Method for predicting solvation energy of small molecule compounds based on graph convolutional neural network

Abstract

The application discloses a method for predicting solvation energy of small molecule compounds based on a graph convolutional neural network. The method introduces an atomic feature descriptor containing three-dimensional structure information and two-dimensional topological information, and automatically extracts a chemical pattern related to solvation energy in a compound based on a graph convolutional neural network to construct a prediction model. In addition, in order to improve the robustness of the prediction model, the method does not directly predict the solvation energy of the compound, but predicts the energy contribution of each atom in the compound. The application uses solvation energy data and three-dimensional structures of 1.7 million compounds calculated by a quantum chemistry method to train the model. The method not only retains the calculation accuracy and extrapolation performance of the quantum chemistry method, but also has the calculation efficiency of the machine learning method. By applying the application, the solvation energy of small molecule compounds can be quickly and accurately predicted, and the efficiency of drug design and virtual screening is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of computer-aided drug design, and is a method for rapidly predicting the solvation energy of a small molecule compound based on a graph convolutional neural network, which can be applied in the fields of drug virtual screening and drug molecule design, can greatly shorten the calculation time of drug virtual screening, and can guide the modification of drug molecule structures and optimize the activity, solubility and other properties of small molecule drugs. BACKGROUND

[0002] Solvation is the process of transferring molecules from vacuum to solution, which occurs in various aspects of nature and affects various biological processes. Solvation energy is a measure of the strength of interaction between molecules and solvents, and chemists evaluate the solubility of molecules through solvation energy. The size of the solvation energy of a drug molecule in an aqueous solution significantly affects the binding of a protein-drug molecule. Therefore, accurately and quickly calculating the solvation energy of a ligand molecule has important significance and practical value in drug design and drug virtual screening.

[0003] At present, many methods for calculating solvation energy have been developed, mainly divided into two methods based on physical theory and machine learning. In the physical-based method, the most rigorous method is the thermodynamic integration method (TI) or the free energy perturbation method (FEP). In addition, implicit solvent-based methods are popular due to their low computational cost, such as the Poisson-Boltzmann surface area method (PBSA) and the generalized Born surface area method (GBSA), which highly depend on empirical parameters and cannot explain specific interactions between solutes and solvents, such as hydrogen bond interactions between solutes and solvents. There is also a class of continuous medium solvation models that describe solute-solvent interactions based on the quantum mechanical charge density of the solute molecule and the dielectric constant of the solvent. These physical-based calculation methods are very expensive, requiring several minutes to several hours per compound on a single core, which severely limits the size of the molecule library that can be evaluated.

[0004] Deep learning has become an effective prediction technique in chemical engineering, biological science and material science. In the past decade, many efforts have been made to replace physical-based methods with deep neural networks. However, a major problem often encountered in the field of chemistry is data scarcity. Compared with other disciplines such as image recognition and natural language processing, the availability and size of chemical engineering and material science data sets are very limited.

[0005] Physical-based models have better extrapolation than machine learning models. Therefore, using deep learning methods to learn the calculation data of quantum chemistry continuous medium models can not only retain the calculation accuracy and excellent extrapolation of quantum chemistry methods, but also improve the calculation efficiency. SUMMARY

[0006] The purpose of the present application is to provide a method for predicting the solvation energy of small molecule compounds based on graph convolutional neural network, which has a very fast calculation speed while having the accuracy of quantum chemical calculation. The method establishes a general small molecule compound solvation energy prediction model based on graph convolutional neural network, introduces three-dimensional structure information and two-dimensional topological structure information in the atomic descriptor, and predicts the energy contribution of each atom in the compound. The solvation energy prediction model is trained using the solvation energy data and three-dimensional structure of 1.7 million compounds calculated by quantum chemical method. Using this method, the solvation energy of small molecule compounds can be quickly predicted, the drug molecule library can be filtered, and virtual screening of drugs can be assisted. The method can also guide the optimization of drug molecular structure, and improve the activity and various physical and chemical properties of drugs.

