TestReferenceNonbondedForce.cpp

/* -------------------------------------------------------------------------- *
 *                                   OpenMM                                   *
 * -------------------------------------------------------------------------- *
 * This is part of the OpenMM molecular simulation toolkit originating from   *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org.               *
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 * Authors: Peter Eastman                                                     *
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/**
 * This tests all the different force terms in the reference implementation of NonbondedForce.
 */

#include "openmm/internal/AssertionUtilities.h"
#include "openmm/Context.h"
#include "ReferencePlatform.h"
#include "openmm/NonbondedForce.h"
#include "openmm/System.h"
#include "openmm/VerletIntegrator.h"
#include "SimTKOpenMMRealType.h"
#include "openmm/HarmonicBondForce.h"
#include "sfmt/SFMT.h"
#include <iostream>
#include <vector>

using namespace OpenMM;
using namespace std;

const double TOL = 1e-5;

void testCoulomb() {
    ReferencePlatform platform;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* forceField = new NonbondedForce();
    forceField->addParticle(0.5, 1, 0);
    forceField->addParticle(-1.5, 1, 0);
    system.addForce(forceField);
    ASSERT(!forceField->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(2, 0, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    double force = ONE_4PI_EPS0*(-0.75)/4.0;
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(ONE_4PI_EPS0*(-0.75)/2.0, state.getPotentialEnergy(), TOL);
}

void testLJ() {
    ReferencePlatform platform;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* forceField = new NonbondedForce();
    forceField->addParticle(0, 1.2, 1);
    forceField->addParticle(0, 1.4, 2);
    system.addForce(forceField);
    ASSERT(!forceField->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(2, 0, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    double x = 1.3/2.0;
    double eps = SQRT_TWO;
    double force = 4.0*eps*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/2.0;
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_TOL(4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0)), state.getPotentialEnergy(), TOL);
}

void testExclusionsAnd14() {
    ReferencePlatform platform;
    System system;
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    for (int i = 0; i < 5; i++) {
        system.addParticle(1.0);
        nonbonded->addParticle(0, 1.5, 0);
    }
    vector<pair<int, int> > bonds;
    bonds.push_back(pair<int, int>(0, 1));
    bonds.push_back(pair<int, int>(1, 2));
    bonds.push_back(pair<int, int>(2, 3));
    bonds.push_back(pair<int, int>(3, 4));
    nonbonded->createExceptionsFromBonds(bonds, 0.0, 0.0);
    int first14, second14;
    for (int i = 0; i < nonbonded->getNumExceptions(); i++) {
        int particle1, particle2;
        double chargeProd, sigma, epsilon;
        nonbonded->getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
        if ((particle1 == 0 && particle2 == 3) || (particle1 == 3 && particle2 == 0))
            first14 = i;
        if ((particle1 == 1 && particle2 == 4) || (particle1 == 4 && particle2 == 1))
            second14 = i;
    }
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    for (int i = 1; i < 5; ++i) {
 
        // Test LJ forces
        
        vector<Vec3> positions(5);
        const double r = 1.0;
        for (int j = 0; j < 5; ++j) {
            nonbonded->setParticleParameters(j, 0, 1.5, 0);
            positions[j] = Vec3(0, j, 0);
        }
        nonbonded->setParticleParameters(0, 0, 1.5, 1);
        nonbonded->setParticleParameters(i, 0, 1.5, 1);
        nonbonded->setExceptionParameters(first14, 0, 3, 0, 1.5, i == 3 ? 0.5 : 0.0);
        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0.0);
        positions[i] = Vec3(r, 0, 0);
        context.reinitialize();
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        double x = 1.5/r;
        double eps = 1.0;
        double force = 4.0*eps*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/r;
        double energy = 4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0));
        if (i == 3) {
            force *= 0.5;
            energy *= 0.5;
        }
        if (i < 3) {
            force = 0;
            energy = 0;
        }
        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[i], TOL);
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);

