Method, system and computer program product for calculating transition states of chemical reactions

Abstract

The present invention relates to a computer-implemented method for calculating transition states of chemical reactions, and a system for data processing, the system comprising means for executing the method, a computer program comprising instructions for causing a computer to execute the method, and uses of the computer program.

Description

Technical Field

[0001] The present invention relates to a computer-implemented method for calculating transition states of chemical reactions, and a system for data processing, the system comprising means for performing the method, a computer program comprising instructions for causing a computer to perform the method, and uses of the computer program. The present invention also relates to systems, methods and devices for automatically and efficiently determining kinetic data of chemical reactions. Background Art

[0002] During a chemical reaction, the atoms involved change their geometry, and bonds break and form new bonds. Here, the energy of the atoms involved also changes and reaches a state of maximum energy during the course of change of the chemical reaction, the so-called transition state. The transition state represents a barrier or activation barrier that separates the reactants and products of a chemical reaction. If the activation barrier is overcome, the product is formed. The energy during a chemical reaction can be represented by means of a so-called potential energy hypersurface, which maps the potential energy of the atoms involved in the reaction according to the geometry of the atoms involved in the reaction. Here, the potential energy hypersurface also maps a state in which no product is formed. The direct reaction path to form a product under the condition of overcoming the transition state can be displayed as a curve in which the distance between the atoms of the molecule and the energy are plotted. With the help of quantum chemical methods and mathematical approximation methods, the geometric structure energy of a system of molecules or multiple molecules can be calculated, wherein the function space to be observed here includes the degrees of freedom of the molecules. These methods make it possible to determine the geometry during the transition state and allow the reaction kinetics of a chemical reaction to be predicted.

[0003] A known method for determining the geometric structure when the transition state can be used is the Newton-Raphson method. However, calculating the transition state by means of the Newton-Raphson method has some disadvantages. First, the Newton-Raphson algorithm cannot be applied to each arbitrary starting geometry of the molecule, but can only be applied to the molecular geometry that is very close to the geometric structure of the transition state. This is troublesome, because the molecular geometry is usually manually approximated to the geometric structure of the transition state, that is, the bond length is manually set on the computer. The following method is also known, in which other methods are first used to calculate the potential energy hypersurface, and possible saddle points are identified from the potential energy hypersurface. Therefore, in these methods, the geometry of the geometry that is very close to the transition state must also be determined first. For these reasons, using current computer technology, it is particularly time-consuming and costly to calculate the transition state by means of the Newton-Raphson algorithm, especially for molecules with more than 100 atoms. In order to use the Newton-Raphson program and the approximation based on the Newton-Raphson program, the second derivative of energy must also be forced to be calculated according to the nuclear coordinates of the observed molecule. The computational cost of the second derivative scales squared with the size of the molecule and therefore determines the speed with which the activation energy can be calculated.

[0004] Lin et al. ("A flexible transition state searching method for atmospheric reaction systems", Chemical Physics 450-451, 2015, pp. 21-31) disclose a method for studying atmospheric chemical reactions in the gas phase. In the first step, the method includes using a force field method to screen a potential hypersurface based on a Monte Carlo method, wherein an approximate saddle-like region is identified. In the document, the observed value used for the corresponding Monte Carlo method is the value of the energy function. Based on this, an attempt is then made to locate the chemical transition state with the aid of the Newton-Raphson method. Using the Monte Carlo method disclosed in the document, the entire potential hypersurface must first be simulated before the approximate saddle-like region can be identified. Therefore, the saddle-like region cannot be optimized in a targeted manner using this Monte Carlo method. For this reason, it is impossible to effectively use the computing resources used to locate the desired saddle point. Using current computer technology, the use of the method disclosed in the document is limited to small molecules with 7 to 30 atoms. In addition, a mathematically highly simplified method is used.

[0005] E. et al. (“An automated transition state search using classical trajectories initialized at multiple minimas”, Phys Chem Chem Phys, June 14, 2015, 17(22): 14912-21; “tsscds2018: A code for automated discovery of chemical reaction mechanisms and solving the kinetics”, J. Comp. Chem., September 24, 2018, 39(23): 1922-1930) disclose methods for studying chemical reaction pathways. In these documents, the potential energy hypersurface of chemical molecules is calculated using mathematical simplification methods. Then, attempts are made to calculate the chemically relevant transition states using the ordinary pseudo-Newton-Raphson method. It is also disadvantageous in these documents that the entire potential energy hypersurface must first be calculated, which is time-consuming and requires computing power. In addition, the method can only be applied to smaller molecules.

[0006] Jacobson et al. ("Automated Transition State Search and Its Application to Diverse Types of Organic Reactions", J. Chem. Theory Comput. 13, 11, 5780-5797) disclose a method for automatically calculating chemical transition states. In this document, chemical transition states are calculated from chemical equilibrium states. This process requires a separate calculation of the chemical equilibrium state before the obtained geometry can be interpolated and the obtained geometry can be used to approximate the transition state. Then in a further step, an attempt is made to calculate the transition state geometry based on this approximation. The creation of the desired equilibrium state requires additional work by the technician. The interpolation used in the disclosed method cannot be successfully applied to arbitrary molecular geometries.

[0007] Hu et al. ("A gradient-directed Monte Carlo method for global optimization a discrete space: Application to protein sequence design and folding", J Chem Phys. 2009 Oct 21; 131(15): 154117) disclose a method for calculating protein structures. In this method, the folding of protein structures is calculated using the Monte Carlo method. In order to accelerate the convergence of the Monte Carlo procedure, gradients are calculated, which influence the direction and magnitude of the deflection of the atomic positions. The publication fails to identify any possible use of this method for the targeted calculation of saddle points.

[0008] Therefore, a method for calculating transition state is needed, in which a simple method, particularly a computer-implemented method, can be used to approximate the molecular geometry of the transition state of a chemical reaction. In particular, a method for determining transition state without calculating the potential energy hypersurface in advance is needed. Here, a method that requires a large amount of computational expenditure and qualitatively low precision is used. In particular, the application of a method including calculating the second derivative of energy according to atomic coordinates, such as Newton-Raphson method or pseudo-Newton-Raphson method, should be avoided as much as possible. These methods either provide a poor success rate when locating the transition state, or prohibit requiring resources, particularly for macromolecules. In this way, the utilization of resources such as processors and storage media can be reduced. Summary of the invention

[0009] The task of the present invention is to provide a computer-implemented method, wherein using an easy-to-use, particularly computer-implemented method to calculate the geometric structure of the transition state by means of a quantum chemical method. Preferably, the following quantum chemical method should not be used as much as possible, in which the second-order derivative of energy must be calculated according to the nuclear coordinates of the observed molecule, so that the transition state can be calculated. In particular, the molecular geometry of the transition state of the chemical reaction should be determined without having to calculate the potential energy hypersurface of the chemical reaction in advance. In particular, a computer-implemented method for calculating the transition state of a molecule preferably having more than 100 atoms should be provided.

