at the set of coordinates on the energy plane being at least in part on the energy or force in (e) and the energy or force in (c).

[0010] In some embodiments, the energy surface is the potential energy surface. In some embodiments, the energy surface is the free energy surface. In some embodiments, the set of coordinates is conformal coordinates. In some embodiments, the set of coordinates is Cartesian coordinates. In some embodiments, the Cartesian coordinates include the direction of motion. In some embodiments, (e) includes evaluating the first-principles energy or first-principles force in the coordinates.

[0011] In some embodiments, the method further includes, until a completion criterion is met, (i) if the reliability index is less than the threshold reliability value, (c) evaluating the energy or force at the coordinate, selecting another coordinate on the energy surface, and using the trained model to evaluate the energy or force at the other coordinate to determine a reliability index for the energy or force at the other coordinate; and (ii) if the reliability index is greater than the threshold reliability value, selecting another coordinate on the energy surface, and using the trained model to evaluate the energy at the other coordinate to determine a reliability index for the energy or force at the other coordinate. In some embodiments, in (i), the method further includes saving the energy or force for retraining, and retraining the trained model based on the energy or force in (i). In some embodiments, the step of selecting the alternative coordinates on the energy surface includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band, growth string, variational reaction path optimization method, and intrinsic reaction coordinate method.

[0012] In some embodiments, the method further includes (e) saving the energy or force for retraining and (c) retraining the trained model based on the energy or force. In some embodiments, the method further includes using the trained model to evaluate a first energy or first force at initial coordinates. In some embodiments, the method further includes determining a reliability index for the first energy or first force at initial coordinates. In some embodiments, (f) further includes outputting a transition state or reaction pathway on the energy plane. In some embodiments, the reaction pathway is a minimum energy pathway.

[0013] In some embodiments, the step of providing a set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band, growth string, variational reaction pathway optimization, and eigencoordinate method. In some embodiments, the trained model includes a machine learning algorithm. In some embodiments, the machine learning algorithm includes a neural network. In some embodiments, the machine learning algorithm includes an ensemble learning method. In some embodiments, (d) includes combining results from one or more submodels to create a metamodel, calculating the energy for each of the one or more submodels, and calculating the standard deviation of the energy for the one or more submodels, the standard deviation constituting part of the reliability index. In some embodiments, the metamodel includes an ANI deep learning potential. In some embodiments, the one or more submodels include one or more of PAINN deep learning potentials, DimeNet++ deep learning potentials, or PauliNet.

[0014] In some embodiments, (e) includes evaluating the first-principles energy or first-principles force in the above coordinates, which is calculated by the Hartree-Fock method, coupled cluster method, full configuration interaction, incremental full configuration interaction, density functional theory, Moller-Plesset perturbation theory, mixed quantum mechanical and molecular mechanical methods, density matrix embedding theory, or the ONIOM model.

[0015] In another embodiment, the Disclosure provides a computer-aided method for determining a reaction pathway. This method may include: (a) providing instructions for reactants and at least one of products or driving coordinates; (b) providing a set of coordinates, the set of coordinates being on an energy plane connecting the reactants and at least one of the products or driving coordinates; (c) evaluating the energy or force at the coordinates of the set of coordinates using a trained model; (d) evaluating the energy or force at the coordinates being at least in part on quantum chemical calculations corresponding to a training dataset of the trained model; and (e) retraining the trained model based on the energy or force in (d).

[0016] In some embodiments, the energy surface is a potential energy surface. In some embodiments, the energy surface is a free energy surface. In some embodiments, the set of coordinates is a conformal coordinate system. In some embodiments, the set of coordinates is a Cartesian coordinate system. In some embodiments, the Cartesian coordinate system includes a direction of motion. In some embodiments, (d) includes evaluating first-principles energy or first-principles force in the coordinate system. In some embodiments, the method further includes outputting a set of energy or force in the set of coordinates on the energy surface, at least in part, based on the energy or force in (d).

[0017] In some embodiments, the trained model includes a machine learning algorithm. In some embodiments, the machine learning algorithm includes a neural network. In some embodiments, the machine learning algorithm includes an ensemble learning method. In some embodiments, (c) includes combining results from one or more submodels to create a metamodel, calculating the energy for each of the one or more submodels, and calculating the standard deviation of the energy for the one or more submodels, the standard deviation constituting a reliability index. In some embodiments, the metamodel includes an ANI deep learning potential. In some embodiments, the one or more submodels include one or more of the PAINN deep learning potential, DimeNet++ deep learning potential, or PauliNet. In some embodiments, (d) includes evaluating the first-principles energy or first-principles force in the coordinates, the first-principles energy or first-principles force being calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or ONIOM model.

[0018] In some embodiments, the method further includes the steps of: (i) if the reliability index is less than the threshold reliability value, (c) evaluating the energy or force at the coordinate, selecting another coordinate on the energy surface, evaluating the energy or force at the other coordinate using the trained model, and determining the reliability index for the energy or force at the other coordinate, until a completion criterion is met; and (ii) if the reliability index is greater than the threshold reliability value, selecting another coordinate on the energy surface, evaluating the energy at the other coordinate using the trained model, and determining the reliability index for the energy or force at the other coordinate. In some embodiments, the method further includes (i) saving the energy or force for retraining, and (i) retraining the trained model based on the energy or force.

[0019] In some embodiments, the method further includes the step of using the trained model to evaluate the first energy or first force in the initial coordinates. In some embodiments, the method further includes the step of determining a reliability index for the first energy or first force in the initial coordinates. In some embodiments, the step of providing the set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method. In some embodiments, the step of selecting the other coordinates on the energy surface includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

[0020] In another embodiment, the disclosure provides a computer-aided method for determining a reaction pathway. The method may include: (a) providing instructions for reactants and at least one of products or driving coordinates; (b) providing a set of coordinates, wherein the set of coordinates lies on an energy plane connecting the reactants and at least one of the products or driving coordinates; (c) providing threshold confidence values ​​for energy or force at the coordinates of the set of coordinates, wherein, until a completion criterion is met, (i) if the confidence index is less than the threshold confidence value, the energy or force at the coordinates is evaluated, another coordinate on the energy plane is selected, the energy or force at the other coordinate is evaluated using a trained model to determine the confidence index for the energy or force at the other coordinate; and (ii) if the confidence index is greater than the threshold confidence value, another coordinate on the potential energy plane is selected, the energy at the other coordinate is evaluated using a trained model to determine the confidence index for the energy or force at the other coordinate; and (d) outputting a set of energy or force at the set of coordinates on the energy plane.

[0021] In some embodiments, the energy surface is a potential energy surface. In some embodiments, the energy surface is a free energy surface. In some embodiments, the set of coordinates is a conformal coordinate system. In some embodiments, the set of coordinates is a Cartesian coordinate system. In some embodiments, the Cartesian coordinate system includes the direction of motion. In some embodiments, (c) includes evaluating first-principles energy or first-principles force in the coordinate system.

[0022] In some embodiments, the method further includes the step of retraining the trained model based on at least one energy or at least one force within the set set of coordinates. In some embodiments, the method further includes the trained model to evaluate a first energy or first force in the initial coordinates. In some embodiments, the method further includes the step of determining a reliability index for the first energy or first force in the initial coordinates. In some embodiments, (f) further includes outputting a transition state or reaction pathway on the energy surface. In some embodiments, the reaction pathway is a minimum energy pathway. In some embodiments, the step of providing the set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method. In some embodiments, the step of selecting another coordinate on the energy surface includes a method selected from the group consisting of first-principles molecular dynamics method, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

[0023] In some embodiments, the trained model includes a machine learning algorithm. In some embodiments, the machine learning algorithm includes a neural network. In some embodiments, the machine learning algorithm includes an ensemble learning method. In some embodiments, (d) includes combining results from one or more submodels to create a metamodel, calculating the energy for each of the one or more submodels, and calculating the standard deviation of the energy for the one or more submodels, the standard deviation constituting part of the reliability index. In some embodiments, the metamodel includes an ANI deep learning potential. In some embodiments, the one or more submodels include one or more PAINN deep learning potentials, DimeNet++ deep learning potentials, or PauliNet. In some embodiments, (e) includes evaluating first-principles energy or first-principles force in the coordinates, the first-principles energy or first-principles force being calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or ONIOM model.

[0024] In another embodiment, the Disclosure provides a computer-aided method for determining a reaction pathway. The method may include: (a) providing instructions for reactants and at least one of products or driving coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting the reactants and at least one of the products or driving coordinates; (c) using a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) determining that a reliability index in the conformational coordinates is less than a threshold reliability value; (e) evaluating the first-principles energy or first-principles force in the conformational coordinates; and (f) outputting a set of energy or force in the set of conformational coordinates on the potential energy plane, at least in part based on the first-principles energy or first-principles force and the energy or force in (c).

[0025] In some embodiments, the method further includes the step of: (i) if the reliability index is less than the threshold reliability value, evaluating the first-principles energy or first-principles force in the conformational coordinates, selecting another conformational coordinate on the potential energy surface, evaluating the energy or force in the other conformational coordinate using the trained model, and determining the reliability index of the energy or force in the other conformational coordinate; and (ii) if the reliability index is greater than the threshold reliability value, selecting another conformational coordinate on the potential energy surface, evaluating the energy in the other conformational coordinate using the trained model, and determining the reliability index of the energy or force in the other conformational coordinate. In some embodiments, the method further includes (e) saving the first-principles energy or first-principles force for retraining, and retraining the trained model based on the first-principles energy or first-principles force. In some embodiments, the method further includes (i) storing the first-principles energy or first-principles force for retraining, and retraining the trained model based on the first-principles energy or first-principles force.

[0026] In some embodiments, the method further includes the step of using the trained model to evaluate a first energy or first force in the initial conformational coordinates. In some embodiments, the method further includes the step of determining a reliability index for the first energy or first force in the initial conformational coordinates. In some embodiments, (f) further includes outputting a transition state or reaction pathway on the potential energy surface. In some embodiments, the reaction pathway is a minimum energy pathway. In some embodiments, the step of providing a set of conformational coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method. In some embodiments, the step of selecting another conformational coordinate on the potential energy surface includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

[0027] In some embodiments, the trained model includes a machine learning algorithm. In some embodiments, the machine learning algorithm includes a neural network. In some embodiments, the machine learning algorithm includes an ensemble learning method. In some embodiments, (d) includes combining results from one or more submodels to create a meta-model, calculating energy for each of the one or more submodels, and calculating a standard deviation of the energy for the one or more submodels, the standard deviation constituting part of the reliability index. In some embodiments, the meta-model includes an ANI deep learning potential. In some embodiments, the one or more submodels include one or more of a PAINN deep learning potential, a DimeNet++ deep learning potential, or a PauliNet. In some embodiments, the ab initio energy or the ab initio force is calculated by a Hartree–Fock method, a coupled cluster method, a full configuration interaction method, an incrementally augmented full configuration interaction method, density functional theory, Møller–Plesset perturbation theory, a hybrid quantum mechanics–molecular mechanics method, density matrix embedding theory, or an ONIOM model.

[0028] In another aspect, the present application provides a computer-implemented method for determining a reaction pathway. The method may include: (a) providing an indication of at least one of a reactant and a product or a driving coordinate; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy surface connecting the reactant and the at least one of the product or the driving coordinate; (c) using a trained model to evaluate energy or force at the conformational coordinates of the set of conformational coordinates; (d) evaluating an ab initio energy or an ab initio force at the conformational coordinates; and (e) retraining the trained model based on the ab initio energy or the ab initio force.