        // Test Coulomb forces
        
        nonbonded->setParticleParameters(0, 2, 1.5, 0);
        nonbonded->setParticleParameters(i, 2, 1.5, 0);
        nonbonded->setExceptionParameters(first14, 0, 3, i == 3 ? 4/1.2 : 0, 1.5, 0);
        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0);
        nonbonded->updateParametersInContext(context);
        state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces2 = state.getForces();
        force = ONE_4PI_EPS0*4/(r*r);
        energy = ONE_4PI_EPS0*4/r;
        if (i == 3) {
            force /= 1.2;
            energy /= 1.2;
        }
        if (i < 3) {
            force = 0;
            energy = 0;
        }
        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces2[0], TOL);
        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces2[i], TOL);
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
    }
}

void testCutoff() {
    ReferencePlatform platform;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* forceField = new NonbondedForce();
    forceField->addParticle(1.0, 1, 0);
    forceField->addParticle(1.0, 1, 0);
    forceField->addParticle(1.0, 1, 0);
    forceField->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
    const double cutoff = 2.9;
    forceField->setCutoffDistance(cutoff);
    const double eps = 50.0;
    forceField->setReactionFieldDielectric(eps);
    system.addForce(forceField);
    ASSERT(!forceField->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(3);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(0, 2, 0);
    positions[2] = Vec3(0, 3, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    const double krf = (1.0/(cutoff*cutoff*cutoff))*(eps-1.0)/(2.0*eps+1.0);
    const double crf = (1.0/cutoff)*(3.0*eps)/(2.0*eps+1.0);
    const double force1 = ONE_4PI_EPS0*(1.0)*(0.25-2.0*krf*2.0);
    const double force2 = ONE_4PI_EPS0*(1.0)*(1.0-2.0*krf*1.0);
    ASSERT_EQUAL_VEC(Vec3(0, -force1, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, force1-force2, 0), forces[1], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, force2, 0), forces[2], TOL);
    const double energy1 = ONE_4PI_EPS0*(1.0)*(0.5+krf*4.0-crf);
    const double energy2 = ONE_4PI_EPS0*(1.0)*(1.0+krf*1.0-crf);
    ASSERT_EQUAL_TOL(energy1+energy2, state.getPotentialEnergy(), TOL);
}

void testCutoff14() {
    ReferencePlatform platform;
    System system;
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    for (int i = 0; i < 5; i++) {
        system.addParticle(1.0);
        nonbonded->addParticle(0, 1.5, 0);
    }
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffNonPeriodic);
    const double cutoff = 3.5;
    nonbonded->setCutoffDistance(cutoff);
    const double eps = 30.0;
    nonbonded->setReactionFieldDielectric(eps);
    vector<pair<int, int> > bonds;
    bonds.push_back(pair<int, int>(0, 1));
    bonds.push_back(pair<int, int>(1, 2));
    bonds.push_back(pair<int, int>(2, 3));
    bonds.push_back(pair<int, int>(3, 4));
    nonbonded->createExceptionsFromBonds(bonds, 0.0, 0.0);
    int first14, second14;
    for (int i = 0; i < nonbonded->getNumExceptions(); i++) {
        int particle1, particle2;
        double chargeProd, sigma, epsilon;
        nonbonded->getExceptionParameters(i, particle1, particle2, chargeProd, sigma, epsilon);
        if ((particle1 == 0 && particle2 == 3) || (particle1 == 3 && particle2 == 0))
            first14 = i;
        if ((particle1 == 1 && particle2 == 4) || (particle1 == 4 && particle2 == 1))
            second14 = i;
    }
    system.addForce(nonbonded);
    ASSERT(!nonbonded->usesPeriodicBoundaryConditions());
    ASSERT(!system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(5);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(1, 0, 0);
    positions[2] = Vec3(2, 0, 0);
    positions[3] = Vec3(3, 0, 0);
    positions[4] = Vec3(4, 0, 0);
    for (int i = 1; i < 5; ++i) {
 
        // Test LJ forces
        
        nonbonded->setParticleParameters(0, 0, 1.5, 1);
        for (int j = 1; j < 5; ++j)
            nonbonded->setParticleParameters(j, 0, 1.5, 0);
        nonbonded->setParticleParameters(i, 0, 1.5, 1);
        nonbonded->setExceptionParameters(first14, 0, 3, 0, 1.5, i == 3 ? 0.5 : 0.0);
        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0.0);
        context.reinitialize();
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces = state.getForces();
        double r = positions[i][0];
        double x = 1.5/r;
        double e = 1.0;
        double force = 4.0*e*(12*std::pow(x, 12.0)-6*std::pow(x, 6.0))/r;
        double energy = 4.0*e*(std::pow(x, 12.0)-std::pow(x, 6.0));
        if (i == 3) {
            force *= 0.5;
            energy *= 0.5;
        }
        if (i < 3 || r > cutoff) {
            force = 0;
            energy = 0;
        }
        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[0], TOL);
        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[i], TOL);
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);

