CN111326217B - Metal nanocluster structure optimization method - Google Patents
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Abstract
The invention discloses a metal nanocluster structure optimization method, which comprises the steps of randomly generating a metal nanocluster group based on point group symmetry and removing metal nanoclusters with similar structures; and updating the speed and the coordinates of the locally optimized metal nanoclusters through a speed updating formula and a coordinate updating formula in an RPSO algorithm, locally optimizing the metal nanoclusters by using density functional theory calculation software, replacing the metal nanoclusters, and comparing the fitness values to obtain the optimal metal nanoclusters. The method for optimizing the structure of the metal nanocluster provided by the invention can directly solve the global optimal structure of the metal nanocluster only from chemical components of the metal nanocluster without providing an initial configuration by a user. On the basis, the search space can be effectively reduced, the calculation amount is reduced, the iteration step number is reduced, the iteration times are reduced, the convergence rate is improved, the accuracy of the generated initial configuration is improved, and the optimization method has higher accuracy and convergence rate.
Description
Technical Field
The invention relates to the technical field of nano materials, in particular to a method for optimizing a metal nanocluster structure.
Background
The metal nanoclusters have some special structures, compositions, properties and the like, and are widely used in the fields of catalysis, optics, magnetism, biological diagnosis and the like. Particularly in catalytic applications, metal nanoclusters are considered as one of the most promising metal nanocatalysts, referred to as "fourth generation catalysts". The catalytic activity of the surface of the metal nanocluster is increased mainly due to the characteristics that the metal nanocluster is small in size and large in specific surface area, the bonding state and the electronic state of surface atoms are different from those of the interior of the metal nanocluster, coordination of the surface atoms is incomplete, and the like. In addition, the metal nanocluster catalyst has good selectivity, and can reduce the generation of byproducts, thereby reducing the pollution to the environment. Therefore, the metal nanoclusters are also a new direction and a new field in the research of nanoscience and technology.
Methods for describing the relationship between metal nanocluster structure and energy can be roughly divided into two categoriesEmpirical potential energy and density functional theory. The empirical potential energy is mainly characterized in that parameters are determined through fitting of experimental data, so that the purpose of describing the potential energy of a certain metal nano-cluster is achieved, but the calculation accuracy cannot be guaranteed. The density functional theory does not depend on any experimental facts or empirical rules, and is the most accurate mode for calculating the potential energy of the metal nanocluster at present. However, the core of the density functional theory is to solve
The equations, their complexity and computation time, grow explosively with increasing size of the computing system. Meanwhile, in both description modes in the prior art, a user is required to provide an initial configuration, if the initial configuration is relatively close to a global optimal solution, the calculation can be finished quickly, but if the initial configuration is not ideal, a large amount of time is often spent on calculation, and meanwhile, in most cases, the accuracy of a result obtained by calculation is poor, and the global optimal solution cannot be obtained.
Therefore, the development of a metal nanocluster structure optimization method with high accuracy and small calculation amount has important significance for the theoretical research of metal cluster structure optimization.
Disclosure of Invention
The invention aims to provide a method for optimizing a metal nanocluster structure with high accuracy and small calculation amount.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for optimizing a metal nanocluster structure, the method comprising the steps of:
s1, setting the size of a metal nanocluster to be optimized and the metal atom species forming the metal nanocluster;
s2, randomly generating a metal nano cluster group with the scale of N in a sphere with the radius of R or a cube with the side length of R by taking a system timestamp as a random number seed, wherein the metal nano cluster group is composed of N symmetrical metal nano clusters, and the metal nano clusters are composed of N metal atoms;
s3, removing metal nanoclusters with similar structures in the metal nanocluster group, supplementing new metal nanoclusters, and ensuring that the metal nanocluster group comprises N metal nanoclusters;
s4, updating the speed of the metal nanoclusters through a speed updating formula in an RPSO algorithm, and updating the coordinates of the metal nanoclusters through a coordinate updating formula in the RPSO algorithm;
s5, if the metal nanoclusters are the bimetallic nanoclusters, performing small-probability variation operation on the metal nanoclusters with the speed and coordinate updating completed, and then turning to the step S6; if the metal nanoclusters are single metal nanoclusters, directly transferring to the step S6;
s6, respectively carrying out force balance optimization calculation on the metal nanoclusters after the speed and the coordinates are updated in the step S4 and the speed and the coordinates of metal atoms in the metal nanoclusters generated in the step S5 by using density functional theory calculation software to obtain a first locally optimized metal nanocluster and a second locally optimized metal nanocluster;
s7, respectively calculating the fitness values of the metal nanoclusters before local optimization, the first locally optimized metal nanoclusters and the second locally optimized metal nanoclusters;
s8, taking the metal nanocluster with the high adaptability value as a metal nanocluster to be selected to obtain the structure and the energy value of the metal nanocluster to be selected;
s9, judging whether the maximum updating iteration frequency is reached, if so, turning to a step S11, otherwise, turning to a step S10;
s10, replacing the corresponding metal nanoclusters in the metal nanocluster group with the first locally optimized metal nanocluster and the second locally optimized metal nanocluster according to the corresponding replacement probabilities of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster to form a new metal nanocluster group, and turning to the step S3;
s11, comparing the plurality of metal nanoclusters to be selected, taking the metal nanoclusters with high adaptability as optimal metal nanoclusters, and outputting the structure of the optimal metal nanoclusters and the energy value of the optimal metal nanoclusters.