[0029] In some embodiments, the method further includes the step of outputting a set of energy or force in the set of conformational coordinates on the potential energy surface, at least in part on the first-principles energy or first-principles force. In some embodiments, the trained model includes a machine learning algorithm. In some embodiments, the machine learning algorithm includes a neural network. In some embodiments, the machine learning algorithm includes an ensemble learning method. In some embodiments, (c) includes combining results from one or more submodels to create a metamodel, calculating the energy for each of the one or more submodels, and calculating the standard deviation of the energy for the one or more submodels, the standard deviation constituting the reliability index. In some embodiments, the metamodel includes an ANI deep learning potential. In some embodiments, the one or more submodels include one or more PAINN deep learning potentials, DimeNet++ deep learning potentials, or PauliNet.

[0030] In another aspect, the present disclosure provides a computer-implemented method for determining a reaction pathway. The method includes: (a) providing an indication of at least one of a reactant and a product or a driving coordinate; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy surface connecting the reactant and at least one of the product or the driving coordinate; (c) providing a threshold reliability value of energy or force at the conformational coordinates of the set of conformational coordinates, and until a completion criterion is met, (i) when a reliability metric is less than the threshold reliability value, evaluating a first-principles energy or a first-principles force at the conformational coordinates, selecting another set of conformational coordinates on the potential energy surface, and evaluating the energy or the force at the another set of conformational coordinates using a trained model to determine the reliability metric of the energy or the force at the another set of conformational coordinates, and (ii) when the reliability metric is greater than the threshold reliability value, selecting another set of conformational coordinates on the potential energy surface, evaluating the energy at the another set of conformational coordinates using the trained model, and determining the reliability metric of the energy or the force at the another set of conformational coordinates; and (d) outputting a set of energy or force at the set of conformational coordinates on the potential energy surface.

[0031] In some embodiments, the method further includes retraining the trained model based on at least one first-principles energy or at least one first-principles force within the set of conformational coordinates that has been set.

[0032] Another aspect of the present disclosure provides a system including one or more computer processors and a computer memory coupled to the one or more computer processors. The computer memory includes machine-executable code that, when executed by the one or more computer processors, performs any of the methods described above or elsewhere in this specification.

[0033] In some embodiments, the system further includes a quantum computer, which is configured to perform a step of any of the methods described above or elsewhere in this specification.

[0034] Further aspects and advantages of the present disclosure will be readily apparent to those skilled in the art from the following detailed description, which shows and describes only exemplary embodiments of the present disclosure. As should be understood, other different embodiments of the present disclosure are possible, and some of their details can be modified in various obvious ways without departing from the present disclosure. Therefore, the drawings and description should be considered as illustrative and not limiting in nature.

[0035] Reference All publications, patents, and patent applications referenced herein are incorporated herein by reference to the same extent as each individual publication, patent, or patent application is specifically and individually indicated as being incorporated by reference. In the event of any conflict between any publication, patent, or patent application incorporated by reference and any disclosure herein, this specification shall prevail and / or supersede any such conflict. [Brief explanation of the drawing]

[0036] This patent or application document includes at least one color drawing. Copies of this patent or publication of the patent application, including the color drawing, are available from the Patent Office upon request and payment of the necessary fees. Novel features of the present invention are described in detail in the appended claims. The features and advantages of the present invention will be better understood by referring to the following detailed description illustrating exemplary embodiments utilizing the principles of the present invention, and to the appended drawings (also referred to herein as "Figure" and "FIG").

[0037] [Figure 1] A flowchart shows an example of a method for determining a reaction pathway according to several embodiments. [Figure 2] A flowchart shows another example of a method for determining a reaction pathway when reliability is below a threshold, according to several embodiments. [Figure 3] This flowchart shows an example of a method for determining a reaction pathway and updating a trained model using data from quantum chemical calculations, according to several embodiments. [Figure 4] A flowchart shows an example of a method for determining a reaction pathway that exhibits a branching path based on a reliability index, according to several embodiments. [Figure 5] An example of a schematic diagram of a system for determining the reaction pathway is shown according to several embodiments. [Figure 6] This document describes a computer system programmed or otherwise configured to carry out the methods described herein. [Figure 7] This diagram shows the chemical reaction between s-cis-butadiene and ethene to produce cyclohexene. [Figure 8] This plot shows the reaction pathway energy profiles for DFT (solid line), ANI / ANIlx (dashed line), and ANI / Transitionlx (dotted line), the GSM node energy (without a center), and the median value (regression line) estimated by cubic spline interpolation. [Figure 9A] This is computational data showing the molecular structures of the reactants (left), transition state (center), and product (right) predicted by GSM using the ANI / ANIlx model. [Figure 9B] This is computational data showing the molecular structures of the reactants (left), transition state (center), and product (right) predicted by GSM using the ANI / Transitionlx model. [Figure 9C] This is computational data showing the molecular structures of the reactants (left), transition state (center), and product (right) predicted by GSM using a DFT model. [Figure 10]The transition state structures predicted by GSM are superimposed using DFT (filled, 1030), ANI / ANIlx (outlined, 1010), and ANI / Transitionlx (textured, 1020), with all structures transformed so that the overall center of mass is the same. [Modes for carrying out the invention]

[0038] While various embodiments of the present invention have been shown and described herein, it will be apparent to those skilled in the art that these embodiments are merely illustrative. Those skilled in the art can conceive of various modifications, changes, and substitutions without departing from the present invention. It should be understood that various alternatives to the embodiments of the present invention described herein are applicable.

[0039] When the terms “at least” precede the first number in a sequence of two or more numbers, and “greater than” or “greater than or equal to” follow it, the terms “at least,” “greater than,” or “greater than or equal to” apply to each number in that sequence. For example, 1, 2, or 3 or more is equivalent to 1 or more, 2 or more, or 3 or more.

[0040] When the terms “not greater than,” “less than,” or “less than or equal to” are appended to the first number in a sequence of two or more numbers, those terms apply to each number in that sequence. For example, 3, 2, and 1 are equivalent to 3 or less, 2 or less, or 1 or less.

[0041] In certain embodiments of this specification, numerical ranges are assumed. If a range exists, it includes both ends of the range. Furthermore, all subranges and values ​​within the range exist as if they were explicitly described.

[0042] The terms “approximately” or “about” may mean within an acceptable margin of error for a particular value, and the acceptable margin of error will depend in part on the method of measuring and determining the value, for example, the limits of the measuring system. For example, “approximately” may mean within or beyond one standard deviation, according to the practice in the art. Alternatively, “approximately” may mean a range of up to 20%, up to 10%, up to 5%, or up to 1% of a given value. Where a particular value is stated in the application documents and claims, unless otherwise specified, the term “approximately” is assumed to mean within an acceptable margin of error for that particular value.

[0043] The following detailed description refers to the accompanying drawings, which constitute part of this specification. In the drawings, unless otherwise specified in the context, similar symbols generally indicate similar components. The exemplary embodiments described in the detailed description, drawings, and claims are not limiting. Other embodiments may be used or other modifications made without departing from the scope of the subject matter presented herein. It will be readily apparent that the aspects of this disclosure outlined herein and shown in the drawings can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are expressly assumed herein.

[0044] This disclosure provides a method and system for predicting reaction pathways using a general-purpose machine learning (ML) potential that can detect when it is unreliable and switch to a more reliable equivalent first-principles calculation instead. The ML potential may be a potential generated from an ML model that incorporates at least a molecular conformational instruction and returns at least the energy of that conformation. Energy and force from first-principles calculations can be used directly instead of the ML potential, and the data can be saved to retrain the ML potential later. Combined with an overall reaction pathway prediction algorithm, this technique can form a robust and rapid method for computing reaction pathways and transition states, continuously improving the underlying ML model.

[0045] The present invention provides a computational chemistry platform that can accurately and efficiently predict chemical reaction pathways by flexibly switching energy and force solvers between quantum chemical methods or other chemical potential methods such as DFT, CCSD(T), iFCI, QM / MM, DMET, ONIOM, and force-field-based potentials, and machine learning (ML) models trained to the level of quantum chemical or chemical potential methods, depending on the reliability of the inferences provided by the ML models. If the platform indicates that the ML inference of the structure along the reaction pathway is reliable, the platform continues to use the ML model for that structure. However, if the platform indicates that the reliability of the ML inference is low, the platform can switch to quantum chemical methods to elucidate the structure in question. In this way, the present invention improves both accuracy and efficiency.

[0046] As another example of improving accuracy and efficiency, results obtained from quantum chemical calculations can be stored in the platform's database as training datasets to improve ML models. This allows the platform to reduce the number of times it uses quantum chemical methods to elucidate target structures and continuously improve ML models to predict chemical reactions more quickly and accurately.

[0047] Figure 1 is a flowchart of an example of method 100 for determining a reaction pathway. In step 110, the method may include providing indications of reactants and products or driving coordinates. In step 120, the method may include providing a set of coordinates on the energy plane. In step 130, the method may include evaluating energy or force using a trained model. In step 140, the method may include determining a reliability index for energy or force at the coordinates determined using the trained model. In step 150, the method may optionally include evaluating energy or force based on quantum chemical calculations, depending on the reliability index.

[0048] Figure 2 is a flowchart illustrating an example of a method 200 for determining a reaction pathway when reliability is below a threshold. Method 200 may include embodiments, modifications, or examples of Method 100. In step 201, Method 200 may include providing indications of reactants and products or at least one of the driving coordinates. Step 201 may include embodiments, modifications, or examples of step 110 of Method 100. In step 210, Method 200 may include providing a set of coordinates. The set of coordinates may lie on an energy plane connecting reactants and products or at least one of the driving coordinates. Step 210 may include embodiments, modifications, or examples of step 120 of Method 100. In step 220, Method 200 may include evaluating energy or force at the coordinates of the set of coordinates using a trained model. Step 220 may include embodiments, modifications, or examples of step 130 of Method 100. In step 230, method 200 may include a step of determining that the reliability index at the coordinates is less than a threshold reliability value. If the reliability index is less than a threshold, step 230 may include an embodiment, modification, or example of step 140 of method 100. In step 240, method 200 may include a step of evaluating the energy or force at the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of the trained model. If the energy or force is calculated using quantum chemical calculations, step 240 may include an embodiment, modification, or example of step 150 of method 100. In step 250, method 200 may include a step of outputting a set of energy or force at a set of coordinates on the energy plane, based at least in part on the energy or force in step 240 and the energy or force in step 220.

[0049] In an example of Method 200, the Disclosure provides a computer-implemented method for determining a reaction pathway. This method may include: (a) providing instructions for reactants and products or at least one of drive coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting the reactants and products or at least one of drive coordinates; (c) using a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) determining that a reliability index in the conformational coordinates is less than a threshold reliability value; (e) evaluating first-principles energy or first-principles force in the conformational coordinates; and (f) outputting a set of energy or force in the conformational coordinates on the potential energy plane, at least in part, based on the first-principles energy or first-principles force and the energy or force in (c).

[0050] Figure 3 is a flowchart illustrating an example of Method 300 for determining a reaction pathway and updating a trained model using data from quantum chemical calculations. Method 300 may include embodiments, modifications, or examples of Method 100. In step 301, Method 300 may include providing indications of reactants and products or at least one of the driving coordinates. Step 301 may include embodiments, modifications, or examples of Step 110 of Method 100. In step 310, Method 300 may include providing a set of coordinates. The set of coordinates may lie on an energy plane connecting reactants and products or at least one of the driving coordinates. Step 310 may include embodiments, modifications, or examples of Step 320 of Method 100. In step 320, Method 300 may include evaluating the energy or force at the coordinates of the set of coordinates using the trained model. Step 320 may include embodiments, modifications, or examples of Step 130 of Method 100. In step 330, method 300 may include the step of determining that the reliability index at the coordinates is less than a threshold reliability value. If the reliability index is less than a threshold, step 330 may include an embodiment, modification, or example of step 140 of method 100. In step 340, method 300 may include the step of evaluating the energy or force at the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of the trained model. If the energy or force is calculated using quantum chemical calculations, step 340 may include an embodiment, modification, or example of step 150 of method 100. In step 350, method 300 may include the step of retraining the trained model based on the energy or force in 340.