[0007] The purpose of the present application is achieved as follows:

[0008] A method for predicting the solvation energy of small molecule compounds based on graph convolutional neural network, comprising the following specific steps:

[0009] Step 1: Extract all compound structures from the PubChem database, neutralize salt-containing compounds, and filter compounds containing non-C, H, O, N, S, P, F, Cl, Br, and I elements;

[0010] Step 2: Calculate the formal charge of the compounds in step 1, and divide all the compounds into neutral compound data set and charged compound data set according to the charged state;

[0011] Step 3: Use RDKit to generate the initial three-dimensional conformation of the neutral compounds and charged compounds in step 2;

[0012] Step 4: Use quantum chemical method to optimize the initial three-dimensional conformation of the neutral compounds and charged compounds in step 3 to obtain the optimized fine three-dimensional conformation;

[0013] Step 5: Based on the fine three-dimensional conformation of step 4, apply high-precision quantum chemical method to calculate the solvation energy of neutral compounds and charged compounds in aqueous solution;

[0014] Step 6: Based on the fine three-dimensional conformation optimized in step 4, calculate the molecular graph of each compound, including node features and edge features, and record its solvation energy data, and construct the training data set of the solvation energy prediction model;

[0015] Step 7: Based on the training data set obtained in step 6, use graph convolutional neural network to train the solvation energy prediction model of neutral molecules and charged molecules respectively;

[0016] Step 8: Use the mean relative error MAE, root mean square error RMSE and correlation coefficient R 2The performance of the model is evaluated, and the model with the best performance is selected from the models saved in step 7 as the final prediction model using the index;

[0017] Step 9: When the solvation energy model is applied to predict the solvation energy of the compound, for each compound, first use RDKit to generate a maximum of 50 initial conformations;

[0018] Step 10: Then use the ANI-2x model to optimize the initial conformations generated by RDKit, and take the conformation with the lowest energy after ANI-2x optimization as the optimal conformation, and the optimal conformation as the input for solvation energy calculation;

[0019] Step 11: Based on the optimal conformation obtained in step 10, use the model obtained in step 8 to predict the solvation energy of the compound.

[0020] Step 3: The initial three-dimensional conformation of each compound is generated only once based on the initial three-dimensional conformation of the compound generated by RDKit.

[0021] Step 4: The quantum chemistry method used to optimize the three-dimensional conformation of the compound uses B3LYP / 6-31G* to optimize the three-dimensional conformation of the compound in vacuum.

[0022] Step 5: The high-precision quantum chemistry method used to calculate the solvation energy of neutral compounds and charged compounds in aqueous solution uses the M06 / 6-31G*SMD continuous medium model.

[0023] The node features described in step 6 include two-dimensional topological information and three-dimensional structural information, which describe the basic properties of the atom represented by the node and its surrounding chemical environment, wherein the two-dimensional topological information includes atom type, hybridization state, aromaticity, and ring state, the atom type includes C, H, O, N, S, F, and Cl, the hybridization state includes sp, sp2, sp3, sp3d, sp3d2, and sp3d3, the aromaticity indicates whether the atom is in an aromatic ring, and the ring state includes three rings, four rings, five rings, six rings, and seven rings; the three-dimensional structural information includes atom environment fingerprint and atom surface solvent accessible surface area, the atom surface solvent accessible surface area is calculated using a numerical integration method, and the atom environment fingerprint is calculated using a symmetry function, including a radial symmetry function and an angular symmetry function, the two symmetry functions have a common truncation function part, and the specific calculation method of the symmetry function is as follows:

[0024] Truncation function

[0025] 1)

[0026] where R ijis the distance between central atom i and neighbor atom j, Rc is the cutoff radius, a is the element type including C, H, O, N, S, P, F, Cl, Br and I;

[0027] Radial symmetry function

[0028] 2)

[0029] wherein f is a cutoff function; and η and Rs are set to 0.5, 0.0, 0.5 and 0.00001, respectively; Z b and Z c are the atomic numbers of central atom i and neighbor atom j, respectively; N is the number of neighbor atoms; R ij is the distance between central atom i and neighbor atom j; the cutoff radius Rc uses 7 values, 1.5, 2.0, 2.5, 3.0, 4.0, 6.0 and 10.0, respectively; a is the element type including C, H, O, N, S, P, F, Cl, Br and I;

[0030] Angular symmetry function

[0031]

[0032] wherein f is a cutoff function; and λ, θ s , ζ and η are set to 0.5, 0.0, 0.5 and 0.00001, respectively; Z b and Z c are the atomic numbers of central atom i and neighbor atom j, respectively; θ ijk is the angle between atoms i, j and k; R ij is the distance between central atom i and neighbor atom j; R ik is the distance between central atom i and neighbor atom k; R jk is the distance between central atom j and neighbor atom k; Z b and Z c are the atomic numbers of neighbor atom i and neighbor atom k, respectively; a and β are the element types.

