Construction method of photolysis full-dimensional potential energy surface of first excited state of nitrous acid molecule

Abstract

The invention discloses a construction method of a photolysis full-dimensional potential energy surface of a first excited state of nitrite molecules, and relates to the technical field of computational chemistry and molecular reaction kinetics. According to the invention, a multi-reference configuration interaction method is adopted to carry out system evaluation and optimization selection on a molecular active space, sampling and calculation of data points are carried out in a molecular full-dimensional global configuration space, and a key reaction channel for generating hydroxyl and nitric oxide products through dissociation of nitrous acid molecules is completely covered. A multi-reference configuration interaction method is adopted to systematically evaluate and optimally select an active space, so that a key reaction channel for generating hydroxyl and nitric oxide products through dissociation of nitrous acid molecules is completely covered, and the potential energy description precision in a strong electron association region such as O-N bond dissociation is improved by the strategy; the problem of potential energy surface deviation possibly caused by insufficient theoretical precision of an existing method is solved, and a reliable full-dimensional potential energy surface data basis is provided for accurately describing the dynamic evolution process of excited state molecules along a main reaction channel.

Description

Technical Field

[0001] This invention relates to the fields of computational chemistry and molecular reaction dynamics, and in particular to a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules. Background Technology

[0002] The first excited state full-dimensional potential energy surface of nitrous acid (HONO) molecules refers to the (3N-6)-dimensional potential energy hypersurface obtained by high-precision ab initio electronic structure calculations within the Born–Oppenheimer approximation framework. This hypersurface systematically describes the variation of the electronic energy of the system with nuclear coordinates when it is in the first electronically excited state. This potential energy can characterize the overall change of the excited state potential energy of the system as it evolves from the Franck–Condon region along the main reaction coordinates towards the OH + NO dissociation exit channel. It is a key theoretical basis for conducting quantum dynamics simulations of HONO photodissociation and predicting product distribution.

[0003] Existing theoretical studies on the photodissociation process of nitrous acid molecules mainly rely on the construction of potential energy surfaces in the ground state and excited state. Early works mostly employed quantum chemical calculation methods such as CASSCF, MRCI, and CASPT2 to explore one-dimensional or two-dimensional potential energy profiles of key reaction coordinates, including the equilibrium configuration of the molecule, the cis-trans isomerization barrier, and stretching along the O–N bond. In recent years, machine learning-based potential energy surface construction methods based on large-scale ab initio data points have been gradually applied to this system, expanding the coverage of potential energy surfaces to some extent. However, their reliability in the dissociation region still needs further verification.

[0004] Existing methods still have significant limitations: on the one hand, due to the quantum chemical calculation methods used, the conventional CASSCF method is difficult to achieve quantitative accuracy when calculating regions such as O–N bond breaking; on the other hand, existing data sampling strategies are mostly concentrated in the molecular equilibrium configuration region, which does not adequately cover the configuration space of the dissociation exit channel, resulting in large errors in the potential energy surface along the key path of photodissociation; in addition, the influence of different energy ranges on the accuracy of the potential energy surface is not fully considered during the fitting process, further limiting the kinetic applicability of the potential energy surface. These problems restrict the reliable theoretical description of the HONO photodissociation rate and product state distribution, thus limiting the in-depth understanding and prediction of the atmospheric photochemical behavior of nitrous acid.

[0005] To address this issue, we provide a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules. Summary of the Invention

[0006] The purpose of this invention is to provide a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules. By adopting a strategy that combines multi-reference configuration interaction calculation with neural network fitting, the problem of insufficient accuracy in describing high-energy regions such as dissociation channels and sparse sampling in the prior art is solved.

[0007] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: This invention discloses a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules, comprising the following steps: Step a: The multi-reference configuration interaction method is used to systematically evaluate and optimize the selection of the active space, and based on this, data points are sampled and calculated in the full-dimensional configuration space, which fully covers the key reaction channels for the dissociation of nitrous acid molecules to generate hydroxyl and nitric oxide products; Step b: In the full-dimensional configuration space covering the dissociation channel, a large-scale ab initio energy point sampling is performed by combining sampling in the normal mode space with a dense sampling strategy targeting key dissociation coordinates. Step c: Based on the geometric differences between configurations, the initial data points obtained from sampling are filtered to construct a high-quality, low-redundancy training dataset; Step d: Fit the potential energy surface using a neural network. Use a multi-layer feedforward neural network architecture with one input layer, two hidden layers and one output layer. Each hidden layer contains 50 neurons. The neural network input layer is constructed using low-order permutation invariant polynomials (PIPs) to achieve permutation invariance to equivalent atoms. Step e: Set segmented weights in neural network training. Set segmented weights for samples in different energy ranges. The weight values ​​decrease step by step as the energy increases. Use the same weights when fitting the potential energy surfaces of S0 and S1. Step f: Iteratively update the neural network parameters by minimizing the loss function, determine the weights and biases of the neural network by minimizing the sum of squared residuals, and iteratively optimize the weights and biases of the neural network using the Levenberg-Marquardt algorithm; Step g: Calculate molecular properties using the trained neural network potential surface, perform structure optimization and frequency calculation, and obtain... trans -HONO、 cis -Hono and the geometric parameters and vibration frequencies of the transition state; Step h: Compare and verify the root mean square error of the ground state and excited state of the potential energy surface obtained after fitting by the neural network method, and compare the obtained geometric parameters and vibration frequencies with existing theoretical and experimental data to verify the accuracy and reliability of the potential energy surface.