[0051] In one example of Method 300, the present application provides a computer-implemented method for determining a reaction pathway. This method may include the steps of: (a) providing instructions for reactants and products or at least one of drive coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting the reactants and products or at least one of drive coordinates; (c) using a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) evaluating the first-principles energy or first-principles force in the conformational coordinates; and (e) retraining the trained model based on the first-principles energy or first-principles force.

[0052] Figure 4 is a flowchart showing an example of a method 400 for determining a reaction pathway that shows a branching path based on a reliability index. Method 400 may include embodiments, modifications, or examples of Method 100.

[0053] In step 401, method 400 may include the step of providing a reactant indication. In step 402, method 400 may include the step of providing at least one of the product or the drive coordinates. The indications in step 401, step 402, or both, may be inputs to the computer implementation methods described herein, for example, step 110 of method 100. Steps 401, step 402, or both, may include the step of providing an indication of a reactant and at least one of the product or the drive coordinates. In step 410, method 400 may include the step of selecting a structure for energy evaluation, force evaluation, or both. Step 410 may include the step of providing a set of coordinates, the set of coordinates being on an energy plane connecting the reactant and at least one of the product or the drive coordinates. In step 420, method 400 may include the step of evaluating the energy or force at the coordinates of the set of coordinates using a trained model. Step 420 may include embodiments, variations, or examples of step 130 of method 100. In step 420, method 400 may further include the step of determining a reliability index in the coordinates. Step 420 may include an embodiment, modification, or example of step 140 of method 100. After step 420, method 400 may branch based on reliability. In some cases, method 400 may include the step of providing a threshold reliability value for energy or force in the coordinates of a set of coordinates. If the reliability index is less than the threshold reliability value, method 400 may proceed to step 425. If the reliability index is greater than the threshold reliability value, method 400 may proceed to step 435. In step 425, method 400 may include the step of evaluating energy or force in the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of a trained model. Step 340 may include embodiments, variations, or examples of Step 150 of Method 100 when calculating energy or force using quantum chemical calculations, selecting a different coordinate on the energy plane, using a trained model to evaluate the energy or force at the different coordinate, and determining a reliability index for the energy or force at the different coordinate.In step 430, method 400 may include the steps of selecting an alternative coordinate on the potential energy surface if the reliability index is greater than a threshold reliability value, using a trained model to evaluate the energy at the alternative coordinate, and determining a reliability index for the energy or force at the alternative coordinate. In some cases, method 400 may include repeating steps 410, 420, 425, and 430 until a stopping criterion is met. In step 440, method 400 may include outputting a set of energy or force at a set of coordinates on the energy surface, at least in part based on the energy or force at 430.

[0054] In one example of Method 400, the present disclosure provides a computer-aided method for determining a reaction pathway. The method may include (a) providing instructions for reactants and products or at least one of drive coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting reactants and products or at least one of drive coordinates; (c) providing threshold confidence values ​​for energy or force in the conformational coordinates of the set of conformational coordinates, until a completion criterion is met, (i) if the confidence index is less than the threshold confidence value, evaluating the first-principles energy or first-principles force in the conformational coordinates, selecting another conformational coordinate on the potential energy plane, evaluating the energy or force in the other conformational coordinate using a trained model, and determining a confidence index for the energy or force in the other conformational coordinate; and (ii) if the confidence index is greater than the threshold confidence value, selecting another conformational coordinate on the potential energy plane, evaluating the energy in the other conformational coordinate using a trained model, and determining a confidence index for the energy or force in the other conformational coordinate; and (d) outputting a set of energy or force in the set of conformational coordinates on the potential energy plane.

[0055] Reaction pathway sampling and initialization Reaction pathway sampling (also called transition pathway sampling) can be a form of simulation that calculates the trajectory of a physical or chemical transition of a system from one stable state to another. Examples of systems targeted by reaction pathway sampling include protein folding, chemical reactions, and crystal nucleation. The transition state is crucial in reaction pathway sampling calculations. In a simple example, states A and B may be stable states of a system. States A and B can be connected by a trajectory along a reaction pathway. The reaction can be characterized by the maximum local energy between the stable states. The maximum local energy can be the transition state. The transition state can be characterized by the activation energy barrier. In some cases, the reaction pathway can be characterized by a set of transition pathways. The structure of the transition state and the activation energy barrier can be important for understanding chemical reactions (e.g., what chemical reactions occur) and rate constants (e.g., how fast the reaction occurs). These calculations can help understand important phenomena such as ligand docking to proteins and perfluoroalkyl and polyfluoroalkyl (PFAS) reactions.

[0056] However, these types of calculations can be difficult to perform. The transition states themselves are non-equilibrium states and may be difficult to model quantum chemically. Furthermore, from a molecular dynamics perspective, the size of the set of paths used to achieve chemical accuracy can be very large. Therefore, these may be promising systems for advanced quantum chemical methods.

[0057] Step 110 may include a step of providing instructions for reactants and products or drive coordinates. Step 201 may include an embodiment, variation, or example of step 110 of method 100. Step 301 may include an embodiment, variation, or example of step 110 of method 100.

[0058] In step 401, method 400 may include the step of providing instructions for the reactants. In step 402, method 400 may include the step of providing at least one of the product or the drive coordinates. Instructions in step 401, step 402, or both may be inputs to the computer implementation described in the specification, for example, step 110 of method 100. Steps 401, step 402, or both may include the step of providing instructions for the reactants and at least one of the product or the drive coordinates. Instructions in step 401, step 402, or both may be provided by the user.

[0059] In some cases, the method may include a step of providing a reactant designation. In some cases, the method may include a step of providing a product designation or a driving coordinate. The reactant designation, product designation, or both may include a chemical structure designation. In some cases, the structure is provided in a set of coordinates. In some cases, the set of coordinates is conformal coordinates. In some cases, the set of coordinates is Cartesian coordinates. In some embodiments, the Cartesian coordinates include a direction of movement. In some cases, the reactant designation, product designation, driving coordinate, or any combination thereof includes a simplified molecular-input line-entry system (SMILES) string. In some cases, the reactant designation, product designation, driving coordinate, or any combination thereof includes a 2D drawing. In some cases, the reactant designation, product designation, driving coordinate, or any combination thereof includes a 3D model.

[0060] In some cases, the products may be unknown at the start of the calculation. If the products are unknown, driving coordinates may be provided. Driving coordinates may include bond bending coordinates, bond cutting coordinates, torsional coordinates, stretching coordinates, bending coordinates, geometric strains of all types of reactants, etc. In some cases, the driving coordinates are the direction of movement in the geometric coordinate system. In some cases, the driving coordinates are the direction of movement in the energy coordinate system. If the products are unknown, they can be found using reaction pathway sampling calculations.

[0061] Instructions may be provided by the user. In some cases, the user provides instructions through an interface that is separate from the computing platform.

[0062] Steps to provide a set of coordinates on an energy plane: In step 120, method 100 may include the step of providing a set of coordinates on an energy plane. Step 210 may include an embodiment, variation, or example of step 120 of method 100. Step 310 may include an embodiment, variation, or example of step 320 of method 100. In step 410, method 400 may include the step of selecting a structure for energy evaluation, force evaluation, or both. Step 410 may include the step of providing a set of coordinates, the set of coordinates being on an energy plane connecting reactants and products or at least one of the driving coordinates.

[0063] Given reactants and products or driving coordinates, a space is provided through which the reaction pathway is determined. In some cases, the set of coordinates includes a set of conformational coordinates. In some cases, the set of conformational coordinates lies on an energy plane connecting the reactants and products or at least one of the driving coordinates. In some cases, the energy plane is the potential energy plane. In some cases, the energy plane is the free energy plane.

[0064] In some cases, methods 100, 200, 300, or 400 may further include the step of selecting conformational coordinates within a set of conformational coordinates. In some cases, methods 100, 200, 300, or 400 may further include the step of generating a first or initial coordinate. In some cases, methods 100, 200, 300, or 400 may further include the step of using a trained model described herein to evaluate a first energy or first force in the initial coordinate. In some cases, methods 100, 200, 300, or 400 may further include the step of determining a reliability index for the first energy or first force in the initial coordinate.

[0065] In some cases, the process of providing a set of coordinates in 120 may include a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and intrinsic reaction coordinate method. Any of these methods can be used to generate a set of coordinates and move to the next coordinate within that set. For example, there are various approaches to generate an intermediate or next molecular structure and track the trajectory of molecules in a chemical reaction, such as first-principles molecular dynamics (AIMD), NEB (nudged elastic band method), GSM (growth string method), variational reaction pathway optimization method, and IRC (intrinsic reaction coordinate method).

[0066] Reaction pathway prediction methods sometimes attempt to determine the minimum energy path (MEP) between a given point on the potential energy surface and a target such as the product, the next conformational state, or the next molecular coordinates. In the two-ended method, the target is another point on the potential energy surface. In the one-ended method, on the other hand, this target is the first saddle point on the potential energy surface in approximately a given direction.

[0067] Numerous methods can be used to calculate MEP. Some rely on surface sampling via metadynamics (e.g., Vaughn-Oppenheimer molecular dynamics), while others use string-based methods (e.g., nudged elastic banding (NEB) or grown string method (GSM)) to more directly explore the surface. There are also methods that construct reaction pathways from transition states (e.g., eigenreaction coordinate method). Examples of these methods can be integrated into the schematic diagrams shown in Figures 1-4.

[0068] Trained model In step 130, the method may include a step of evaluating energy or force using a trained model. Step 220 may include an embodiment, variation, or example of step 130 of method 100. Step 320 may include an embodiment, variation, or example of step 130 of method 100. Step 420 may include an embodiment, variation, or example of step 130 of method 100.

[0069] Due to the high computational cost of certain computational methods, machine learning models have been proposed as alternatives to computationally expensive calculations. Machine learning (ML) methods can be used in various fields, including quantum chemistry and materials simulation. For example, ML methods can be used to provide predictive models for interatomic potential energy surfaces, intermolecular forces, electron density, density functionals, and molecular response properties such as polarizability and infrared spectra. Large datasets of molecular properties, whether computed from quantum chemistry or measured experimentally, can be used to explore vast compound spaces, discover new sustainable catalytic materials, and build predictive models for designing novel synthetic routes. In some cases, machine learning can be used to build approximate quantum chemical methods, such as predicting MP2 or bond cluster energy from Hartree-Fock orbitals. In some cases, neural networks may be used as basis representations of wave functions. Generally, ML models can learn from quantum chemical datasets and describe molecular properties as scalar fields, vector fields, or tensor fields. For example, separate ML models can be built for each property using quantum chemical data of different electronic properties such as energy and dipole moment. ML can sometimes enable efficient exploration of the chemical space related to these properties.

[0070] Examples of machine learning techniques - In some cases, step 130 may include a step of evaluating energy or force using a trained model. In some cases, the trained model may include a machine learning algorithm. In some cases, ML may generally include a step of identifying and recognizing patterns in existing data to facilitate prediction of subsequent data. ML may include an ML model (e.g., an ML algorithm). Machine learning can provide deductive or inductive reasoning based on real or simulated data, whether analytical or statistical in nature. The ML model may be a trained model.