[0010] The object is achieved by a computer-implemented method for calculating transition states of a chemical reaction, the method comprising the following steps

[0011] A Generates the starting geometry

[0012] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0013] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0014] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0015] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0016] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0017] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0018] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0019] C determines the precursor of the transition state of the chemical reaction

[0020] C1 applies a Monte Carlo algorithm to change the starting geometry of the optimization, where

[0021] C1.1 randomly select at least one atom from the function space selected in step B1,

[0022] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0023] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0024] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0025] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0026] D determines the transition state

[0027] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0028] D1.1 Select atoms from the function space selected in step B1,

[0029] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0030] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0031] D2 optimizes the geometry of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions, thereby obtaining two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energy of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the value of the gradient norm C3 or B3 of the precursor used in step D1,

[0032] D4.1 If the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively smaller than the energy C3 or B3 values ​​of the precursor used in step D1, the precursor used in step D1 is classified as a transition state. D4.2 If the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively smaller than the energy C3 or B3 values ​​of the precursor used in step D1, the method is repeated starting from step C1.

[0033] Surprisingly, it is found that by using a suitable Monte Carlo method to change different molecular geometries and approximate the geometry of the transition state by means of a quality standard, the task can be solved. In addition, it is surprisingly found that by using the gradient of the curve of the direct reaction path as an observable in the Monte Carlo method, the task can be solved. Thus, the function space to be processed can be reduced, and the molecular geometry of the function space should be mapped in the transition state of the chemical reaction, so that the saddle point can be calculated without calculating the potential energy hypersurface in advance or manually searching the molecular geometry. In addition, it is surprisingly found that the saddle point in the high-dimensional function space can be calculated using the method according to the present invention without using the method based on Newton-Raphson. Instead of calculating the second-order derivative of energy according to the nuclear coordinates, the area around the saddle point is verified by infinitesimal deflection and subsequent geometry optimization. Here, the deflection along the bond dissociation must lead to a reduction in total energy. In this way, the time-consuming second-order derivative calculation of energy according to the nuclear coordinates as in the method based on Newton-Raphson can be completely bypassed. With current computer technology, the method according to the invention can also be used to calculate transition states of molecules with more than 100 atoms significantly shorter and faster, in particular by reducing the human effort required for handling the corresponding conventional processes. Computer resources are also saved in this case.

[0034] In the method according to the invention, a starting geometry is first generated in step A by providing a three-dimensional representation of at least one molecule in the high-energy ground state in step A1. Then, in step A2, the bonds of the molecule are selected and the length of the bonds is selected, which is different from the bond length in the high-energy ground state, so that the starting geometry is obtained. The selected bonds are preferably those bonds that are formed or broken in the chemical reaction to be considered. The bond length that is different from the bond length in the high-energy ground state is 10 to 90%, preferably 20% to 40% greater than the bond in the high-energy ground state.

[0035] Preferably, at least one molecule from step A1 has a size of more than 100 atoms, more preferably more than 80 atoms, more preferably more than 60 atoms, and / or the length of the bond selected in step A2 is at most 230 pm, preferably at most 200 pm, more preferably at most 180 pm, more preferably 150 pm.

[0036] Step A is preferably performed by a user who enters the three-dimensional representation of the molecule in the high-energy ground state in step A1, the selection of bonds and their lengths in step A2 and the display of the starting geometry in step A3 into an input mask for the computer-implemented method.

[0037] In another preferred embodiment of the method according to the invention, at least two molecules I and II are provided in step A1, and in step A2, instead of or in addition to the at least one bond, at least one distance between at least one atom from molecule I and at least one atom from molecule II and the length of the at least one distance can also be selected, wherein the length of the distance is in particular at most 230 pm, preferably at most 200 pm, more preferably at most 180 pm, more preferably 150 pm. If the method is performed with at least two molecules I and II and the length of the distance between the atoms of different molecules is selected, the method can preferably be used to calculate the transition state of the synthesis reaction. Preferably, molecule I has a size of 2 to 1000 atoms, molecule II has a size of 2 to 1000 atoms, more preferably molecule I has a size of 2 to 800 atoms, molecule II has a size of 2 to 800 atoms, more preferably molecule I has a size of 2 to 600 atoms, and molecule II has a size of 2 to 600 atoms. The sum of atoms from molecule I and from molecule II is preferably greater than 100 atoms.

[0038] Preferably, molecule I is a catalyst for a chemical reaction, in particular for polymer synthesis, and molecule II is a reactant for the chemical reaction. In this embodiment, polymer synthesis is preferably polyurethane synthesis. The chemical reaction in this embodiment is preferably also the synthesis of monomers for polymerization, basic chemicals required industrially, additives, surfactants and pharmacologically active substances. In particular, the chemical reaction is the synthesis of basic chemicals obtained using a catalyst or a reactant for chemical synthesis. Additives are generally understood to be additives for plastics, such as plasticizers, antioxidants, regulators, and additives for fuels, and catalysts are used when synthesizing these additives.

[0039] In step A3, the starting geometry selected in step A2 is expressed in Cartesian coordinates and / or internal coordinates. Internal coordinates describe the spatial arrangement of atoms relative to each other using bond lengths, bond angles, and torsion angles.

[0040] In step B of the method according to the invention, the optimized starting geometry is determined. To this end, a function space is first set in step B1. The function space includes the spatial coordinates of the selected atoms, wherein the spatial coordinates in the vector space of all atomic coordinates contained in the molecule span a subspace. The atoms selected for the function space are a group of atoms that participate in bond dissociation or preferably participate in a synthesis reaction. In addition, the function space includes at least one bond from step A2. In a preferred embodiment with at least two molecules I and II, the function space includes the distance between at least one atom from molecule I and at least one atom from molecule II.

[0041] In the following step B2, the starting geometry is geometrically optimized by means of quantum chemical methods, with the boundary condition that the length of at least one bond selected in step A2 remains constant, thereby obtaining an optimized starting geometry. Here, the geometry optimization includes all atoms of the molecule selected as the starting geometry. In a preferred embodiment with at least two molecules I and II, the distance between at least one atom from molecule I and at least one atom from molecule II remains constant during the geometry optimization, thereby obtaining an optimized starting geometry.

[0042] In the case of geometry optimization with boundary conditions, the total energy of the molecule is minimized as a function of the nuclear coordinates of the atoms contained in the molecule using quantum chemical methods. To obtain a local energy minimum, the energy is minimized according to a gradient (e.g., steepest descent), wherein the energy is minimized as long as the boundary conditions allow.

[0043] In step B3, a gradient norm B3 is determined for the previously obtained optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) with the aid of quantum chemical methods, where E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry. In step B3, the same quantum chemical methods as in step B2 are used. The Euclidean norm of the vector is the gradient norm. In other words, the gradient vector of the energy is calculated. The gradient vector spans the same vector space as the molecule. Each component of the vector is determined by taking the first derivative of the function E=f(x) with the aid of quantum chemical methods. i Partial derivatives of energy expressed in coordinates Composition, and in x i The coordinates are stretched in the direction of the unit vector. The (Euclidean) norm of this vector is then determined.

