Method for predicting nonlinear optical performance of atomic cluster

Abstract

The invention discloses a method for predicting the nonlinear optical performance of an atomic cluster. The method comprises the following steps: randomly generating an enough number of atomic cluster isomers; optimizing the generated initial configuration based on a density functional theory, and collecting geometric parameters (dmax, dx, dy, dz and psi) of each atomic cluster; performing fractional occupancy number weighted electron density (FOD) analysis to remove a multi-reference feature strong system; performing density functional theory simulation to obtain orientation average polarizability (alpha ave) and second-order hyperpolarizability (gamma ave) of each atomic cluster; fitting the geometrical parameters of the atomic cluster with the alpha ave value and the gamma ave value, determining the optimal geometrical parameters for measuring the alpha ave value and the gamma ave value based on statistical analysis, and obtaining a fitting curve of the geometrical parameters and the nonlinear optical performance. According to the method, the nonlinear optical performance of the atomic cluster can be quickly and accurately predicted without expensive and time-consuming quantum chemical calculation by describing the relation curve of the geometrical parameters and the optical performance of the atomic cluster, and the method is expected to be applied to development of nonlinear optical materials.

Description

Technical Field

[0001] The invention relates to the field of nonlinear optics, and in particular to a method for efficiently predicting the nonlinear optical properties of atomic clusters. Background Art

[0002] Precise control of light signal intensity, frequency and phase has a significant impact on existing and future photonic and optoelectronic technologies. The preparation of materials with ideal nonlinear optical properties is the key to realizing these technologies. In the history of science, the creation of high-performance nonlinear optical materials benefited from researchers' deep understanding of the relationship between the geometric structure and performance of materials. For example, the anion group theory explains the relationship between the crystal structure and nonlinear optical properties of oxides, and promotes the preparation of barium metaborate (BBO), lithium triborate (LBO), and potassium beryllium fluoroborate (KBBF) crystals; the multi-level model explains the structure-activity relationship of the nonlinear optical effect of organic molecules quite well, and promotes the design and synthesis of various molecules with D-π-A structure.

[0003] Atomic clusters are a new level of material structure between microscopic atoms and macroscopic condensed matter. Their continuously adjustable geometric structure and electronic configuration have broken through the limitations of traditional materials and have great application potential in the field of nonlinear optics. Screening geometric configurations with good nonlinear optical properties is crucial to realizing the application of atomic clusters in the field of nonlinear optics. However, the complex bonding patterns of clusters make it difficult to directly transfer and apply previous understandings of traditional nonlinear optical materials to atomic clusters. At present, the nonlinear optical response of atomic clusters can be qualitatively evaluated with the help of multi-level models and bonding analysis, while the quantitative determination of the nonlinear optical properties of atomic clusters depends entirely on expensive and time-consuming quantum chemical calculations.

[0004] Atomic clusters usually lack clear characteristic excited states, which makes it difficult for multi-level models to reasonably explain the nonlinear optical response of atomic clusters. Although bonding analysis provides meaningful insights into the nonlinear optical behavior of small-sized atomic clusters, the bonding patterns of medium-sized atomic clusters are quite complex. In particular, local bonding information is difficult to reveal the overall nonlinear optical response characteristics of atomic clusters. Therefore, multi-level models and bonding analysis often make qualitative errors in predicting the nonlinear optical properties of atomic clusters. Theoretical simulations to predict the nonlinear optical properties of atomic clusters require expensive and time-consuming quantum chemical calculations. In addition, theoretical simulations are highly professional, and their calculation accuracy depends on the executor's expertise and simulation experience. Summary of the invention

[0005] In order to solve the above problems in the prior art, the present invention provides a method for predicting the nonlinear optical properties of atomic clusters. First, the initial configuration of the cluster is generated, and then the geometric configuration and light response performance of the cluster are analyzed, and then the geometric parameters of the cluster are fitted with the (hyper)polarizability value, and finally the structure-activity relationship curve describing the nonlinear optical properties of the atomic cluster is obtained and the accuracy of the model prediction is evaluated. The method comprises:

[0006] Step S100, generating 100 to 200 cluster initial configurations containing n atoms respectively by randomly moving atoms, where n represents a preset number of atoms;