[0071] ML techniques may include one or more supervised ML techniques, semi-supervised ML techniques, self-supervised ML techniques, or unsupervised ML techniques. For example, an ML model may be a trained model learned through supervised learning (e.g., various parameters are determined as weights or scaling factors). ML may include one or more regression analysis, regularization, classification, dimensionality reduction, ensemble learning, meta-learning, association rule learning, cluster analysis, anomaly detection, deep learning, or hyper-deep learning. ML is not limited to these, but includes k-means clustering, k-nearest neighbors, learning vector quantization, linear regression, nonlinear regression, least squares regression, partial least squares regression, logistic regression, stepwise regression, multivariate adaptive regression splines, ridge regression, principal component regression, lasso regression, minimum angle regression, canonical correlation analysis, factor analysis, independent component analysis, linear discriminant analysis, multidimensional scaling, non-negative matrix factorization, principal component analysis, principal coordinate analysis, projection tracking, summon mapping, t-distribution type stochastic neighbor embedding, AdaBoost, boosting, gradient boosting, bootstrap aggregation, ensemble mean, decision tree, conditional decision tree, boosting decision tree, gradient boosting decision tree, random forest, stack generalization (stacked This may include generalizations, Bayesian networks, Bayesian belief networks, naive Bayes, Gaussian naive Bayes, polynomial naive Bayes, hidden Markov models, hierarchical hidden Markov models, support vector machines, encoders, decoders, autoencoders, stacked autoencoders, perceptrons, multilayer perceptrons, artificial neural networks, feedforward neural networks, convolutional neural networks, recurrent neural networks, long-term memory, deep belief networks, deep Boltzmann machines, deep convolutional neural networks, deep recurrent neural networks, or generative adversarial networks.

[0072] Training Data - Trained models can be trained using datasets of quantum chemical information. For example, datasets may include the Transition IX dataset (see https: / / arxiv.org / abs / 2207.12858), which is incorporated herein by reference for all purposes. In some cases, the base dataset may be supplemented with data from the user base. For example, it is possible to generate custom datasets or supplement existing datasets using prior quantum chemical calculations. Training datasets may include coordinates and energies of reactant and product sets. In some cases, training datasets may also include forces. The more samples similar to the data points being computed, the higher the accuracy of the dataset may be. In some cases, datasets with more data points having structures similar to transition states may be more accurate.

[0073] The process of training an ML model may, in some cases, include selecting one or more untrained data models to be trained on a training dataset. The selected untrained data models may include any type of untrained ML model for supervised, semi-supervised, self-supervised, or unsupervised machine learning. The selected untrained data models may be specified based on inputs (e.g., user inputs) that specify relevant parameters to be used as predictors and other variables to be used as potential explanatory variables. For example, the selected untrained data models may be specified to produce outputs (e.g., predictions) based on the inputs. Similarly, conditions for training the ML model from the selected untrained data models (e.g., limits on the complexity of the ML model, or limits on improving the ML model beyond a certain point) may also be selected. The ML model may be trained on the training dataset (e.g., via a computer system such as a server). In some cases, a first subset of the training dataset may be selected to train the ML model. The selected untrained data models may then be trained on the first subset of the training dataset using appropriate ML techniques, based on the type of ML model selected and any conditions specified for training the ML model. In some cases, due to the processing power requirements needed to train an ML model, the selected untrained data model may be trained using additional computing resources (e.g., cloud computing resources). Such training may continue until at least one aspect of the ML model is validated and meets the selection criteria for use as a predictive model.

[0074] In some cases, to determine the accuracy and robustness of an ML model, one or more aspects of the ML model may be validated using a second subset of the training dataset (e.g., different from the first subset of the training dataset). Such validation may involve applying the ML model to the second subset of the training dataset and making predictions derived from the second subset of training data. The ML model can then be evaluated to determine whether its performance is sufficient based on the derived predictions. The sufficiency criteria applied to the ML model may vary depending on the size of the training dataset available for training, the performance of past iterations of the trained model, or user-specified performance requirements. If the ML model does not achieve sufficient performance, additional training may be performed. Additional training may involve refining the ML model or retraining using a different first subset of the training dataset, after which the new ML model may be validated and evaluated again. If the ML model achieves sufficient performance, it may, in some cases, be saved for current or future use. ML models may be stored as sets of parameter values ​​or weights for analysis of further inputs (e.g., further predictor variables, further explanatory variables, further relevant parameters to be used as further user interaction data, etc.), and may also include analytical logic and instructions for model validity. In some cases, multiple ML models may be stored to generate predictions under different sets of input data conditions. In some embodiments, ML models may be stored in a database (e.g., one associated with a server).

[0075] Neural Networks - In some embodiments, machine learning algorithms include neural networks. Artificial neural networks (ANNs), a type of machine learning algorithm, may be part of the trained models described herein. For example, feedforward neural networks (such as convolutional neural networks (CNNs)) and recurrent neural networks (RNNs) may be used. In some cases, multiple layers of neural networks may be employed to create deep neural networks. Using deep neural networks can improve the predictive power of neural network algorithms. In some cases, machine learning algorithms using neural networks may further include Adam optimization (e.g., adaptive learning rate), regularization, etc. The number of layers, the number of nodes in a layer, the stride length in convolutional neural networks, padding, filters, etc., may be tunable parameters in a neural network.

[0076] Ensemble Learning - In some embodiments, machine learning algorithms include ensemble learning methods. Ensemble learning can be a machine learning technique that improves the accuracy and resilience of predictions by integrating predictions from multiple models.

[0077] Ensemble learning can create a large metamodel by statistically combining results from multiple smaller and simpler models. These smaller models do not need to have the same architecture, but can predict similar or identical features to the large model. In some cases, the output of the metamodel and each submodel is the energy of the molecular system. The energy from the metamodel is the average of the energies from the submodels and can be expressed as follows:

[0078]

number

[0079] In some cases, ensemble learning methods include ANI architectures. A description of ANI architectures is provided at https: / / arxiv.org / ftp / arxiv / papers / 1801 / 1801.09319.pdf, which is incorporated herein by reference for all purposes. If the confidence criterion is greater than the tolerance, the structure may be used to retrain the model.

[0080] The ANI model incorporates atomic number and coordinates in orthogonal coordinate space to predict the energy of the entire molecule. An example using ANI-1 is shown, for example, at https: / / arxiv.org / ftp / arxiv / papers / 1610 / 1610.08935.pdf, which is incorporated herein by reference for all purposes.

[0081] The ANI model is a type of chemical potential method using general machine learning. The ANI model is not specific to any particular atom or system type. However, in some cases, certain trained instances, such as ANI-lx and ANI-2x, may restrict the set of atoms that are allowed. For example, ML models like the ANI model can directly predict the energy of a molecular system. For more details on the ANI model, see, for example, https: / / arxiv.org / ftp / arxiv / papers / 1610 / 1610.08935.pdf, which is incorporated herein by reference for all purposes. Since the input parameters of the ANI model include atomic coordinates, the forces acting on the molecule can be determined by automatic differentiation.

[0082] In some cases, the ensemble learning method includes the step of combining results from one or more submodels to create a metamodel. In some cases, the ensemble learning method includes a MACE or espaloma architecture. In some cases, the submodels within the metamodel include a MACE or an espaloma. A MACE may include an equivariant message passing neural network (see https: / / arxiv.org / pdf / 2206.07697.pdf), which is incorporated herein by reference in its entirety. An Espaloma may include a machine-learned molecular dynamics force field (see https: / / arxiv.org / abs / 2307.07085), which is incorporated herein by reference in its entirety. In some embodiments, the submodels within the metamodel include an ANI deep learning potential. In some embodiments, one or more submodels include one or more polarizable atom interaction neural networks (PaiNN), DimeNet++ deep learning potentials, or PauliNet. PaiNN (Deep Learning Potential) is described, for example, at https: / / arxiv.org / abs / 2102.03150, and the entire work is incorporated herein by reference. DimeNet++ is described, for example, at https: / / arxiv.org / abs / 2011.14115, and the entire work is incorporated herein by reference. PauliNet is described, for example, at https: / / arxiv.org / abs / 1909.08423, and the entire work is incorporated herein by reference. In some cases, one or more submodels include SchNET, OCP, etc., and SchNET is described, for example, at https: / / arxiv.org / abs / 1712.06113, and the entire work is incorporated herein by reference.The Open Catalyst Project (OCP) also generates an Al model that can be used as a sub-model herein (see, for example, https: / / opencatalystproject.org / ), and the entire OCP is incorporated herein by reference.

[0083] Automated reliability In step 140, the method may include a step of determining a reliability index for energy or force at coordinates determined using a trained model. In some cases, the method may include a step of determining a reliability index. By combining the trained model with reaction pathway prediction, highly reliable reaction pathway prediction and transition state determination can be provided simultaneously. In some cases, the method may also continuously improve the ML model used to provide potentials along this pathway. For example, a structure for investigation may be generated using a reaction pathway prediction algorithm, and a set of molecular coordinates may be generated. Then, the energy, force, and reliability at this set of molecular coordinates can be evaluated using an ensemble general-purpose ML potential.

[0084] From there, two things can happen. If the ML potential is sufficiently reliable (e.g., the standard deviation is below an acceptable threshold), these energies and forces can be passed directly to the reaction pathway prediction algorithm. If the ML potential is not sufficiently reliable, quantum chemical calculations can be initiated to calculate the energies and forces in first principles. The type of quantum chemical calculation initiated can match that used to generate the original training dataset for the ML potential. For example, if the original training set was calculated using single and double bond clusters with cc-pVTZ basis sets, that calculation can be initiated. The energies, forces, atomic numbers, and atomic coordinates obtained from this calculation can be saved for further training of the ML potential.

[0085] In some cases, Method 100, 200, 300, or 400 further includes, until the completion criterion is met, (i) if the reliability index is below a threshold reliability value, the steps of evaluating the energy or force at the unreliable coordinate, selecting another coordinate on the energy surface, using a trained model to evaluate the energy or force at the other coordinate, and determining a reliability index for the energy or force at the other coordinate; and (ii) if the reliability index is greater than a threshold reliability value, the steps of selecting another coordinate on the energy surface, using a trained model to evaluate the energy at the other coordinate, and determining a reliability index for the energy or force at the other coordinate.

[0086] In some cases, in (i), the method further includes the steps of conserving energy or force for retraining and retraining the trained model based on the energy or force in (i). In some embodiments, the step of selecting a different coordinate on the energy plane includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

[0087] Returning to Figure 4, in some cases, the method may include step 425: if the reliability index is below a threshold reliability value, evaluate the first-principles energy or first-principles force in the conformational coordinates. After step 425, the method may include the steps of selecting an alternative conformational coordinate on the potential energy surface, using a trained model to evaluate the energy or force in the alternative conformational coordinate, and determining a reliability index for the energy or force in the alternative conformational coordinate.

[0088] In some cases, the method may include step 430: selecting an alternative conformation on the potential energy surface if the reliability index is greater than a threshold reliability value. After step 425, the method may include using a trained model to evaluate the energy at the alternative conformation and determining a reliability index for the energy or force at the alternative conformation.

[0089] In some cases, the method may include a step 440 for determining whether the completion conditions have been met. If the completion conditions have not been met, the method may include a step of repeating steps 410, 420, 425, and 430 until the completion conditions are met.

[0090] Reliability Metrics – In some cases, methods 100, 200, 300, or 400 further include a step of determining a reliability metric. In some cases, computational chemistry models can output their own reliability metrics. For example, if a computational chemistry method outputs an error estimate, that error estimate can be used as a reliability metric. Bayesian models can be an example of models that generate a measure of uncertainty. For example, Gaussian process regression can generate a measure of uncertainty. In some cases, if the computed reaction pathway is not smooth, the uncertainty of values ​​that deviate significantly from a smooth curve may be high. In some cases, the same ML model may be run multiple times and the standard deviation calculated.

