CN102937946A - Complicated function minimal value searching method based on constrained regular pattern - Google Patents

Complicated function minimal value searching method based on constrained regular pattern Download PDF

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CN102937946A
CN102937946A CN2012104219396A CN201210421939A CN102937946A CN 102937946 A CN102937946 A CN 102937946A CN 2012104219396 A CN2012104219396 A CN 2012104219396A CN 201210421939 A CN201210421939 A CN 201210421939A CN 102937946 A CN102937946 A CN 102937946A
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刘智攀
商城
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Fudan University
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Abstract

The invention belongs to the technical fields of computational chemistry and physics and particularly relates to a complicated function minimal value searching method based on a constrained regular pattern. In the complicated function minimal value searching method, an atomic coordinate corresponding to an energy minimal value is solved by virtue of the input atomic coordinate, a known potential energy surface energy function and a first-order derivative of the energy function corresponding to the coordinate. The method comprises the steps: starting from a coordinate system corresponding to one minimal value, carrying out optional generating and analyzing to obtain one constrained regular pattern, realizing a purpose of surpassing an energy maximal value of the potential energy surface by continuously adding bias potential functions and repeating optimizing of the energy minimal value, and finally obtaining the coordinate system corresponding to a new minimal value. The complicated function minimal value searching method based on the constrained regular pattern has the effect that the overall minimal values can be quickly searched, is suitable for complicated function systems, and meanwhile has a function of searching an optimal reaction channel. The complicated function minimal value searching method based on the constrained regular pattern can be used for traversing the potential energy surfaces of complicated molecules and periodic crystal systems.

Description

A kind of complicated function minimal value searching method of Constraint-based regular pattern
Technical field
The invention belongs to chemistry and physical technique field, be specifically related to a kind of fast complicated function minimal value searching method, can be used for traveling through the potential energy surface of complex molecule, periodicity crystal system.
Background technology
Structure prediction and response path are searched for the core missions as present age chemistry and physical computing modeling effort, for understanding and predicting that macroscopic property and the kinetic property of material have irreplaceable effect.Although molecular dynamics simulation is widely used as a kind of conventional instrument of searching for potential energy surface and simulation chemical reaction process, the predictive ability of this method can decline to a great extent when processing high-dimensional complicated potential energy surface system or having the chemical process system of high reaction activity.Such as Molecular Dynamics method, can not fine processing protein folding or the growth course of carbon nano-tube.
Have the chemical process of higher reaction activity for these, a kind of method relatively more commonly used is to search for first the corresponding transition state of chemical process, finds the reaction channel through this transition state again.The most obvious shortcoming of this method be exactly it highly depend on the scientific research personnel by chemical intuition in advance the conjecture possible reaction channel, and this guess in advance in the higher-dimension system may make hardly.Another kind of method commonly used is the sampling probability that increases overactivity energy process by increase restrictive condition (such as adding the biasing potential function) in predefined reaction coordinate, such as metadynamics method (Phys. Rev. Lett. 2003,90,238302) and the umbrella methods of sampling (umbrella sampling) (J. Chem. Phys. 1998,109,7737).Since need to be according to the pre-defined restrictive condition of system, these methods can only be used for search single step chemical reaction usually, can not be used for possible energy level point on the traversal potential energy surface.
Opposite with previous methods, global optimization's method, such as BH method (Basin-Hopping method, J. Phys. Chem. A 1997,101,5111) and genetic algorithm (Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Reading, MA, 1989) be that to obtain functional minimum value be final goal, the rock-steady structure on the potential energy surface namely.These methods have generally adopted radical structural deformation, reach the purpose of jumping out minimum energy value zone on the potential energy surface, so these methods have been ignored on the potential energy surface reaction channel information of change between different minimal values fully, and also greatly reduce for the treatment effeciency of complicated potential energy surface.