[0007] Step S200, performing fractional occupation number weighted electron density (FOD) analysis and density functional theory simulation to obtain the polarizability (α ave ) and the second-order hyperpolarizability (γ ave ) parameters, and collect the geometric parameters of each atomic cluster at the same time;

[0008] Step S300, comparing the geometric parameters of the atomic cluster with the α obtained in step S200 ave and γ ave Perform fitting to obtain the relationship curve between the geometric parameters of the atomic cluster and the nonlinear optical performance;

[0009] Step S400, based on the method in step S100, obtain 30 to 50 stable configurations of clusters containing n atoms, collect geometric parameters of each atomic cluster, and use density functional theory to simulate and calculate the α of each atomic cluster. ave and γ ave The values ​​are used to evaluate the accuracy of the fitting curve in predicting the nonlinear optical properties of atomic clusters.

[0010] The above method first obtains the geometric parameters and α of a certain type of atomic cluster ave and γ ave The fitting relationship curve of the value is then obtained. For this type of atomic cluster with arbitrary structure, its α can be quantitatively determined based on its geometric parameters. ave and γ ave The method can obtain a value and give the confidence level of the value. Compared with the existing technology, the method has the advantages of being fast and effective.

[0011] In some preferred embodiments, in step S100, 100 to 200 initial cluster configurations containing n atoms are generated, and the construction method is:

[0012] Step S110, controlling atomic coordinate parameters, regulating the initial configuration of the clusters, and expanding the initial structural differences of the clusters;

[0013] Step S120, setting 10 groups of parameters, each group of parameters generates 10 to 20 structures, and a total of 100 to 200 required cluster initial configurations are generated;

[0014] Step S130, using density functional theory to optimize the generated initial structure and ensure that the optimized structure is at the minimum point of the potential energy surface, and finally obtaining 100 to 200 stable cluster configurations containing n atoms.

[0015] In some preferred embodiments, the method for controlling the atomic coordinate parameters in step S110 is: presetting the minimum allowable value r between atoms min , and by regulating the maximum (minimum) allowable value of atoms in the three directions of the Cartesian coordinate system, namely x max (x min ),y max (y min ) and z max (z min ) coordinate values ​​to enhance the diversity and exploration scope of cluster structures.

[0016] In some preferred embodiments, when performing FOD analysis in step S200, the FOD isosurface of the cluster and N FOD The value is used as a criterion to remove systems with strong multi-reference features. Among them, the FOD isosurface refers to the surface formed by the fractional occupation number weighted electron density in three-dimensional space, N FOD The value reflects the strength of the multi-reference feature of the system. The larger the value, the stronger the multi-reference feature of the system, and vice versa. FOD Clusters with values ​​greater than a preset threshold are excluded to improve the accuracy of the prediction of nonlinear optical properties;

[0017] In some preferred embodiments, the polarizability and second-order hyperpolarizability obtained by density functional theory simulation in step S200 are tensors whose component values ​​depend on the coordinate system. Therefore, in order to reflect the intrinsic linear and nonlinear optical properties of the atomic cluster and avoid the dispersion effect, the directional average static polarizability α is introduced. ave and the second-order superscaling rate γ ave , defined as follows:

[0018] α ave =(α xx +α yy +α zz ) / 3

[0019] γ ave =(γ xxxx +γ yyyy +γ zzzz +2γ xxyy +2γ xxzz +2γ yyzz) / 5

[0020] In some preferred embodiments, the geometric parameters of each atomic cluster in step S200 include: the maximum interatomic distance d max , the length (d x )、Width(d y ) and high (d z ) and sphericity (Ψ), geometric parameters are the core input variables for predicting the nonlinear optical properties of atomic clusters.

[0021] In some preferred embodiments, the geometric parameters and α are combined in step S300. ave and γ ave The values ​​are fitted, and the influence of geometric parameters on optical properties is judged based on the significance analysis and fitting degree in statistics. The structure-activity relationship curve of the atomic cluster is determined according to the best fitting result. The structure-activity relationship curve is used to describe the intrinsic connection between geometric structure and optical response.

[0022] In some preferred embodiments, the optimal fitting model between the cluster geometric parameters and the optical properties is determined by the structure-activity relationship curve in step S400, and the fitting model includes the α ave and γ ave The prediction range of the values ​​is given, and a fitting curve prediction band with a 95% confidence interval is set to evaluate the prediction accuracy of the model for the nonlinear optical properties of atomic clusters.