Optionally, step S2 further comprises:
s21, defining a region where metal atoms are generated;
s22, randomly selecting a point group;
s23, randomly generating a coordinate of a metal atom;
s24, carrying out corresponding point group symmetry operation on the coordinates of the metal atoms to obtain the coordinates of the metal atoms after the point group symmetry operation;
s25, judging whether the coordinates of the metal atoms after the point group symmetry operation coincide with the coordinates of the metal atoms in the specified area, if so, merging the metal atoms with coincident coordinates, and then turning to the step 26; otherwise, directly go to step 26;
and S26, judging whether the number of the metal atoms in the specified area reaches a preset value, if so, outputting the metal nanocluster, and otherwise, turning to the step S23.
Optionally, step S3 further comprises:
s31, respectively calculating bonding characteristic matrixes of the metal nanoclusters;
and S32, comparing the bonding characteristic matrixes of the metal nanoclusters, and when the Euclidean distance between the bonding characteristic matrixes of the two metal nanoclusters is smaller than a preset value, excluding the metal nanoclusters with higher energy values.
Optionally, the definition of the key-forming feature matrix is as follows:
wherein, delta AB Denotes the kind of bond, AB denotes the atom of the bond, N AB Indicates the number of the corresponding keys and,
Y lm euclidean distance D of a key-forming feature matrix which is a spherical harmonic function uv Is defined as follows:
optionally, in step S4,
the velocity update formula of the ith metal nanocluster is:
coordinate update formula of ith metal nanocluster:
wherein the coordinates of the ith metal nanocluster in the kth update iteration are represented as
The velocity is expressed as
c 1 、c 2 、c 3 Respectively, introduced random learning operator, r 1 、r 2 、r 3 Is [0,1]Uniform random constant within a range, r 4 Is [0,N-1 ]]A uniform random integer within; p i The coordinates with the lowest energy for the i metal nanoclusters in all update iterations; p g The coordinate with the lowest energy for all metal nanoclusters in the metal nanocluster cluster is found in all update iterations.
Optionally, the calculation formula of the fitness value is as follows:
f i ＝exp(-αρ i )；
wherein f is i Is the fitness value of the ith metal nanocluster, alpha is a set constant,
V i is the ithEnergy value, V, of the metal nanocluster min Is the minimum value, V, among the energy values of the current metal nanoclusters max Is the maximum value among the energy values of the current metal nanoclusters.
Optionally, the step S5 further includes:
s51, selecting a numerical value in the range of [0,1] as a variation rate;
s52, correspondingly generating a uniform random number within the range of [0,1] in a random manner for each speed and coordinate updated bimetal nanocluster;
and S53, comparing the uniform random number corresponding to each speed and coordinate updated bimetal nanocluster with the variation rate, and randomly exchanging the positions of a plurality of different types of metal atoms in the bimetal nanoclusters after the speed and coordinate updated corresponding to the uniform random number are updated if the corresponding uniform random number is smaller than the variation rate.
Optionally, step S10 further comprises:
s101, respectively calculating the replacement probability of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster;
s102, respectively and randomly generating a uniform random number within the range of [0,1] corresponding to each metal nanocluster in the metal nanocluster group;
s103, comparing the uniform random number corresponding to each metal nanocluster with the replacement probability of the first locally optimized metal nanocluster and the replacement probability of the second locally optimized metal nanocluster, and replacing the locally optimized metal nanocluster corresponding to the replacement probability with the metal nanocluster corresponding to the uniform random number if the uniform random number is smaller than the replacement probability.
Optionally, the calculation formula of the replacement probability is as follows:
wherein E is old Is the energy of a certain metal nanocluster in a metal nanocluster group, E new Is E old The energy corresponding to the first and second locally optimized metal nanoclusters of the corresponding metal nanocluster.
Alternatively, the energy value of the metal nanocluster is calculated according to the structure and density functional theory calculation software of the metal nanocluster.
The invention has the following beneficial effects:
the method for optimizing the structure of the metal nanocluster provided by the invention can directly solve the global optimal structure of the metal nanocluster only from chemical components of the metal nanocluster without providing an initial configuration by a user. On the basis, the metal nanocluster structure optimization method provided by the invention can effectively reduce the search space, reduce the calculated amount, reduce the number of steps required by iteration, reduce the iteration times, improve the convergence rate, and improve the accuracy of the generated initial configuration, so that the metal nanocluster structure optimization method has higher accuracy and convergence rate, can realize the rapid simulation of the metal nanocluster structure optimization within 100 atoms, and meanwhile, the optimal metal nanocluster optimized by the optimization method has better symmetry and stability, the error range is within 0.01ev/atom, and the accuracy is higher than that of the existing optimization method; meanwhile, compared with the existing method, the optimization method of the metal nanocluster structure provided by the invention has higher convergence rate, and can generally improve the convergence rate by about 2-8 times. The technical scheme of the invention is easy to realize, simple to operate and can be automatically and intelligently realized.
Drawings
The following describes embodiments of the present invention in further detail with reference to the accompanying drawings;
fig. 1 shows a flow chart of a metal nanocluster structure optimization method disclosed in the present invention.
FIG. 2 shows Au optimized by the metal nanocluster structure optimization method disclosed by the invention 20 Energy relaxation pattern of the clusters.
FIG. 3 illustrates a method for optimizing the structure of a metal nanocluster according to the present disclosureThe structure diagram of the optimized metal cluster, wherein, FIG. 3-a is Ag 19 Structure of cluster, FIG. 3-b is Ag 20 Structural diagram of the clusters, and FIG. 3-c is Au 19 Structure of clusters, FIG. 3-d is Au 20 Structure of the clusters, FIG. 3-e is Pt 19 Structure of the clusters, FIG. 3-f is Pt 20 Structure of clusters.