Summary of the invention
The objective of the invention is for a kind of easy pervasive potential energy surface Selecting Function System method is provided, overcome in the previous methods shortcoming that the complex system predictive ability for high-dimensional potential energy surface reduces greatly.
Another object of the present invention provides a kind of method, can be used for simultaneously the structure prediction of minimum energy value and the prediction of reaction channel.
For achieving the above object, the present invention is based on the biasing potential function and drive molecular dynamics thought, by structure motor pattern at random, and the constraint regular pattern that obtains along optimization, configuration minimum energy value on the potential energy surface is transformed to another minimum energy value, utilize at last the Metropolis monte carlo method to determine whether new-found minimum energy value configuration is accepted.The method for solving of wherein describing the energy function of potential energy surface comprises the force field method, Ab initio method, first principle DFT method.
The inventive method synoptic diagram as shown in Figure 1, concrete steps are:
Utilize the atomic coordinates q of input i, i=1,2 ... n, known potential energy surface energy function E= f(q i), i=1,2 ... n, energy function is to the first order derivative F=of coordinate g(q i), i=1,2 ... n finds the solution atomic coordinates corresponding to all minimal values of energy, and connects these minimizing reaction channels, and concrete steps are as follows:
Step 1, minimum energy value coordinate A of input, and produce at random a pattern N0
Step 2, in the pattern that produces at random N0On the basis, obtain the regular pattern N of a constraint by the optimization of constraint Shuangzi method;
Step 3, on original potential function basis, newly add one of this N direction biasing Gauss potential function, then total potential energy surface V Tot Can be expressed as true potential energy surface V Real With the biasing potential function V G And, namely
Figure 330572DEST_PATH_IMAGE001
, along this NThe direction current coordinate of extrapolating is near the minimum energy value that is produced by biasing potential function and the stack of original potential function;
Step 4, minimum energy value are optimized current coordinate;
Step 5, determine whether the upper limit of the biasing Gauss potential function number (NG) that reaches maximum, or reach default energy threshold E r(satisfy E Max＜E r); Reach and then forward step 6 to, otherwise repeating step two, step 3, step 4;
Step 6, remove the biasing Gauss potential function of all interpolations, the optimization of minimum energy value obtains new coordinate-system B;
Step 7 adopts the Metropolis monte carlo method, judges whether B accepts; If accept, A is substituted by B;
Step 8, repeating step one is sought next minimum energy value to step 7, or EOP (end of program).
Among the present invention, the method for solving of potential energy surface energy function comprises the force field method, Ab initio method, or first principle DFT method.
Among the present invention, the pattern that step 1 produces at random N0Formed by two parts: first N g , being the Maxwell-Boltzmann rate distribution under the uniform temperature condition, this part is global schema, second portion N l , be the mutual close motor pattern of any two the non-conterminous atoms in system inside; N0By N g With N l Constructive method as follows:
Figure 762690DEST_PATH_IMAGE002
?，
The value of parameter lambda is a random number between 0.1 to 10.
Among the present invention, the step of the Shuangzi of constraint described in step 2 method is: two coordinate points on the definition potential energy surface are designated as respectively R0, R1, and so that R0, R1Satisfy relation
Figure 918865DEST_PATH_IMAGE003
, wherein Δ RBe the Shuangzi spacing, generally be redefined for 0.005 dust. R1Upper effect biasing potential function V N, use afterwards the optimization of Shuangzi method to obtain N.
Among the present invention, the concrete form of the Gauss potential of biasing described in step 3 function is as follows:
Figure 523110DEST_PATH_IMAGE004
Figure 102176DEST_PATH_IMAGE006
Figure 112857DEST_PATH_IMAGE007
Wherein, i is biasing Gaussian function counting. Be current coordinate,
Figure 52311DEST_PATH_IMAGE009
System coordinate when adding current corresponding Gauss potential function; N iBe current constraint regular pattern N, it is obtained by step 2; Parameter w i, ds is height and the width of biasing Gaussian function.