[0008] A multi-reference configuration interaction method is employed to systematically evaluate and optimize the selection of the active space, and based on this, data point sampling calculations are performed in the global configuration space. Then, within the full-dimensional configuration space encompassing the dissociation channels, a large-scale ab initio energy point sampling is conducted by combining normal mode space sampling and a dense sampling strategy targeting key dissociation coordinates. The sampling points are then filtered based on the geometric differences between configurations to construct a high-quality, low-redundancy training dataset. Subsequently, a multilayer feedforward neural network with low-order permutation invariant polynomials (PIPs) as input is used to fit the potential energy surface, with piecewise weights decreasing as energy increases during training. The loss function containing a regularization term is then minimized, and the Levenberg-Marquardt algorithm is used to optimize the neural network parameters. The root mean square error of the ground state and excited state of the potential energy surface obtained by the neural network fitting method is calculated. Finally, the trained potential energy surface is used for structure optimization and frequency calculation to obtain... trans -HONO、 cis - The geometric parameters and vibrational frequencies of the HONO and transition states are calculated, and the results are compared with existing theoretical and experimental data to verify the accuracy and reliability of the potential energy surface.

[0009] The present invention is further configured such that step a specifically includes: employing the multi-reference configuration interaction (MRCI) method, and using the aug-cc-pVTZ basis set to perform state-averaged fully self-consistent active space field (SA-CASSCF) calculations within an active space containing at least five singlet states; further employing the multi-reference configuration interaction method (MRCI+Q) with Davidson correction; testing several active spaces containing different numbers of electrons and orbitals, and based on these active spaces, lengthening the ON bond length at the MRCI+Q level while fixing other coordinates in the ground state equilibrium configuration; finally, selecting an active space with a smooth potential energy curve in the dissociation region for subsequent calculations; wherein, the finally selected active space contains 14 electrons and 9 orbitals, i.e. (14e, 9o). Through the multi-reference configuration interaction method and the active space optimization screening process, the physical correctness of the potential energy behavior in the strongly electron-correlated region of the dissociation channel is ensured, providing a high-quality data foundation for the full-dimensional and full-range potential energy surface.

[0010] The present invention is further configured such that step b specifically includes: firstly in state trans -HONO、 cis Initial points are sampled in the normal mode space of -HONO and transition states (TS), followed by sampling at the ON atomic spacing (R O-N Dense sampling is performed within the range [1.0, 10.0] Å, and the remaining five coordinates are randomly distributed in the following intervals: R H-O ∈[0.7,3.0]Å、R N=O ∈[0.8,2.5]Å、θONO ∈[0.0,180.0]°、θ HON ∈[0.0,180.0]°、φ HONO ∈[0.0,180.0]°, the number of energy points selected after sampling for potential energy surface fitting is approximately 63,000, and the energy is relative to [0.0,180.0]°. state trans -HONO, with a voltage below 10.0 eV, efficiently obtained large-scale training data covering the entire space and encompassing high-energy regions related to photodissociation, through a specific and operable global sampling scheme and a strategy of dense sampling in key areas and random exploration of the remaining space, with controllable computational cost.

[0011] The present invention further specifies that step c specifically involves: introducing Euclidean distance as a screening criterion; when the Euclidean distance between a new molecular configuration and an existing molecular configuration is less than 0.1 Å, the two configurations are considered to be highly similar, and the sampling result will not be included in the subsequent dataset construction; wherein the formula for calculating the Euclidean distance is:

[0012] The redundancy configuration judgment criteria and calculation formula are highly operable and can effectively ensure the uniformity of the distribution of training data points in the configuration space, avoiding training bias caused by excessive local data density.

[0013] The present invention is further configured such that the symmetric polynomial expression of the low-order permutation invariant polynomials (PIPs) in step d is:

[0014] in l ij Let the order be the order of the monomial. This represents the symmetry operator, where N represents the number of atomic nuclei. For Morse-like variables (parameter α = 2 / 3 Å) -1 ), r ij Indicates the interatomic distance.