Detailed Description
In order to more clearly illustrate the invention, the invention is further described below with reference to preferred embodiments and the accompanying drawings. Similar components in the figures are denoted by the same reference numerals. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
As shown in fig. 1, the method for optimizing a metal nanocluster structure disclosed by the present invention includes the following steps:
s1, setting the size of a metal nanocluster to be optimized and the metal atom species forming the metal nanocluster;
in a specific embodiment, the metal nanoclusters are 2 to 20 in size, the metal nanoclusters contain 2 to 20 atoms in number, and the metal atom species contain all metals that can be calculated by existing calculation software (e.g., DFT).
S2, randomly generating a metal nano cluster group with the scale of N in a sphere with the radius of R or a cube with the side length of R by taking a system timestamp as a random number seed, wherein the metal nano cluster group is formed by N symmetrical metal nano clusters, and each metal nano cluster is formed by N metal atoms;
here, the metal nanoclusters having symmetry refer to metal nanoclusters having a symmetric structure.
In a specific embodiment, step S2 further comprises:
the region where the predetermined metal atoms are generated in S21 may be, for example, a sphere having a radius R or a cube having a side length R.
S22, randomly selecting a point group which can be C 1 ,C 2 ,C 3 ,C 4 ,C 5 ,C 6 Any one of the point groups has a corresponding symmetry matrix, as will be understood by those skilled in the art.
S23, randomly generating a coordinate of a metal atom;
s24, carrying out corresponding point group symmetry operation on the coordinates of the metal atoms to obtain the coordinates of the metal atoms after the point group symmetry operation; i.e. the coordinates of the metal atoms are multiplied by the symmetry matrix corresponding to the randomly selected group of points, thereby obtaining the new coordinates of the metal atoms.
S25, judging whether the coordinates of the metal atoms after the point group symmetry operation coincide with the coordinates of the metal atoms in the specified area, if so, merging the metal atoms with coincident coordinates, and then turning to the step 26; otherwise, directly go to step 26;
and S26, judging whether the number of the metal atoms in the specified area reaches a preset value, if so, outputting the metal nanocluster, otherwise, turning to the step S23.
According to the first technical scheme of the embodiment, a user can automatically generate the initial configuration without providing the initial configuration, and the embodiment considers that the stable metal nanocluster structure has higher symmetry relative to other structures under the normal condition, so that the whole search space can be effectively reduced by adopting symmetry limitation when the initial configuration is generated, the search efficiency is improved, and meanwhile, the calculation amount is reduced, so that the calculation of the metal nanocluster structure optimization method is accelerated, and the convergence speed is improved; moreover, the energy distribution of the metal nanocluster structure after being limited by the symmetry of the embodiment is lower and more uniform as a whole, which means that the structure of the metal nanocluster is more stable, and the improvement of the accuracy of the initial configuration is facilitated. This embodiment may implement symmetry constraints, for example, by the open source item spglib.
S3, removing metal nanoclusters with similar structures in the metal nanocluster group, supplementing new metal nanoclusters, and ensuring that the metal nanocluster group comprises N metal nanoclusters;
in a specific embodiment, similar structures are excluded by comparing euclidean distances of the bonding feature matrix of the metal nanoclusters. Step S3 further includes:
s31, respectively calculating the bonding characteristic matrix of each metal nanocluster;
and S32, comparing the bonding characteristic matrixes of the metal nanoclusters, and when the Euclidean distance between the bonding characteristic matrixes of the two metal nanoclusters is smaller than a preset value, excluding the metal nanoclusters with higher energy values. In a specific embodiment, the preset value may be 0.1.
Further, in the step S31,
the definition of the bonding feature matrix is shown as follows:
wherein, delta AB Denotes the kind of bond, AB denotes the atom of the bond, N AB Indicates the number of the corresponding keys and,
Y lm for spherical harmonics, l is the order of the spherical harmonics, l =0,2,4,6, …, m = l, l-1, …, θ ij ,
The elevation angle and the azimuth angle between the metal atom i and the metal atom j in the spherical coordinate system are respectively.
For the elements in the key-forming feature matrix,
is a key sequence parameter.
Euclidean distance D of key-forming feature matrix uv Is defined as follows:
in the embodiment, the Euclidean distance between bonding characteristic matrixes of the metal nanoclusters is adopted to remove the metal nanoclusters with similar structures, so that the similar metal nanocluster structures with similar energy values can be effectively avoided, the diversity of the metal nanoclusters in the metal nanocluster group in the iteration process is ensured, the number of steps required by iteration is reduced, the iteration times are reduced, the calculation of the optimization method of the metal nanocluster structure is accelerated, and the convergence speed is improved; by adopting the synergistic effect of symmetry limitation and elimination of similar structures, the accuracy of the generated initial configuration and the convergence speed of the metal nanocluster structure optimization method can be further improved.
S4, updating the speed of the metal nanocluster through a speed updating formula in an RPSO algorithm, and updating the coordinates of the metal nanocluster through a coordinate updating formula in the RPSO algorithm;
in a specific embodiment, in step S4, the velocity update formula of the ith metal nanocluster is as follows:
coordinate update formula of ith metal nanocluster:
wherein the coordinates of the ith metal nanocluster in the kth update iteration are represented as
The velocity is expressed as
Omega is an inertia constant, usually taking the value 0.5 1 、c 2 、c 3 Respectively, introduced random learning operator, r 1 、r 2 、r 3 Is [0,1]Uniform random constant within a range, r 4 Is [0,N-1]Uniform random integers within; p is i The coordinate with the lowest energy for the i metal nanoclusters in all update iterations; p is g The coordinate with the lowest energy for all metal nanoclusters in the metal nanocluster cluster in all update iterations.
