MD程序

//
// lj_md.C
//
// Molecular dynamics simulation code for a Lennard-Jones system.
//
// Written by: Yanting Wang                      October 22, 2009
//

#include <iostream>
#include <fstream>
using namespace std;

#include <stdlib.h>

#include "vector.h"

//
// Define reduced units
//

double m = 1.0;         // particle mass
double epsilon = 1.0;   // LJ energy coefficient
double sigma = 1.0;     // LJ distance coefficient
double kB = 1.0;        // Boltzmann constant

//
// Define global variables
//

Vector *r;               // particle positions
Vector *v;               // particle velocities
Vector *a;               // particle accelerations
Vector *pa;              // previous accelerations

int np;                  // number of particles
double L;                // cubic simulation box size

double Ek;               // total kinetic energy
double Ep;               // total potential energy

double Ecut;             // potential energy contribution beyond cutoff
double rc;               // cutoff distance of the potential

int step;                // total simulation steps
int sample_int;          // sampling interval
double dt;               // integration time interval
bool scale;              // whether scale temperature
double T = 0.01;         // temperature

//
// Periodic boundary condition (PBC)
//

Vector pbc( Vector r )
{
//
// PBC correction
//

double hL = L / 2.0;

if( r.x > hL )  r.x -= L;
if( r.x < -hL ) r.x += L;

if( r.y > hL )  r.y -= L;
if( r.y < -hL ) r.y += L;

if( r.z > hL )  r.z -= L;
if( r.z < -hL ) r.z += L;

//
// Check if the vector is now inside the box
//

if( r.x > hL || r.x < -hL )
{
cerr << "r.x = " << r.x << " is out of simulation box." << endl;

exit( -1 );
}

if( r.y > hL || r.y < -hL )
{
cerr << "r.y = " << r.y << " is out of simulation box." << endl;

exit( -1 );
}

if( r.z > hL || r.z < -hL )
{
cerr << "r.z = " << r.z << " is out of simulation box." << endl;

exit( -1 );
}

return r;
}

//
// Update particle positions with the Velocity Verlet algorithm
//

void position()
{
for( int i=0; i<np; ++i )
{
r[i] += v[i] * dt + 0.5 * a[i] * dt * dt;   // Velocity Verlet integration

r[i] = pbc( r[i] );    // put back into the box if out of boundary
}
}

//
// Calculate forces and potentials according to the current positions
//

void force()
{
Ep = 0.0;

for( int i=0; i<np; ++i )
{
pa[i] = a[i];
a[i].clear();        // set all three components to be 0
}

//
// Calculate pair forces and update the system potential
//

for( int i=0; i<np-1; ++i )
{
for( int j=i+1; j<np; ++j )
{
Vector dr = pbc( r[i] - r[j] );

double d = dr.r();          // modulus of vector dr

if( d < rc )       // within cutoff distance
{
double id = sigma / d;
double i2 = id * id;
double i6 = i2 * i2 * i2;

// Below is actually f/r to save computational time
double f = 24.0 * epsilon * i2 * i6 * ( 2.0 * i6 - 1.0 );

a[i] += f * dr / m;
a[j] -= f * dr / m;

Ep += 4.0 * epsilon * i6 * ( i6 - 1.0 ) - Ecut;
}
}
}
}

//
// Update velocities with the velocity Verlet algorithm
//

void velocity()
{
Ek = 0.0;

for( int i=0; i<np; ++i )
{
v[i] += 0.5 * dt * ( a[i] + pa[i] );

Ek += v[i] * v[i];
}

Ek *= 0.5;
}

//
// Scale temperature with the isokinetics (Evans) thermostat
//

void scale_T()
{
double Tc = 2.0 / 3.0 * Ek / np / kB;   // current temperature
double fs = sqrt( T / Tc );             // scaling factor

for( int i=0; i<np; ++i ) v[i] *= fs;   // scale velocity of each particle

Ek *= fs * fs;                          // update kinetic energy
}

//
// System and variable initialization
//

void init()
{
//
// Read initial configuration
//

ifstream fc( "md_init.xyz" );

if( !fc.is_open() )       // failed to open the file
{
cerr << "File md_init.xyz can not be opened for reading." << endl;
exit( -4 );
}

fc >> np >> L;

r = new Vector[np];
v = new Vector[np];
a = new Vector[np];
pa = new Vector[np];

string pname;                // particle name;

for( int i=0; i<np; ++i )
{
fc >> pname >> r[i] >> v[i] >> a[i] >> pa[i];
}

fc.close();

//
// Read simulation parameters
//

ifstream fp( "md_para.dat" );

if( !fp.is_open() )        // failed to open the file
{
cerr << "File md_para.dat can not be opened for reading." << endl;
exit( -4 );
}

fp >> step >> sample_int >> dt >> rc >> scale;

if( scale ) fp >> T;

fp.close();

if( step <= 0 || sample_int <= 0 || dt <= 0.0 || rc <= 0.0 || T <= 0.0 )
{
cerr << "Error: input parameter is less than 0." << endl;
cerr << "Input parameters: " << step << " " << sample_int << " "
<< dt << " " << rc << " " << T << endl;

exit( -3 );
}

//
// Determine if rc is valid
//

if( rc > 0.5 * L )
{
cerr << "Error: rc=" << rc
<< " is larger than half of the box size L=" << L << endl;
exit( -2 );
}

//
// Calculate ecut
//

double id = sigma / rc;
double i2 = id * id;
double i6 = i2 * i2 * i2;

Ecut = 4.0 * epsilon * i6 * ( i6 - 1.0 );

//
// Refresh output files
//

ofstream od( "md_out.dat" );
od.close();

ofstream oc( "md_out.xyz" );
oc.close();
}

//
// Sample and dump thermodynamic data and configurations
//
// Input: cstep -- current step
//

void sample( int cstep )
{
//
// Output thermodynamic data
//

ofstream od( "md_out.dat", ios::app );

od << cstep * dt             // current simulation time
<< " " << (Ek + Ep) / np  // average total energy per particle
<< " " << Ek / np         // average kinetic energy per particle
<< " " << Ep / np         // average potential energy per particle
<< endl;

od.close();

//
// Output an instantaneous configuration
//

ofstream oc( "md_out.xyz", ios::app );

oc << np << endl             // number of particles
<< L  << endl;            // simulation box size

for( int i=0; i<np; ++i )
{
oc << "He"                 // particle name
<< " " << r[i]          // positions
<< " " << v[i]          // velocities
<< " " << a[i]          // accelerations
<< " " << pa[i]         // previous accelerations
<< endl;
}

oc.close();
}

//
// Termination process
//

void end()
{
//
// Release memory allocated for the arrays
//

delete []r;
delete []v;
delete []a;
delete []pa;
}

int main()
{
init();

for( int i=0; i<step; ++i )
{
position();
force();
velocity();

if( scale ) scale_T();

if( i % sample_int == 0 ) sample( i+1 );
}

end();

return 0;
}