[0015] By employing specific mathematical transformations for permutation invariance and methods for constructing input descriptors, the correct symmetry of the neural network input is ensured. This is crucial for constructing a high-precision potential energy surface with physical meaning.

[0016] The present invention is further configured such that the mathematical expression of the k-th neuron in the (i+1)-th layer of the neural network in step d is:

[0017] in Ni This represents the number of neurons in the i-th layer. The weights connecting the j-th neuron in layer i to the k-th neuron in layer (i+1) It is the deviation of the k-th neuron in the (i+1)-th layer. The transfer function representing the (i+1)th layer, through the core mathematical expression of the neural network model, increases the clarity and repeatability of the technical solution, making it easier for those skilled in the art to understand and implement.

[0018] The present invention is further configured such that the specific values ​​of the segment weights in step e are: The weights are 1.0 for energies < 6.0 eV, 0.8 for 6-6.5 eV, 0.6 for 6.5-7 eV, 0.4 for 7-7.5 eV, 0.1 for 7.5-8 eV, and 0.001 for 8-10 eV. By assigning differentiated weights to samples in different energy ranges, the fitting error in low-energy configuration regions is significantly reduced during training, thereby ensuring the prediction accuracy of the geometric parameters of the balanced configuration.

[0019] The present invention is further configured such that the expression for the loss function minimized in step f is:

[0020] Where N dat This represents the total number of energy points. w Energy-dependent weighting factor E Represents the adiabatic energy of state S0 or S1, where The term is the regularization term, and p represents all the parameters to be optimized in the neural network function (weights and biases). t It is a small constant (taken as 10 in the calculation). -5 By incorporating a loss function with a regularization term, the network parameters are suppressed from becoming too large, effectively improving the model's generalization ability and preventing overfitting to the training data, thus resulting in a smoother and physically more reasonable potential energy surface.

[0021] The present invention is further configured such that the geometric parameters in step g include bond length R. O-H R N=O R O-N and bond angle θ HON θ ONO and dihedral angle φ HONO The vibration frequencies include those corresponding to HO stretching ( v 1), N=O telescopic ( v 2) HON bending ( v 3) ON telescopic ( v 4) ONO bending ( v 5) and twist ( v6) The harmonic frequency of the mode, through specific molecular characteristic indicators used to verify the accuracy of the potential energy surface, provides a clear, comprehensive and quantifiable benchmark for accuracy verification.

[0022] The present invention is further configured such that the reliability of the potential energy surface in step h is verified by the following methods: ① Calculating the root mean square error (RMSE) between the ground state (S0) and the excited state (S1); ② Comparing the optimized geometric parameters (bond length, bond angle, dihedral angle) and vibrational frequency with reported experimental data and high-precision theoretical results to confirm their agreement. According to the appendix... Figure 3 The graph shows the root mean square error (RMSE) of the potential energy surfaces of the ground state (S0) and the first excited state (S1) obtained by fitting using a neural network method, as a function of energy. The horizontal axis represents energy (eV), the left vertical axis reflects the fitting error (RMSE, eV), and the right vertical axis corresponds to the cumulative number of data points below the current energy value. This graph simultaneously displays the distribution of fitting accuracy and the number of training samples with energy.

[0023] Overall, as the energy increases, the RMSE of both the ground state and excited state gradually increases. This increase occurs against the backdrop of a continuous increase in the total number of data points. Within the energy range below 6.0 eV, the fitting errors of both states remain at a low level. Specifically, the RMSE of both the ground state and excited state energy surfaces does not exceed 8 meV at energies < 6.0 eV, indicating that the neural network has high accuracy in fitting both state energy surfaces in the low-energy region.

[0024] As the energy increases to the mid-to-high energy range (e.g., >8 eV), the number of data points involved in the fitting for both the ground state and excited state increases significantly. However, the RMSE does not improve; instead, it increases significantly. This is because different weights are assigned to samples from different energy ranges during the fitting process. Furthermore, the absolute value of the RMSE for the excited state is higher than that for the ground state in the high-energy region. For example, at 13.0 eV, the ground state RMSE is 46.23 meV, while the excited state RMSE reaches 52.6 meV, reflecting the higher complexity of the excited state potential surface in the high-energy region.

[0025] For excited state S1, at energy relative to trans Within the range of 5.0 eV from the minimum point of -HONO(S0), the total root mean square error of the potential energy surface is only 6.5 meV, which proves that the fitting results have high reliability and the accuracy of the constructed full-dimensional potential energy surface meets the requirements of subsequent high-precision dynamic simulations.