[0044] The further execution of the method depends on the size of the gradient norm B3 obtained. The optimized starting geometry can then be classified as a precursor to a transition state of a chemical reaction, and step C of the method can be omitted, and the method can be continued with step D1. Step C of the method is then carried out and the precursor of the transition state of the chemical reaction is first determined, starting from the optimized starting geometry. h represents Hartree energy, where 1E h =4.3597·10 - 18 J, and a0 represents the Bohr radius, where 1a0 = 5.29·10 -11 m.

[0045] In step C, the precursors of the transition state of the chemical reaction are determined. For this purpose, a Monte Carlo algorithm is applied to change the optimized starting geometry by randomly generated deflections of the atoms in the collection consisting of the geometries of one molecule or preferably at least two molecules I and II.

[0046] The Monte Carlo algorithm or method is a simulation method that solves mathematical problems that cannot be solved analytically or are difficult to solve by numerical approximation. Here, the most likely course of an experiment is described by a large number of randomly arranged individual experiments.

[0047] In the Monte Carlo algorithm used according to the invention in step C, randomly generated deflections are applied to the atoms in the collection of geometric structures of a molecule or at least two molecules I and II and the change in an observable is observed. The observable is the norm of the gradient. In this case, the method according to the invention changes only a subspace whose dimension is significantly smaller than the entire function space of the collection and the change in the observable of the entire collection is considered as a function of the reduced function space.

[0048] To this end, in step C1.1, at least one atom is selected from the function space selected in step B1. This is done with the aid of a random number Z1. In step C1.2, the direction of deflection of the atom selected by Z1 or the direction of the vector used for the deflection is selected by means of a further random number Z2. The direction is preferably defined by selecting the position of an atom different from the atom selected in step C1.1 from the reduced function space in a preferred step C1.2a and then selecting the direction of the deflection in a preferred step C1.2b, wherein the position of the atom selected in step C1.2a determines the direction of the vector. In a preferred step C1.2c, the amplitude of the deflection is preferably determined by means of a third random number Z3.

[0049] In a preferred embodiment of the method according to the present invention, step C1.2 includes the following other steps: Cl.2a determines other atoms that are inconsistent with the atoms selected in step C1.1 from the function space selected in step B1, Cl.2b selects the direction of the vector, wherein the position of the atom selected in step Cl.2.a determines the direction of the vector, and C1.2c randomly selects the length of the vector, wherein the length value of the vector can take a positive or negative value.

[0050] The weighting of the randomly selected component of the vector in step C1.2 is preferably performed by multiplying the value of the randomly selected component of the vector by the value of the gradient norm B3.

[0051] Since the positions of the atoms selected in step C1.2 determine the direction of the vector, the function space is restricted as strongly as possible and this measure also leads to a change in the main bond lengths, which have the lengths that are most likely to be actually achieved during the reaction.

[0052] In step C1.3, the atoms selected in step C1.1 are deflected from their positions in the optimized starting geometry based on the vectors from step C1.2, thereby obtaining precursors of the transition state of the chemical reaction.

[0053] In step C2, the obtained precursor of the transition state is subjected to a geometry optimization by means of quantum chemical methods, with the boundary condition that at least one bond from step A2 has the length determined in step C1.3. In step C2, the same quantum chemical methods as in steps B2 and B3 are used. Then in step C3, a gradient norm C3 is determined for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) by means of quantum chemical methods, where E=total energy of the precursor of the transition state and x=nuclear coordinate of the molecule in the precursor of the transition state. In step C3, the same quantum chemical methods as in steps B2, B3 and C2 are used.

[0054] The further execution of the method depends on the size of the obtained gradient norm C3. Then, step D1 of the method can be performed on the precursor of the transition state. h represents Hartree energy, where 1E h =4.3597·10 -18 J, and a0 represents the Bohr radius, where 1a0 = 5.29·10 -11 m.

[0055] If the gradient norm C3 is Then repeat steps C1 to C3 in step 4.2 until the gradient norm is obtained By repeating steps C1 to C3, an iterative method is shown, with which the gradient norm should be minimized. Therefore, as the starting point for repeating the method, the molecular geometry that already has the lowest possible gradient norm should be selected respectively. Therefore, when repeating steps C1 to C3, not only the optimized starting geometry can be changed in step C1, but also the precursor of the transition state can be changed, as long as the value of its gradient norm C3 is less than the value of the gradient norm C3 of the optimized starting geometry. Preferably, the optimized starting geometry obtained when executing the method and the (one or more) precursors of the transition state obtained and the value of each gradient norm C3 are stored.

[0056] In the case where steps C1 to C3 have been performed once, the molecular geometry with the lowest gradient norm can be selected from the two molecular geometries for the purpose of performing the repetition, i.e. the optimized starting geometry or the precursor of the transition state obtained in the first iteration. In the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1.

[0057] In the case where steps C1 to C3 have already been carried out, the molecular geometry with the lowest gradient norm can be selected from more than two molecular geometries for carrying out the repetition, i.e. the optimized starting geometry or the precursor(s) of the transition state obtained in the repetition. In the case where steps C1 to C3 have already been carried out several times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, said precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far.

[0058] Preferably, in step C4.1, the gradient norm C3≤0.02E h a0 -1 , preferably C3≤0.01E h a0 -1 , and continue to execute step C4.2 until the gradient norm C3≤0.02E is obtained h a0 -1 , preferably C3≤0.01E h a0 -1 .

[0059] Preferably, step C4.2 is repeated at most 50 times, preferably at most 40 times, more preferably at most 30 times, more preferably at most 10 times, in particular at most 3 times. Preferably, when performing step C4.2, different atoms can be selected when repeating step C1 than in the previous performance of the method.

[0060] An advantage of the method according to the invention is that when the Monte Carlo algorithm is applied to change, only the atomic coordinates of the selected function space (i.e., the subspace of the atoms participating in the observed bond dissociation or preferred synthesis reaction) span in the vector space of all atomic coordinates contained in the molecule or molecular assembly. That is to say, the Monte Carlo algorithm according to the invention only operates in this subspace, because its function is defined only in this subspace. Thus, the subspace of the coordinates participating in the dissociation or preferred synthesis reaction is the function space of the Monte Carlo algorithm. Although the calculation of energy and gradient vector (or its norm) depends on all coordinates in the molecule, the Monte Carlo algorithm according to the invention only observes the calculation according to the coordinates of the subspace. In order to make the function value, i.e., the gradient norm to be minimized, remain unique when observing the calculation, before observing the function value each time, the entire molecular structure is relaxed by optimizing the geometry with (one or more) boundary conditions. Here, the (one or more) boundary conditions are the bond distances generated by the Monte Carlo algorithm.

[0061] In step D1, the precursor from step C4.1 or the precursor from step B4.1 is relaxed by means of quantum chemical methods and the pseudo-Newton-Raphson algorithm to obtain the transition state. In step D1, the same quantum chemical methods as in steps B2, B3, C2 and C3 are used.

[0062] If the gradient norm has been minimized sufficiently, the negative curvature behavior in the obtained fixed point region is verified in step D by infinitesimal deflections and subsequent geometry optimization. In this case, the deflection along the bond dissociation necessarily leads to a reduction in the total energy. A further advantage of the invention is that in this way the complex calculation of the second derivative of the energy according to the nuclear coordinates can be completely bypassed.