The speed updating formula consists of four parts, wherein the first part is an inertia part, reflects the motion habit of the metal nanocluster and represents that the metal nanocluster has the tendency of maintaining the previous state of the metal nanocluster; the second part is a cognitive part, reflects the memory of the metal nanocluster to self historical experience and represents the trend that the metal nanocluster approaches to self historical optimal solution; the third part is a social part and reflects the trend that the metal nanoclusters approach to the optimal solution of other metal nanoclusters in the metal nanocluster group; the fourth part is a random part, reflects the influence of random factors in the metal nanocluster group and represents the tendency that the metal nanoclusters approach solutions of any other metal nanoclusters.
It should be noted that the fourth part of the velocity update formula
Instead of acting each time the velocity of the metal nanoclusters is updated, a uniform random number in the range of 0 to 1 is generated, and the fourth part will only act if this random number is smaller than a set threshold (typically 0.4).
S5, if the metal nanoclusters are the bimetallic nanoclusters, performing small-probability variation operation on the metal nanoclusters with the speed and coordinate updating completed, and then turning to the step S6; if the metal nanoclusters are single metal nanoclusters, directly transferring to step S6;
s6, respectively carrying out force balance optimization calculation on the metal nanoclusters after the speed and the coordinates are updated in the step S4 and the speed and the coordinates of metal atoms in the metal nanoclusters generated in the step S5 by using density functional theory calculation software to obtain a first locally optimized metal nanocluster and a second locally optimized metal nanocluster;
s7, respectively calculating the fitness values of the metal nanoclusters before local optimization, the first locally optimized metal nanoclusters and the second locally optimized metal nanoclusters;
s8, taking the metal nanocluster with the high adaptability value as a metal nanocluster to be selected to obtain the structure and the energy value of the metal nanocluster to be selected; it can be understood that during the update iteration, a plurality of candidate metal nanoclusters may occur, and these candidate metal nanoclusters correspond to the local optimal solution.
S9, judging whether the maximum updating iteration frequency is reached, if so, turning to a step S11, otherwise, turning to a step S10; the maximum number of update iterations is adjusted according to the requirements of the calculation precision and the calculation amount.
S10, replacing the corresponding metal nanoclusters in the metal nanocluster group with the first locally optimized metal nanocluster and the second locally optimized metal nanocluster according to the corresponding replacement probabilities of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster to form a new metal nanocluster group, and turning to the step S3;
in a specific embodiment, step S10 further includes:
s101, respectively calculating the replacement probability of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster;
s102, respectively and randomly generating a uniform random number within the range of [0,1] corresponding to each metal nanocluster in the metal nanocluster group;
s103, comparing the uniform random number corresponding to each metal nanocluster with the replacement probability of the first locally optimized metal nanocluster and the replacement probability of the second locally optimized metal nanocluster, and replacing the locally optimized metal nanocluster corresponding to the replacement probability with the metal nanocluster corresponding to the uniform random number if the uniform random number is smaller than the replacement probability, that is, replacing the metal nanocluster corresponding to the uniform random number with the first locally optimized metal nanocluster or the second locally optimized metal nanocluster if the uniform random number corresponding to the metal nanocluster is smaller than the replacement probability of the first locally optimized metal nanocluster or smaller than the replacement probability of the second locally optimized metal nanocluster.
The calculation formula of the replacement probability is as follows:
wherein, E old Is the energy of a certain metal nanocluster in a metal nanocluster group, E new Is E old The energy corresponding to the first locally optimized metal nanocluster and the second locally optimized metal nanocluster of the corresponding metal nanocluster. Meanwhile, T in the formula is a set parameter, and the T linearly decreases along with the increase of the number of iteration steps. Details of the specific influence and numerical setting of T are as follows: the larger the value of T, the smaller the probability of accepting a bad solution at the beginning of the program run. For more complex metal nanoclusters, T may be chosen to be a smaller value.
As shown in the formula, the energy E corresponding to the first and second locally optimized metal nanoclusters of the corresponding metal nanocluster new Less than the energy E of the corresponding metal nanoclusters in the metal nanocluster group old When the replacement probability is 1, directly replacing the corresponding metal nanoclusters in the metal nanocluster group with the first locally optimized metal nanocluster and the second locally optimized metal nanocluster; if the energy E corresponding to the first and second locally optimized metal nanoclusters of the corresponding metal nanocluster new Greater than the energy E of the corresponding metal nanoclusters in the metal nanocluster group old And meanwhile, as iteration is carried out, T is linearly reduced along with the increase of iteration steps, so that the replacement probability is increased, and the corresponding metal nanoclusters in the metal nanocluster group are more likely to be replaced. This embodiment pairs metal nanocluster groups by employing alternative probabilitiesThe replacement of the metal nanoclusters reflects the idea of accepting inferior solutions according to a certain probability, ensures the diversity of the metal nanoclusters in the iteration process, and improves the accuracy of the metal nanocluster structure optimization method.
When the metal nanoclusters are single metal nanoclusters, the metal nanoclusters updated in the speed and coordinate step S4 are subjected to force balance optimization in step S6 to obtain first locally optimized metal nanoclusters, the first locally optimized metal nanoclusters are substituted for corresponding metal nanoclusters in the metal nanocluster group according to the substitution probability of the first locally optimized metal nanoclusters, that is, the substitution probability corresponding to the first locally optimized metal nanoclusters is calculated according to the calculation formula of the substitution probability, and the substitution probability is compared with the uniform random number corresponding to the single metal nanoclusters.