The w of biasing Gauss potential function iNeed to satisfy following formula with the value of ds: get current coordinate
Figure 576965DEST_PATH_IMAGE008
=
Figure 707732DEST_PATH_IMAGE010
, biasing Gauss potential function satisfies
Figure 908906DEST_PATH_IMAGE011
Wherein the scope of optimum ds is between the 0.2-0.8.
Among the present invention, the Optimal units of biasing Gauss potential function number (NG) is between 10 to 20.
Among the present invention, the method for described minimum energy value optimization can adopt method of steepest descent, method of conjugate gradient, or intend Newton method.
Among the present invention, in the step 5, default energy threshold E rThe required highest energy scope that is used for control one-step reaction process, this parameter can determine according to the temperature of reaction of system, and this parameter can be set as according to the temperature of reaction of system 0 to+infinitely-great any value, the value difference then among the result product distribute different.
By the present invention, require potential energy surface continuous, the potential-energy function single order can be led.
By the present invention, to the system of studying, except system elements and atom number, search procedure does not need to introduce in advance any other information, such as system shape, symmetry.
By the present invention, research system both can be molecule, nano particle, also can be the periodicity crystal.If periodic structure, both fixedly structure cell search also can change the structure cell search.
By the present invention, unless specify, otherwise can not guarantee accurately to find all transition state structures.If specify the search transition state will obviously affect efficient.
By the present invention, at first can obtain several local minimums, and can in limited optimization step number, can search the energy smallest point of system.Secondly dynamic information be can obtain, the approximate value of reaction activity and the reaction channel between the connection energy level point comprised.
By the present invention, the searched probability that arrives of specific chemical process not with the reaction activity exponent function relation, and relevant with the selected probability of pattern.This probability can be realized by adjusting parameter lambda.
The present invention has following advantage: than traditional global optimization's method, such as BH method and genetic algorithm, the present invention is applied widely to potential-energy function and studied system, and the single step structural change is little, reaction channel is complete, and the electronic structure that is particularly useful for first principle calculates.Than traditional restrictive condition Molecular Dynamics method, such as metadynamics and the umbrella methods of sampling, automaticity of the present invention is high, only need the initial setting parameter just can search for whole potential energy surface, do not need human-computer interaction in the search procedure, and easy and simple to handle, left-hand seat is low to scientific research personnel's specialty background requirement easily.
Description of drawings
Fig. 1: the present invention is the synoptic diagram from structure A to structure B on the one dimension potential energy surface.
The three kinds of mutual conversion reaction passage of rock-steady structure figure among Fig. 2: the embodiment 2.
Fig. 3: embodiment 3 result schematic diagrams.(a) be result of the present invention; (b) result who searches for for the BH method.Ordinate is the Monte Carlo step number, and horizontal ordinate is corresponding to atomicity.Different gray scales and line style are corresponding to the probability that finds energy-minimum, and energy-minimum is found in white expression 100%.
Fig. 4: embodiment 4 result schematic diagrams.(a) be result of the present invention; (b) be the result of BH.Ordinate is the Monte Carlo step number, and horizontal ordinate is corresponding to atomicity.Different gray scales and line style are corresponding to the probability that finds energy-minimum, and energy-minimum is found in white expression 100%.
Fig. 5: embodiment 5 is figure as a result.Product distribution plan under the different-energy threshold value.
Fig. 6: left figure is initial configuration, i.e. diamond lattic structure, and right figure is target configuration, i.e. graphite-structure.
Embodiment
Below by embodiment in detail the present invention is described in detail, but content of the present invention is not limited to this.
Embodiment 1:
C 4H 6The conformation change of molecule under meteorology.Use the first principle density functional theory to describe potential energy surface, optimized altogether for 30000 steps (number of times of calculating energy and power).The Monte Carlo Temperature Setting is 1000 Kelvins, and ds is made as 15 of 0.4, the NG number upper limits.The result in the step, finds 13 kinds of different chemical materials 151 Monte Carlos.