[0026] The present invention has the following beneficial effects: 1. This invention employs a multi-reference configuration interaction method to determine and optimize the active space, ensuring complete coverage of key reaction pathways for the dissociation of nitrous acid molecules to generate hydroxyl and nitric oxide products. This strategy improves the accuracy of potential energy description in regions with strong electronic correlations, such as ON bond dissociation, and overcomes the potential energy surface deviation problem that may be caused by insufficient theoretical accuracy in existing methods. It provides a reliable full-dimensional potential energy surface data foundation for accurately describing the dynamic evolution of excited-state molecules along the main reaction pathways, thereby supporting a more reliable theoretical description of the key mechanisms of photodissociation dynamic processes.

[0027] 2. This invention combines normal mode spatial sampling with dense sampling of key dissociation coordinates, and introduces a redundancy judgment mechanism based on geometric differences in the data screening stage to construct a uniformly distributed training dataset that covers the full-dimensional configuration space. Furthermore, the neural network training process is optimized by setting segmented weights, which enhances the fitting accuracy. This comprehensive approach effectively solves the problems caused by the sparsity of sampling in high-energy regions and the failure to distinguish the importance of energy in the fitting process in the past. Through systematic comparison and verification with a variety of independent theoretical and experimental data, the accuracy and reliability of the constructed potential energy surface are comprehensively enhanced. Attached Figure Description

[0028] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0029] Figure 1 A schematic diagram of the nine orbitals included in the CASSCF calculation for a method of constructing the photolysis full-dimensional potential energy surface of the first excited state of a nitrous molecule; Figure 2 HONO is used in a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules. trans and cis Molecular configuration diagram; Figure 3 Neural network fitting in a method for constructing the full-dimensional potential energy surface of the first excited state of nitrous acid molecules via photolysis. and Root mean square error distribution of the potential energy surface; Figure 4 This is a one-dimensional potential energy curve along six coordinates in a method for constructing the full-dimensional potential energy surface of the first excited state of nitrous acid molecules through photolysis. Figure 5 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the bond length R in the excited state (S1) is... N-O With R O-H Two-dimensional potential energy surface plot; Figure 6In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the bond length R in the excited state (S1) is... N-O With R N=O Two-dimensional potential energy surface plot; Figure 7 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the bond length R in the excited state (S1) is... N-O With bond angle θ HON Two-dimensional potential energy surface plot; Figure 8 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the bond length R in the excited state (S1) is... N-O With bond angle θ ONO Two-dimensional potential energy surface diagram.

[0030] Figure 9 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the bond length R in the excited state (S1) is... N-O With dihedral angle φ HONO Two-dimensional potential energy surface diagram.

[0031] Figure 10 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the lower bond angle θ of the excited state (S1) is... HON With θ ONO Two-dimensional potential energy surface diagram.

[0032] Figure 11 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the lower bond angle θ of the excited state (S1) is... HON With dihedral angle φ HONO Two-dimensional potential energy surface diagram.

[0033] Figure 12 In a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecule, the lower bond angle θ of the excited state (S1) is... ONO With dihedral angle φ HONO Two-dimensional potential energy surface diagram. Detailed Implementation

[0034] The technical solutions of the present invention will be described below with reference to the accompanying drawings. The described embodiments are only some embodiments of the present invention, and not all embodiments.

[0035] Please see Figures 1-12 This invention relates to a method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules, comprising the following steps: Step a: The multi-reference configuration interaction method is used to systematically evaluate and optimize the selection of the active space, and based on this, data points are sampled and calculated in the full-dimensional configuration space, which fully covers the key reaction channels for the dissociation of nitrous acid molecules to generate hydroxyl and nitric oxide products; Step b: In the full-dimensional configuration space covering the dissociation channel, a large-scale ab initio energy point sampling is performed by combining sampling in the normal mode space with a dense sampling strategy targeting key dissociation coordinates. Step c: Based on the geometric differences between configurations, the initial data points obtained from sampling are filtered to construct a high-quality, low-redundancy training dataset; Step d: Fit the potential energy surface using a neural network. Use a multi-layer feedforward neural network architecture with one input layer, two hidden layers and one output layer. Each hidden layer contains 50 neurons. The neural network input layer is constructed using low-order permutation invariant polynomials (PIPs) to achieve permutation invariance to equivalent atoms. Step e: Set segmented weights in neural network training. Set segmented weights for samples in different energy ranges. The weight values ​​decrease step by step as the energy increases. Use the same weights when fitting the potential energy surfaces of S0 and S1. Step f: Iteratively update the neural network parameters by minimizing the loss function, determine the weights and biases of the neural network by minimizing the sum of squared residuals, and iteratively optimize the weights and biases of the neural network using the Levenberg-Marquardt algorithm; Step g: Calculate molecular properties using the trained neural network potential surface, perform structure optimization and frequency calculation, and obtain... trans -HONO、 cis -Hono and the geometric parameters and vibration frequencies of the transition state; Step h: Compare and verify the root mean square error of the ground state and excited state of the potential energy surface obtained after fitting by the neural network method, and compare the obtained geometric parameters and vibration frequencies with existing theoretical and experimental data to verify the accuracy and reliability of the potential energy surface.