When the metal nanoclusters are bimetallic nanoclusters, respectively performing force balance optimization on the metal nanoclusters subjected to speed and coordinate updating in the step S4 and the metal nanoclusters subjected to the small probability variation operation in the step S5 through a step S6 to respectively obtain a first locally optimized metal nanocluster and a second locally optimized metal nanocluster, and then replacing the corresponding metal nanoclusters in the metal nanocluster group according to respective replacement probability; that is, a first replacement probability of the first locally optimized metal nanocluster and a second replacement probability of the second locally optimized metal nanocluster are respectively calculated through the calculation formula of the replacement probability, and the first replacement probability and the second replacement probability are respectively compared with the uniform random number corresponding to the bimetal nanocluster.
S11, comparing the plurality of metal nanoclusters to be selected, taking the metal nanoclusters with high adaptability as optimal metal nanoclusters, and outputting the structure of the optimal metal nanoclusters and the energy value of the optimal metal nanoclusters. Namely, a metal nanocluster to be selected with the highest fitness value is selected from all metal nanoclusters to be selected as a global optimal solution.
The optimization method of the metal nanocluster structure provided by the embodiment enables a user to directly solve the global optimal structure of the metal nanocluster structure only from the chemical components of the metal nanocluster without providing an initial configuration. Meanwhile, optimization modes of initial configuration such as symmetry limitation and similar structure elimination are combined into the optimization method of the metal nanocluster structure, so that the optimization method is simpler, the search space is effectively reduced, the calculated amount is reduced, the number of steps required by iteration can be reduced, the iteration number is reduced, the convergence speed is increased, the accuracy of the generated initial configuration is increased, the metal nanocluster structure optimization method has higher accuracy and convergence speed, and the rapid simulation of the metal nanocluster structure optimization within 100 atoms can be realized; meanwhile, the optimal metal nanocluster obtained by optimization through the optimization method has good symmetry and structural stability, the error range is within 0.01ev/atom, and the accuracy is higher than that of the existing optimization method; meanwhile, compared with the existing method, the optimization method of the metal nanocluster structure provided by the invention has higher convergence rate, and can generally improve the convergence rate by about 2-8 times. The technical scheme of the invention is easy to realize, simple to operate and can be automatically and intelligently realized.
In a specific embodiment, the fitness value is calculated as follows:
f i ＝exp(-αρ i )；
wherein f is i Which is the fitness value of the ith metal nanocluster, alpha is a set constant, alpha may be 0.3,
V i is the energy value, V, of the ith metal nanocluster min Is the minimum value, V, among the energy values of the current metal nanoclusters max Is the maximum value among the energy values of the current metal nanoclusters. Normalizing the energy values of all the metal nanoclusters in the current metal nanocluster group to obtain rho i . Fitness value f i The larger metal nanoclusters indicate that the structures are more stable and have lower energy, so that more opportunities are provided for the next iteration so as to gradually improve the average fitness value of the metal nanocluster groups and the optimal metal nanoclustersThe performance of (c). Therefore, the quality of the metal nanoclusters is evaluated according to the size of the fitness value, and the characteristics of high quality and low cost are reflected.
In a specific embodiment, the step S5 further includes:
s51, selecting a numerical value in the range of [0,1] as a variation rate;
s52, corresponding to each speed and coordinate updated bimetal nanocluster, respectively and randomly generating a uniform random number in the range of [0,1 ];
and S53, comparing the uniform random number corresponding to each speed and coordinate updated bimetal nanocluster with the variation rate, and randomly exchanging the positions of a plurality of different types of metal atoms in the bimetal nanoclusters after the speed and coordinate updated corresponding to the uniform random number are updated if the corresponding uniform random number is smaller than the variation rate.
In one embodiment, the energy value of the metal nanoclusters is calculated according to functional theory calculation software of the structure and density of the metal nanoclusters.
The structure of the optimal metal nanocluster is characterized by coordinates of metal atoms in the optimal metal nanocluster, which can be input into a drawing software to observe the morphological characteristics of the structure of the metal nanocluster.
The method for optimizing the structure of the metal nanocluster according to the present disclosure is further described below with reference to specific examples in which data such as specific metal atom types and sizes of the metal nanoclusters are substituted.
Example 1
Setting the atomic species as Ag and the atomic number as 2, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence as 5, executing the method, and iterating for 5 times to obtain Ag 2 Cluster stable structure and energy-2000.561397 eV.
Example 2
Setting the atomic species as Ag and the atomic number as 3, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, setting the maximum iteration number as 50, and collectingThe number of convergence times is 5, the invention is executed, 5 iterations are carried out, and Ag is obtained 3 Cluster stable structure and energy-3000.934651 eV.
Example 3
Setting the atomic species as Ag and the atomic number as 4, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Ag 4 Cluster stable structure and energy-4002.222333 eV.
Example 4
Setting the atomic species as Ag and the atomic number as 5, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Ag 5 Cluster stable structure and energy-5003.356977 eV.
Example 5
Setting the atomic species as Ag and the atomic number as 6, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Ag 6 Cluster stable structure and energy-6004.970377 eV.
Example 6
Setting the atom type as Ag and the atom number as 7, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 5 times to obtain Ag 7 Cluster stable structure and energy-7006.073436 eV.
Example 7
Setting the atom type as Ag and the atom number as 8, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 6 times to obtain Ag 8 Cluster stable structure and energy-8007.634316 eV.
Example 8
Setting the atomic species as Ag and the atomic number as 9, calculating the local optimization calculation by PWscf, and setting goldThe scale of the cluster group belonging to the nanometer is 10, the maximum iteration frequency is 50, the convergence frequency is 5, the invention is executed, the iteration is 5 times, and the Ag is obtained 9 Cluster stable structure and energy-9008.469442 eV.
