CN102867125B - A kind of method calculating molecular dynamics dynamic time step-length - Google Patents
A kind of method calculating molecular dynamics dynamic time step-length Download PDFInfo
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- CN102867125B CN102867125B CN201210340172.4A CN201210340172A CN102867125B CN 102867125 B CN102867125 B CN 102867125B CN 201210340172 A CN201210340172 A CN 201210340172A CN 102867125 B CN102867125 B CN 102867125B
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Abstract
Calculate a method for molecular dynamics dynamic time step-length, is concrete calculation procedure as follows: 1) calculate the distance between every two molecules
, judge array
numerical value whether be all greater than truncation radius <i>r
c</i>; 2) relative velocity between every two molecules is calculated
; 3) time t (n) moved between every two molecules required for truncation radius is calculated; 4) in array t (n), minimum value t is taken out
minas next step time step.Dynamic molecular dynamics simulation algorithm of the present invention can eliminate invalid calculation procedure, accelerates computing velocity, saves computing time, makes molecular dynamics simulation non-agglomerated state, extends the range of application of molecular dynamics simulation.
Description
Technical field
The present invention relates to molecular dynamics field, particularly a kind of method calculating next step time step.
Background technology
At the beginning of the sixties, first Alder and Wainwright adopt hard-sphere model, carried out molecular dynamics simulation research, and this is acknowledged as first time molecular dynamics simulation.Verlet etc. then depict Lennard-Jones system phasor, and propose famous Verlet algorithm, and this algorithm makes molecular dynamics simulation more effective, and its range of application have also been obtained wide spread.
After the seventies, along with the new theories such as density functional theory (Density-FunctionTheory), fluctuation Dissipative Theory (FluctuationDissipationTheory) are introduced into molecular dynamics one after another, this analogy method obtains flourish.Because molecular dynamics is combined with subjects such as statistical physics again, classical molecular dynamics theory is enriched, and to the end of the eighties, this system is perfect gradually.To the nineties, computer hardware achieves the development of advancing by leaps and bounds, and makes molecular dynamics simulation further strengthened.In addition because the method can regard the bridge of linking up macroscopic property and micromechanism as, can explain to a certain extent from molecular scale many theoretical and experimental study observe on all inscrutable microphenomenon, therefore in field and crossing domains such as chemistry, physics, biology, material science, tribology, molecular dynamics simulation is obtained for be applied widely.
Molecular dynamics simulation hypothetical particle observes Newton mechanics law, molecule (atom, ion etc. is calculated by solving various potential function, below be referred to as molecule) between interaction between two particles, obtain the acting force suffered by each molecule and movement velocity, the characteristics of motion of molecule can be obtained after certain hour simulation.Again according to statistical mechanics principle, utilize suitable statistical method just can obtain the macroscopic property of whole system.
In microcanonical ensemble, an isolated system comprising N number of atom can be regarded as, if total potential energy of system is used
represent, then for this classical formalism, the stressed Newton's equation of particle is described as:
Wherein: m is the quality of particle,
afor acceleration, acceleration is the continuous function of time, and in the calculation, we are expressed as time discrete:
Wherein:
it is the time of arrival n-th step; N is step number; H is time step.In calculating, the initial position of given particle and initial velocity, then can carry out numerical solution to this equation.In simulations, in order to save computing time, when intermolecular distance exceedes a certain value, intermolecular interaction is more weak, can ignore, and this distance is called truncation radius.
The basic thought of Molecular Dynamics Calculation be give molecular system initial motion state after utilize the proper motion of molecule sample drawn in phase space to carry out statistical computation, time step be exactly sampling interval, thus time step choose dynamics simulation extremely important.Oversize time step can cause intermolecular fierceness collision, system data from overflow; Too short time step can reduce the ability of simulation process search phase space.Therefore the time step generally chosen is 10
-14about s.This method is applicable for most system.
But, in the middle of system, the mean distance of particle is much larger than (distance between pressure gas molecule as usual) during truncation radius, if time step is fixed, at this moment because time step is less, in effective simulated time, molecule mainly when mutually not colliding, does invalid motion in space, the intermolecular number of times collided is limited, and system is difficult to balance.Existing molecular dynamics can only simulate the situation of aggregative state, as analog gas can only simulate dense gas (densegas).
Summary of the invention
Object of the present invention is just to provide a kind of method calculating molecular dynamics dynamic time step-length, when intermolecular distance be greater than cut half radius time, dynamic time step-length is long, and this algorithm can calculate next step time step, reduces the simulated time that molecule does lost motion in space.
The object of the invention is by such technical scheme realize, it includes multiple molecule, and concrete calculation procedure is as follows:
1) measure the coordinate of all molecules, calculate the distance between every two molecules
, i and j is molecule numbering, judges array
numerical value whether be all greater than truncation radius
r c if be greater than, proceed to step 2), if be less than, terminate;
2) measure the movement velocity of all molecules, calculate the relative velocity between every two molecules
;
3) according to step 1) and step 2) in distance between measured every two molecules
and speed
, calculate time t (n) moved between every two molecules required for truncation radius;
4) in array t (n), minimum value t is taken out
minas next step time step.
Further, the spacing of every two molecules is calculated in step 1)
formula be
，
In formula, x, y and z are the spatial value of molecule, i and j is molecule numbering.
Further, step 2) in calculate every two molecules the formula of spacing be
In formula,
for molecule is in the speed in x direction,
for molecule is in the speed in y direction,
for molecule is in the speed in z direction.