[0023] Beneficial effects of the present invention:

[0024] (1) The method disclosed in the present invention has the advantages of being fast and effective. According to the technical solution, the geometric parameters and α of a certain type of atomic cluster are obtained. ave and γ ave The structure-activity relationship curve of this type of arbitrary atomic cluster can be quantitatively determined based on its geometric parameters. ave and γ ave value and give a degree of confidence in that value without the need for expensive ab initio calculations or complex machine learning simulations.

[0025] (2) The present invention uses fractional occupancy weighted electron density analysis to effectively screen out cluster structures with multiple reference features, ensuring that the polarizability and hyperpolarizability of the remaining clusters are accurately evaluated.

[0026] (3) The present invention generates structure-activity relationship curves of atomic clusters, reveals the intrinsic relationship between geometric structure and nonlinear optical response, and can provide guidance for the design of new nonlinear optical materials and optimize material performance. By fitting the model to generate a prediction band with a 95% confidence interval, it provides material designers with a credible range for optical performance prediction, helping the decision-making process to be more accurate and reliable.

[0027] (4) The present invention is applicable to various types of atomic clusters, and the prediction results are accurate and efficient, and can be applied to the development of various nonlinear optical materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Other features, objects and advantages of the present application will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0029] Figure 1 It is a system flow chart of a method for predicting nonlinear optical properties of atomic clusters in the present invention;

[0030] Figure 2 It is a schematic diagram of the prediction accuracy of the fitting curve corresponding to the example content in the present invention. DETAILED DESCRIPTION

[0031] The present application will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the relevant invention, rather than to limit the invention. It is also necessary to explain that, for ease of description, only the parts related to the relevant invention are shown in the accompanying drawings.

[0032] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0033] A method for predicting the nonlinear optical properties of atomic clusters of the present invention, such as Figure 1 Said, including the following:

[0034] Step S100, generating 100 to 200 cluster initial configurations containing n atoms respectively by randomly moving atoms, where n represents a preset number of atoms;

[0035] Step S200, performing fractional occupation number weighted electron density (FOD) analysis and density functional theory simulation to obtain the polarizability (α ave ) and the second-order hyperpolarizability (γ ave ) parameters, and collect the geometric parameters of each atomic cluster at the same time;

[0036] Step S300, comparing the geometric parameters of the atomic cluster with the α obtained in step S200 ave and γ ave Perform fitting to obtain the relationship curve between the geometric parameters of the atomic cluster and the nonlinear optical performance;

[0037] Step S400, based on the method in step S100, obtain 30 to 50 stable configurations of clusters containing n atoms, collect geometric parameters of each atomic cluster, and use density functional theory to simulate and calculate the α of each atomic cluster. ave and γ ave The values ​​are used to evaluate the accuracy of the fitting curve in predicting the nonlinear optical properties of atomic clusters.

[0038] Example 1

[0039] Taking a silicon cluster containing 20 atoms as an example, a method for predicting the nonlinear optical properties of an atomic cluster includes the following steps:

[0040] Step S100, generating 200 initial structures of silicon clusters containing 20 atoms respectively by randomly moving atoms, and adjusting the initial geometric configuration of the atomic clusters by controlling the atomic coordinate parameters to expand the diversity of the structure. Here, 20 groups of parameters are set, each group of parameters generates 10 structures, and a total of 200 required cluster initial configurations are generated;

[0041] Step S200, using density functional theory to calculate and optimize the generated initial structure and ensure that the optimized structure is at the minimum point of the potential energy surface, 182 silicon isomers are obtained, among which those isomers that do not converge in the geometry optimization are removed. Atomic clusters usually have multi-reference characteristics. Single reference theory cannot accurately evaluate the physical and chemical properties of such systems. FOD analysis is used to remove systems with significant multi-reference characteristics. Among them, the FOD integral value of the entire space, i.e., N FOD Value as standard, remove N FOD The silicon clusters with values ​​greater than 3.2 were selected, and finally 131 clusters that met the conditions were retained. The second-order hyperpolarizability of silicon clusters was calculated using density functional theory to obtain the α of each atomic cluster. ave and γ ave value;

[0042] Step S300, collecting the lengths (d x ) and α ave , γ ave The relationship curve between the linear and nonlinear optical properties of silicon clusters is obtained by fitting the values ​​and the prediction band (95%) of the fitting curve is given;

[0043] Step S400, using the method of step S100, obtain 20 stable configurations of silicon clusters containing 20 atoms, collect the atomic clusters d x The density functional theory was used to simulate and calculate the α ave and γ ave The evaluation results show that the fitting curve has the advantages of being fast and effective in predicting the linear and nonlinear optical properties of atomic clusters.