        // Test Coulomb forces
        
        const double q = 0.7;
        nonbonded->setParticleParameters(0, q, 1.5, 0);
        nonbonded->setParticleParameters(i, q, 1.5, 0);
        nonbonded->setExceptionParameters(first14, 0, 3, i == 3 ? q*q/1.2 : 0, 1.5, 0);
        nonbonded->setExceptionParameters(second14, 1, 4, 0, 1.5, 0);
        nonbonded->updateParametersInContext(context);
        state = context.getState(State::Forces | State::Energy);
        const vector<Vec3>& forces2 = state.getForces();
        force = ONE_4PI_EPS0*q*q/(r*r);
        energy = ONE_4PI_EPS0*q*q/r;
        if (i == 3) {
            force /= 1.2;
            energy /= 1.2;
        }
        if (i < 3 || r > cutoff) {
            force = 0;
            energy = 0;
        }
        ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces2[0], TOL);
        ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces2[i], TOL);
        ASSERT_EQUAL_TOL(energy, state.getPotentialEnergy(), TOL);
    }
}

void testPeriodic() {
    ReferencePlatform platform;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->addException(0, 1, 0.0, 1.0, 0.0);
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    const double cutoff = 2.0;
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(4, 0, 0), Vec3(0, 4, 0), Vec3(0, 0, 4));
    system.addForce(nonbonded);
    ASSERT(nonbonded->usesPeriodicBoundaryConditions());
    ASSERT(system.usesPeriodicBoundaryConditions());
    Context context(system, integrator, platform);
    vector<Vec3> positions(3);
    positions[0] = Vec3(0, 0, 0);
    positions[1] = Vec3(2, 0, 0);
    positions[2] = Vec3(3, 0, 0);
    context.setPositions(positions);
    State state = context.getState(State::Forces | State::Energy);
    const vector<Vec3>& forces = state.getForces();
    const double eps = 78.3;
    const double krf = (1.0/(cutoff*cutoff*cutoff))*(eps-1.0)/(2.0*eps+1.0);
    const double crf = (1.0/cutoff)*(3.0*eps)/(2.0*eps+1.0);
    const double force = ONE_4PI_EPS0*(1.0)*(1.0-2.0*krf*1.0);
    ASSERT_EQUAL_VEC(Vec3(force, 0, 0), forces[0], TOL);
    ASSERT_EQUAL_VEC(Vec3(-force, 0, 0), forces[1], TOL);
    ASSERT_EQUAL_VEC(Vec3(0, 0, 0), forces[2], TOL);
    ASSERT_EQUAL_TOL(2*ONE_4PI_EPS0*(1.0)*(1.0+krf*1.0-crf), state.getPotentialEnergy(), TOL);
}

void testTriclinic() {
    ReferencePlatform platform;
    System system;
    system.addParticle(1.0);
    system.addParticle(1.0);
    Vec3 a(3.1, 0, 0);
    Vec3 b(0.4, 3.5, 0);
    Vec3 c(-0.1, -0.5, 4.0);
    system.setDefaultPeriodicBoxVectors(a, b, c);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->addParticle(1.0, 1, 0);
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    const double cutoff = 1.5;
    nonbonded->setCutoffDistance(cutoff);
    system.addForce(nonbonded);
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    OpenMM_SFMT::SFMT sfmt;
    init_gen_rand(0, sfmt);
    const double eps = 78.3;
    const double krf = (1.0/(cutoff*cutoff*cutoff))*(eps-1.0)/(2.0*eps+1.0);
    const double crf = (1.0/cutoff)*(3.0*eps)/(2.0*eps+1.0);
    for (int iteration = 0; iteration < 50; iteration++) {
        // Generate random positions for the two particles.

        positions[0] = a*genrand_real2(sfmt) + b*genrand_real2(sfmt) + c*genrand_real2(sfmt);
        positions[1] = a*genrand_real2(sfmt) + b*genrand_real2(sfmt) + c*genrand_real2(sfmt);
        context.setPositions(positions);

        // Loop over all possible periodic copies and find the nearest one.