Embodiment 2:
C 4H 6The conformation change of molecule under meteorology.Use the first principle density functional theory to describe potential energy surface, optimized altogether for 30000 steps (number of times of calculating energy and power).The Monte Carlo Temperature Setting is 1000 Kelvins, and ds is made as 45 of 0.1, the NG number upper limits.The result in the step, finds 4 kinds of different chemical materials 94 Monte Carlos.The reaction channel that wherein mutually transforms between three the most stable species as shown in Figure 2.
Embodiment 3
Describe potential energy surface with the Lenard-Jones potential function, research is from the energy-minimum of the system of 5 atom to 100 atoms.Its concrete functional form is:
Figure 39804DEST_PATH_IMAGE012
Limiting the Monte Carlo step number is 5000.The Monte Carlo Temperature Setting is 9000 Kelvins, and ds is made as 15 of 0.6, the NG number upper limits.Search efficiency and BH method result relatively contrasts from figure and can find out that optimization efficiency of the present invention obviously is better than the BH method as shown in Figure 3.
Embodiment 4
Describe potential energy surface with the Lenard-Jones potential function, research is from the energy-minimum of the system of 5 atom to 100 atoms.Its concrete functional form is:
Figure 555099DEST_PATH_IMAGE013
Limiting the Monte Carlo step number is 10000.The Monte Carlo Temperature Setting is 9000 Kelvins, and ds is made as 15 of 0.6, the NG number upper limits.Search efficiency and BH method result relatively contrasts from figure and can find out that optimization efficiency of the present invention is apparently higher than the BH method as shown in Figure 4.For the system atomicity〉60 complex system, efficient of the present invention is more than ten times of BH method.
Embodiment 5
Describe potential energy surface with the Lenard-Jones potential function, research comprises the stability of BCB structure of 74 atoms, the reaction channel obtaining from the BCB structure to rock-steady structure conversion process.Move respectively five independently operations, and set energy threshold (E r) be 1,2,3,4,5.The result as shown in Figure 5, the system configuration obtains different product and distributes from BCB under different energy thresholds.The selectivity that is set as the structural stability (GM) that obtained at energy threshold at 3 o'clock is maximum.
Embodiment 6
The periodic structure that contains 8 C atoms is from the change of configuration of diamond lattic structure.Adopt the first principle density functional theory to describe potential energy surface, calculated a track.The cell parameter of initial configuration is a=b=c=3.58.α=β=γ=90 ° are diamond lattic structure, as shown in Figure 6.The result shows that the step is found crystal structure of graphite in the 41st Monte Carlo.Cell parameter is a=4.97, and b=3.92, and c=4.31, α=104.28, and β=90.00, γ=100.81, as shown in Figure 6.

Claims (10)

1. the complicated function minimal value searching method of a Constraint-based regular pattern is characterized in that, utilizes the atomic coordinates q of input i, i=1,2 ... n, known potential energy surface energy function E= f(q i), i=1,2 ... n, energy function is to the first order derivative F=of coordinate g(q i), i=1,2 ... n finds the solution atomic coordinates corresponding to all minimal values of energy, and connects these minimizing reaction channels, and concrete steps are as follows:
Step 1, minimum energy value coordinate A of input, and produce at random a pattern N0
Step 2, in the pattern that produces at random N0On the basis, obtain the regular pattern of a constraint by the optimization of constraint Shuangzi method N
Step 3, on original potential function basis, newly add one of this N direction biasing Gauss potential function, then total potential energy surface V Tot Can be expressed as true potential energy surface V Real With the biasing potential function V G And, namely
Figure 964079DEST_PATH_IMAGE001
, along this NThe direction current coordinate of extrapolating is near the minimum energy value that is produced by biasing potential function and the stack of original potential function;
Step 4, minimum energy value are optimized current coordinate;
Step 5, determine whether the upper limit of the biasing Gauss potential function number (NG) that reaches maximum, or reach default energy threshold E rReach and then forward step 6 to, otherwise repeating step two, step 3, step 4;
Step 6, remove the biasing Gauss potential function of all interpolations, the optimization of minimum energy value obtains new coordinate-system B;
Step 7, employing Metropolis monte carlo method judge whether B accepts; If accept, A is substituted by B;
Step 8, repeating step one are sought next minimum energy value to step 7, or EOP (end of program).