[0091] In some cases, reliability testing involves calculating the standard deviation using inference results based on multiple ML models. In some cases, the multiple ML models are part of an ensemble learning model. In some cases, reliability testing involves similarity searching between the training dataset and the input query to identify the rarity of the input query. In some cases, inference reliability testing involves instance selection strategies to select important instances for refining the ML model. Instance selection strategies include uncertainty sampling approaches, query by committee approaches, expected model change approaches, expected error reduction approaches, and density weighted methods.

[0092] In some cases, the process of determining a reliability metric involves combining results from one or more submodels to create a metamodel, calculating the energy for each of the one or more submodels, and calculating the standard deviation of the energy for each of the one or more submodels. In some cases, the standard deviation constitutes part of the reliability metric. For example, the reliability of a particular assessment can be estimated by taking the standard deviation of the energy predicted by the submodels of an ensemble learning method. In some cases, the standard deviation may be normalized based on the model architecture to produce a consistent estimate of the model's reliability. For example, in an ensemble ANI architecture, the normalized standard deviation is given as follows:

[0093]

number

[0094] quantum chemical calculation In step 150, the method may optionally include a step of evaluating energy or force based on quantum chemical calculations, depending on the reliability index. The quantum chemical calculations may correspond to the training dataset of the trained model described above. For example, the type of quantum chemical calculation to be started may match that used to generate the original training dataset of the ML potential. For example, if the original training set was calculated on single and double bond clusters using cc-pVTZ basis functions, that calculation may be started. The energy, force, atomic number, and atomic coordinates obtained from this calculation may be saved for further training of the ML potential.

[0095] For example, if the reliability of the ML potential is insufficient, quantum chemical calculations can be initiated to first-principlesally calculate the energy and force. The type of quantum chemical calculation initiated can match that used to generate the original training dataset for the ML potential. For instance, if the original training set was calculated using single and double bond clusters with cc-pVTZ basis sets, that calculation can be initiated. The energy, force, atomic number, and atomic coordinates obtained from this calculation can be saved for further training of the ML potential.

[0096] In some cases, the process of evaluating energy or force based on quantum chemical calculations includes the process of evaluating first-principles energy or first-principles force in coordinates. In some cases, first-principles energy or first-principles force is calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or ONIOM model.

[0097] In some cases, the process of calculating energy or force may involve at least one of the following methods: Hartree-Fock method (HF), density functional theory (DFT), coupled cluster single, double, and perturbative triple excitation (CCSD(T)), full configuration interaction (FCI), heat-bath configuration interaction (HBCI), quantum Monte Carlo full configuration interaction (QMCFCI), density matrix embedding theory (DMET), fragment molecular orbital method (FMO), incremental full configuration interaction (iFCI), hybrid quantum mechanics-molecular mechanics (QM / MM), first-principles molecular dynamics (AIMD) simulation, variational Monte Carlo method, and diffusion Monte Carlo method.

[0098] In some cases, methods 100, 200, 300, or 400 further include a step of saving energy or force from quantum chemical calculations in order to retrain the trained model.

[0099] In some cases, methods 100, 200, 300, or 400 further include the step of selecting an alternative conformation on the potential energy surface after calculating the force or energy at a higher-order theoretical level. In the next conformation, the method may include the step of using a trained model to evaluate the energy or force in the new conformation. In the new conformation, the method may include the step of determining a reliability index for the energy or force in the new conformation.

[0100] Model Output In some cases, methods 100, 200, 300, or 400 further include the step of selecting an alternative conformation on the potential energy surface if the reliability index is greater than a threshold reliability value. This method may include the steps of using a trained model to evaluate the energy at the alternative conformation and determining a reliability index for the energy or force at the alternative conformation.

[0101] In some cases, methods 100, 200, 300, or 400 further include a step of determining whether completion conditions have been met. If the completion conditions have not been met, the method may include a step of repeating steps 410, 420, 425, and 430 until the completion conditions are met. Completion conditions may include reaching thresholds such as the maximum number of cycles, the threshold change in energy, or the threshold change in a reliability index.

[0102] In some cases, methods 100, 200, 300, or 400 further include a step of outputting a transition state or reaction pathway on the energy plane. In some cases, the reaction pathway is a minimum energy pathway. In some cases, methods 100, 200, 300, or 400 further include a step of outputting a set of energies or forces in a set of coordinates on the energy plane, at least partially based on energies or forces calculated from higher-order theoretical methods (e.g., quantum chemical methods).

[0103] In some cases, methods 100, 200, 300, or 400 further include the step of outputting a set of energy or force in a set of conformational coordinates on the potential energy surface. In some cases, the outputted set of energy or force is output after a completion condition is met.

[0104] ML retraining The methods and systems of this disclosure may also be integrated with retraining or updating a trained model. For example, this application provides a method and system for determining a reaction pathway, including retraining a trained model. Referring again to Figure 3, a flowchart is shown illustrating an example of method 300 for determining a reaction pathway and updating a trained model using data from quantum chemical calculations. In step 301, method 300 may include providing indications of reactants and products or at least one of the driving coordinates. In step 310, method 300 may include providing a set of coordinates. The set of coordinates may lie on an energy plane connecting reactants and products or at least one of the driving coordinates. In step 320, method 300 may include evaluating the energy or force at the coordinates of the set of coordinates using the trained model. In step 330, method 300 may include determining that a confidence index at the coordinates is less than a threshold confidence value. In step 340, method 300 may include evaluating the energy or force at the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of the trained model. In step 350, method 300 may include a step of retraining the trained model based on the energy or force in 340.

[0105] In one example of Method 300, the present application provides a computer-aided method for determining a reaction pathway. This method may include the steps of: (a) providing instructions for reactants and products or at least one of drive coordinates; (b) providing a set of conformational coordinates, the set of conformational coordinates being on a potential energy plane connecting the reactants and products or at least one of drive coordinates; (c) using a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) evaluating the first-principles energy or first-principles force in the conformational coordinates; and (e) retraining the trained model based on the first-principles energy or first-principles force.

[0106] In some cases, methods 100, 200, 300, or 400 further include passing energy and force based on training data to a machine learning model. In some cases, energy and force from the model corresponding to the training data can be fed back to the reaction pathway prediction algorithm. In some cases, energy and force from quantum chemical calculations can be fed back to the machine learning model. In some cases, energy and force from quantum chemical calculations can be fed back to the reaction pathway prediction algorithm. Once the reaction pathway prediction algorithm receives these quantities, it can continue as is. In some cases, it can continue without making any other changes. The step of retraining the ML potential to incorporate the new data points generated above can be performed separately from the reaction pathway prediction process. This retraining does not need to be performed during the reaction pathway prediction process, but it may be.

[0107] Computer system The systems and methods of this disclosure may perform various processes on a digital computer. In some cases, the digital computer includes one or more hardware central processing units (CPUs) that perform the functions of the digital computer. In some cases, the digital computer further includes an operating system configured to execute executable instructions. In some cases, the digital computer is connected to a computer network. In some cases, the digital computer is connected to the Internet to access the World Wide Web. In some cases, the digital computer is connected to a cloud computing infrastructure. In some cases, the digital computer is connected to an intranet. In some cases, the digital computer is connected to a data storage device.

[0108] Various types of digital computers may be used. In fact, suitable digital computers may include, but are not limited to, server computers, desktop computers, laptop computers, notebook computers, subnotebook computers, netbook computers, set-top computers, media streaming devices, handheld computers, internet appliances, mobile smartphones, tablet computers, personal digital assistants, video game consoles, and vehicles. Smartphones may be suitable for use with one or more examples of the methods and systems described herein. Certain televisions, video players, and digital music players (possibly with computer network connectivity) may be suitable for use with some of the systems and methods described herein. Suitable tablet computers may include those having booklet, slate, and convertible configurations.

[0109] In some cases, a digital computer includes an operating system configured to execute executable instructions. An operating system is software, for example, containing programs and data, that manages the device's hardware and provides services for running applications. Various types of operating systems can be used. For example, suitable server operating systems include, but are not limited to, FreeBSD, OpenBSD, NetBSD®, Linux, Apple® Mac OS X Server®, Oracle® Solaris®, Windows Server®, and Novell® NetWare®. Suitable personal computer operating systems may include, but are not limited to, Microsoft® Windows®, Apple® Mac OS X®, UNIX®, and UNIX-like operating systems such as GNU / Linux®. In some cases, operating systems are provided through cloud computing. Suitable mobile smartphone operating systems may include, but are not limited to, Nokia® Symbian® OS, Apple® iOS®, Research In Motion® BlackBerry OS®, Google® Android®, Microsoft® Windows Phone® OS, Microsoft® Windows Mobile® OS, Linux®, and Palm® WebOS®. Suitable media streaming device operating systems may include, but are not limited to, Apple TV®, Roku®, Boxee®, Google TV®, Google Chromecast®, Amazon Fire®, and Samsung® HomeSync®.Appropriate video game console operating systems may include, but are not limited to, Sony® PS3®, Sony® PS4®, Microsoft® Xbox 360®, Microsoft® Xbox One®, Nintendo® Wii®, Nintendo® Wii U®, and Ouya®.

[0110] In some cases, a digital computer includes storage devices and / or memory devices. Various types of storage and / or memory may be used in a digital computer. In some cases, storage devices and / or memory devices include one or more physical devices used to temporarily or permanently store data or programs. In some cases, devices include volatile memory, which requires power to maintain the stored information. In some cases, devices include non-volatile memory, which retains the stored information even when the digital computer is powered off. In some cases, non-volatile memory includes flash memory. In some cases, non-volatile memory includes dynamic random access memory (DRAM). In some cases, non-volatile memory includes ferroelectric random access memory (FRAM). In some cases, non-volatile memory includes phase-change random access memory (PRAM). In some cases, devices include storage devices, including, but not limited to, CD-ROMs, DVDs, flash memory devices, magnetic disk drives, magnetic tape drives, optical disk drives, and cloud computing-based storage. In some cases, storage devices and / or memory devices include combinations of devices such as those disclosed herein.

[0111] In some cases, a digital computer includes a display used to provide visual information to the user. Various types of displays may be used. In some cases, the display includes a cathode ray tube (CRT). In some cases, the display includes a liquid crystal display (LCD). In some cases, the display includes a thin-film transistor liquid crystal display (TFT-LCD). In some cases, the display includes an organic light-emitting diode (OLED) display. In some cases, the OLED display includes a passive-matrix OLED (PMOLED) display or an active-matrix OLED (AMOLED) display. In some cases, the display includes a plasma display. In some cases, the display includes a video projector. In some cases, the display includes a combination of devices such as those disclosed herein.

[0112] In some cases, a digital computer includes an input device for receiving information from a user. Various types of input devices may be used. In some cases, the input device includes a keyboard. In some cases, the input device includes a pointing device, including, but not limited to, a mouse, trackball, trackpad, joystick, game controller, or stylus. In some cases, the input device includes a touchscreen or multitouchscreen. In some cases, the input device includes a microphone for acquiring audio or other acoustic input. In some cases, the input device includes a video camera or other sensor for acquiring motion or visual input. In some cases, the input device includes Kinect®, Leap Motion®, etc. In some cases, the input device includes a combination of devices such as those disclosed herein.

[0113] Referring to Figure 5, an illustrative schematic diagram of a system for determining reaction pathways is shown. This system is configured to determine reaction pathways using one or more machine learning (ML) models, such as neural networks or ensemble machine learning models.