[0033] The edge features described in step 6 include single bond, double bond, triple bond and aromatic bond.

[0034] In the step 7 prediction model training process, first, the solvation energy model of neutral molecules is trained, and then based on the solvation energy model of neutral molecules, the solvation energy model of charged molecules is trained by applying transfer learning.

[0035] The graph convolutional neural network described in step 7 is divided into two parts, namely a graph convolution module and an information reading module. First, the graph convolution module is used to extract the vector representation of the compound, and then the information reading module is used to fit the solvation energy; the neural network updates the information of the node and fits the solvation energy data using the following formula:

[0036]

[0037]

[0038]

[0039] wherein A is an adjacency matrix, D is a degree matrix, H is a feature matrix, W is a parameter matrix, l is the number of graph convolution layers, ReLu is an activation function, and MLP is a multi-layer perception.

[0040] The average relative error MAE, the root mean square error RMSE and the correlation coefficient R in step 8 2 The index calculation method is as follows:

[0041]

[0042]

[0043]

[0044] wherein x i is the experimental value, x′ i is the predicted value, and N is the sample number.

[0045] Compared with other methods, the beneficial effects of the present application are:

[0046] (1) The present application learns the solvation energy of small molecule compounds based on a graph convolutional neural network. The model automatically learns the relationship between the molecular structure and the solvation energy using a deep neural network, realizes an end-to-end training process, and compared with other methods, does not need to manually write molecular descriptors, and is more convenient and faster to construct a solvation energy model.

[0047] (2) The present application constructs a prediction model based on a graph convolutional neural network. Not only does it introduce solvent accessible surface area and atomic environment fingerprint to represent the three-dimensional conformation information around the atom, but also contains the two-dimensional topological structure information of the compound, so that the neural network can accurately fit the solvation energy data.

[0048] (3) Since experimental data of solvation energy is very rare, the solvation energy prediction model is not directly fitted by using experimental data in the application, but the solvation energy data calculated by a high-precision quantum chemistry method is learned, so that the solvation energy prediction model has a wide scope of action of physical methods and has the ability of fast prediction of machine learning methods.

[0049] (4) Since the distribution intervals of solvation energy of neutral compounds and charged compounds are obviously different, the prediction model is trained for neutral compounds and charged compounds respectively in the application, so that the differences between the two types of compounds can be fully considered, noise can be avoided, and the model is easier to converge during training.

[0050] (5) The deep neural network is used for nonlinear fitting in the application, which is easier to fit the relationship between the structure of the compound and the solvation energy than the traditional linear fitting method.

[0051] (6) The results show that the solvation energy of small molecule compounds can be more quickly and accurately predicted by using the application, which is suitable for evaluating the filtration of large compound library before virtual screening, reducing the time of drug virtual screening, and can also be used to guide the structural modification of drug molecules and improve the solubility of drug molecules. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a workflow diagram of the application;

[0053] Figure 2 is an energy distribution histogram of the solvation energy training set;

[0054] Figure 3 is a training flowchart of the solvation energy prediction model;

[0055] Figure 4 is a performance performance diagram of the solvation energy prediction model on the independent test set;

[0056] Figure 5 is a performance performance diagram of the solvation energy prediction model on different similarity intervals;

[0057] Figure 6 is a performance performance diagram of the solvation energy prediction model on the independent experimental test set;

[0058] Figure 7 is a performance performance diagram of the solvation energy prediction model on a larger molecular weight test set. DETAILED DESCRIPTION

[0059] The application will be described in detail below in combination with the drawings and examples.

[0060] Reference Figure 1The application discloses a small molecule compound solvation energy prediction method based on a graph convolutional neural network.

[0061] Step 1: extracting all compound structures from the PubChem database, filtering compounds containing salts and special elements, and finally obtaining a compound dataset containing only 10 chemical elements (C, H, O, N, S, P, F, Cl, Br and I);

[0062] Step 2: calculating the charge size of the compounds in step 1, and dividing all the compounds into a neutral compound dataset and a charged compound dataset according to the charged state, all the calculations being realized by using a chemical informatics software package RDKit, and the solvation energy data distribution in the final neutral compound dataset and charged compound dataset being as shown in Figure 2 .