Example 9
Setting the atomic species as Ag and the atomic number as 10, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 7 times to obtain Ag 10 Cluster stable structure and energy-10009.904944 eV.
Example 10
Setting the atomic species as Ag and the atomic number as 11, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 8 times to obtain Ag 11 Cluster stable structure and energy-11011.112775 eV.
Example 11
Setting the atom type as Ag and the atom number as 12, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 8 times to obtain Ag 12 Cluster stable structure and energy-12012.563274 eV.
Example 12
Setting the atomic species as Ag and the atomic number as 13, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 10 times to obtain Ag 13 Cluster stable structure and energy-13013.887596 eV.
Example 13
Setting the atomic species as Ag and the atomic number as 14, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 9 times to obtain Ag 14 Cluster stable structure and energy-14015.554633 eV.
Example 14
Setting sourceThe sub-species is Ag, the atomic number is 15, the local optimization calculation is calculated by PWscf, the scale of the metal nano cluster group is set to be 10, the maximum iteration number is 50, and the convergence number is 5, the method is executed, the iteration is carried out for 14 times, and the Ag is obtained 15 Cluster stable structure and energy-15016.76998 eV.
Example 15
Setting the atomic species as Ag and the atomic number as 16, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 10 times to obtain Ag 16 Cluster stable structure and energy-16018.217606 eV.
Example 16
Setting the atomic species as Ag and the atomic number as 17, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 11 times to obtain Ag 17 Cluster stable structure and energy-17019.763622 eV.
Example 17
Setting the atom type as Ag and the atom number as 18, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 12 times to obtain Ag 18 Cluster stable structure and energy-18021.486569 eV.
Example 18
Setting the atom type as Ag and the atom number as 19, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 5, executing the invention, and iterating for 14 times to obtain the Ag shown in figure 3-a 19 Cluster stable structure and energy-19023.01885 eV.
Example 19
Setting the atom type to be Ag, the atom number to be 20, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster to be 10, the maximum iteration number to be 50 and the convergence number to be 5, executing the invention, and iterating for 16 times to obtain the Ag shown in the figure 3-b 20 Cluster stabilizing structure andenergy-20024.658728 eV.
Example 20
Setting the atomic species as Au and the atomic number as 2, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Au 2 Cluster stable structure and energy-2384.972606 eV.
Example 21
Setting the atomic species as Au and the atomic number as 3, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 5 times to obtain Au 3 Cluster stable structure and energy-3577.699225 eV.
Example 22
Setting the atomic species as Au and the atomic number as 4, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Au 4 Cluster stable structure and energy-4771.485236 eV.
Example 23
Setting the atomic species as Au and the atomic number as 5, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Au 5 Cluster stable structure and energy-5965.122184 eV.
Example 24
Setting the atomic species as Au and the atomic number as 6, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 5 times to obtain Au 6 Cluster stable structure and energy-7159.431603 eV.
Example 25
Setting the atomic species as Au and the atomic number as 7, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50, the convergence number as 5, and executingThe invention iterates for 8 times to obtain Au 7 Cluster stable structure and energy-8352.473071 eV.
Example 26
Setting the atomic species as Au and the atomic number as 8, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 9 times to obtain Au 8 Cluster stable structure and energy-9546.487916 eV.
Example 27
Setting the atomic species as Au and the atomic number as 9, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 9 times to obtain Au 9 Cluster stable structure and energy-10739.508504V.
Example 28
Setting the atomic species as Au and the atomic number as 10, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 14 times to obtain Au 10 Cluster stable structure and energy-11933.870661 eV.
Example 29
Setting the atomic species as Au and the atomic number as 11, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 16 times to obtain Au 11 Cluster stable structure and energy-13127.307127 eV.
Example 30
Setting the atomic species as Au, the atomic number as 12, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 15 times to obtain Au 12 Cluster stable structure and energy-14320.989776 eV.
Example 31
Setting the atomic species as Au and the atomic number as 13, calculating the local optimization calculation by PWscf, and setting goldThe scale of the cluster group belonging to the nanometer is 10, the maximum iteration frequency is 50, the convergence frequency is 10, the invention is executed, the iteration is 14 times, and Au is obtained 13 Cluster stable structure and energy-15514.682177 eV.
Example 32
Setting the atomic species as Au, the atomic number as 14, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 15 times to obtain Au 14 Cluster stable structure and energy-16708.41167 eV.
Example 33
Setting the atomic species as Au and the atomic number as 15, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 25 times to obtain Au 15 Cluster stable structure and energy-17902.251217 eV.
Example 34
Setting the atomic species as Au, the atomic number as 16, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 24 times to obtain Au 16 Cluster stable structure and energy-19095.877722 eV.
Example 35
Setting the atomic species as Au and the atomic number as 17, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 10, executing the method, and iterating for 28 times to obtain Au 17 Cluster stable structure and energy-20290.196973 eV.
Example 36
Setting the atomic species as Au and the atomic number as 18, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 10, executing the method, and iterating for 33 times to obtain Au 18 Cluster stable structure and energy-21484.233999 eV.
Example 37
Setting the atomic species as Au and the atomic number as 19, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 10, executing the invention, and iterating for 30 times to obtain Au as shown in figure 3-c 19 Cluster stable structure and energy-22678.063823 eV.
Example 38
Setting the atomic species as Au and the atomic number as 20, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 10, executing the invention, and iterating for 38 times to obtain Au as shown in FIG. 3-d 20 Cluster stable structure and energy-23872.402085eV 20 The energy relaxation pattern of the cluster is shown in fig. 2.
Example 39
Setting the atomic type as Pt and the atomic number as 2, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 5 times to obtain Pt 2 Cluster stable structure and energy-2350.498541 eV.