[0044] Example 2

[0045] Taking a cluster containing 20 phosphorus atoms as an example, a method for predicting the nonlinear optical properties of an atomic cluster includes the following steps:

[0046] Step S100, generating 200 initial structures of phosphorus clusters containing 20 atoms respectively by randomly moving atoms, and adjusting the initial geometric configuration of the atomic clusters by controlling the atomic coordinate parameters to expand the diversity of the structure. Here, 20 groups of parameters are set, each group of parameters generates 10 structures, and a total of 200 required cluster initial configurations are generated;

[0047] Step S200, using density functional theory to calculate and optimize the generated initial structure and ensure that the optimized structure is at the minimum point of the potential energy surface, 185 isomers are obtained, among which those isomers that do not converge in the geometry optimization are removed. Atomic clusters usually have multi-reference characteristics, and single reference theory cannot accurately evaluate the physical and chemical properties of such systems. FOD analysis is used to remove systems with significant multi-reference characteristics. Among them, the FOD integral value of the entire space, i.e., N FOD Value as standard, remove N FOD Finally, 149 clusters that meet the conditions are retained, and the second-order hyperpolarizabilities of phosphorus atomic clusters are calculated using density functional theory simulation to obtain the α of each atomic cluster. ave and γ ave value;

[0048] Step S300, collecting the lengths (d x ) and α ave , γ ave The values ​​were fitted to obtain the relationship curves of linear and nonlinear optical properties of phosphorus clusters and the predicted band (95%) of the fitting curve was given;

[0049] Step S400, using the method of step S100, obtain 20 stable configurations of 20 atomic phosphorus clusters, collect the atomic clusters d x The density functional theory was used to simulate and calculate the α ave and γ ave The evaluation results show that the fitting curve has the advantages of being fast and effective in predicting the linear and nonlinear optical properties of atomic clusters.

[0050] Example 3

[0051] Taking a sulfur cluster containing 20 atoms as an example, a method for predicting the nonlinear optical properties of the atomic cluster includes the following steps:

[0052] Step S100, generating 200 initial structures of sulfur clusters containing 20 atoms respectively by randomly moving atoms, and adjusting the initial geometric configuration of the atomic clusters by controlling the atomic coordinate parameters to expand the diversity of the structure. Here, 20 groups of parameters are set, each group of parameters generates 10 structures, and a total of 200 required cluster initial configurations are generated;

[0053] Step S200, using density functional theory to calculate and optimize the generated initial structure and ensure that the optimized structure is at the minimum point of the potential energy surface, respectively obtain 180 sulfur isomers, among which those isomers that do not converge in the geometry optimization are removed. Atomic clusters usually have multi-reference characteristics, and single reference theory cannot accurately evaluate the physical and chemical properties of such systems. FOD analysis is used to remove systems with significant multi-reference characteristics. Among them, the FOD integral value of the entire space, i.e., N FOD Value as standard, remove N FOD Finally, 130 sulfur clusters that meet the conditions are retained, and the density functional theory is used to simulate and calculate the second-order hyperpolarizability of sulfur atomic clusters to obtain the α ave and γ ave value;

[0054] Step S300, collecting the lengths (d x ) and α ave , γ ave The values ​​were fitted to obtain the relationship curves of the linear and nonlinear optical properties of the sulfur clusters and the predicted bands (95%) of the fitting curves were given;

[0055] Step S400, using the method of step S100, respectively obtain 20 stable configurations of 20 atomic sulfur clusters, collect the atomic clusters d x The density functional theory was used to simulate and calculate the α ave and γ ave The evaluation results show that the fitting curve has the advantages of being fast and effective in predicting the linear and nonlinear optical properties of atomic clusters.