[0063] Step 3: using RDKit to generate initial three-dimensional conformations for the neutral compounds and charged compounds in step 2;

[0064] Step 4: using a quantum chemistry method to optimize the initial three-dimensional conformations of the neutral compounds and charged compounds in step 3, to obtain fine three-dimensional conformations after optimization;

[0065] Step 5: based on the three-dimensional conformations obtained by the quantum chemistry method in step 4, applying a high-precision quantum chemistry method to calculate the solvation energy of the neutral compounds and charged compounds in aqueous solution;

[0066] Step 6: based on the fine three-dimensional conformations obtained in step 4, calculating the molecular graph of each compound, including node features and edge features, and recording the solvation energy data, to build a training dataset for a solvation energy prediction model;

[0067] Step 7: based on the training dataset calculated in step 6, using a graph convolutional neural network to train solvation energy prediction models for neutral molecules and charged molecules respectively, and the specific training process being referred to in Figure 3 .

[0068] Step 8: using mean relative error MAE, root mean square error RMSE and correlation coefficient R 2 to evaluate the performance of the model, and using the indexes to screen a model with the optimal performance from the models saved in step 7 as a final prediction model;

[0069] Step 9: testing the performance of the solvation energy prediction model on an external test set and an experimental dataset, and the results being referred to in Figure 4 、 Figure 5 and Figure 6 ;

[0070] Step 10: To verify the robustness of the solvation energy prediction model network architecture, the performance of the model was tested on an external test set containing larger number of atoms, see Figure 7 , and the results show that the model predicting the energy contribution of each atom has significantly better extrapolation performance than the model directly predicting the total solvation energy;

[0071] Step 11: In the prediction, for each compound, RDKit is used to generate a maximum of 50 initial conformations;

[0072] Step 12: The initial conformations generated by RDKit are optimized using the ANI-2x model, and the optimized conformations are used as input for the solvation energy calculation;

[0073] Step 13: Based on the optimized conformations obtained in step 10, the solvation energy of the compound is predicted using the model obtained in step 8;

[0074] In step 3, only one initial conformation is generated for each compound;

[0075] In step 4, the quantum chemistry method uses B3LYP / 6-31G* to optimize the geometric structure of the molecule in vacuum, and the calculation is realized using Gaussian 16 software;

[0076] In step 5, the quantum chemistry method uses M062X / 6-31G*SMD method to calculate the solvation energy of the small molecule compound, and the calculation is realized using Gaussian 16 software;

[0077] The node features in step 6 include two-dimensional topological information and three-dimensional structural information, which describe the basic properties of the atom represented by the node and the surrounding chemical environment, where the two-dimensional topological information includes atom type, hybridization state, aromaticity, ring state, atom type includes C, H, O, N, S, F, Cl, hybridization state includes sp, sp2, sp3, sp3d, sp3d2, sp3d3, aromaticity indicates whether the atom is in an aromatic ring, and ring state includes three rings, four rings, five rings, six rings, seven rings; The three-dimensional structural information includes atomic environment fingerprint and atomic surface solvent accessible surface area, the atomic surface solvent accessible surface area is calculated using numerical integration method, and the atomic environment fingerprint is calculated using symmetry function, including radial symmetry function and angular symmetry function, the two symmetry functions have common truncation function part, and the specific calculation method of the symmetry function is as follows:

[0078] Truncation function

[0079] 3)

[0080] where R ijRc is the distance between the central atom i and its neighboring atom j, Rc is the cutoff radius, and α is the element type, including C, H, O, N, S, P, F, Cl, Br, and I.

[0081] radially symmetric function

[0082] 4)

[0083] Where f is the truncation function; η and Rs are used to adjust the width and peak height of the Gaussian weights, and η and Rs are set to 0.0001 and 0, respectively; Z b and Z c These are the atomic numbers of the central atom i and its neighboring atom j, respectively; N is the number of neighboring atoms; R ij It is the distance between the central atom i and its neighboring atom j; the cutoff radius Rc uses 7 values, namely 1.5, 2.0, 2.5, 3.0, 4.0, 6.0 and 10.0; α is the element type, including C, H, O, N, S, P, F, Cl, Br and I;

[0084] Angular symmetric function

[0085]

[0086] Where f is the truncation function; λ, θ s ζ and η are set to 0.5, 0.0, 0.5, and 0.00001 respectively; Z b and Z c These are the atomic numbers of the central atom i and its neighboring atom j, respectively; θ ijk R is the angle between atoms i, j, and k; ij R is the distance between the central atom i and its neighboring atom j; ik R is the distance between the central atom i and its neighboring atom k; jk Z is the distance between the central atom j and its neighboring atom k; b and Z c α and β are the atomic numbers of neighboring atoms i and k, respectively; α and β are the element types.