Example 40
Setting the atomic type as Pt and the atomic number as 3, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 5 times to obtain Pt 3 Cluster stable structure and energy-3527.717327 eV.
EXAMPLE 41
Setting the atomic type as Pt and the atomic number as 4, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 8 times to obtain Pt 4 Cluster stable structure and energy-4704.103296 eV.
Example 42
Setting the atomic type as Pt and the atomic number as 5, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50, the convergence number as 5, and executingThe invention iterates for 5 times to obtain Pt 5 Cluster stable structure and energy-5881.392917 eV.
Example 43
Setting the atom type as Pt and the atom number as 6, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 10 times to obtain Pt 6 Cluster stable structure and energy-7059.105873 eV.
Example 44
Setting the atomic type as Pt and the atomic number as 7, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating 19 times to obtain Pt 7 Cluster stable structure and energy-8236.364502 eV.
Example 45
Setting the atomic type as Pt and the atomic number as 8, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating 17 times to obtain Pt 8 Cluster stable structure and energy-9413.996941 eV.
Example 46
Setting the atom type as Pt and the atom number as 9, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 14 times to obtain Pt 9 Cluster stable structure and energy-10591.766256V.
Example 47
Setting the atom type as Pt and the atom number as 10, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 13 times to obtain Pt 10 Cluster stable structure and energy-11770.153715 eV.
Example 48
Setting the atomic species as Pt and the atomic number as 11, calculating by PWscf through local optimization calculation, and setting metal nanoThe cluster size is 10, the maximum iteration number is 50, the convergence number is 5, the method is executed, the iteration is performed for 15 times, and Pt is obtained 11 Cluster stable structure and energy-12947.357919 eV.
Example 49
Setting the atomic type as Pt and the atomic number as 12, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 10 times to obtain Pt 12 Cluster stable structure and energy-14125.096752 eV.
Example 50
Setting the atom type as Pt and the atom number as 13, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 15 times to obtain Pt 13 Cluster stable structure and energy-15302.817758 eV.
Example 51
Setting the atomic type as Pt and the atomic number as 14, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration frequency as 50 and the convergence frequency as 5, executing the method, and iterating for 12 times to obtain Pt 14 Cluster stable structure and energy-16480.571501 eV.
Example 52
Setting the atom type as Pt and the atom number as 15, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 14 times to obtain Pt 15 Cluster stable structure and energy-17658.365623 eV.
Example 53
Setting the atom type as Pt and the atom number as 16, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 24 times to obtain Pt 16 Cluster stable structure and energy-18835.992585 eV.
Example 54
Setting sourceThe subclass is Pt, the atomic number is 17, the local optimization calculation is calculated by PWscf, the scale of the metal nano cluster group is set to be 10, the maximum iteration frequency is 50, the convergence frequency is 5, the invention is executed, the iteration is carried out for 21 times, and Pt is obtained 17 Cluster stable structure and energy-20014.061953 eV.
Example 55
Setting the atomic type as Pt and the atomic number as 18, calculating local optimization calculation by PWscf, setting the scale of the metal nano cluster group as 10, the maximum iteration number as 50 and the convergence number as 5, executing the method, and iterating for 22 times to obtain Pt 18 Cluster stable structure and energy-21192.571947 eV.
Example 56
Setting the atomic species as Pt and the atomic number as 19, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 5, executing the invention, and iterating for 22 times to obtain Pt as shown in FIG. 3-e 19 Cluster stable structure and energy-22369.850002 eV.
Example 57
Setting the atomic species as Pt and the atomic number as 20, calculating the local optimization calculation by PWscf, setting the scale of the metal nano cluster as 10, the maximum iteration number as 50 and the convergence number as 5, executing the invention, and iterating for 24 times to obtain Pt as shown in figure 3-f 20 Cluster stable structure and energy-23547.668665 eV.
It should be understood that the above-described exemplary embodiments of the present invention are merely examples for clearly illustrating the invention and are not to be construed as limiting the embodiments of the present invention, and it will be apparent to those skilled in the art that other variations and modifications can be made on the basis of the above description.
Claims (10)
1. A method for optimizing the structure of a metal nanocluster, comprising the steps of:
s1, setting the size of a metal nanocluster to be optimized and the metal atom species forming the metal nanocluster;
s2, randomly generating a metal nano cluster group with the scale of N in a sphere with the radius of R or a cube with the side length of R by taking a system timestamp as a random number seed, wherein the metal nano cluster group is composed of N symmetrical metal nano clusters, and the metal nano clusters are composed of N metal atoms;
s3, removing metal nanoclusters with similar structures in the metal nanocluster group, supplementing new metal nanoclusters, and ensuring that the metal nanocluster group comprises N metal nanoclusters;
s4, updating the speed of the metal nanocluster through a speed updating formula in an RPSO algorithm, and updating the coordinates of the metal nanocluster through a coordinate updating formula in the RPSO algorithm;
s5, if the metal nanoclusters are the bimetallic nanoclusters, performing small-probability variation operation on the metal nanoclusters with the speed and coordinate updating completed, and then turning to the step S6; if the metal nanoclusters are single metal nanoclusters, directly transferring to the step S6;
s6, respectively carrying out force balance optimization calculation on the metal nanoclusters after the speed and the coordinates are updated in the step S4 and the speed and the coordinates of metal atoms in the metal nanoclusters generated in the step S5 by using density functional theory calculation software to obtain a first locally optimized metal nanocluster and a second locally optimized metal nanocluster;
s7, respectively calculating the fitness values of the metal nanoclusters before local optimization, the first locally optimized metal nanoclusters and the second locally optimized metal nanoclusters;
s8, taking the metal nanocluster with the high adaptability value as a metal nanocluster to be selected to obtain the structure and the energy value of the metal nanocluster to be selected;
s9, judging whether the maximum updating iteration number is reached, if so, turning to a step S11, otherwise, turning to a step S10;
s10, replacing the corresponding metal nanoclusters in the metal nanocluster group with the first locally optimized metal nanocluster and the second locally optimized metal nanocluster according to the corresponding replacement probabilities of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster to form a new metal nanocluster group, and turning to the step S3;
s11, comparing the plurality of metal nanoclusters to be selected, taking the metal nanoclusters with high adaptability as optimal metal nanoclusters, and outputting the structure of the optimal metal nanoclusters and the energy value of the optimal metal nanoclusters.