[0114] The system may include a digital computer 500. The digital computer can be of various types, such as, for example, a digital computer as described elsewhere in this specification. The digital computer may include at least one processing unit 506 and at least one memory 512. At least one memory may contain a computer program executable by the processing unit 506, and the processing unit 506 may be configured to provide or receive instructions for reactants and products or driving coordinates, provide or receive sets of coordinates on an energy plane, evaluate energy or force using a trained model, determine a reliability index for energy or force at the coordinates determined by the trained model, and optionally evaluate energy or force based on quantum chemical calculations depending on the reliability index.

[0115] The system may include a computing platform 502 operably connected to a digital computer 500. The computing platform 502 may include at least one processor 516. The at least one processor 516 can be any type of processor, such as, for example, a processor of the type described elsewhere in this specification. The at least one processor may include noisy medium-scale quantum (NISQ) technology, any quantum device, any high-performance computing device, any quantum annealer, any optical computing device, an integrated photon coherent Ising machine, etc. For example, the at least one processor may include at least one field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), central processing unit (CPU), graphics processing unit (GPU), tensor processing unit (TPU), tensor streaming processor (TSP), quantum computer, quantum annealer, integrated photon coherent Ising machine, optical quantum computer, etc., or any combination thereof. The computing platform 502 may be provided by a cloud computing system. In some cases, the computing platform 502 includes an array of distributed high-performance computing units. Distributed high-performance computing units may include various types of processing units as described herein.

[0116] Each component of the system (e.g., hardware) may be used as part of the system to execute the whole method or a part of it, either alone or in combination with other components (e.g., other hardware). In some cases, these components may be used to take a request containing at least one property of a molecule and a task instruction, to perform inference with at least one machine learning (ML) model using the acquired instruction, to perform an inference reliability test, to obtain a task result using the inference result if the reliability is satisfactory, or to perform the task and obtain a task result if the reliability is not satisfactory.

[0117] The computing platform 502 may be operably connected to the digital computer 500. The computing platform may be communicatively coupled to the digital computer. The computing platform may include a read control system 518. The read control system may be configured to read information (e.g., calculation results, parameters, etc.) from at least one processor 516. For example, the read control system may be configured to convert data from the FPGA into data usable by the digital computer.

[0118] The system may include a database 504. Database 504 may be operably connected to a digital computer 500. Database 504 can be of various types. Database 504 may refer to a central repository configured to store task specifications and task results. In some cases, the database may be, for example, MongoDB. Database 504 may be used to store molecular properties, corresponding tasks, and resulting instructions. Database 504 may be used to store task results. Database 504 may further be used to store output from the chemical discovery toolbox. Database 504 may further be used to store datasets for training ML models. The datasets for training ML models may be a subset or the complete set of task results. The datasets for training ML models may further be a subset or the complete set of output from the chemical discovery toolbox. The processing unit 506 may further be configured to store molecular properties, corresponding tasks, and resulting instructions in database 504 and to read molecular property instructions from database 504.

[0119] The computing platform 502 and database 504 may be connected to the digital computer 500 via a network. The computing platform, database, and / or digital computer may have a network communication device. The network communication device may enable the computing platform, database, and / or digital computer to communicate with each other and with any number of user devices via the network. The network may be a wired or wireless network. For example, the network may be a fiber optic network, an Ethernet® network, a satellite network, a cellular network, a Wi-Fi® network, a Bluetooth® network, etc. In one or more embodiments, the computing platform, database, and / or digital computer may be multiple distributed computing platforms, databases, and / or digital computers accessible via the Internet. Such computing platforms, databases, and / or digital computers may be considered cloud computing devices. In some cases, one or more processors of at least one processor may be located in the cloud.

[0120] At least one processor 516 may contain one or more virtual machines. One or more virtual machines may be one or more emulations of one or more computer systems. A virtual machine may be a process virtual machine (e.g., a virtual machine configured to implement a process in a platform-independent environment). A virtual machine may be a system virtual machine (e.g., a virtual machine configured to run an operating system and associated programs). A virtual machine may be configured to emulate an architecture different from at least one processor. For example, a virtual machine may be configured to emulate a quantum computing architecture on a silicon computer chip. Examples of virtual machines may include, but are not limited to, VMware®, VirtualBox®, Parallels®, QEMU®, Citrix® Hypervisor, Microsoft® Hyper-V®, etc.

[0121] The system in Figure 5 can provide or receive instructions for reactants and products or at least one of the drive coordinates, provide or receive a set of conformal coordinates on the potential energy plane connecting the reactants and products or at least one of the drive coordinates, use a trained model to evaluate the energy or force in the conformal coordinates of the set of conformal coordinates, determine a reliability index in the conformal coordinates, and optionally evaluate first-principles energy or first-principles force in the conformal coordinates.

[0122] In some cases, the digital computer 500 may receive, in the input device 516, a set of conformational coordinates, instructions for at least one of reactants and products or drive coordinates, or any combination thereof. In some cases, the system may, in the processor 506, provide, based on instructions from the user, a set of conformational coordinates, instructions for at least one of reactants and products or drive coordinates, or any combination thereof. In some cases, the digital computer 500 is a user's device that provides the user with access to an application programming interface.

[0123] In some cases, the system is configured to use a trained model to evaluate the energy or force in the conformal coordinates of a set of conformal coordinates. In some cases, the system is configured to have the processing unit 516 perform any of the following: use a trained model to evaluate the energy or force in the conformal coordinates of a set of conformal coordinates, determine a reliability index in the conformal coordinates, evaluate first-principles energy or first-principles force in the conformal coordinates, or any combination thereof. The system may run the trained model via a communication port. In some cases, the system is configured to have the CPU 506 perform any of the following: use a trained model to evaluate the energy or force in the conformal coordinates of a set of conformal coordinates, determine a reliability index in the conformal coordinates, evaluate first-principles energy or first-principles force in the conformal coordinates, or any combination thereof. In some cases, the processing unit 516 includes an array of distributed high-performance computing units. Distributed high-performance computing units may include various types of processing units as described herein.

[0124] This disclosure provides a computer system programmed to carry out the method of this disclosure. Figure 6 shows a computer system 601 programmed or configured to perform steps of the method for determining a reaction pathway disclosed herein. Computer system 601 may include modifications or examples of embodiments of the digital computer 500 of Figure 5. For example, computer system 601 may be programmed or configured to (a) provide or receive instructions for at least one of reactants and products or drive coordinates; (b) provide or receive a set of conformational coordinates on the potential energy plane connecting the reactants and products or drive coordinates; (c) use a trained model to evaluate the energy or force in the conformational coordinates of the set of conformational coordinates; (d) determine that a reliability index in the conformational coordinates is less than a threshold reliability value; (e) evaluate the first-principles energy or first-principles force in the conformational coordinates; and (f) output a set of energy or force in the set of conformational coordinates on the potential energy plane, at least in part, based on the first-principles energy or first-principles force and the energy or force.

[0125] The computer system 601 can be a computer system located on the user's electronic device or remotely from the electronic device. The electronic device can be a mobile electronic device.

[0126] The computer system 601 includes a central processing unit (CPU, e.g., CPU 506, also referred to herein as “processor” and “computer processor”) 605, the central processing unit may be a single-core processor, a multi-core processor, or multiple processors for parallel processing. The computer system 601 also includes memory or memory locations 610 (e.g., random-access memory, read-only memory, flash memory, e.g., memory 512), an electronic storage unit 615 (e.g., a hard disk), a communication interface 620 for communicating with one or more other systems (e.g., a network adapter, e.g., a communication port 514), and peripherals 625 such as a cache, other memory, data storage, and / or an electronic display adapter. The memory 610, storage unit 615, interface 620, and peripherals 625 communicate with the CPU 605 via a communication bus (solid line), such as a motherboard. The storage unit 615 may be a data storage unit (or data repository) for storing data. Computer system 601 can be operationally connected to computer network ("Network") 630 via communication interface 620. Network 630 may be the Internet, the Internet and / or an extranet, or an intranet and / or extranet communicating with the Internet. Network 630 may, in some cases, be a telecommunications network and / or a data network. Network 630 may include one or more computer servers that enable distributed computing, such as cloud computing. Network 630 may, in some cases, implement a peer-to-peer network with the assistance of computer system 601, thereby enabling devices connected to computer system 601 to act as clients or servers.

[0127] The CPU 605 can execute a sequence of machine-readable instructions that can be embodied in a program or software. Instructions may be stored in a memory location, such as memory 610. Instructions are sent to the CPU 605, which can then be programmed or configured to perform the methods of this disclosure. Examples of steps performed by the CPU 605 may include fetching, decoding, executing, and writing back.

[0128] The CPU 605 can be part of a circuit, such as an integrated circuit. One or more other components of system 601 can be included in this circuit. In some cases, this circuit is an application-specific integrated circuit (ASIC).

[0129] The storage unit 615 can store files such as drivers, libraries, and saved programs. The storage unit 615 can also store user data (e.g., user settings and user programs). The computer system 601 may, in some cases, include one or more additional data storage units located outside of the computer system 601, such as on a remote server communicating with the computer system 601 via an intranet or the internet.

[0130] Computer system 601 can communicate with one or more remote computer systems via network 630. For example, computer system 601 can communicate with a user's remote computer system. Examples of remote computer systems include personal computers (e.g., portable PCs), slate PCs or tablet PCs (e.g., Apple® iPad, Samsung® Galaxy Tab), telephones, smartphones (e.g., Apple® iPhone, Android devices, Blackberry®), or personal digital assistants. Users can access computer system 601 via network 630.

[0131] The methods described in this specification can be implemented by machine-executable code (e.g., computer processor) stored in an electronic storage location (e.g., memory 610 or electronic storage unit 615) of the computer system 601. The machine-executable code or machine-readable code can be provided in the form of software. When in use, the code can be executed by the processor 605. In some cases, the code can be retrieved from the storage unit 615 and stored in memory 610 for easy access by the processor 605. In some cases, the electronic storage unit 615 can be omitted, and machine-executable instructions are stored in memory 610.

[0132] The code can be pre-compiled and configured for use on a machine with a processor adapted to run the code, or it can be compiled at runtime. The code can be provided in a selectable programming language so that it can run in either a pre-compiled or compiled form.

[0133] Embodiments of systems and methods provided herein, such as computer system 601, can be embodied by programming. Various embodiments of the art may typically be considered “products” or “manufactured goods” in the form of machine (or processor) executable code and / or related data held or embodied in some kind of machine-readable medium. Machine executable code may be stored in electronic storage units such as memory (e.g., read-only memory, random-access memory, flash memory) or hard disks. “Storage” type media may include any or all tangible memories provided by a computer or processor, or related modules thereof (e.g., various semiconductor memories, tape drives, disk drives), that can provide non-temporary storage for software programming from time to time, such as various semiconductor memories, tape drives, disk drives, etc. All or part of the software may, in some cases, be communicated over the Internet or other various communication networks. Such communication may enable loading software from one computer or processor to another, for example, from a management server or host computer to an application server computer platform. Therefore, other types of media that can hold software elements include optical waves, electrical waves, and electromagnetic waves, such as those used in physical interfaces between local devices, wired and optical fixed-line networks, and various air links. Physical elements such as wired or wireless links and optical links that transmit such waves may also be considered media that hold software. In this specification, unless limited to non-temporary tangible “storage” media, terms such as computer or machine “readable media” mean any medium involved in providing instructions for execution to a processor.