[0063] Preferably, in step D3, the energies of the two optimized precursors (i) and (II) are expressed in units of E h a0 -1 The unit is expressed as .

[0064] If both the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are less than the value of the energy C3 or B3 of the precursor used in step D1, the precursor is classified as a transition state in step D4.1. If one of the two energy values ​​of the optimized precursor (i) or (ii), or both energy values ​​of the optimized precursors (i) and (ii) are greater than the value of the energy C3 or B3 of the precursor used in step D1, the method is repeated starting from step C. Starting from step C, the method is preferably repeated up to 10 times, preferably up to 3 times.

[0065] In steps B2, B3, C2, C3, D2 and D3, the same quantum chemical method is used respectively. Preferably, the quantum chemical method from steps B2, B3, C2, C3, D2 and D3 is an approximation of a semi-empirical method, a density functional theory method or a Schrödinger equation, and particularly preferably a density functional theory method, such as a TPSS density functional with a def2-SVP basic setting, as implemented in a standard manner in the Turbomole program package. In a preferred embodiment, quantum mechanical calculations are performed using the program package TURBOMOLE. Preferably, a computer with 16 core processors and 25MB of intermediate memory is used for the calculations, the clock frequency of the core processor being 3.20GHz, and the intermediate memory having a RAM memory of 128GB DDR42400 rgECC.

[0066] Preferably, the chemical reaction is a synthesis selected from the group consisting of polymer synthesis (in particular polyurethane synthesis), monomers for polymerization, basic chemical substances required for industry, additives, surfactants and pharmacologically active substances. In particular, the chemical reaction is the synthesis of basic chemical substances or reactants for chemical synthesis obtained using a catalyst. Additives are generally understood to be additives for plastics, such as plasticizers, antioxidants, regulators, and additives for fuels, in the synthesis of which catalysts are used.

[0067] If in a preferred embodiment of the method at least two molecules I and II are provided, the steps of the method mentioned under the letters A, B and C can preferably be repeated, wherein in each repetition molecule I is changed or a molecule other than molecule I is provided compared to the previous execution of the method, and

[0068] does not change molecule II, and does not provide molecules other than molecule II,

[0069] And perform an additional step D0:

[0070] D0 compares the gradient norms C3 of different precursors of the transition state obtained in the repetitions, selects the precursor of the transition state having the lowest gradient norm C3, and performs steps D1 and / or D2 on the selected precursor of the transition state.

[0071] In the above preferred embodiment of the method, the gradient norm C3 is first calculated for different combinations of molecules and the results are stored. Then, in a preferred step D0, the values ​​of the gradient norm C3 obtained can be compared and the combination of molecules with the lowest gradient norm C3 can be selected. Therefore, this preferred embodiment of the method enables direct comparison of different combinations of molecules.

[0072] Another subject matter of the invention is a system for data processing, which comprises means for carrying out the method according to the invention.

[0073] Furthermore, other subjects of the present invention are a computer program and a computer-readable storage medium, comprising instructions which, when the program is executed by a computer, cause the computer to perform the following steps of a method: A. generating a starting geometry;

[0074] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0075] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0076] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0077] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0078] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0079] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0080] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0081] C determines the precursor of the transition state of the chemical reaction

[0082] C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where

[0083] C1.1 randomly select at least one atom from the function space selected in step B1,

[0084] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0085] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0086] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0087] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0088] D determines the transition state

[0089] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0090] D1.1 Select atoms from the function space selected in step B1,

[0091] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0092] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0093] D2 optimizes the geometric structure of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions to obtain two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energies of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the energy C3 or B3 value of the precursor used in step D1, D4.1 if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively less than the energy C3 or B3 value of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively less than the energy C3 or B3 value of the precursor used in step D1, then the method is repeated starting from step C1.

[0094] Preferably, the computer program and / or the computer-readable storage medium comprises instructions which, when the program is executed by a computer, cause the computer to perform steps B to D of the method.

[0095] Furthermore, the invention relates to the use of a computer program according to the invention or a computer-readable storage medium according to the invention for evaluating transition states of a chemical reaction, in particular of a polymer synthesis.

[0096] The present invention particularly relates to the following embodiments:

[0097] In a first embodiment, the present invention relates to a computer-implemented method for calculating a transition state of a chemical reaction, comprising the following steps:

[0098] A Generates the starting geometry

[0099] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0100] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0101] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0102] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0103] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0104] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0105] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0106] C determines the precursor of the transition state of the chemical reaction

[0107] C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where

[0108] C1.1 randomly select at least one atom from the function space selected in step B1,

[0109] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0110] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0111] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0112] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0113] D determines the transition state

[0114] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0115] D1.1 Select atoms from the function space selected in step B1,

[0116] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0117] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0118] D2 optimizes the geometric structure of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions to obtain two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energies of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the energy C3 or B3 value of the precursor used in step D1, D4.1 if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively less than the energy C3 or B3 value of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively less than the energy C3 or B3 value of the precursor used in step D1, then the method is repeated starting from step C1.

[0119] In a second embodiment, the invention relates to a method according to embodiment 1, characterized in that at least one molecule from step A1 has a size of more than 100 atoms and / or the length of the bond selected in step A2 is at most 230 pm.

[0120] In a third embodiment, the present invention relates to a method according to embodiment 1 or 2, characterized in that step C1.2 comprises the following further steps:

[0121] Cl.2a determines other atoms that are inconsistent with the atoms selected in step C1.1 from the function space selected in step B1, Cl.2b selects the direction of the vector, where the position of the atom selected in step Cl.2.a determines the direction of the vector, and C1.2c randomly selects the length of the vector, where the length value of the vector can be positive or negative.

[0122] In a fourth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that the weighting of the randomly selected amount of the vector in step C1.2 is performed by multiplying the value of the randomly selected amount of the vector by the value of the gradient norm B3.

[0123] In a fifth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that in step C4.1 the gradient norm C3≤0.02E h a0 -1 , preferably ≤0.01E h a0 -1 , and continue to execute step C4.2 until the gradient norm C3≤0.02E is obtained h a0 -1 , preferably ≤0.01E h a0 -1 .

[0124] In a sixth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that step C4.2 is repeated at most 50 times, preferably at most 30 times, in particular at most 3 times.

[0125] In a seventh embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that, when performing step C4.2, different atoms can be selected when repeating step C1 than in a previous execution of the method.

[0126] In an eighth embodiment, the present invention relates to a method according to one of the preceding embodiments, characterized in that the quantum chemical method from steps B2, B3, C2, C3, D2 and D3 is a semi-empirical method, a density functional theory method or an approximation of the Schrödinger equation, and the quantum chemical method from steps B2, B3, C2, C3, D2 and D3 is in particular a density functional theory method.

[0127] In a ninth embodiment, the present invention relates to a method according to one of the preceding embodiments, characterized in that the chemical reaction is a synthesis selected from the group consisting of polymer synthesis (in particular polyurethane synthesis), monomers for polymerization reactions, basic chemical platform compounds required for industrial use, additives, surfactants and synthesis of pharmacologically active substances.

