Neural network model and method for predicting molecular static third-order nonlinear optical coefficients

Abstract

The application belongs to the field of molecular static third-order nonlinear optical coefficient calculation, and particularly relates to a neural network model and method for predicting a molecular static third-order nonlinear optical coefficient. The construction method of the neural network model comprises the following steps: A, calculating the molecular orbital energy and the third-order nonlinear optical coefficient of a compound to be predicted and similar compounds, expanding the molecular orbital energy using a Gaussian function to obtain DOS data, performing MinMaxScaler transformation on the DOS data and the third-order nonlinear optical data to obtain a training data set; B, importing the training data set into a neural network for training to obtain a neural network model. The screening speed of the application is faster, the rate is higher, and the accuracy is also higher.

Description

Technical Field

[0001] This invention belongs to the field of molecular static third-order nonlinear optical coefficient calculation, specifically involving a neural network model and method for predicting molecular static third-order nonlinear optical coefficients. This method calculates the third-order nonlinear optical coefficients of molecules using molecular density of states data. Background Technology

[0002] Nonlinear optical materials have advantages such as high nonlinear optical polarizability, fast response speed, low DC dielectric constant, high optical damage threshold, easy processing and simple molecular design, and have broad application prospects in fields such as optical modulators, frequency converters, optical computing, optical information processing and all-optical switches.

[0003] Designing materials with significant third-order nonlinear optical responses is a challenging problem in materials design. Existing materials design methods involve large-scale screening from material structure databases using theoretical simulations or experimental methods. However, the above methods have significant limitations: on the one hand, general experimental methods can only synthesize a small number of materials each time, and after synthesis, it is necessary to measure the third-order nonlinear optical response to determine whether the synthesized material has a significant third-order nonlinear optical response. Both synthesis and testing require a lot of time and cost, making it difficult to solve the problems of automation and high throughput in material design and screening; on the other hand, for theoretical calculation methods, although it is easy to automate the operation through programming, at present, due to the limited computing power of computers, it is also difficult to perform high-throughput calculations on a large scale of materials (ORR BJ, WARD J F. Perturbation theory of the non-linear optical polarization of anisolated system[J / OL]. Molecular Physics,1971,20(3):513-526.DOI:10.1080 / 00268977100100481.), and it is also difficult to screen out the required third-order nonlinear optical response materials within a limited time.

[0004] Therefore, given the vast and ever-growing database of material structures, how to quickly and accurately select materials that meet the performance requirements is an urgent problem to be solved. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention aims to provide a neural network model for predicting the static third-order nonlinear optical coefficients (DOS) of molecules. An end-to-end machine learning computational process is developed to establish the relationship between DOS and the third-order nonlinear optical coefficients of molecules. This computational process demonstrates good predictive performance for substituted benzene compounds, solves the problem of slow calculation speed using density functional theory for molecular third-order nonlinear optical coefficients, and improves the screening speed for potential high-quality third-order nonlinear optical response molecules in databases.

[0006] A method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules includes the following steps:

[0007] A. Calculate the molecular orbital energies and third-order nonlinear optical coefficients of the compound to be predicted and its similar compounds. Expand the molecular orbital energies using a Gaussian function to obtain DOS data. Perform MinMaxScaler transformation on the DOS data and the third-order nonlinear optical data to obtain the training dataset.

[0008] B. Import the training dataset into the neural network for training to obtain the neural network model.

[0009] According to an embodiment of the present invention, step A includes the following steps:

[0010] S1. Identify several compounds to be used for training;

[0011] S2. Calculate the molecular orbital energies and third-order nonlinear optical coefficients of all compounds to be trained;

[0012] S3. Expand the molecular orbital energies using the Gaussian function as shown in equation (1) to obtain the corresponding DOS data. The Gaussian function is:

[0013]

[0014] In equation (1), F is the broadening of the Gaussian function, and the range of F is 0.001-1.0. N is the number of molecular orbitals, and Ei is the energy of the i-th molecular orbital.

[0015] S4. Uniformly sample the Gaussian function G(x) in equation (1) to obtain the corresponding high-dimensional vector a;

[0016] S5. Stack the high-dimensional vectors a corresponding to all compounds vertically to obtain the input two-dimensional array X. Perform MinMaxScaler transformation on all high-dimensional vectors a and their corresponding third-order nonlinear optical coefficients according to equation (2) to obtain the training dataset:

[0017]

[0018] In equation (2), minX and maxX are the extreme values ​​of each feature, γ is the calculated third-order nonlinear optical coefficient, X' is the input data of the model, and γ' is the label of the model.

[0019] According to an embodiment of the present invention, the training compounds in step S1 have similar structures, and the number of training compounds is greater than 100. Preferably, the number of training compounds is greater than 200, for example, 200, 300, 400, 500, or 600.