        Vec3 delta;
        double distance2 = 100.0;
        for (int i = -1; i < 2; i++)
            for (int j = -1; j < 2; j++)
                for (int k = -1; k < 2; k++) {
                    Vec3 d = positions[1]-positions[0]+a*i+b*j+c*k;
                    if (d.dot(d) < distance2) {
                        delta = d;
                        distance2 = d.dot(d);
                    }
                }
        double distance = sqrt(distance2);

        // See if the force and energy are correct.

        State state = context.getState(State::Forces | State::Energy);
        if (distance >= cutoff) {
            ASSERT_EQUAL(0.0, state.getPotentialEnergy());
            ASSERT_EQUAL_VEC(Vec3(0, 0, 0), state.getForces()[0], 0);
            ASSERT_EQUAL_VEC(Vec3(0, 0, 0), state.getForces()[1], 0);
        }
        else {
            const Vec3 force = delta*ONE_4PI_EPS0*(-1.0/(distance*distance*distance)+2.0*krf);
            ASSERT_EQUAL_TOL(ONE_4PI_EPS0*(1.0/distance+krf*distance*distance-crf), state.getPotentialEnergy(), TOL);
            ASSERT_EQUAL_VEC(force, state.getForces()[0], TOL);
            ASSERT_EQUAL_VEC(-force, state.getForces()[1], TOL);
        }
    }
}

void testDispersionCorrection() {
    // Create a box full of identical particles.

    int gridSize = 5;
    int numParticles = gridSize*gridSize*gridSize;
    double boxSize = gridSize*0.7;
    double cutoff = boxSize/3;
    ReferencePlatform platform;
    System system;
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    vector<Vec3> positions(numParticles);
    int index = 0;
    for (int i = 0; i < gridSize; i++)
        for (int j = 0; j < gridSize; j++)
            for (int k = 0; k < gridSize; k++) {
                system.addParticle(1.0);
                nonbonded->addParticle(0, 1.1, 0.5);
                positions[index] = Vec3(i*boxSize/gridSize, j*boxSize/gridSize, k*boxSize/gridSize);
                index++;
            }
    nonbonded->setNonbondedMethod(NonbondedForce::CutoffPeriodic);
    nonbonded->setCutoffDistance(cutoff);
    system.setDefaultPeriodicBoxVectors(Vec3(boxSize, 0, 0), Vec3(0, boxSize, 0), Vec3(0, 0, boxSize));
    system.addForce(nonbonded);
    ASSERT(nonbonded->usesPeriodicBoundaryConditions());
    ASSERT(system.usesPeriodicBoundaryConditions());

    // See if the correction has the correct value.

    Context context(system, integrator, platform);
    context.setPositions(positions);
    double energy1 = context.getState(State::Energy).getPotentialEnergy();
    nonbonded->setUseDispersionCorrection(false);
    context.reinitialize();
    context.setPositions(positions);
    double energy2 = context.getState(State::Energy).getPotentialEnergy();
    double term1 = (0.5*pow(1.1, 12)/pow(cutoff, 9))/9;
    double term2 = (0.5*pow(1.1, 6)/pow(cutoff, 3))/3;
    double expected = 8*M_PI*numParticles*numParticles*(term1-term2)/(boxSize*boxSize*boxSize);
    ASSERT_EQUAL_TOL(expected, energy1-energy2, 1e-4);

    // Now modify half the particles to be different, and see if it is still correct.