[0087] In step 7, the solvation energy dataset is divided into a training set, a validation set, and a test set in an 8:1:1 ratio. First, a solvation energy model for neutral molecules is trained. Then, based on the solvation energy model for neutral molecules, transfer learning is applied to train a solvation energy model for charged molecules.

[0088] The graph convolutional neural network in step 7 consists of two parts: a graph convolution module and an information readout module. First, the graph convolution module is used to extract the vector representation of the compound, and then the information readout module is used to fit the solvation energy. The neural network updates the node information and fits the solvation energy data using the following formula:

[0089]

[0090]

[0091]

[0092] where A is the adjacency matrix, D is the degree matrix, H is the eigen matrix, W is the parameter matrix, L is the number of graph convolution layers, ReLu is the activation function, and MLP is the multi-layer perceptron.

[0093] In step 7, the contribution of each atom in the compound to the total solvation energy is first fitted based on the graph convolutional neural network, and then the energy contributions of each atom are summed to obtain the final solvation energy, as described in Figure 1 ;

[0094] The three evaluation index calculation methods in step 8 are as follows:

[0095]

[0096]

[0097]

[0098] where xi is the experimental value, x'i is the predicted value, and N is the number of samples.

[0099] In step 9, the prediction performance of the solvation energy prediction model for neutral molecules and charged molecules is evaluated based on the test set. For neutral molecules, the correlation between the predicted value and the quantum chemistry calculation result is 0.99, the RMSE is 0.43 kcal / mol, and the MAE is 0.26 kcal / mol. For charged molecules, the correlation between the predicted value and the quantum chemistry calculation result is 0.94, the RMSE is 2.72 kcal / mol, and the MAE is 1.83 kcal / mol, with excellent performance. At the same time, the influence of the similarity between the molecules in the test set and the training set on the performance of the model is analyzed, and the results are described in Figure 5 , Figure 5 The left graph is the similarity analysis of neutral molecules, and the right graph is the similarity analysis of charged molecules. It can be found that as the similarity decreases, the prediction performance of the model decreases, but the overall impact is small, indicating that the method has good robustness. In addition, the solvation energy experimental data set FreeSolv is extracted from the literature, and the performance differences between the solvation energy prediction model in this method and other three physical theory-based methods are compared, as described in Figure 6 , Figure 6 A is the performance of the method on the experimental data set, Figure 6 B is the performance of the Alchemical method,Figure 6 C is the performance of the quantum chemistry-based continuum model SMD method, Figure 6 D is the performance of the GBSA method, and it can be found from the figure that the prediction performance of the present method is comparable to that of the physical theory-based method.

[0100] In step 11, the number of generated conformations can be selected according to the size of the molecule, and the final number of conformations cannot be greater than 50.

[0101] In step 12, in order to speed up the calculation speed, a machine learning potential energy function is used instead of a quantum chemistry method to optimize the conformation of the compound.

Claims

1. A method for predicting the solvation energy of small molecule compounds based on graph convolutional neural networks, characterized in that, The method includes the following specific steps: Step 1: Extract all compound structures from the PubChem database, neutralize salt-containing compounds, and filter compounds containing elements other than C, H, O, N, S, P, F, Cl, Br, and I. Step 2: Calculate the formal charge of the compounds in Step 1, and divide all compounds into neutral compound datasets and charged compound datasets according to their charged states; Step 3: Use RDKit to generate initial three-dimensional conformations for the neutral and charged compounds from Step 2; Step 4: Optimize the initial three-dimensional conformations of the neutral and charged compounds in Step 3 using quantum chemical methods to obtain the optimized fine three-dimensional conformations; Step 5: Based on the refined three-dimensional conformation obtained in Step 4, the solvation energies of neutral and charged compounds in aqueous solution are calculated using high-precision quantum chemical methods. Step 6: Based on the refined 3D conformation obtained in Step 4, calculate the molecular graph of each compound, including node features and edge features, and record its solvation energy data to construct the training dataset for the solvation energy prediction model. Step 7: Based on the training dataset obtained in Step 6, use a graph convolutional neural network to train solvation energy prediction models for neutral molecules and charged molecules respectively. Step 8: Use the mean relative error (MAE), root mean square error (RMSE), and correlation coefficient (R²) 2 The performance of the model is evaluated using the indicators, and the best-performing model is selected from the models saved in step 7 as the final prediction model. Step 9: When applying the solvation energy model to predict the solvation energy of a compound, for each compound, first use RDKit to generate up to 50 initial conformations; Step 10: Then, use the ANI-2x model to optimize the initial conformation generated by RDKit, and take the conformation with the lowest energy after ANI-2x optimization as the optimal three-dimensional conformation. The optimal three-dimensional conformation is used as the input for solvation energy calculation. Step 11: Based on the optimal three-dimensional conformation obtained in Step 10, predict the solvation energy of the compound using the model obtained in Step 8; where: In step 7, during the prediction model training process, the solvation energy model of neutral molecules is first trained, and then, based on the solvation energy model of neutral molecules, transfer learning is applied to train the solvation energy model of charged molecules. The graph convolutional neural network described in step 7 consists of two parts: a graph convolution module and an information readout module. First, the graph convolution module extracts the vector representation of the compound, and then the information readout module fits the solvation energy. The neural network updates the node information and fits the solvation energy data using the following formula: ； ； ； Where A is the adjacency matrix, D is the degree matrix, H is the feature matrix, W is the parameter matrix, l is the number of graph convolutional layers, ReLU is the activation function, and MLP is a multilayer perceptron.