[0020] According to an embodiment of the invention, the training in step B includes performing at least 100 cycles, for example, at least 200 cycles.

[0021] According to an embodiment of the present invention, the neural network is a fully connected neural network, preferably the fully connected neural network includes an input layer, an output layer and at least one hidden layer, wherein the input layer is connected to the output layer through the hidden layer.

[0022] According to an embodiment of the present invention, the fully connected neural network includes 1 to 5 hidden layers, for example, 1, 2, 3, 4 or 5 hidden layers.

[0023] According to an embodiment of the present invention, the number of neurons in the input layer is 10-1000, preferably 100-800, and more preferably 300-500.

[0024] According to an embodiment of the present invention, the number of neurons in the output layer is 10-1000, preferably 100-800, and more preferably 300-500.

[0025] According to an embodiment of the present invention, the number of neurons in the hidden layer is 10-1000, preferably 100-800, and more preferably 300-500.

[0026] According to an embodiment of the present invention, the activation function of the hidden layer is a ReLU function, and the ReLU function is defined as follows:

[0027]

[0028] In equation (4), x is the transformation value of the current layer neural network after the linear transformation.

[0029] According to an embodiment of the present invention, the output layer comprises a linear function as shown in equation (5):

[0030] f(x)=x……(5)

[0031] In equation (5), x is the transformation value of the current layer neural network after the linear transformation.

[0032] According to an embodiment of the present invention, the fully connected neural network further includes the loss function shown in equation (6):

[0033] L=(y p -y t ) 2 ……(6)

[0034] In equation (6), y p The value of the third-order nonlinear optical coefficient predicted by the neural network, y t Rather, it refers to the value of the third-order nonlinear optical coefficient calculated using theoretical chemical methods.

[0035] According to an embodiment of the present invention, the optimization algorithm for the fully connected neural network is the Adam optimization algorithm.

[0036] According to an embodiment of the present invention, the learning rate of the fully connected neural network is 0.1-0.00001.

[0037] According to an embodiment of the present invention, in step S2, the molecular orbital energies and third-order nonlinear optical coefficients of all compounds to be predicted are determined by chemical calculation or experimental detection methods, such as the DFT method.

[0038] According to an embodiment of the present invention, before expanding the molecular orbital energy in step S3, the following step is further included:

[0039] Determine whether the molecular orbital energy distribution meets the following requirements: a. The highest occupied orbital energy and the lowest unoccupied orbital energy of each molecule must be included in the current molecular orbital energy range; b. It contains at least 5 empty orbitals. If yes, proceed to step S3; otherwise, modify the current energy range to include the highest occupied orbital energy and the lowest unoccupied orbital energy.

[0040] According to an embodiment of the present invention, the Gaussian function in step S3 has the following characteristics: Figure 1 The structural distribution is shown.

[0041] According to an embodiment of the present invention, in step S4, the number of samples for uniformly sampling the Gaussian function G(x) is greater than 500, preferably greater than 600.

[0042] According to an embodiment of the present invention, the horizontal length of the two-dimensional array X in step S5 is the length of the high-dimensional vector x, and the vertical length is the size of the number of molecules in the training set.

[0043] The present invention also provides a method for predicting the static third-order nonlinear optical coefficients of a molecule, comprising the following steps: preprocessing the DOS data of the molecule to be predicted and inputting it into the above-mentioned neural network model to obtain the third-order nonlinear optical coefficients of the molecule to be predicted.

[0044] According to an embodiment of the present invention, the preprocessing of the DOS data of the molecule to be predicted includes the following steps: after performing MinMaxScaler transformation on the DOS data of the molecule to be predicted, the data is imported into a neural network model to obtain the predicted value of the third-order nonlinear optical coefficient of the molecule to be predicted.

[0045] According to an embodiment of the present invention, the predicted value of the third-order nonlinear optical coefficient of the molecule to be predicted is calculated according to equation (3):

[0046] γ=γ′×(maxγ-minγ)+minγ……(3)

[0047] In equation (3), γ' is the output value of the neural network model, minγ is the minimum value of the third-order nonlinear optical coefficients in the training set, and maxγ is the maximum value of the third-order nonlinear optical coefficients in the training set.

[0048] Beneficial effects

[0049] Higher-order nonlinear optical effects generally involve the absorption of multiple photons and transitions between multiple orbitals. Therefore, this invention uses the electronic structure of compounds as the input feature of a neural network model. The electronic structure refers to the energy distribution of occupied and unoccupied orbitals of electrons in a molecule. The energy distribution of molecular orbitals can be regarded as a special fingerprint of a molecule. Moreover, from the perspective of electronic transitions and electronic orbital energy distribution, this invention uses a neural network model to establish the relationship between the molecular density of states (DOS) and the third-order nonlinear optical response of matter, which can simultaneously ensure speed and accuracy.