Further, calculate in step 3) and move to the formula of time t (n) required for truncation radius between every two molecules and be
T (n) serves as reasons
the array of composition.
Owing to have employed technique scheme, the present invention has following advantage:
Dynamic molecular dynamics simulation algorithm of the present invention can eliminate invalid calculation procedure, accelerates computing velocity, saves computing time, makes molecular dynamics simulation non-agglomerated state, extends the range of application of molecular dynamics simulation.
Other advantages of the present invention, target and feature will be set forth to a certain extent in the following description, and to a certain extent, based on will be apparent to those skilled in the art to investigating hereafter, or can be instructed from the practice of the present invention.Target of the present invention and other advantages can be realized by instructions below and claims and be obtained.
Accompanying drawing explanation
Accompanying drawing of the present invention is described as follows.
Fig. 1 is the view of molecule in the one-dimensional space;
Fig. 2 is the view of molecule at two-dimensional space;
Fig. 3 is that molecule is in three-dimensional view;
Fig. 4 is algorithm flow chart of the present invention.
Embodiment
Below in conjunction with drawings and Examples, the invention will be further described.
Calculate a method for molecular dynamics dynamic time step-length, include multiple molecule, concrete calculation procedure is as follows:
1) measure the coordinate of all molecules, calculate the distance between every two molecules
, i and j is molecule numbering, judges array
numerical value whether be all greater than truncation radius
r c if be greater than, proceed to step 2), if be less than, terminate;
2) measure the movement velocity of all molecules, calculate the relative velocity between every two molecules
;
3) according to step 1) and step 2) in distance between measured every two molecules
and speed
, calculate time t (n) moved between every two molecules required for truncation radius;
4) in array t (n), minimum value t is taken out
minas next step time step.
The spacing of every two molecules is calculated in step 1)
formula be
，
In formula, x, y and z are the spatial value of molecule, i and j is molecule numbering.
Step 2) in calculate every two molecules the formula of spacing be
In formula,
for molecule is in the speed in x direction,
for molecule is in the speed in y direction,
for molecule is in the speed in z direction.
Calculate in step 3) and move to the formula of time t (n) required for truncation radius between every two molecules and be
T (n) serves as reasons
the array of composition.
The present invention can calculate dynamic time step-length in one dimension, two and three dimensions space.
As shown in Figure 1, when the one-dimensional space is implemented, can calculate every two intermolecular relative velocities and distance very easily, namely relative velocity is:
, relative distance
, and then calculate two molecules interact required for time
, obtain array
t ij in minimum value
t min .
t min as next step time step.
As shown in Figure 2, when two-dimensional space is implemented, need the relative velocity obtaining them according to molecule in the speed of X, Y-direction
, relative distance
, and then calculate two molecules interact at two-dimensional space required for time
, obtain array
t ij in minimum value
t min .
t min as next step time step.
As shown in Figure 3, when three dimensions is implemented, need the relative velocity obtaining them according to molecule in the speed of X, Y, Z-direction
, relative distance
, and then calculate two molecules interact at three dimensions required for time
, obtain array
t ij in minimum value
t min .
Dynamic molecular dynamics simulation algorithm of the present invention can eliminate invalid calculation procedure, accelerates computing velocity, saves computing time, makes molecular dynamics simulation non-agglomerated state, extends the range of application of molecular dynamics simulation.
What finally illustrate is, above embodiment is only in order to illustrate technical scheme of the present invention and unrestricted, although with reference to preferred embodiment to invention has been detailed description, those of ordinary skill in the art is to be understood that, can modify to technical scheme of the present invention or equivalent replacement, and not departing from aim and the scope of the technical program, it all should be encompassed in the middle of right of the present invention.
Claims (3)
1. calculate a method for molecular dynamics dynamic time step-length, include multiple molecule, it is characterized in that, concrete calculation procedure is as follows:
1) measure the coordinate of all molecules, calculate the distance l between every two molecules
ij, i and j is molecule numbering, judges array l
ijnumerical value whether be all greater than truncation radius r
cif be greater than, proceed to step 2), if be less than, terminate;
2) measure the movement velocity of all molecules, calculate the relative velocity v between every two molecules
ij;
3) according to step 1) and step 2) in distance l between measured every two molecules
ijand speed v
ij, calculate time t (n) moved between every two molecules required for truncation radius,
t
ij＝(l
ij-r
c)/v
ij
T (n) is by t
ijthe array of composition;
4) in array t (n), minimum value t is taken out
minas next step time step.
2. a kind of method calculating molecular dynamics dynamic time step-length as claimed in claim 1, is characterized in that: step 1) the middle spacing l calculating every two molecules
ijformula be
001"/>
In formula, x, y and z are the spatial value of molecule, i and j is molecule numbering.
3. a kind of method calculating molecular dynamics dynamic time step-length as claimed in claim 1, is characterized in that: step 2) in calculate the formula of relative velocity between every two molecules and be
002"/>
In formula, v
xfor molecule is in the speed in x direction, v
yfor molecule is in the speed in y direction, v
zfor molecule is in the speed in z direction.
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| CN108595842B (en) * | 2018-04-25 | 2021-12-21 | 中国科学院合肥物质科学研究院 | Time step optimization method for simulating particle irradiation damage |
| CN111307754A (en) * | 2020-03-13 | 2020-06-19 | 中国科学院上海高等研究院 | Method for detecting gas effect based on terahertz technology |
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| MEMS粘附的分子动力学研究;申海兰;《中国优秀硕士学位论文全文数据库工程科技I辑》;20090115(第01期);第28页第21-26行，第38页1-25行 * |
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