[0128] In a tenth embodiment, the invention relates to a method according to one of the preceding embodiments, characterized in that in step A1 at least two molecules I and II are provided and in step A2 instead of or in addition to the at least one bond, at least one distance between at least one atom from molecule I and at least one atom from molecule II and the length of the at least one distance are also selected, wherein the length of the distance is in particular at most 230 pm.

[0129] In an eleventh embodiment, the invention relates to a method according to embodiment 10, characterized in that the steps mentioned under the letters A, B and C of said method are repeated, wherein at each repetition molecule I is changed or a molecule other than molecule I is provided compared to the previous execution of said method, and

[0130] The molecule II is not changed, and no molecule other than the molecule II is provided, and an additional step D0 is performed:

[0131] D0 compares the gradient norms C3 of different precursors of the transition state obtained in the repetition, selects the precursor of the transition state having the lowest gradient norm C3, and performs steps D1 and / or D2 on the selected precursor of the transition state.

[0132] In a twelfth embodiment, the invention relates to a method according to one of embodiments 10 or 11, characterized in that molecule I is a catalyst for said chemical reaction, in particular for polymer synthesis, and molecule II is a reactant of said chemical reaction.

[0133] In a thirteenth embodiment, the present invention relates to a method according to one of embodiments 10 to 13, characterized in that molecule I has a size of 2 to 1000 atoms and molecule II has a size of 2 to 1000 atoms, preferably the sum of atoms from molecule I and from molecule II is greater than 100 atoms.

[0134] In a fourteenth embodiment, the present invention relates to a system for data processing, the system comprising means for performing a method comprising the following steps:

[0135] A Generates the starting geometry

[0136] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0137] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0138] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0139] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0140] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0141] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0142] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0143] C determines the precursor of the transition state of the chemical reaction

[0144] C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where

[0145] C1.1 randomly select at least one atom from the function space selected in step B1,

[0146] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0147] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0148] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0149] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0150] D determines the transition state

[0151] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0152] D1.1 Select atoms from the function space selected in step B1,

[0153] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0154] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0155] D2 optimizes the geometric structure of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions to obtain two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energies of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the energy C3 or B3 value of the precursor used in step D1, D4.1 if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively less than the energy C3 or B3 value of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively less than the energy C3 or B3 value of the precursor used in step D1, then the method is repeated starting from step C1.

[0156] In a fifteenth embodiment, the present invention relates to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to perform the following steps of a method:

[0157] A Generates the starting geometry

[0158] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0159] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0160] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0161] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0162] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0163] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0164] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0165] C determines the precursor of the transition state of the chemical reaction

[0166] C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where

[0167] C1.1 randomly select at least one atom from the function space selected in step B1,

[0168] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0169] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0170] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0171] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0172] D determines the transition state

[0173] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0174] D1.1 Select atoms from the function space selected in step B1,

[0175] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0176] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0177] D2 optimizes the geometric structure of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions to obtain two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energies of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the energy C3 or B3 value of the precursor used in step D1, D4.1 if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively less than the energy C3 or B3 value of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively less than the energy C3 or B3 value of the precursor used in step D1, then the method is repeated starting from step C1.

[0178] In a sixteenth embodiment, the present invention relates to a computer-readable storage medium comprising instructions, which, when executed by a computer, cause the computer to perform the following steps of a method:

[0179] A Generates the starting geometry

[0180] A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state,

[0181] A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to a length of the bond in the high-energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performing a three-dimensional representation of the starting geometry in Cartesian coordinates and / or internal coordinates, and B determining an optimized starting geometry

[0182] B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond,

[0183] B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant,

[0184] B3 determining the gradient norm B3 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry,

[0185] B4.1 If the gradient norm B3 is then classifying the optimized starting geometry as a precursor to the transition state of the chemical reaction and continuing the method with step D1, or

[0186] B4.2 If the gradient norm B3 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps:

[0187] C determines the precursor of the transition state of the chemical reaction

[0188] C1 applies a Monte Carlo algorithm to change the starting geometry of the optimization, where

[0189] C1.1 randomly select at least one atom from the function space selected in step B1,

[0190] C1.2 randomly selects a vector for deflecting the atom selected in step C1, wherein the random selection of the vector is weighted using the gradient norm B3,

[0191] C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction,

[0192] C2 performs geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C3, C3 determines a gradient norm C3 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state,

[0193] C4.1 If the gradient norm C3 is The method is continued with step D1, or C4.2 if the gradient norm C3 is Then repeat steps C1 to C3 until the gradient norm C3 is obtained wherein (a) in the case where steps C1 to C3 have been performed once, if the value of the gradient norm C3 of the geometry of the precursor of the transition state is lower than the value of the gradient norm B3 of the optimized starting geometry, the geometry of the precursor of the transition state is changed in step C1, or (b) in the case where steps C1 to C3 have been performed multiple times, the geometry of the optimized starting geometry or the geometry of the following precursor of the transition state from the previous repetition is changed in step C1, the precursor having the lowest value of the gradient norm C3 or B3 compared to all the gradient norms C3 and B3 obtained so far,

[0194] D determines the transition state

[0195] D1 changes the precursor from step C4.1 or the precursor from step B4.1 by performing the following steps on the atoms in the function space defined in B1,

[0196] D1.1 Select atoms from the function space selected in step B1,

[0197] D1.2 Select the vector used to deflect the atom selected in step D1.1,

[0198] D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D.1.3,

[0199] D2 optimizes the geometric structure of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions to obtain two optimized precursors (i) and (ii), wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energies of the two optimized precursors (i) and (ii) from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the energy C3 or B3 value of the precursor used in step D1, D4.1 if the energy value of the optimized precursor (i) and the energy value of the optimized precursor (ii) are respectively less than the energy C3 or B3 value of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 if the energy value of the optimized precursor (i) or the energy value of the optimized precursor (ii) is not respectively less than the energy C3 or B3 value of the precursor used in step D1, then the method is repeated starting from step C1.

[0200] In a seventeenth embodiment, the present invention relates to the use of the computer program according to embodiment 15 or the computer readable storage medium according to embodiment 16 for evaluating transition states of a chemical reaction, in particular of a polymer synthesis.

[0201] In an eighteenth embodiment, the invention relates to a method according to one of the first to thirteenth embodiments, characterized in that information about the transition state determined according to step D.1 and / or the equilibrium state determined according to step D.2 is reported to a user.

[0202] In a nineteenth embodiment, the invention relates to a method according to one of the first to thirteenth embodiments, characterized in that information about the transition state determined according to step D.1 and / or the equilibrium state determined according to step D.2 is received by a user.

[0203] In a twentieth embodiment, the invention relates to a method according to one of the ninth to thirteenth embodiments, characterized in that molecule I is synthesized after step D.1 and / or after step D.2.

[0204] In a twenty-first embodiment, the invention relates to a method according to one of the ninth to thirteenth embodiments, characterized in that after step D.1 and / or step D.2, a chemical reaction is carried out using molecule I as a catalyst.