[0050] This invention uses a neural network model to predict the third-order nonlinear optical coefficients of molecules. Compared with existing methods that rely on theoretical simulation or experiments, this invention offers faster screening speed, higher rate, and higher accuracy. Attached Figure Description

[0051] Figure 1 This is a distribution plot of DOS data, where the horizontal axis represents molecular orbital energy and the vertical axis represents the density of states of electrons in the molecule.

[0052] Figure 2 This is a flowchart illustrating the use of neural networks to predict the third-order nonlinear optical coefficients of molecules in this invention. Detailed Implementation

[0053] The method and application of the present invention will be further described in detail below with reference to specific embodiments. It should be understood that the following embodiments are merely illustrative and explanatory of the present invention and should not be construed as limiting the scope of protection of the present invention. All technologies implemented based on the above content of the present invention are covered within the scope of protection intended by the present invention.

[0054] Example 1

[0055] S1. Determine the compound to be calculated, wherein the compound is selected from substituted benzene and disubstituted benzene (disubstituted benzene can be ortho, meta or para substituted, the ortho substituted compounds are shown below) with the following structures.

[0056]

[0057] The substituents R1, R2, and R3 are independently selected from any one of the following 15 substituents: -NO2, -CN, -SO3, -COOH, -CHO, -COCH, -NH2, -N(CH3)2, -NHCH3, -NHCOCH3, -OCOCH3, CH3, F, Cl, and OH.

[0058] Through calculation, a total of 375 different monosubstituted and disubstituted benzene structures were obtained.

[0059] S2. The configurations of all monosubstituted and disubstituted benzenes in S1 were optimized using the DFT (Density Function Theory) method. Specifically, optimization was performed using the B3LYP hybrid functional and the 6-31G(d) basis set, and the energies of each molecular orbital of all molecules were obtained during the optimization.

[0060] S3. Randomly select 200 molecular structures from the optimized molecular structures in step S2, calculate the third-order nonlinear optical coefficients of the corresponding molecules using the Gaussian16 program, and convert the energy of the molecular orbitals into DOS data using a Gaussian function.

[0061] S4. Establish a fully connected neural network model. The basic parameters of the three hidden layers of the neural network are as follows: the number of neurons in each hidden layer is 100, 200, and 500 respectively, and the activation function of each hidden layer is ReLU.

[0062] The parameters for training the fully connected neural network model are as follows: the optimizer algorithm used is Adam, and the learning rate is 1×10⁻⁶. -4 A total of 500 epochs were trained to obtain the neural network model.

[0063] Example 2: Prediction of third-order nonlinear optical coefficients of CNc1ccccc1C#N

[0064] The geometry of the CNc1ccccc1C#N molecule was optimized using a B3LYP hybrid functional and a 6-31G(d) basis set. The input DOS data was constructed and preprocessed, then input into the model trained in Example 1 and inversely scaled to obtain the molecule's third-order nonlinear optical coefficient 11109.13.

[0065] To ensure the accuracy of the model, the third-order nonlinear optical coefficient of the molecule was calculated using the DFT method, which was 13420.76. Compared with the data calculated by DFT, the error of the data given by the model was 17.2%.

[0066] Example 3: Prediction of third-order nonlinear optical coefficients of CNc1ccccc1C(=O)O

[0067] The geometry of the CNc1ccccc1C(=O)O molecule was optimized using a B3LYP hybrid functional and a 6-31G(d) basis set. The input DOS data was constructed and preprocessed, then input into the model trained in Example 1, yielding a third-order nonlinear optical coefficient of 17740.66. To ensure model accuracy, the third-order nonlinear optical coefficient of the molecule was calculated using the DFT method, resulting in 13882.26. Compared to the DFT-calculated data, the model's error was 27.0%.

[0068] Example 4: Prediction of third-order nonlinear optical coefficients: CC(=O)Nc1cccc(NC(C)=O)c1

[0069] The geometry of the CC(=O)Nc1cccc(NC(C)=O)c1 molecule was optimized using a B3LYP hybrid functional and a 6-31G(d) basis set. The input DOS data was constructed and preprocessed, then input into the model trained in Example 1, yielding a third-order nonlinear optical coefficient of 22548.20. To ensure model accuracy, the third-order nonlinear optical coefficient of the molecule was calculated using the DFT method, resulting in 24742.51. Compared to the DFT-calculated data, the model's error was 9.0%.