    int numType2 = 0;
    for (int i = 0; i < numParticles; i += 2) {
        nonbonded->setParticleParameters(i, 0, 1, 1);
        numType2++;
    }
    int numType1 = numParticles-numType2;
    nonbonded->updateParametersInContext(context);
    energy2 = context.getState(State::Energy).getPotentialEnergy();
    nonbonded->setUseDispersionCorrection(true);
    context.reinitialize();
    context.setPositions(positions);
    energy1 = context.getState(State::Energy).getPotentialEnergy();
    term1 = ((numType1*(numType1+1))/2)*(0.5*pow(1.1, 12)/pow(cutoff, 9))/9;
    term2 = ((numType1*(numType1+1))/2)*(0.5*pow(1.1, 6)/pow(cutoff, 3))/3;
    term1 += ((numType2*(numType2+1))/2)*(1*pow(1.0, 12)/pow(cutoff, 9))/9;
    term2 += ((numType2*(numType2+1))/2)*(1*pow(1.0, 6)/pow(cutoff, 3))/3;
    double combinedSigma = 0.5*(1+1.1);
    double combinedEpsilon = sqrt(1*0.5);
    term1 += (numType1*numType2)*(combinedEpsilon*pow(combinedSigma, 12)/pow(cutoff, 9))/9;
    term2 += (numType1*numType2)*(combinedEpsilon*pow(combinedSigma, 6)/pow(cutoff, 3))/3;
    term1 /= (numParticles*(numParticles+1))/2;
    term2 /= (numParticles*(numParticles+1))/2;
    expected = 8*M_PI*numParticles*numParticles*(term1-term2)/(boxSize*boxSize*boxSize);
    ASSERT_EQUAL_TOL(expected, energy1-energy2, 1e-4);
}

void testSwitchingFunction(NonbondedForce::NonbondedMethod method) {
    ReferencePlatform platform;
    System system;
    system.setDefaultPeriodicBoxVectors(Vec3(6, 0, 0), Vec3(0, 6, 0), Vec3(0, 0, 6));
    system.addParticle(1.0);
    system.addParticle(1.0);
    VerletIntegrator integrator(0.01);
    NonbondedForce* nonbonded = new NonbondedForce();
    nonbonded->addParticle(0, 1.2, 1);
    nonbonded->addParticle(0, 1.4, 2);
    nonbonded->setNonbondedMethod(method);
    nonbonded->setCutoffDistance(2.0);
    nonbonded->setUseSwitchingFunction(true);
    nonbonded->setSwitchingDistance(1.5);
    nonbonded->setUseDispersionCorrection(false);
    system.addForce(nonbonded);
    if (method == NonbondedForce::PME) {
        ASSERT(nonbonded->usesPeriodicBoundaryConditions());
        ASSERT(system.usesPeriodicBoundaryConditions());
    }
    else {
        ASSERT(!nonbonded->usesPeriodicBoundaryConditions());
        ASSERT(!system.usesPeriodicBoundaryConditions());
    }
    Context context(system, integrator, platform);
    vector<Vec3> positions(2);
    positions[0] = Vec3(0, 0, 0);
    double eps = SQRT_TWO;
    
    // Compute the interaction at various distances.
    
    for (double r = 1.0; r < 2.5; r += 0.1) {
        positions[1] = Vec3(r, 0, 0);
        context.setPositions(positions);
        State state = context.getState(State::Forces | State::Energy);
        
        // See if the energy is correct.
        
        double x = 1.3/r;
        double expectedEnergy = 4.0*eps*(std::pow(x, 12.0)-std::pow(x, 6.0));
        double switchValue;
        if (r <= 1.5)
            switchValue = 1;
        else if (r >= 2.0)
            switchValue = 0;
        else {
            double t = (r-1.5)/0.5;
            switchValue = 1+t*t*t*(-10+t*(15-t*6));
        }
        ASSERT_EQUAL_TOL(switchValue*expectedEnergy, state.getPotentialEnergy(), TOL);
        
        // See if the force is the gradient of the energy.
        
        double delta = 1e-3;
        positions[1] = Vec3(r-delta, 0, 0);
        context.setPositions(positions);
        double e1 = context.getState(State::Energy).getPotentialEnergy();
        positions[1] = Vec3(r+delta, 0, 0);
        context.setPositions(positions);
        double e2 = context.getState(State::Energy).getPotentialEnergy();
        ASSERT_EQUAL_TOL((e2-e1)/(2*delta), state.getForces()[0][0], 1e-3);
    }
}

int main() {
    try {
        testCoulomb();
        testLJ();
        testExclusionsAnd14();
        testCutoff();
        testCutoff14();
        testPeriodic();
        testTriclinic();
        testDispersionCorrection();
        testSwitchingFunction(NonbondedForce::CutoffNonPeriodic);
        testSwitchingFunction(NonbondedForce::PME);
    }
    catch(const exception& e) {
        cout << "exception: " << e.what() << endl;
        return 1;
    }
    cout << "Done" << endl;
    return 0;
}