[0134] Therefore, machine-readable media such as computer executable code can take many forms, including but not limited to tangible storage media, carrier media, or physical transmission media. Non-volatile storage media include optical and magnetic disks, such as optical disks and magnetic disks, in any storage device such as any computer, which may be used to implement, for example, a database as shown in the drawing. Volatile storage media include dynamic memory, such as the main memory of such a computer platform. Tangible transmission media include coaxial cables, copper wires, and optical fibers, which also include wiring that makes up buses in computer systems. Carrier media can take the form of electrical or electromagnetic signals, or sound or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Therefore, common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, and other magnetic media; CD-ROMs, DVDs or DVD-ROMs, and other optical media; punch cards, paper tapes, and other physical storage media with perforated patterns; RAM, ROMs, PROMs and EPROMs, flash EPROMs, and other memory chips or cartridges; carriers for transmitting data or instructions; cables or links for transmitting such carriers; or other media from which a computer can read programming code and / or data. Many of these forms of computer-readable media can be involved in transmitting one or more sequences of one or more instructions to a processor for execution.

[0135] The computer system 601 includes, or can communicate with, an electronic display 635 (e.g., display device 508) equipped with a user interface (UI) 640 (e.g., input device 510) for providing outputs such as coordinates, structure, energy, and geometric structure. Examples of UIs include, but are not limited to, graphical user interfaces (GUIs) and web-based user interfaces.

[0136] The methods and systems disclosed herein can be implemented by one or more algorithms. The algorithms can be implemented by software during execution by the central processing unit 605. The algorithms can, for example, perform one or more steps of the method for determining a reaction pathway disclosed herein.

[0137] Quantum computer system In some cases, the systems and methods disclosed herein may be carried out with the help of a quantum computing system. In some cases, the computer implementations of the disclosure may be carried out at least partially by a quantum computer. In some cases, the computing systems of the disclosure may include a hybrid computing unit. In some cases, the hybrid computing unit may include a classical computer and a quantum computer. The quantum computer may be configured to execute one or more quantum algorithms for solving a computational problem (e.g., at least part of a reaction pathway calculation). The quantum processor may include the processing unit QC of element 516 in Figure 5.

[0138] One or more quantum algorithms may be executed using a quantum computer, a quantum-ready computing service, or a quantum-enabled computing service. For example, one or more quantum algorithms may be executed using the system or method described in U.S. Patent Publication 2018 / 0107526, “Methods and Systems for Quantum Ready and Quantum-Enabled Computations,” which is incorporated herein by reference. A classical computer may include at least one classical processor and computer memory and may be configured to execute one or more classical algorithms for solving a computational problem (e.g., at least a portion of a reaction pathway calculation).

[0139] A digital computer may include at least one computer processor and computer memory, and may include a computer program having instructions executable by at least one computer processor, and may render applications. These applications may facilitate the use of quantum and / or classical computers by users.

[0140] In some implementations, quantum computers could be used in conjunction with classical computers that operate at the bit level, such as personal desktops, laptops, supercomputers, distributed computing, clusters, cloud-based computing resources, smartphones, or tablets.

[0141] The system may include an interface for the user. In some cases, the interface may include an application programming interface (API). The interface may provide a programming model that removes the internal details of the quantum computer (e.g., architecture and operation) (e.g., by concealing them from the user). In some cases, the interface may minimize the need to update application programs in response to changes in quantum hardware. In some cases, the interface may remain unchanged even if the internal structure of the quantum computer changes.

[0142] This disclosure provides non-classical (e.g., quantum) computing, or systems and methods that may involve the use of non-classical (e.g., quantum) computing. Quantum computers may be able to solve certain types of computing tasks more efficiently than classical computers. However, quantum computing resources can be scarce and expensive, and using them efficiently or effectively (e.g., cost-effective or cost-efficient) may require certain expertise. Several parameters can be tuned for a quantum computer to realize its potential computing power.

[0143] Quantum computers (or other types of non-classical computers) may be able to operate in parallel with classical computers as coprocessors. Hybrid architectures (e.g., computing systems) including classical and quantum computers may be highly efficient in dealing with complex computational tasks such as quantum chemical simulations. The systems and methods disclosed herein may be able to efficiently and accurately decompose or subdivide quantum chemical problems and delegate appropriate elements of quantum chemical simulations to quantum computers or classical computers.

[0144] While this disclosure refers to quantum computers, the methods and systems described herein are also applicable in conjunction with other types of computers that may be non-classical computers. Such non-classical computers may include quantum computers, hybrid quantum computers, quantum-type computers, or other computers that are not classical. Examples of non-classical computers may include, but are not limited to, the Hitachi Ising solver, coherent Ising machines based on optical parameters, and other solvers that utilize different physical phenomena to solve certain types of problems more efficiently.

[0145] In some cases, a quantum computer may include one or more adiabatic quantum computers, quantum gate arrays, one-way quantum computers, topological quantum computers, quantum Turing machines, superconducting-based quantum computers, trapped-ion quantum computers, trapped-atom quantum computers, optical lattices, quantum dot computers, spin-based quantum computers, space-based quantum computers, Loss-DiVincenzo quantum computers, nuclear magnetic resonance (NMR)-based quantum computers, solution-state NMR quantum computers, solid-state NMR quantum computers, solid-state NMR Kane quantum computers, electrons-on-helium quantum computers, cavity quantum electrodynamics-based quantum computers, molecular magnet quantum computers, fullerene-based quantum computers, linear optical quantum computers, diamond-based quantum computers, nitrogen vacancy (NV) diamond-based quantum computers, Bose-Einstein condensate-based quantum computers, transistor-based quantum computers, and rare-earth metal ion-doped inorganic crystal-based quantum computers. A quantum computer may include one or more of the following: quantum annealers, Ising solvers, optical parametric oscillators (OPOs), and gate models of quantum computation.

[0146] In some cases, the non-classical computers of this disclosure may include noisy, medium-scale quantum devices. "Noisy" may mean that control over the qubits is imperfect, and "medium-scale" may mean that the number of qubits can range from 50 to several hundred. Several physical systems consisting of superconducting qubits, artificial atoms, and ion traps have been proposed to date as feasible candidates for constructing NISQ quantum devices and ultimately general-purpose quantum computers.

[0147] In some cases, classical simulators for quantum circuits can be used, which are run on classical computers such as MacBook Pro laptops, Windows laptops, or Linux laptops. In some cases, classical simulators can be run on cloud computing platforms that provide parallel or distributed access to multiple computing nodes. In some cases, all or part of quantum mechanical energy and / or electronic structure calculations can be performed using classical simulators.

[0148] The methods described herein can be implemented on an analog quantum simulator. An analog quantum simulator may be a quantum mechanical system consisting of multiple fabricated qubits. An analog quantum simulator may be designed to simulate a quantum system using a system that is physically different but mathematically equivalent or nearly equivalent. In an analog quantum simulator, each qubit may be realized as an ion in a sequence of atomic ions trapped in a linear radio frequency trap. Each qubit may be coupled with a bias source called a local field bias. The local field bias on a qubit may be programmable and controllable. In some cases, a qubit control system including a digital processing unit may be connected to the qubit system to program and adjust the local field bias on the qubits.

[0149] Examples Example 1: Diels-Alder GSM Experiment Figure 7 is a schematic diagram of the chemical reaction in which s-cis-butadiene reacts with ethene to produce cyclohexene. The growth string method (GSM) was used to predict the transition state and reaction pathway in the "s-cis-butadiene + ethene → cyclohexene reaction" shown in Figure 7. This reaction pathway was predicted using multiple different models to evaluate the effectiveness of ML models with different training data. This experiment proved to be a proof of concept that ML models can effectively model transition states and reaction pathways when retrained with relevant data. It has been shown that when ensemble ML models have high variability, performing quantum chemical calculations and retraining the ML models with that data increases the likelihood of the ML models succeeding in predicting reaction pathways.

[0150] Methodology. The following energy and force evaluation tools were used: 6-31G* / coB97X theoretical-level density functional theory (DFT); ANLlx machine learning (ML) model trained on the original ANLlx dataset (referred to as "ANI / ANIlx"); and ANLlxML model trained on the Transition-lx dataset (referred to as "ANI / Transitionlx"). For each evaluation tool, the reactant and product structures were optimized to local minima before the GSM calculation. Then, the GSM calculation was performed using the corresponding evaluation tool to calculate the energy and force at each GSM node during string growth and optimization processes.

[0151] Results: Reaction pathway prediction algorithms can be evaluated based on both the quality of the predicted transition states and the overall quality of the calculated reaction pathways. In this case, the ANI / ANIlx evaluation tool performed quantitatively worse than the ANI / Transitionlx evaluation tool and failed to qualitatively predict the correct transition states.

[0152] To quantitatively compare these models, the absolute energy and reaction barrier of each ML evaluation tool are compared with those of the DFT evaluation tool (see Table 1 for values). The deviations from the DFT results for the ANI / ANIlx evaluation tool are approximately 0.0117 Hartree for absolute energy and approximately 4.4 kcal / mol for reaction barrier. The deviations from the DFT results for the ANI / Transitionlx evaluation tool are approximately 0.0040 Hartree for absolute energy and approximately 1.2 kcal / mol for reaction barrier. The ANI / Transitionlx evaluation tool not only outperforms the ANI / ANIlx evaluation tool but also predicts the reaction barrier with an accuracy close to the chemical precision of the DFT results (1 kcal / mol).

[0153] Figure 8 is a plot of the calculated data, showing the reaction pathway energy profiles for DFT (solid line), ANI / ANIlx (dashed line), and ANI / Transitionlx (dotted line), the GSM node energy (hollowed out), and the median values ​​estimated by cubic spline interpolation (regression line). Qualitatively, it can be seen that the ANI / ANIlx evaluation tool predicts a different reaction mechanism than DFT and ANI / Transitionlx. DFT and ANI / Transitionlx predict the correct transition state in which ethene approaches butadiene from outside the bond surface, while ANI / ANIlx predicts a transition state involving C2-C3 bond twisting and direct adhesion of ethene across the butadiene bond surface. This suggests that the double-barrier properties of the ANI / ANIlx reaction pathway may be observed in the reaction pathway originating first from butadiene twisting and then bond formation.

[0154] Figure 9A shows computational data illustrating the molecular structures of the reactants (left), transition state (center), and product (right) as predicted by GSM using the ANI / ANIlx model. Figure 9B shows computational data illustrating the molecular structures of the reactants (left), transition state (center), and product (right) as predicted by GSM using the ANI / Transitionlx model. Figure 9C shows computational data illustrating the molecular structures of the reactants (left), transition state (center), and product (right) as predicted by GSM using the DFT model. As can be seen from the snapshots of the transition state structure (center) in Figures 9A to 9C, the ANI / ANIlx evaluation tool predicts a reaction mechanism different from both DFT and ANI / Transitionlx. DFT and ANI / Transitionlx predict the correct transition state in which ethene approaches from the outside of the butadiene bond surface, while ANI / ANIlx predicts a transition state that includes a twist of the C2-C3 bond and direct attachment of ethene across the butadiene bond surface.

[0155] Figure 10 shows the superposition of the transition state structures predicted by GSM using DFT (filled, 1030), ANI / ANIlx (outlined, 1010), and ANI / Transitionlx (textured, 1020), with all structures transformed to have the same overall center of mass. Figure 10 also shows the differences in the transition state geometry.

[0156] [Table 1]

[0157] While preferred embodiments of the present invention have been described and illustrated herein, it will be apparent to those skilled in the art that these embodiments are merely illustrative. The present invention is not intended to be limited by the specific examples provided herein. Although the present invention has been described with reference to the preceding specification, the descriptions and illustrations of embodiments herein should not be construed as restrictive. Those skilled in the art will be able to conceive of various modifications, changes, and alternatives without departing from the present invention. Furthermore, it should be understood that all aspects of the present invention are not limited to the specific descriptions, configurations, or relative proportions described herein, which depend on various conditions and variables. It should be understood that various alternative forms of the embodiments of the present invention described herein may be adopted when carrying out the present invention. Accordingly, the present invention is intended to encompass such alternative forms, modifications, variations, or equivalents. The following claims define the scope of the present invention, and methods and structures within the scope of these claims, as well as their equivalents, are intended to be encompassed by the present invention.