2. described method according to claim 1 is characterized in that, the method for solving of potential energy surface energy function adopts force field method, Ab initio method, or first principle DFT method.
3. described method according to claim 1 is characterized in that, the pattern that produces at random N0Formed by two parts: first N g , being the Maxwell-Boltzmann rate distribution under the uniform temperature condition, this part is global schema, second portion N l , be the mutual close motor pattern of any two the non-conterminous atoms in system inside; N0By N g With N l Constructive method as follows:
Figure 336154DEST_PATH_IMAGE002
?。
4. described method according to claim 3 is characterized in that the value of parameter lambda is a random number between 0.1 to 10.
5. described method according to claim 3, it is characterized in that the step of described constraint Shuangzi method is: two coordinate points on the definition potential energy surface are designated as respectively R0, R1, and so that R0, R1Satisfy relation
Figure 954348DEST_PATH_IMAGE003
, wherein Δ RBe the Shuangzi spacing, R1Upper effect biasing potential function V N, use afterwards the optimization of Shuangzi method to obtain N
6. described method according to claim 1 is characterized in that, in the step 3, the concrete form of biasing Gauss potential function is as follows:
Figure 7755DEST_PATH_IMAGE004
Figure 909852DEST_PATH_IMAGE005
Figure 203561DEST_PATH_IMAGE006
Figure 761581DEST_PATH_IMAGE007
Wherein, i is biasing Gaussian function counting.
Figure 415417DEST_PATH_IMAGE008
Be current coordinate,
Figure 188332DEST_PATH_IMAGE009
System coordinate when adding current corresponding Gauss potential function; N iBe current constraint regular pattern N, it is obtained by step 2; Parameter w i, ds is height and the width of biasing Gaussian function.
7. described method according to claim 6 is characterized in that, the w of biasing Gauss potential function iNeed to satisfy following formula with the value of ds: get current coordinate
Figure 902210DEST_PATH_IMAGE008
=
Figure 681947DEST_PATH_IMAGE010
, biasing Gauss potential function satisfies
Figure 890206DEST_PATH_IMAGE011
The optimized scope of ds is between the 0.2-0.8.
8. described method according to claim 1 is characterized in that, biasing Gauss potential function number (NG) is between 10 to 20.
9. described method according to claim 1 is characterized in that, the method that the minimum energy value is optimized adopts method of steepest descent, method of conjugate gradient, or intend Newton method.
10. described method according to claim 1 is characterized in that, in the step 5, and default energy threshold E rThe required highest energy scope that is used for control one-step reaction process, this parameter can be set as according to the temperature of reaction of system 0 to infinitely-great any value, the value difference then among the result product distribute different.
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Publication number Priority date Publication date Assignee Title
CN103488485A (en) * 2013-09-25 2014-01-01 浪潮电子信息产业股份有限公司 Parallel migration method for optimizing operating performance of application software on server
CN104463846A (en) * 2014-11-04 2015-03-25 浙江捷尚视觉科技股份有限公司 Parameter adjustment method used for digital image processing
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CN109187337A (en) * 2018-09-10 2019-01-11 南京工业职业技术学院 A method of screening obdurability FeAl crystal boundary
CN112823393A (en) * 2018-10-18 2021-05-18 科思创知识产权两合公司 Monte Carlo method for automatically and efficiently calculating kinetic data for chemical reactions
CN111415710A (en) * 2020-03-06 2020-07-14 深圳晶泰科技有限公司 Potential energy surface scanning method and system for molecular conformation space analysis

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