[0036] A multi-reference configuration interaction method is employed to systematically evaluate and optimize the selection of the active space, and based on this, data point sampling calculations are performed in the global configuration space. Then, within the full-dimensional configuration space encompassing the dissociation channels, a large-scale ab initio energy point sampling is conducted by combining normal mode space sampling and a dense sampling strategy targeting key dissociation coordinates. The sampling points are then filtered based on the geometric differences between configurations to construct a high-quality, low-redundancy training dataset. Subsequently, a multilayer feedforward neural network with low-order permutation invariant polynomials (PIPs) as input is used to fit the potential energy surface, with piecewise weights decreasing as energy increases during training. The loss function containing a regularization term is then minimized, and the Levenberg-Marquardt algorithm is used to optimize the neural network parameters. Finally, the trained potential energy surface is used for structure optimization and frequency calculation to obtain... trans -HONO、 cis - The geometric parameters and vibrational frequencies of the HONO and transition states are calculated, and the results are compared with existing theoretical and experimental data to verify the accuracy and reliability of the potential energy surface.

[0037] Step a specifically includes: employing the multi-reference configuration interaction (MRCI) method, and using the aug-cc-pVTZ basis set to perform state-averaged fully active space self-consistent field (SA-CASSCF) calculations within an active space containing at least five singlet states; further employing the multi-reference configuration interaction method with Davidson correction (MRCI+Q); testing several active spaces containing different numbers of electrons and orbitals, and based on these active spaces, lengthening the ON bond length at the MRCI+Q level while fixing other coordinates in the ground state equilibrium configuration; finally, selecting an active space with a smooth potential energy curve in the dissociation region for subsequent calculations; wherein, the finally selected active space contains 14 electrons and 9 orbitals, i.e. (14e, 9o). Step b specifically includes: firstly in state trans -HONO、 cis Initial points are sampled in the normal mode space of -HONO and transition states (TS), followed by sampling at the ON atomic spacing (R O-N Dense sampling is performed within the range [1.0, 10.0] Å, and the remaining five coordinates are randomly distributed in the following intervals: R H-O ∈[0.7,3.0]Å、R N=O ∈[0.8,2.5]Å、θ ONO ∈[0.0,180.0]°、θ HON ∈[0.0,180.0]°、φ HONO ∈[0.0,180.0]°, the number of energy points selected after sampling for potential energy surface fitting is approximately 63,000, and the energy is relative to [0.0,180.0]°. state trans- HONO is below 10.0 eV. Specifically, step c involves: introducing Euclidean distance as a screening criterion. When the Euclidean distance between a new molecular configuration and an existing molecular configuration is less than 0.1 Å, the two configurations are considered highly similar, and this sampling result will not be included in the subsequent dataset construction. The formula for calculating the Euclidean distance is: .

[0038] The symmetric polynomial expression for the low-order permutation invariant polynomials (PIPs) in step d is as follows:

[0039] in l ij Let the order be the order of the monomial. This represents the symmetry operator, where N represents the number of atomic nuclei. For Morse-like variables (parameter α = 2 / 3 Å) -1 ), r ij Indicates the interatomic distance.

[0040] The mathematical expression for the k-th neuron in the (i+1)-th layer of the neural network in step d is:

[0041] in N i This represents the number of neurons in the i-th layer. The weights connecting the j-th neuron in layer i to the k-th neuron in layer (i+1) It is the deviation of the k-th neuron in the (i+1)-th layer. Representing the transfer function of the (i+1)th layer, the specific values ​​of the segment weights in step e are: The weight is 1.0 for energies < 6.0 eV, 0.8 for 6-6.5 eV, 0.6 for 6.5-7 eV, 0.4 for 7-7.5 eV, 0.1 for 7.5-8 eV, and 0.001 for 8-10 eV. Weights in different energy ranges during neural network fitting

[0042] The expression for the loss function minimized in step f is:

[0043] Where N dat This represents the total number of energy points. w Energy-dependent weighting factor ERepresents the adiabatic energy of state S0 or S1, where The term is the regularization term, and p represents all the parameters to be optimized in the neural network function (weights and biases). t It is a small constant (taken as 10 in the calculation). -5 The geometric parameters in steps g and h include bond length R. O-H R N=O R O-N and bond angle θ HON θ ONO and dihedral angle φ HONO ; Based on ab initio calculations and the S0 potential energy surface trans -HONO, cis -HONO and its transition state (TS) bond length parameters, with a comparison of early theoretical and experimental results.

[0044] Based on ab initio calculations and the S0 potential energy surface trans -HONO, cis - HONO and its transition state (TS) bond angle parameters, with a comparison of early theoretical and experimental results.