[0056] from Figure 2 It can be seen that α ave and γ ave The value is related to the length (d x , that is, the x-length parameter in the figure) show linear and exponential dependence respectively. The black points indicate that the fitting curve has very high accuracy in predicting the linear and nonlinear optical properties of atomic clusters, and all black points are located within the 95% prediction band of the fitting curve. Based on the fitting expressions of various atomic clusters, only the d x The α of the structure can be accurately predicted ave and γave The method disclosed in the present invention has the advantages of being fast and accurate in predicting the linear and nonlinear optical properties of atomic clusters.

[0057] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A method for predicting the nonlinear optical properties of atomic clusters, characterized in that: The following steps are involved: Step S100, generating 100 to 200 cluster initial configurations containing n atoms respectively by randomly moving atoms, where n represents a preset number of atoms; Step S200, performing fractional occupation number weighted electron density (FOD) analysis and density functional theory simulation to obtain the polarizability (α ave ) and the second-order hyperpolarizability (γ ave ) parameters, and collect the geometric parameters of each atomic cluster at the same time; Step S300, comparing the geometric parameters of the atomic cluster with the α obtained in step S200 ave and γ ave Perform fitting to obtain the relationship curve between the geometric parameters of the atomic cluster and the nonlinear optical performance; Step S400, based on the method in step S100, obtain 30 to 50 stable configurations of clusters containing n atoms, collect geometric parameters of each atomic cluster, and use density functional theory to simulate and calculate the α of each atomic cluster. ave and γ ave The values ​​are used to evaluate the accuracy of the fitting curve in predicting the nonlinear optical properties of atomic clusters.

2. The method for predicting the nonlinear optical properties of atomic clusters according to claim 1, characterized in that: In step S100, 100 to 200 initial cluster configurations containing n atoms are generated, and the construction method is as follows: Step S110, controlling atomic coordinate parameters, regulating the initial configuration of the clusters, and expanding the initial structural differences of the clusters; Step S120, setting 10 groups of parameters, each group of parameters generates 10 to 20 structures, and a total of 100 to 200 required cluster initial configurations are generated; Step S130, using density functional theory to optimize the generated initial structure and ensure that the optimized structure is at the minimum point of the potential energy surface, and finally obtaining 100 to 200 stable cluster configurations containing n atoms.

3. The method for controlling atomic coordinate parameters in step S110 according to claim 2, characterized in that: Preset the minimum allowed value r between atoms min , and by regulating the maximum (minimum) allowable value of atoms in the three directions of the Cartesian coordinate system, namely x max (x min ),y max (y min ) and z max (z min ) coordinate values ​​to enhance the diversity and exploration scope of cluster structures.

4. The method for predicting the nonlinear optical properties of atomic clusters according to claim 1, characterized in that: When performing FOD analysis in step S200, the FOD isosurface of the cluster and N FOD The value is used as a criterion to remove systems with strong multi-reference features. Among them, the FOD isosurface refers to the surface formed by the fractional occupation number weighted electron density in three-dimensional space, N FOD The value reflects the strength of the multi-reference feature in the system. The larger the value, the stronger the multi-reference feature of the system, and vice versa. FOD Clusters with values ​​greater than a preset threshold are excluded to improve the accuracy of the prediction of nonlinear optical properties.

5. The polarizability and second-order hyperpolarizability obtained by density functional theory simulation in step S200 of claim 4 are tensors whose component values ​​depend on the coordinate system. Therefore, in order to reflect the intrinsic linear and nonlinear optical properties of the atomic cluster and avoid the dispersion effect, the directional average static polarizability α is introduced. ave and the second-order superscaling rate γ ave , the relationship between them is as follows: α ave ＝(α xx +α yy +α zz ) / 3 c ave =(γ xxxx +g yyyy +g zzzz +2c xxyy +2c xxzz +2c yyzz ) / 5。 6. The geometric parameters of each atomic cluster in step S200 according to claim 4 include: Maximum interatomic distance d max , the length (d x )、Width(d y ) and high (d z ) and sphericity (Ψ), geometric parameters are the core input variables for predicting the nonlinear optical properties of atomic clusters.

7. The method for predicting the nonlinear optical properties of atomic clusters according to claim 1, characterized in that: In step S400, the optimal fitting model between the cluster geometric parameters and the optical properties is determined by the structure-activity relationship curve, and the fitting model includes the α ave and γ ave The prediction range of the values ​​is given, and a fitting curve prediction band with a 95% confidence interval is set to evaluate the prediction accuracy of the model for the nonlinear optical properties of atomic clusters.

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