void testIdealGas() {
const int numParticles = 64;
const int frequency = 10;
const int steps = 1000;
const double pressure = 1.5;
const double pressureInMD = pressure*(AVOGADRO*1e-25); // pressure in kJ/mol/nm^3
const double temp[] = {300.0, 600.0, 1000.0};
const double initialVolume = numParticles*BOLTZ*temp[1]/pressureInMD;
const double initialLength = std::pow(initialVolume, 1.0/3.0);
// Create a gas of noninteracting particles.
ReferencePlatform platform;
System system;
system.setDefaultPeriodicBoxVectors(Vec3(initialLength, 0, 0), Vec3(0, 0.5*initialLength, 0), Vec3(0, 0, 2*initialLength));
vector<Vec3> positions(numParticles);
OpenMM_SFMT::SFMT sfmt;
init_gen_rand(0, sfmt);
for (int i = 0; i < numParticles; ++i) {
system.addParticle(1.0);
positions[i] = Vec3(initialLength*genrand_real2(sfmt), 0.5*initialLength*genrand_real2(sfmt), 2*initialLength*genrand_real2(sfmt));
}
MonteCarloAnisotropicBarostat* barostat = new MonteCarloAnisotropicBarostat(Vec3(pressure, pressure, pressure), temp[0], true, true, true, frequency);
system.addForce(barostat);
// Test it for three different temperatures.
for (int i = 0; i < 3; i++) {
barostat->setTemperature(temp[i]);
LangevinIntegrator integrator(temp[i], 0.1, 0.01);
Context context(system, integrator, platform);
context.setPositions(positions);
// Let it equilibrate.
integrator.step(10000);
// Now run it for a while and see if the volume is correct.
double volume = 0.0;
for (int j = 0; j < steps; ++j) {
Vec3 box[3];
context.getState(0).getPeriodicBoxVectors(box[0], box[1], box[2]);
volume += box[0][0]*box[1][1]*box[2][2];
integrator.step(frequency);
}
volume /= steps;
double expected = (numParticles+1)*BOLTZ*temp[i]/pressureInMD;
ASSERT_USUALLY_EQUAL_TOL(expected, volume, 3/std::sqrt((double) steps));
}
}
/**
* Run a constant pressure simulation on an anisotropic Einstein crystal
* using isotropic and anisotropic barostats. There are a total of 15 simulations:
*
* 1) 3 pressures: 9.0, 10.0, 11.0 bar, for each of the following groups:
* 2) 3 groups of simulations that scale just one axis: x, y, z
* 3) 1 group of simulations that scales all three axes in the anisotropic barostat
* 4) 1 group of simulations that scales all three axes in the isotropic barostat
*
* Results that we will check:
*
* a) In each group of simulations, the volume should decrease with increasing pressure
* b) In the three simulation groups that scale just one axis, the compressibility (i.e. incremental volume change
* with increasing pressure) should go like kx > ky > kz (because the spring constant is largest in the z-direction)
* c) The anisotropic barostat should produce the same result as the isotropic barostat when all three axes are scaled
*/
void testEinsteinCrystal() {
const int numParticles = 64;
const int frequency = 2;
const int equil = 10000;
const int steps = 5000;
const double pressure = 10.0;
const double pressureInMD = pressure*(AVOGADRO*1e-25); // pressure in kJ/mol/nm^3
const double temp = 300.0; // Only test one temperature since we're looking at three pressures.
const double pres3[] = {2.0, 8.0, 15.0};
const double initialVolume = numParticles*BOLTZ*temp/pressureInMD;
const double initialLength = std::pow(initialVolume, 1.0/3.0);
vector<double> initialPositions(3);
vector<double> results;
// Run four groups of anisotropic simulations; scaling just x, y, z, then all three.
for (int a = 0; a < 4; a++) {
// Test barostat for three different pressures.
for (int p = 0; p < 3; p++) {
// Create a system of noninteracting particles attached by harmonic springs to their initial positions.
System system;
system.setDefaultPeriodicBoxVectors(Vec3(initialLength, 0, 0), Vec3(0, initialLength, 0), Vec3(0, 0, initialLength));
vector<Vec3> positions(numParticles);
OpenMM_SFMT::SFMT sfmt;
init_gen_rand(0, sfmt);
// Anisotropic force constants.
CustomExternalForce* force = new CustomExternalForce("0.005*(x-x0)^2 + 0.01*(y-y0)^2 + 0.02*(z-z0)^2");
force->addPerParticleParameter("x0");
force->addPerParticleParameter("y0");
force->addPerParticleParameter("z0");
NonbondedForce* nb = new NonbondedForce();
nb->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
for (int i = 0; i < numParticles; ++i) {
system.addParticle(1.0);
positions[i] = Vec3(((i/16)%4+0.5)*initialLength/4, ((i/4)%4+0.5)*initialLength/4, (i%4+0.5)*initialLength/4);
initialPositions[0] = positions[i][0];
initialPositions[1] = positions[i][1];
initialPositions[2] = positions[i][2];
force->addParticle(i, initialPositions);
nb->addParticle(0, initialLength/6, 0.1);
}
system.addForce(force);
system.addForce(nb);
// Create the barostat.