[0045] The vibration frequency includes frequencies corresponding to HO stretching ( v 1), N=O telescopic ( v 2) HON bending ( v 3) ON telescopic ( v 4) ONO bending ( v 5) and twist ( v 6) The simple harmonic frequency of the mode; To comprehensively evaluate the accuracy of the constructed potential energy surface from the perspective of data fitting, a systematic analysis was conducted on the root mean square error (RMSE) between high-precision ab initio reference values. The results are as follows: Figure 3 As shown, Figure 3 It also shows the ground state ( ) and the first excited state ( The RMSE of the potential energy surface and the distribution of the number of training samples with energy; Analysis shows that the key region with energy not exceeding 6.0 eV (covering molecular equilibrium configuration and reaction barrier) is the most affected. and The RMSE of the potential energy surface does not exceed 8 meV, indicating that the neural network has extremely high fitting accuracy in the low-energy region. As the energy increases to the medium-high energy region (>8 eV), although the number of data points involved in the fitting increases significantly, the RMSE of both electronic states shows a reasonable growth trend. This is attributed to the piecewise weighting strategy used in training, which prioritizes the accuracy in the low-energy region. At 13.0 eV, and The RMSEs of the potential energy surface are 46.23 meV and 52.6 meV, respectively, reflecting that the excited state has higher complexity in the high-energy dissociation channel; For excited state S1, at energy relative to trans Within the range of 5.0 eV from the minimum point of -HONO(S0), the total root mean square error of the potential energy surface is only 6.5 meV, which proves that the fitting results have high reliability and the accuracy of the constructed full-dimensional potential energy surface meets the requirements of subsequent high-precision dynamic simulations.

[0046] trans / cis -Hono and the simple harmonic frequency of the transition state (TS) The calculation results are presented, along with a comparison of theoretical and experimental values.

[0047]

[0048] The reliability of the potential energy surface is verified in step h by the following methods: ① Calculating the root mean square error (RMSE) of the ground state (S0) and the excited state (S1); ② Comparing the optimized geometric parameters (bond length, bond angle, dihedral angle) and vibrational frequencies with reported experimental data and high-precision theoretical results to confirm their agreement. (According to Appendix...) Figure 3 The graph shows the root mean square error (RMSE) of the potential energy surfaces of the ground state (S0) and the first excited state (S1) obtained by fitting using a neural network method, as a function of energy. The horizontal axis represents energy (eV), the left vertical axis reflects the fitting error (RMSE, eV), and the right vertical axis corresponds to the cumulative number of data points below the current energy value. This graph simultaneously displays the distribution of fitting accuracy and the number of training samples with energy.

[0049] Overall, as the energy increases, the RMSE of both the ground state and excited state gradually increases. This increase occurs against the backdrop of a continuous increase in the total number of data points. Within the energy range below 6.0 eV, the fitting errors of both states remain at a low level. Specifically, the RMSE of both the ground state and excited state energy surfaces does not exceed 8 meV when the energy is ≤6.0 eV, indicating that the neural network has high accuracy in fitting both energy surfaces in the low-energy region.

[0050] As the energy increases to the mid-to-high energy range (e.g., >8 eV), the number of data points involved in the fitting of both the ground state and excited state increases significantly. However, the RMSE does not improve as a result; instead, it increases significantly. This is because different weights are assigned to samples from different energy ranges. Furthermore, the absolute value of the RMSE of the excited state is higher than that of the ground state in the high-energy region. For example, at 13.0 eV, the ground state RMSE is 46.23 meV, while the excited state RMSE reaches 52.6 meV, reflecting the higher complexity of the excited state potential surface in the high-energy region.

[0051] For excited state S1, at energy relative to trans Within the range of 5.0 eV from the minimum point of -HONO(S0), the total root mean square error of the potential energy surface is only 6.5 meV, which proves that the fitting results have high reliability and the accuracy of the constructed full-dimensional potential energy surface meets the requirements of subsequent high-precision dynamic simulations.