[0205] In a twenty-second embodiment, the invention relates to a method according to one of the ninth to thirteenth or twenty-first embodiments, characterized in that after step D.1 and / or after step D.2, a chemical reaction is carried out using molecule II as reactant.

[0206] The present invention shall be explained based on the following examples, but the present invention is not limited thereto.

[0207] The activity of various catalysts for the reaction of prepolymers with terminal isocyanate groups with water was investigated. For this purpose, the activation energy of the reaction using the corresponding catalyst was first calculated by means of the method according to the invention. The calculated value was then compared with the laboratory test results of the reaction calculated beforehand. As a measure of the activity of the tested catalyst, a reaction temperature was used in the laboratory test at which the catalyst showed activity if exceeded. Whether the catalyst showed activity was determined in the laboratory experiment based on the release of gas and the foaming of the reaction mixture.

[0208] Laboratory testing was performed as follows:

[0209] Synthesis of HDI Prepolymers with Terminal Isocyanate Groups Since commercially available prepolymers contain residues of catalysts which could falsify the test results, a prepolymer for carrying out the test was synthesized. For this purpose, 20.00 g (48.193 mmol; 1.0 equivalent) of polypropylene glycol with an average molecular weight of 415 g / mol (PET 1004) were placed under argon countercurrent and 16.212 g of hexamethylene diisocyanate (2.0 equivalent) were added. The mixture was heated to 80° C. over a period of 3 hours with stirring. After cooling to room temperature and precipitation of the product at room temperature for one week, a viscous, transparent substance was obtained.

[0210] The number-average molecular weight of the HDI prepolymer was determined by means of gel permeation chromatography. The samples were measured in THF on a GPC column of the PSSSDV 5 μm linear S THF type with polystyrene as standard. The molecular weight was determined to be Mn=789.7.

[0211] (In the case where the polypropylene glycol used is extended twice with HDI, the theoretical molecular mass is 751.4 g / mol, and in the case where the polypropylene glycol used is extended once with HDI, the theoretical molecular mass is 583.2 g / mol.)

[0212] Test reaction

[0213] The following catalysts were used for the reaction of HDI prepolymer with water:

[0214] -DBN: 1,5-diazabicyclo[4,3,0]non-5-ene;

[0215] -NEt3: triethylamine;

[0216] -DMA: dimethylaniline.

[0217] 1.0 equivalent of HDI prepolymer and 2.0 equivalent of water were placed in a test tube with a magnetic stirrer. The contents of the test tube were mixed thoroughly, and 0.1 equivalent of the corresponding catalyst was added under stirring. The temperature of the mixture was slowly increased by means of an oil bath with a thermostat until obvious gas evolution could be observed.

[0218] Table 1: Molar masses and substance contents of the substances used

[0219]

[0220] 1) Theoretical molecular weight of a prepolymer made from two equivalents of HDI and one equivalent of the polypropylene glycol used.

[0221] Execution of quantum mechanical calculations

[0222] The quantum mechanical calculations were performed using the program package Turbomole. The density functional theory method used was the TPSS density functional with the def2-SVP basis set, as implemented in the Turbomole program package in a standard manner. For this purpose, an Intel Xeon E5-2667v4 with a 16-core processor and 25MB of intermediate memory was used as a computer, the clock frequency of the core processor being 3.20 GHz, and the intermediate memory having a RAM memory of 128GB DDR42400 rg ECC. These calculations were performed on two processors, respectively, providing a memory volume of 8000MB.

[0223] For each reaction examined, a starting geometry was chosen as the starting point for determining the transition state. The calculation of the corresponding activation energies took up to 36 hours.

[0224] For the simulation of the activation energy, the reaction of a prepolymer containing two terminal isocyanate groups based on HDI and syntactic polypropylene glycol with seven repeating units based on propylene oxide, which consist of a total of 121 atoms, a water molecule and the corresponding catalyst (a total of between 144 and 146 atoms), was investigated. In order to generate the starting geometry of the embodiment in Table 3, in the example of DBN, the prepolymer molecules, the DBN catalyst molecules and the water molecules were drawn according to method step A1 using a program suitable for visualizing three-dimensional molecular structures. According to method step A2, the position of the carbon atom of the isocyanate group under consideration was placed at a distance of 175.5 pm from the oxygen atom of the water molecule under consideration, and the distance of one of the hydrogen atoms in the water molecule to the oxygen of the water molecule was placed at 117.4 pm. The molecular geometry generated in this way is stored according to method step A3 in Cartesian coordinate representation, and the atoms participating in the bond distances thus arranged are used to define the function space according to method step B1.

[0225] The activation energies shown in Table 2 can be obtained using the method according to the invention.

[0226] With the aid of the pseudo-Newton-Raphson based methods known from the prior art for optimizing transition states, under identical conditions, ie with identical starting geometries of the transition state, no transition state and therefore no activation energy could be obtained in any of the cases shown.

[0227] Table 2: Summary of experimental and calculated activation energies

[0228]

[0229] 1) Very vaguely determined temperature points. The reaction can only be identified weakly.

[0230] The data in Table 2 show that, with the aid of the method of the present invention, the user can accurately calculate the molecular geometry of the transition state of a chemical reaction with little effort, thereby being able to make correct statements about the kinetics of the chemical reaction based on the calculated activation energy.

[0231] The number average molecular weight of the HDI prepolymer used in the laboratory tests is in the same range as the theoretically calculated mass of polypropylene glycol extended twice with HDI. Therefore, the laboratory tests are similar to the reaction conditions used for simulations of this reaction to calculate the activation energy and truly mirror the simulations.

[0232] The activation energy of DBN calculated based on the method of the present invention is slightly lower than that of Net3 and significantly lower than that of DMA. The following conclusion can be drawn from the calculation results: When the HDI prepolymer reacts with water, DBN as a catalyst realizes a transition state with lower energy than when Net3 or DMA is used as a catalyst. Therefore, when DBN is used as a catalyst for the reaction, less energy or no energy needs to be supplied (starting from room temperature) in order to make the reaction proceed and obtain the product.

[0233] These conclusions drawn from the calculated activation energies are reflected in the results of the laboratory tests. The reaction of the HDI prepolymer with water and DBN as catalyst already takes place at 23°C, whereas when using Net3 as a catalyst, the reaction mixture must be raised to 40°C. From the calculated activation energies it can already be concluded that a higher activation energy is required for the reaction with Net3.

[0234] The same is true when DMA is used as a catalyst. Here, the calculated activation energy is significantly higher than when Net3 is used as a catalyst. This result can be verified by laboratory tests. When Net3 is used as a catalyst, the reaction can only be detected at temperatures above 100°C, and then only weakly.