Claims

1. A computer-based method for determining a reaction pathway, wherein the method is: (a) A step of providing instructions for at least one of the reactants and the product or the drive coordinate, (b) A step of providing a set of coordinates, wherein the set of coordinates lies on an energy plane connecting the reactants and the products or at least one of the drive coordinates, (c) A step of evaluating the energy or force in the coordinates of the set of coordinates using a trained model, (d) A step of determining whether the reliability index in the coordinates is less than the threshold reliability value, (e) A step of evaluating the energy or force in the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of the trained model, (f) A step of outputting a set of energy or force in the set of coordinates on the energy plane, based at least partially on the energy or force in (e) and the energy or force in (c), A computer implementation method, including

2. The computer implementation method according to claim 1, wherein the energy surface is a potential energy surface.

3. The computer implementation method according to claim 1 or 2, wherein the energy surface is a free energy surface.

4. The computer implementation method according to any one of claims 1 to 3, wherein the set of coordinates is a spatial coordinate system.

5. The computer implementation method according to any one of claims 1 to 4, wherein the set of coordinates is a Cartesian coordinate system.

6. The computer implementation method according to claim 5, wherein the Cartesian coordinates include the direction of movement.

7. (e) a computer implementation method according to any one of claims 1 to 6, comprising evaluating a first-principles energy or first-principles force in the coordinates.

8. Until the completion criteria are met, (i) If the reliability index is less than the threshold reliability value, (c) a step of evaluating the energy or force at the coordinates, selecting another coordinate on the energy plane, evaluating the energy or force at the other coordinate using the trained model, and determining a reliability index for the energy or force at the other coordinate, (ii) If the reliability index is greater than the threshold reliability value, A step of selecting another coordinate on the energy surface, evaluating the energy at the other coordinate using the trained model, and determining a reliability index for the energy or force at the other coordinate, A computer implementation method according to any one of claims 1 to 7, further comprising:

9. A computer implementation method according to any one of claims 1 to 8, further comprising (e) conserving the energy or force for retraining, and (c) retraining the trained model based on the energy or force.

10. The computer implementation method according to claim 8, further comprising (i) conserving the energy or force for retraining, and (i) retraining the trained model based on the energy or force.

11. The computer implementation method according to any one of claims 1 to 10, further comprising the step of evaluating a first energy or a first force at initial coordinates using the trained model.

12. The computer implementation method according to claim 11, further comprising the step of determining a reliability index of the first energy or the first force in the initial coordinates.

13. (f) further comprises outputting a transition state or reaction pathway on the energy plane, according to any one of claims 1 to 12.

14. The computer implementation method according to claim 13, wherein the reaction pathway is the minimum energy pathway.

15. The computer-aided method according to any one of claims 1 to 14, wherein the step of providing the set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

16. The computer implementation method according to claim 8, wherein selecting the other coordinate on the energy plane includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and intrinsic reaction coordinate method.

17. The computer implementation method according to any one of claims 1 to 16, wherein the trained model includes a machine learning algorithm.

18. The computer implementation method according to claim 17, wherein the machine learning algorithm includes a neural network.

19. The computer implementation method according to claim 17, wherein the machine learning algorithm includes an ensemble learning method.

20. (d) a computer implementation of the method according to claim 18 or 19, comprising combining results from one or more submodels to create a metamodel, calculating the energy of each of the one or more submodels, and calculating the standard deviation of the energies of the one or more submodels, wherein the standard deviation constitutes part of the reliability index.

21. The computer implementation method according to claim 20, wherein the metamodel includes an ANI deep learning potential.

22. The computer implementation method according to claim 20 or 21, wherein the one or more submodels include one or more of PAINN deep learning potential, DimeNet++ deep learning potential, or PauliNet.

23. (e) a computer implementation according to any one of claims 1 to 22, comprising evaluating a first-principles energy or first-principles force in the coordinates, wherein the first-principles energy or first-principles force is calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or the ONIOM model.

24. A computer-based method for determining a reaction pathway, wherein the method is: (a) A step of providing instructions for at least one of the reactants and the product or the drive coordinate, (b) A step of providing a set of coordinates, wherein the set of coordinates lies on an energy plane connecting the reactants and the products or at least one of the drive coordinates, (c) A step of evaluating the energy or force in the coordinates of the set of coordinates using a trained model, (d) A step of evaluating the energy or force in the coordinates based at least in part on quantum chemical calculations corresponding to the training dataset of the trained model, (e) A step of retraining the trained model based on the energy or force in (d), A computer implementation method, including

25. The computer implementation method according to claim 24, wherein the energy surface is a potential energy surface.

26. The computer implementation method according to claim 24 or 25, wherein the energy surface is a free energy surface.

27. The computer implementation method according to any one of claims 24 to 26, wherein the set of coordinates is a spatial coordinate system.

28. The computer implementation method according to any one of claims 24 to 27, wherein the set of coordinates is a Cartesian coordinate system.

29. The computer implementation method according to claim 28, wherein the Cartesian coordinates include the direction of movement.

30. (d) a computer implementation according to any one of claims 24 to 29, comprising evaluating a first-principles energy or first-principles force in the coordinates.

31. A computerized implementation according to any one of claims 24 to 30, further comprising outputting a set of energy or force in the set of coordinates on the energy plane, at least in part, based on the energy or force in (d).

32. The computer implementation method according to any one of claims 24 to 31, wherein the trained model includes a machine learning algorithm.

33. The computer implementation method according to claim 32, wherein the machine learning algorithm includes a neural network.

34. The computer implementation method according to claim 32, wherein the machine learning algorithm includes an ensemble learning method.

35. (c) The computer implementation method according to claim 34, comprising combining results from one or more submodels to create a metamodel, calculating the energy of each of the one or more submodels, and calculating the standard deviation of the energies of the one or more submodels, wherein the standard deviation constitutes a reliability index.

36. The computer implementation method according to claim 35, wherein the metamodel includes an ANI deep learning potential.

37. The computer implementation method according to claim 35 or 36, wherein the one or more submodels include one or more of PAINN deep learning potential, DimeNet++ deep learning potential, or PauliNet.

38. (d) a computer implementation according to any one of claims 24 to 37, comprising evaluating a first-principles energy or first-principles force in the coordinates, wherein the first-principles energy or first-principles force is calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or the ONIOM model.

39. Until the completion criteria are met, (i) If the reliability index is less than the threshold reliability value, (c) a step of evaluating the energy or force at the coordinates, selecting another coordinate on the energy plane, evaluating the energy or force at the other coordinate using the trained model, and determining a reliability index for the energy or force at the other coordinate, (ii) If the reliability index is greater than the threshold reliability value, A step of selecting another coordinate on the energy surface, evaluating the energy at the other coordinate using the trained model, and determining a reliability index for the energy or force at the other coordinate, A computer implementation method according to any one of claims 24 to 38, further comprising:

40. A computer implementation of claim 39, further comprising (i) conserving the energy or force for retraining, and (i) retraining the trained model based on the energy or force.

41. The computer implementation method according to any one of claims 24 to 40, further comprising the step of evaluating a first energy or a first force at initial coordinates using the trained model.

42. The computer implementation method according to claim 41, further comprising the step of determining a reliability index of the first energy or the first force in the initial coordinates.

43. The computer-aided method according to any one of claims 24 to 42, wherein the step of providing the set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

44. The computer implementation method according to claim 39, wherein selecting the other coordinate on the energy plane includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and eigencoordinate method.

45. A computer-based method for determining a reaction pathway, wherein the method is: (a) A step of providing instructions for at least one of the reactants and the product or the drive coordinate, (b) A step of providing a set of coordinates, wherein the set of coordinates lies on an energy plane connecting the reactants and the products or at least one of the drive coordinates, (c) A step of providing an energy or force threshold reliability value in the coordinates of the set of coordinates, until the completion criterion is met. (i) If the reliability index is less than the threshold reliability value, Evaluate the energy or force at the aforementioned coordinates, select another coordinate on the energy plane, evaluate the energy or force at the other coordinate using a trained model, and determine the reliability index of the energy or force at the other coordinate, and (ii) If the reliability index is greater than the threshold reliability value, The process involves selecting another coordinate on the potential energy surface, evaluating the energy at the other coordinate using the trained model, and determining a reliability index for the energy or force at the other coordinate. (d) A step of outputting a set of energy or force in the set of coordinates on the energy surface, A computer implementation method, including

46. The computer implementation method according to claim 45, wherein the energy surface is a potential energy surface.

47. The computer implementation method according to claim 45 or 46, wherein the energy surface is a free energy surface.

48. The computer implementation method according to any one of claims 45 to 47, wherein the set of coordinates is a spatial coordinate system.

49. The computer implementation method according to any one of claims 45 to 48, wherein the set of coordinates is a Cartesian coordinate system.

50. The computer implementation method according to claim 49, wherein the Cartesian coordinates include the direction of movement.

51. (c) A computer-aided method according to any one of claims 45 to 50, comprising evaluating a first-principles energy or first-principles force in the coordinates.

52. A computer-assisted method according to any one of claims 45 to 51, further comprising the step of retraining the trained model based on at least one energy or at least one force within the set of coordinates.

53. The computer implementation method according to any one of claims 45 to 52, further comprising the step of evaluating a first energy or a first force at initial coordinates using the trained model.

54. The computer implementation method according to claim 53, further comprising the step of determining a reliability index of the first energy or the first force in the initial coordinates.

55. (f) further comprises outputting a transition state or reaction pathway on the energy plane, according to any one of claims 45 to 54.

56. The computer implementation method according to claim 55, wherein the reaction pathway is the minimum energy pathway.

57. The computer-aided method according to any one of claims 45 to 56, wherein the step of providing the set of coordinates in (b) includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and intrinsic reaction coordinate method.

58. The computer implementation method according to claim 57, wherein selecting the other coordinate on the energy plane includes a method selected from the group consisting of first-principles molecular dynamics, nudged elastic band method, growth string method, variational reaction pathway optimization method, and intrinsic reaction coordinate method.

59. The computer implementation method according to any one of claims 45 to 58, wherein the trained model includes a machine learning algorithm.

60. The computer implementation method according to claim 59, wherein the machine learning algorithm includes a neural network.

61. The computer implementation method according to claim 59, wherein the machine learning algorithm includes an ensemble learning method.

62. (d) a computer implementation of claim 60 or 61, comprising combining results from one or more submodels to create a metamodel, calculating the energy of each of the one or more submodels, and calculating the standard deviation of the energies of the one or more submodels, wherein the standard deviation constitutes part of the reliability index.

63. The computer implementation method according to claim 62, wherein the metamodel includes an ANI deep learning potential.

64. The computer implementation method according to claim 62 or 63, wherein the one or more submodels include one or more of PAINN deep learning potential, DimeNet++ deep learning potential, or PauliNet.

65. (e) a computer implementation according to any one of claims 45 to 64, comprising evaluating a first-principles energy or first-principles force in the coordinates, wherein the first-principles energy or first-principles force is calculated by the Hartree-Fock method, coupled cluster method, exact configuration interaction method, incremental exact configuration interaction method, density functional theory, Möller-Presset perturbation theory, mixed quantum mechanics / molecular mechanics method, density matrix embedding theory, or the ONIOM model.

66. A processor comprising a non-temporary medium on which instructions are stored, wherein when an instruction is executed, it causes one or more processing units to perform the method according to any one of claims 1 to 65.

67. The processor according to claim 66, wherein the one or more processing units comprises a quantum computer, and the quantum computer is configured to perform the operation according to any one of claims 1 to 65.

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