MonteCarloAnisotropicBarostat* barostat = new MonteCarloAnisotropicBarostat(Vec3(pres3[p], pres3[p], pres3[p]), temp, (a==0||a==3), (a==1||a==3), (a==2||a==3), frequency);
system.addForce(barostat);
barostat->setTemperature(temp);
LangevinIntegrator integrator(temp, 0.1, 0.01);
Context context(system, integrator, platform);
context.setPositions(positions);
// Let it equilibrate.
integrator.step(equil);
// Now run it for a while and see if the volume is correct.
double volume = 0.0;
for (int j = 0; j < steps; ++j) {
Vec3 box[3];
context.getState(0).getPeriodicBoxVectors(box[0], box[1], box[2]);
volume += box[0][0]*box[1][1]*box[2][2];
integrator.step(frequency);
}
volume /= steps;
results.push_back(volume);
}
}
for (int p = 0; p < 3; p++) {
// Create a system of noninteracting particles attached by harmonic springs to their initial positions.
System system;
system.setDefaultPeriodicBoxVectors(Vec3(initialLength, 0, 0), Vec3(0, initialLength, 0), Vec3(0, 0, initialLength));
vector<Vec3> positions(numParticles);
OpenMM_SFMT::SFMT sfmt;
init_gen_rand(0, sfmt);
// Anisotropic force constants.
CustomExternalForce* force = new CustomExternalForce("0.005*(x-x0)^2 + 0.01*(y-y0)^2 + 0.02*(z-z0)^2");
force->addPerParticleParameter("x0");
force->addPerParticleParameter("y0");
force->addPerParticleParameter("z0");
NonbondedForce* nb = new NonbondedForce();
nb->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
for (int i = 0; i < numParticles; ++i) {
system.addParticle(1.0);
positions[i] = Vec3(((i/16)%4+0.5)*initialLength/4, ((i/4)%4+0.5)*initialLength/4, (i%4+0.5)*initialLength/4);
initialPositions[0] = positions[i][0];
initialPositions[1] = positions[i][1];
initialPositions[2] = positions[i][2];
force->addParticle(i, initialPositions);
nb->addParticle(0, initialLength/6, 0.1);
}
system.addForce(force);
system.addForce(nb);
// Create the barostat.
MonteCarloBarostat* barostat = new MonteCarloBarostat(pres3[p], temp, frequency);
system.addForce(barostat);
barostat->setTemperature(temp);
LangevinIntegrator integrator(temp, 0.1, 0.001);
Context context(system, integrator, platform);
context.setPositions(positions);
// Let it equilibrate.
integrator.step(equil);
// Now run it for a while and see if the volume is correct.
double volume = 0.0;
for (int j = 0; j < steps; ++j) {
Vec3 box[3];
context.getState(0).getPeriodicBoxVectors(box[0], box[1], box[2]);
volume += box[0][0]*box[1][1]*box[2][2];
integrator.step(frequency);
}
volume /= steps;
results.push_back(volume);
}
// Check to see if volumes decrease with increasing pressure.
ASSERT_USUALLY_TRUE(results[0] > results[1]);
ASSERT_USUALLY_TRUE(results[1] > results[2]);
ASSERT_USUALLY_TRUE(results[3] > results[4]);
ASSERT_USUALLY_TRUE(results[4] > results[5]);
ASSERT_USUALLY_TRUE(results[6] > results[7]);
ASSERT_USUALLY_TRUE(results[7] > results[8]);
// Check to see if incremental volume changes with increasing pressure go like kx > ky > kz.
ASSERT_USUALLY_TRUE((results[0] - results[1]) > (results[3] - results[4]));
ASSERT_USUALLY_TRUE((results[1] - results[2]) > (results[4] - results[5]));
ASSERT_USUALLY_TRUE((results[3] - results[4]) > (results[6] - results[7]));
ASSERT_USUALLY_TRUE((results[4] - results[5]) > (results[7] - results[8]));
// Check to see if the volumes are equal for isotropic and anisotropic (all axis).
ASSERT_USUALLY_EQUAL_TOL(results[9], results[12], 3/std::sqrt((double) steps));
ASSERT_USUALLY_EQUAL_TOL(results[10], results[13], 3/std::sqrt((double) steps));
ASSERT_USUALLY_EQUAL_TOL(results[11], results[14], 3/std::sqrt((double) steps));
}