[0052] Specifically: Through high-precision electronic structure calculation methods and active space optimization screening processes, the physical correctness of potential energy behavior in strongly correlated electron regions such as dissociation channels is ensured, providing a high-quality data foundation for the overall potential energy surface; through a specific and operable global sampling scheme, employing a strategy of dense sampling in key areas and random exploration of the remaining space, large-scale training data covering the entire dimensional space and encompassing photodissociation-related regions is efficiently obtained at a controllable computational cost; through redundancy configuration judgment criteria and calculation formulas, the system is highly operable and effectively ensures the uniform distribution of training data points in the configuration space, avoiding training bias caused by excessive local data density; through specific mathematical transformations of permutation invariance and input descriptor construction methods, the correct symmetry of the neural network input is ensured, which is crucial for constructing physically meaningful high-precision... The key to determining the potential energy surface lies in the following: The core mathematical expression of the neural network model increases the clarity and repeatability of the technical solution, facilitating understanding and implementation by those skilled in the art; By assigning differentiated weights to samples in different energy ranges, the fitting error in low-energy configuration regions is significantly reduced during training, thus ensuring the prediction accuracy of the equilibrium configuration geometric parameters; The specific form of the loss function including a regularization term effectively improves the model's generalization ability by suppressing excessively large network parameters, preventing overfitting to training data and resulting in a smoother, more physically reasonable potential energy; Specific molecular characteristic indicators used to verify the accuracy of the potential energy surface provide a clear, comprehensive, and quantifiable benchmark for accuracy verification; Comparison with data from multiple independent sources greatly enhances the credibility and persuasiveness of the constructed potential energy surface.

[0053] Please see Figures 1-12 Potential energy surface construction based on standard active space and basic sampling strategy.

[0054] Specifically: First, using the multi-reference configuration interaction method with Davidson correction (MRCI+Q), at the aug-cc-pVTZ basis set level, state-averaged self-consistent field (SA-CASSCF) calculations were performed on the active space containing the lowest five singlet states. Multiple candidate active spaces (e.g., (12e, 8o), (14e, 9o), (16e, 10o), and (18e, 11o)) were tested, and the smoothness of their potential energy curves stretched along the ON bonds at the MRCI+Q level was analyzed. Finally, (14e, 9o) was selected as the optimal active space. Based on this, data point sampling was performed: first at… state trans -HONO、 cis Approximately 10,000 initial points were obtained by sampling within the normal mode space of -HONO and transition states (TS); subsequently, the atomic spacing (R) at the dissociation coordinate ON was determined. O-N The range is 1.0 Å to 10.0 Å, with dense sampling at 0.1 Å intervals, while the other five internal coordinates (R) are also sampled. O-H R N=O θ HON θ ono φ HONO Random values ​​were randomly selected within its range, generating approximately 80,000 candidate configurations. MRCI+Q single-point energy calculations were performed on all sampled points. Subsequently, following the method of claim 4, a threshold of 0.1 Å Euclidean distance was used to select configurations with energies lower than [a certain value]. state trans - All computational points at 10.0 eV were screened, and highly similar configurations were removed, resulting in approximately 63,000 high-quality data points without redundancy for training. The neural network adopted the structure of claim 1 (input layer - PIPs, two hidden layers each containing 50 neurons, output layer), and segmented weights were set according to claim 7 (weight 1.0 for energy < 6.0 eV, weight 0.8 for 6-6.5 eV, weight 0.6 for 6.5-7.0 eV, weight 0.4 for 7.0-7.5 eV, weight 0.1 for 7.5-8.0 eV, and weight 0.001 for 8.0-10.0 eV). During training, the regularization term of claim 8 was used ( The loss function of the neural network is calculated and optimized using the Levenberg-Marquardt algorithm. After training, the potential energy of the neural network is applied to the target surface. trans -HONO、 cis -HONO and cis-trans isomerization transition states were structurally optimized and their harmonic frequencies were analyzed to obtain their geometric parameters (R). O-H R O-N R N=O θ HON θ onoφ HON ) and six simple harmonic frequencies ( ), the optimized trans -HONO's R O-N Bond length (1.440 Å) and θ HON The bond angle (101.99°) was compared with the high-precision theoretical reference value (1.434 Å, 101.97°), and the errors were less than 0.42% and 0.02%, respectively, which verified that the potential energy surface constructed by this method is relatively reliable.

[0055] The preferred embodiments of the present invention disclosed above are only for the purpose of illustrating the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation described herein. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can better understand and utilize the present invention.

Claims

1. A method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules, characterized in that, Includes the following steps: Step a: The multi-reference configuration interaction method is used to systematically evaluate and optimize the selection of the active space, and based on this, data points are sampled and calculated in the full-dimensional configuration space, which fully covers the key reaction channels for the dissociation of nitrous acid molecules to generate hydroxyl and nitric oxide products; Step b: In the full-dimensional configuration space covering the dissociation channel, a large-scale ab initio energy point sampling is performed by combining sampling in the normal mode space with a dense sampling strategy targeting key dissociation coordinates. Step c: Based on the geometric differences between configurations, the initial data points obtained from sampling are filtered to construct a high-quality, low-redundancy training dataset; Step d: Fit the potential energy surface using a neural network. Use a multi-layer feedforward neural network architecture with one input layer, two hidden layers and one output layer. Each hidden layer contains 50 neurons. The neural network input layer is constructed using low-order permutation invariant polynomials (PIPs) to achieve permutation invariance to equivalent atoms. Step e: Set segmented weights in neural network training. Set segmented weights for samples in different energy ranges. The weight values ​​decrease step by step as the energy increases. Use the same weights when fitting the potential energy surfaces of S0 and S1. Step f: Iteratively update the neural network parameters by minimizing the loss function, determine the weights and biases of the neural network by minimizing the sum of squared residuals, and iteratively optimize the weights and biases of the neural network using the Levenberg-Marquardt algorithm; Step g: Calculate molecular properties using the trained neural network potential surface, perform structure optimization and frequency calculation, and obtain... trans -HONO、 cis -Hono and the geometric parameters and vibration frequencies of the transition state; Step h: Compare and verify the root mean square error of the ground state and excited state of the potential energy surface obtained after fitting by the neural network method, and compare the obtained geometric parameters and vibration frequencies with existing theoretical and experimental data to verify the accuracy and reliability of the potential energy surface.

2. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: Step a specifically includes: employing the multiple reference configuration interaction (MRCI) method, and using the aug-cc-pVTZ basis set to perform state-averaged fully active space self-consistent field (SA-CASSCF) calculations within an active space containing at least five singlet states; further employing the multiple reference configuration interaction method with Davidson correction (MRCI+Q); testing several active spaces containing different numbers of electrons and orbitals, and based on these active spaces, lengthening the ON bond length at the MRCI+Q level while fixing other coordinates in the ground state equilibrium configuration; finally, selecting an active space with a smooth potential energy curve in the dissociation region for subsequent calculations; wherein, the finally selected active space contains 14 electrons and 9 orbitals, i.e. (14e, 9o).

3. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: Step b specifically includes: firstly in state trans -HONO、 cis Initial points are sampled in the normal mode space of -HONO and transition states (TS), followed by sampling at the ON atomic spacing (R O-N Dense sampling is performed within the range [1.0, 10.0] Å, and the remaining five coordinates are randomly distributed in the following intervals: R H-O ∈[0.7,3.0]Å、R N=O ∈[0.8,2.5]Å、θ ONO ∈[0.0,180.0]°、θ HON ∈[0.0,180.0]°、φ HONO ∈[0.0,180.0]°, the number of energy points selected after sampling for potential energy surface fitting is approximately 63,000, and the energy is relative to [0.0,180.0]°. state trans -HONO is below 10.0 eV.

4. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: Step c specifically involves: introducing Euclidean distance as a screening criterion. When the Euclidean distance between a new molecular configuration and an existing molecular configuration is less than 0.1 Å, the two configurations are considered highly similar, and this sampling result will not be included in the subsequent dataset construction. The formula for calculating the Euclidean distance is as follows:

5. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The symmetric polynomial expression for the low-order permutation invariant polynomials (PIPs) in step d is as follows: ,in l ij The order of the monomial. This represents the symmetry operator, where N represents the number of atomic nuclei. For Morse-like variables (parameter α = 2 / 3 Å) -1 ), r ij Indicates the interatomic distance.

6. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The mathematical expression for the k-th neuron in the (i+1)-th layer of the neural network in step d is: ,in N i This represents the number of neurons in the i-th layer. The weights connecting the j-th neuron in layer i to the k-th neuron in layer (i+1) It is the deviation of the k-th neuron in the (i+1)-th layer. This represents the transfer function of the (i+1)th layer.

7. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The specific values ​​of the segment weights in step e are as follows: 1.0 when the energy is <6.0 eV, 0.8 when it is 6-6.5 eV, 0.6 when it is 6.5-7 eV, 0.4 when it is 7-7.5 eV, 0.1 when it is 7.5-8 eV, and 0.001 when it is 8-10 eV.

8. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The expression for the loss function minimized in step f is: , where N dat This represents the total number of energy points. w Energy-dependent weighting factor E Represents the adiabatic energy of state S0 or S1, where The term is the regularization term, and p represents all the parameters to be optimized in the neural network function (weights and biases). t It is a small constant (taken as 10 in the calculation). -5 ).

9. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The geometric parameters in steps g and h include bond length R. O-H R N=O R O-N and bond angle θ HON θ ONO and dihedral angle φ HONO The vibration frequencies include those corresponding to HO stretching ( v 1), N=O telescopic ( v 2) HON bending ( v 3) ON telescopic ( v 4) ONO bending ( v 5) and twist ( v 6) The simple harmonic frequency of the mode.

10. The method for constructing the photolytic full-dimensional potential energy surface of the first excited state of nitrous acid molecules according to claim 1, characterized in that: The reliability of the potential energy surface in step h is verified by the following methods: ① Calculate the root mean square error (RMSE) of the ground state (S0) and the excited state (S1); ② Compare the optimized geometric parameters (bond length, bond angle, dihedral angle) and vibration frequency with the reported experimental data and high-precision theoretical results to confirm their agreement.

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