Claims

1. A computer-implemented method for calculating transition states of chemical reactions, comprising the following steps: A. generating a starting geometry; A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to the length of the bond in the high energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performs a three-dimensional representation of the starting geometric structure in Cartesian coordinates and / or internal coordinates, B. Determine the starting geometry for optimization B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond, B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant, B3 determining the gradient norm L1 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=the total energy of the optimized starting geometry, and x=the nuclear coordinates of the molecule in the optimized starting geometry, B4 If the gradient norm L1 is The optimized starting geometry is then classified as a precursor to the transition state of the chemical reaction, and the method is continued with step D1, wherein E h represents the Hartree energy, a0 represents the Bohr radius, or B5 If the gradient norm L1 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps: C determines the precursor of the transition state of the chemical reaction C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where C1.1 randomly select at least one atom from the function space selected in step B1, C1.2 randomly selects a vector for deflecting the atom selected in step C1.1, wherein the random selection of the vector is weighted by the gradient norm L1, C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction, C2 performs a geometry optimization of the precursor of the transition state by means of the quantum chemical method and using boundary conditions, wherein at least one bond from step A2 has a length determined in step C1.3, C3 determines a gradient norm L2 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the precursor of the transition state and x=nuclear coordinates of the molecule in the precursor of the transition state, C4 If the gradient norm L2 is The method continues with step D1, or C5 if the gradient norm L2 is Then repeat steps C1 to C3 until the gradient norm L2 is obtained 0 So far, among them (a) when steps C1 to C3 have been performed once, if the value of the gradient norm L2 of the geometric structure of the precursor of the transition state is lower than the value of the gradient norm L1 of the optimized starting geometric structure, then in step C1, the geometric structure of the precursor of the transition state is changed, or (b) in case of a plurality of executions of steps C1 to C3, in step C1 changing the geometry of the optimized starting geometry or the geometry of the following precursor from a previously repeated transition state which has the lowest value of the gradient norm L2 or L1 compared to all the gradient norms L2 and L1 obtained so far, D determines the transition state D1 changes the precursor from step C4 or the precursor from step B4 by performing the following steps on the atoms in the function space defined in B1, D1.1 Select atoms from the function space selected in step B1, D1.2 Select the vector used to deflect the atom selected in step D1.1, D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D1.3, D2 optimizes the geometry of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions, thereby obtaining two optimized precursors i and ii, wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energy of the two optimized precursors i and ii from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the values ​​of the gradient norm L2 or L1 of the precursors used in step D1, D4.1 If the energy value of the optimized precursor i and the energy value of the optimized precursor ii are respectively less than the energy value L2 or L1 of the precursor used in step D1, the precursor used in step D1 is classified as a transition state, D4.2 If the energy value of the optimized precursor i or the energy value of the optimized precursor ii is not smaller than the value of the energy L2 or L1 of the precursor used in step D1, the method is repeated starting from step C1.

2. The method according to claim 1, characterized in that The quantum chemical methods from steps B2, B3, C2, C3, D2 and D3 are semi-empirical methods, density functional theory methods or the Schrödinger equation.

3. The method according to claim 1 or 2, characterized in that: The chemical reaction is a synthesis selected from the group consisting of polymer synthesis, monomers for polymerization, basic chemical platform compounds required in industry, additives, surfactants and synthesis of pharmacologically active substances.

4. The method according to claim 1 or 2, characterized in that: In step A1 at least two molecules I and II are provided and in step A2 instead of or in addition to the at least one bond at least one distance between at least one atom from molecule I and at least one atom from molecule II and the length of the at least one distance are selected.

5. The method according to claim 4, characterized in that Molecule I is a catalyst for the chemical reaction and molecule II is a reactant for the chemical reaction, wherein molecule I has a size of 2 to 1000 atoms and molecule II has a size of 2 to 1000 atoms, and the sum of atoms from molecule I and from molecule II is greater than 100 atoms.

6. The method according to any one of claims 1 to 2, characterized in that Information about the transition state determined according to step D is reported to the user.

7. The method according to any one of claims 1 to 2, characterized in that Information about the transition state determined according to step D is received by a user.

8. The method according to claim 3, characterized in that The polymer synthesis is a polyurethane synthesis.

9. The method according to claim 4, characterized in that The length of the distance is at most 230 pm.

10. A system for data processing, comprising means for performing a method for calculating a transition state of a chemical reaction comprising the steps of: A Generates the starting geometry A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to the length of the bond in the high energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performs a three-dimensional representation of the starting geometric structure in Cartesian coordinates and / or internal coordinates, B. Determine the starting geometry for optimization B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond, B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant, B3 determining the gradient norm L1 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=the total energy of the optimized starting geometry, and x=the nuclear coordinates of the molecule in the optimized starting geometry, B4 If the gradient norm L1 is The optimized starting geometry is then classified as a precursor to the transition state of the chemical reaction, and the method is continued with step D1, wherein E h represents the Hartree energy, a0 represents the Bohr radius, or B5 If the gradient norm L1 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps: C determines the precursor of the transition state of the chemical reaction C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where C1.1 randomly select at least one atom from the function space selected in step B1, C1.2 randomly selects a vector for deflecting the atom selected in step C1.1, wherein the random selection of the vector is weighted by the gradient norm L1, C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction, C2 geometry optimization of the precursor of the transition state by means of the quantum chemical method and using the boundary condition that at least one bond from step A2 has the length determined in step C1.3, C3 determines a gradient norm L2 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, where E=total energy of the precursor of the transition state and x=nuclear coordinates of a molecule in the precursor of the transition state, C4 If the gradient norm L2 is The method continues with step D1, or C5 if the gradient norm L2 is Then repeat steps C1 to C3 until the gradient norm L2 is obtained 0 So far, among them (a) when steps C1 to C3 have been performed once, if the value of the gradient norm L2 of the geometric structure of the precursor of the transition state is lower than the value of the gradient norm L1 of the optimized starting geometric structure, then in step C1, the geometric structure of the precursor of the transition state is changed, or (b) in case of a plurality of executions of steps C1 to C3, in step C1 changing the geometry of the optimized starting geometry or the geometry of the following precursor from a previously repeated transition state which has the lowest value of the gradient norm L2 or L1 compared to all the gradient norms L2 and L1 obtained so far, D determines the transition state D1 changes the precursor from step C4 or the precursor from step B4 by performing the following steps on the atoms in the function space defined in B1, D1.1 Select atoms from the function space selected in step B1, D1.2 Select the vector used to deflect the atom selected in step D1.1, D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D1.3, D2 optimizes the geometry of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions, thereby obtaining two optimized precursors i and ii, wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energy of the two optimized precursors i and ii from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the value of energy L2 or L1 of the precursor used in step D1, D4.1 if the energy value of the optimized precursor i and the energy value of the optimized precursor ii are respectively less than the value of energy L2 or L1 of the precursor used in step D1, then classify the precursor used in step D1 as a transition state, D4.2 If the energy value of the optimized precursor i or the energy value of the optimized precursor ii is not smaller than the value of the energy L2 or L1 of the precursor used in step D1, the method is repeated starting from step C1.