[0070] Example 5: Prediction of third-order nonlinear optical coefficients of CC(=O)Oc1cccc(S(=O)(=O)O)c1

[0071] The geometry of the CC(=O)Oc1cccc(S(=O)(=O)O)c1 molecule was optimized using a B3LYP hybrid functional and a 6-31G(d) basis set. The input DOS data was constructed and preprocessed, then input into the model trained in Example 1, yielding the molecule's third-order nonlinear optical coefficient of 13060.22. To ensure model accuracy, the third-order nonlinear optical coefficient of the molecule was calculated using the DFT method, resulting in 12486.26. Compared to the DFT-calculated data, the model's error was 4.6%.

[0072] The specific embodiments of the present invention have been described above by way of example. However, the scope of protection of the present invention is not limited to the above exemplary embodiments. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules, characterized in that, Includes the following steps: A. Calculate the molecular orbital energies and third-order nonlinear optical coefficients of the compound to be predicted and its similar compounds. Expand the molecular orbital energies using a Gaussian function to obtain DOS data. Perform MinMaxScaler transformation on the DOS data and the third-order nonlinear optical data to obtain the training dataset. Step A includes the following steps: S1. Identify several compounds to be trained; S2. Calculate the molecular orbital energies and third-order nonlinear optical coefficients of all compounds to be trained; S3. Expand the molecular orbital energies using the Gaussian function as shown in equation (1) to obtain the corresponding DOS data. The Gaussian function is: （1） In equation (1), F is the broadening of the Gaussian function, and the range of F is 0.001-1.

0. N is the number of molecular orbitals, and Ei is the energy of the i-th molecular orbital. S4. Uniformly sample the Gaussian function G(x) in equation (1) to obtain the corresponding high-dimensional vector a; S5. Stack the high-dimensional vectors a corresponding to all compounds vertically to obtain the input two-dimensional array X. Perform MinMaxScaler transformation on all high-dimensional vectors a and their corresponding third-order nonlinear optical coefficients according to equation (2) to obtain the training dataset: （2） In equation (2), minX and maxX are the extreme values ​​of each feature, γ is the calculated third-order nonlinear optical coefficient, X' is the input data of the model, and γ' is the label of the model. B. Import the training dataset into the neural network for training to obtain the neural network model.

2. The method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules according to claim 1, characterized in that, The training compounds in step S1 have similar structures, the number of training compounds is greater than 100, and the number of training compounds is greater than 200. The training described in step B includes performing at least 100 cycles and at least 200 cycles.

3. The method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules according to claim 1, characterized in that, In step S2, the molecular orbital energies and third-order nonlinear optical coefficients of all compounds to be predicted are determined by chemical calculations or experimental detection methods.

4. The method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules according to claim 1, characterized in that, Before expanding the molecular orbital energy in step S3, the following steps are also included: Determine whether the molecular orbital energy distribution meets the following requirements: a. The highest occupied orbital energy and the lowest unoccupied orbital energy of each molecule must be included in the current molecular orbital energy range; b. It contains at least 5 empty orbitals. If yes, proceed to step S3; otherwise, modify the energy range.

5. The method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules according to claim 1, characterized in that, In step S4, the number of samples for uniform sampling of the Gaussian function G(x) is greater than 500, and the number of samples is greater than 600. In step S5, the horizontal length of the two-dimensional array X is the length of the high-dimensional vector x, and the vertical length is the size of the number of molecules in the training set.

6. The method for constructing a neural network model for predicting the static third-order nonlinear optical coefficients of molecules according to claim 1, characterized in that, The neural network is a fully connected neural network, which includes an input layer, an output layer, and at least one hidden layer. The input layer is connected to the output layer through the hidden layer.

7. A method for predicting the static third-order nonlinear optical coefficients of a molecule, comprising the following steps: preprocessing the DOS data of the molecule to be predicted and inputting it into the neural network model according to any one of claims 1-6 to obtain the third-order nonlinear optical coefficients of the molecule to be predicted.

8. The method for predicting the static third-order nonlinear optical coefficient of a molecule according to claim 7, characterized in that, The preprocessing of the DOS data of the molecule to be predicted includes the following steps: after performing MinMaxScaler transformation on the DOS data of the molecule to be predicted, the data is imported into the neural network model to obtain the predicted value of the third-order nonlinear optical coefficient of the molecule to be predicted.

9. The method for predicting the static third-order nonlinear optical coefficient of a molecule according to claim 7 or 8, characterized in that, The predicted value of the third-order nonlinear optical coefficient of the molecule to be predicted is calculated according to equation (3): （3） In equation (3), γ' is the output value of the neural network model, minγ is the minimum value of the third-order nonlinear optical coefficients in the training set, and maxγ is the maximum value of the third-order nonlinear optical coefficients in the training set.

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