2. The method according to claim 1, characterized in that, In step 3, only one initial three-dimensional conformation is generated for each compound based on RDKit.

3. The method according to claim 1, characterized in that, Step 4 describes the optimization of the three-dimensional conformation of the compound using quantum chemical methods. B3LYP / 6-31G* is used to optimize the three-dimensional conformation of the compound in a vacuum.

4. The method according to claim 1, characterized in that, The solvation energies of neutral and charged compounds in aqueous solution were calculated using the high-precision quantum chemical method described in step 5, employing the M06 / 6-31G* SMD continuum model.

5. The method according to claim 1, characterized in that, The node features described in step 6 include two-dimensional topological information and three-dimensional structural information. These features describe the basic properties of the atom represented by the node and its surrounding chemical environment. The two-dimensional topological information includes atom type, hybridization state, aromaticity, and ring state. Atom types include C, H, O, N, S, F, and Cl. Hybridization states include sp, sp2, sp3, sp3d, sp3d2, and sp3d3. Aromaticity indicates whether the atom is in an aromatic ring, and ring states include tricyclic, tetracyclic, pentacyclic, hexacyclic, and heptacyclic rings. The three-dimensional structural information includes the atomic environment fingerprint and the solvent-accessible surface area of ​​the atomic surface. The solvent-accessible surface area is calculated using numerical integration. The atomic environment fingerprint is calculated using symmetry functions, including radial and angular symmetry functions. The two symmetry functions share a common cutoff function. The specific calculation method for the symmetry functions is as follows: Truncation function ； Where R ij Rc is the distance between the central atom i and its neighboring atom j, Rc is the cutoff radius, and α is the element type, including C, H, O, N, S, P, F, Cl, Br, and I. radially symmetric function ； η and Rs are used to adjust the width and peak height of the Gaussian weights, and η and Rs are set to 0.0001 and 0, respectively; Z b and Z c These are the atomic numbers of the central atom i and its neighboring atom j, respectively; N is the number of neighboring atoms; R ij It is the distance between the central atom i and its neighboring atom j; the cutoff radius Rc uses 7 values, namely 1.5, 2.0, 2.5, 3.0, 4.0, 6.0 and 10.0; α is the element type, including C, H, O, N, S, P, F, Cl, Br and I; Angular symmetric function ； Where f is the cutoff function; λ, θ s ζ and η are set to 0.5, 0.0, 0.5 and 0.00001 respectively; Z b and Z c These are the atomic numbers of the central atom i and its neighboring atom j, respectively; θ ijk R is the angle between atoms i, j, and k; ij R is the distance between the central atom i and its neighboring atom j; ik R is the distance between the central atom i and its neighboring atom k; jk Z is the distance between the central atom j and its neighboring atom k; b and Z c α and β are the atomic numbers of neighboring atoms i and k, respectively; α and β are the element types.

6. The method according to claim 1, characterized in that, The edge features described in step 6 include single bonds, double bonds, triple bonds, and aromatic bonds.

7. The method according to claim 1, characterized in that, The mean relative error (MAE), root mean square error (RMSE), and correlation coefficient (R) mentioned in step 8 2 The calculation method for the indicator is as follows: ； ； ； in These are experimental values. is the predicted value, and N is the sample size.

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