11. A computer program product comprising instructions which, when executed by a computer, cause the computer to perform the following steps of a method for calculating a transition state of a chemical reaction: A Generates the starting geometry A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to the length of the bond in the high energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performs a three-dimensional representation of the starting geometric structure in Cartesian coordinates and / or internal coordinates, B. Determine the starting geometry for optimization B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond, B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant, B3 determining the gradient norm L1 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=the total energy of the optimized starting geometry and x=the nuclear coordinates of the molecule in the optimized starting geometry, B4 If the gradient norm L1 is The optimized starting geometry is then classified as a precursor to the transition state of the chemical reaction, and the method is continued with step D1, wherein E h represents the Hartree energy, a0 represents the Bohr radius, or B5 If the gradient norm L1 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps: C determines the precursor of the transition state of the chemical reaction C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where C1.1 randomly select at least one atom from the function space selected in step B1, C1.2 randomly selects a vector for deflecting the atom selected in step C1.1, wherein the random selection of the vector is weighted by the gradient norm L1, C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction, C2 geometry optimization of the precursor of the transition state by means of the quantum chemical method and using the boundary condition that at least one bond from step A2 has the length determined in step C1.3, C3 determines a gradient norm L2 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, where E=total energy of the precursor of the transition state and x=nuclear coordinates of a molecule in the precursor of the transition state, C4 If the gradient norm L2 is The method continues with step D1, or C5 if the gradient norm L2 is Then repeat steps C1 to C3 until the gradient norm L2 is obtained 0 So far, among them (a) when steps C1 to C3 have been performed once, if the value of the gradient norm L2 of the geometric structure of the precursor of the transition state is lower than the value of the gradient norm L1 of the optimized starting geometric structure, then in step C1, the geometric structure of the precursor of the transition state is changed, or (b) in case of a plurality of executions of steps C1 to C3, in step C1 changing the geometry of the optimized starting geometry or the geometry of the following precursor from a previously repeated transition state which has the lowest value of the gradient norm L2 or L1 compared to all the gradient norms L2 and L1 obtained so far, D determines the transition state D1 changes the precursor from step C4 or the precursor from step B4 by performing the following steps on the atoms in the function space defined in B1, D1.1 Select atoms from the function space selected in step B1, D1.2 Select the vector used to deflect the atom selected in step D1.1, D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D1.3, D2 optimizes the geometry of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions, thereby obtaining two optimized precursors i and ii, wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energy of the two optimized precursors i and ii from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the value of energy L2 or L1 of the precursor used in step D1, D4.1 if the energy value of the optimized precursor i and the energy value of the optimized precursor ii are respectively less than the value of energy L2 or L1 of the precursor used in step D1, then classify the precursor used in step D1 as a transition state, D4.2 If the energy value of the optimized precursor i or the energy value of the optimized precursor ii is not smaller than the value of the energy L2 or L1 of the precursor used in step D1, the method is repeated starting from step C1.

12. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the following steps of a method for calculating a transition state of a chemical reaction: A Generates the starting geometry A1 provides a three-dimensional representation of at least one molecule in a high-energy ground state, A2 selecting at least one bond of the at least one molecule and selecting a length of the bond, wherein the selected length does not correspond to the length of the bond in the high energy ground state of the molecule, thereby obtaining a starting geometry for the chemical reaction, A3 performs a three-dimensional representation of the starting geometric structure in Cartesian coordinates and / or internal coordinates, B. Determine the starting geometry for optimization B1 sets a function space, the function space including at least one bond from step A2 and atoms connected by the bond, B2: performing a geometry optimization of the function space selected in step B1 by means of a quantum chemical method and with boundary conditions, thereby obtaining an optimized starting geometry, wherein the boundary condition is that the length of at least one bond selected in step A2 remains constant, B3 determining the gradient norm L1 of the optimized starting geometry, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, wherein E=total energy of the optimized starting geometry and x=nuclear coordinates of the molecule in the optimized starting geometry, B4 If the gradient norm L1 is The optimized starting geometry is then classified as a precursor to the transition state of the chemical reaction, and the method is continued with step D1, wherein E h represents the Hartree energy, a0 represents the Bohr radius, or B5 If the gradient norm L1 is Starting from the optimized starting geometry, the precursor of the transition state of the chemical reaction is determined by a method comprising the following steps: C determines the precursor of the transition state of the chemical reaction C1 applies a Monte Carlo algorithm to change the optimized starting geometry, where C1.1 randomly select at least one atom from the function space selected in step B1, C1.2 randomly selects a vector for deflecting the atom selected in step C1.1, wherein the random selection of the vector is weighted by the gradient norm L1, C1.3 deflecting the atom selected in step C1.1 from the position of the atom in said optimized starting geometry based on the vector from step C1.2, thereby obtaining a precursor of the transition state of said chemical reaction, C2 geometry optimization of the precursor of the transition state by means of the quantum chemical method and using the boundary condition that at least one bond from step A2 has the length determined in step C1.3, C3 determines a gradient norm L2 for the precursor of the transition state from step C2, wherein the gradient norm is obtained by taking the first derivative of the function E=f(x) of the quantum chemical method, where E=total energy of the precursor of the transition state and x=nuclear coordinates of a molecule in the precursor of the transition state, C4 If the gradient norm L2 is The method continues with step D1, or C5 if the gradient norm L2 is Then repeat steps C1 to C3 until the gradient norm L2 is obtained 0 So far, among them (a) when steps C1 to C3 have been performed once, if the value of the gradient norm L2 of the geometric structure of the precursor of the transition state is lower than the value of the gradient norm L1 of the optimized starting geometric structure, then in step C1, the geometric structure of the precursor of the transition state is changed, or (b) in case of a plurality of executions of steps C1 to C3, in step C1 changing the geometry of the optimized starting geometry or the geometry of the following precursor from a previously repeated transition state which has the lowest value of the gradient norm L2 or L1 compared to all the gradient norms L2 and L1 obtained so far, D determines the transition state D1 changes the precursor from step C4 or the precursor from step B4 by performing the following steps on the atoms in the function space defined in B1, D1.1 Select atoms from the function space selected in step B1, D1.2 Select the vector used to deflect the atom selected in step D1.1, D1.3 deflecting the atom selected in step D1.1 from its position in said precursor based on the vector from step D1.2, wherein said position is deflected once by the positive value of the amount of said vector and once by the negative value of the amount of said vector, thereby obtaining two deflected precursors when performing steps D1.1 to D1.3, D2 optimizes the geometry of the two deflected precursors from step D1 by means of the quantum chemical method under boundary conditions, thereby obtaining two optimized precursors i and ii, wherein the boundary condition is that the bond distance obtained in D1 remains constant, D3 calculates the energy of the two optimized precursors i and ii from step D2 by means of the quantum chemical method, D4 compares the energy values ​​of the two optimized precursors with the value of energy L2 or L1 of the precursor used in step D1, D4.1 if the energy value of the optimized precursor i and the energy value of the optimized precursor ii are respectively less than the value of energy L2 or L1 of the precursor used in step D1, then classify the precursor used in step D1 as a transition state, D4.2 If the energy value of the optimized precursor i or the energy value of the optimized precursor ii is not smaller than the value of the energy L2 or L1 of the precursor used in step D1, the method is repeated starting from step C1.

13. Use of the computer program product according to claim 11 or the computer readable storage medium according to claim 12 for evaluating a transition state of a chemical reaction.

14. The use according to claim 13, characterized in that The chemical reaction is a polymer synthesis.

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