2. The method of optimizing the structure of metal nanoclusters according to claim 1, wherein step S2 further includes:
s21, defining a region where metal atoms are generated;
s22, randomly selecting a point group;
s23, randomly generating a coordinate of a metal atom;
s24, carrying out corresponding point group symmetry operation on the coordinates of the metal atoms to obtain the coordinates of the metal atoms after the point group symmetry operation;
s25, judging whether the coordinates of the metal atoms after the point group symmetry operation coincide with the coordinates of the metal atoms in the specified area, if so, merging the metal atoms with coincident coordinates, and then turning to the step 26; otherwise, directly go to step 26;
and S26, judging whether the number of the metal atoms in the specified area reaches a preset value, if so, outputting the metal nanocluster, and otherwise, turning to the step S23.
3. The method for optimizing the structure of metal nanoclusters according to claim 1, wherein step S3 further includes:
s31, respectively calculating bonding characteristic matrixes of the metal nanoclusters;
and S32, comparing the bonding characteristic matrixes of the metal nanoclusters, and when the Euclidean distance between the bonding characteristic matrixes of the two metal nanoclusters is smaller than a preset value, excluding the metal nanoclusters with higher energy values.
4. The method of optimizing the structure of metal nanoclusters according to claim 3,
the definition of the bonding feature matrix is shown as follows:
wherein, delta AB Denotes the kind of bond, AB denotes the atom of bond, N AB Indicates the number of the corresponding keys and,
is a parameter of the key sequence,
being elements of the bonding feature matrix, θ ij ,
Respectively the elevation angle and the azimuth angle Y between the metal atom i and the metal atom j in the spherical coordinate system lm For spherical harmonics, l is the order of the spherical harmonics, l =0,2,4,6, …, m = l, l-1, …, euclidean distance D of the keyed feature matrix uv Is defined as follows:
5. the method for optimizing the structure of metal nanoclusters according to claim 1, wherein in step S4,
the velocity update formula of the ith metal nanocluster is:
coordinate update formula of ith metal nanocluster:
wherein the coordinates of the ith metal nanocluster in the kth update iteration are represented as
The velocity is expressed as
Omega is the inertia constant, c 1 、c 2 、c 3 Respectively, introduced random learning operator, r 1 、r 2 、r 3 Is [0,1]Uniform random constant within a range, r 4 Is [0,N-1]Uniform random integers within; p i The coordinates with the lowest energy for the i metal nanoclusters in all update iterations; p g The coordinate with the lowest energy for all metal nanoclusters in the metal nanocluster cluster is found in all update iterations.
6. The method for optimizing a structure of a metal nanocluster according to claim 1, wherein the calculation formula of the fitness value is as follows:
f i ＝exp(-αρ i )；
wherein f is i Is the fitness value of the ith metal nanocluster, alpha is a set constant,
V i is the energy value, V, of the ith metal nanocluster min Is the minimum value, V, among the energy values of the current metal nanoclusters max Is the maximum value among the energy values of the current metal nanoclusters.
7. The method for optimizing the structure of metal nanoclusters according to claim 1, wherein said step S5 further comprises:
s51, selecting a numerical value in the range of [0,1 as a variation rate;
s52, correspondingly generating a uniform random number within the range of [0,1] in a random manner for each speed and coordinate updated bimetal nanocluster;
and S53, comparing the uniform random number corresponding to each speed and coordinate updated bimetal nanocluster with the variation rate, and randomly exchanging the positions of a plurality of different types of metal atoms in the bimetal nanoclusters after the speed and coordinate updated corresponding to the uniform random number are updated if the corresponding uniform random number is smaller than the variation rate.
8. The method for optimizing the structure of metal nanoclusters according to claim 1, wherein step S10 further includes:
s101, respectively calculating the replacement probability of the first locally optimized metal nanocluster and the second locally optimized metal nanocluster;
s102, respectively and randomly generating a uniform random number within the range of [0,1] corresponding to each metal nanocluster in the metal nanocluster group;
s103, comparing the uniform random number corresponding to each metal nanocluster with the replacement probability of the first locally optimized metal nanocluster and the replacement probability of the second locally optimized metal nanocluster, and replacing the locally optimized metal nanocluster corresponding to the replacement probability with the metal nanocluster corresponding to the uniform random number if the uniform random number is smaller than the replacement probability.
9. The method for optimizing a structure of a metal nanocluster according to claim 1, wherein the calculation formula of the replacement probability is as follows:
wherein E is old Is the energy of a certain metal nanocluster in the metal nanocluster group, T is a set parameter, E new Is E old The energy corresponding to the first locally optimized metal nanocluster and the second locally optimized metal nanocluster of the corresponding metal nanocluster.
10. The method for optimizing the structure of a metal nanocluster according to claim 1, wherein the energy value of the metal nanocluster is calculated by functional theory calculation software based on the structure and density of the metal nanocluster.
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