// ******************************************************************************
   //
   // Title:       Force Field X.
   // Description: Force Field X - Software for Molecular Biophysics.
   // Copyright:   Copyright (c) Michael J. Schnieders 2001-2025.
   //
   // This file is part of Force Field X.
   //
   // Force Field X is free software; you can redistribute it and/or modify it
  // under the terms of the GNU General Public License version 3 as published by
  // the Free Software Foundation.
  //
  // Force Field X is distributed in the hope that it will be useful, but WITHOUT
  // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
  // FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
  // details.
  //
  // You should have received a copy of the GNU General Public License along with
  // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
  // Place, Suite 330, Boston, MA 02111-1307 USA
  //
  // Linking this library statically or dynamically with other modules is making a
  // combined work based on this library. Thus, the terms and conditions of the
  // GNU General Public License cover the whole combination.
  //
  // As a special exception, the copyright holders of this library give you
  // permission to link this library with independent modules to produce an
  // executable, regardless of the license terms of these independent modules, and
  // to copy and distribute the resulting executable under terms of your choice,
  // provided that you also meet, for each linked independent module, the terms
  // and conditions of the license of that module. An independent module is a
  // module which is not derived from or based on this library. If you modify this
  // library, you may extend this exception to your version of the library, but
  // you are not obligated to do so. If you do not wish to do so, delete this
  // exception statement from your version.
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  // ******************************************************************************
  package ffx.potential;
  
  import edu.rit.pj.ParallelRegion;
  import edu.rit.pj.ParallelSection;
  import edu.rit.pj.ParallelTeam;
  import ffx.crystal.Crystal;
  import ffx.crystal.CrystalPotential;
  import ffx.crystal.SymOp;
  import ffx.numerics.Potential;
  import ffx.numerics.switching.UnivariateSwitchingFunction;
  import ffx.potential.bonded.Atom;
  import ffx.potential.bonded.LambdaInterface;
  import ffx.potential.openmm.OpenMMEnergy;
  import ffx.potential.parameters.ForceField;
  import ffx.potential.utils.EnergyException;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.List;
  import java.util.logging.Level;
  import java.util.logging.Logger;
  
  import static ffx.crystal.SymOp.applyCartesianSymOp;
  import static ffx.crystal.SymOp.applyCartesianSymRot;
  import static ffx.crystal.SymOp.invertSymOp;
  import static ffx.potential.utils.Superpose.rmsd;
  import static ffx.utilities.StringUtils.parseAtomRanges;
  import static ffx.utilities.StringUtils.writeAtomRanges;
  import static java.lang.Double.parseDouble;
  import static java.lang.String.format;
  import static java.util.Arrays.fill;
  import static org.apache.commons.math3.util.FastMath.sqrt;
  
  /**
   * Compute the potential energy and derivatives for a dual-topology system.
   *
   * @author Michael J. Schnieders
   * @since 1.0
   */
  public class DualTopologyEnergy implements CrystalPotential, LambdaInterface {
  
    /**
     * Logger for the DualTopologyEnergy class.
     */
    private static final Logger logger = Logger.getLogger(DualTopologyEnergy.class.getName());
    /**
     * Shared atoms between topologies 1 and 2.
     */
    private final int nShared;
    /**
     * Total number of variables
     */
    private final int nVariables;
    /**
     * Region for computing energy/gradient in parallel.
     */
    private final EnergyRegion energyRegion;
    /**
     * Mass array for shared and softcore atoms.
     */
    private final double[] mass;
    /**
    * VARIABLE_TYPE array for shared and softcore atoms.
    */
   private final VARIABLE_TYPE[] variableTypes;
   /**
    * Coordinates for topology 1.
    */
   private final double[] x1;
   /**
    * Coordinates for topology 2.
    */
   private final double[] x2;
   /**
    * Topology 1 coordinate gradient.
    */
   private final double[] g1;
   /**
    * Topology 2 coordinate gradient.
    */
   private final double[] g2;
   /**
    * Topology 1 restraint gradient for end state bonded terms.
    */
   private final double[] rg1;
   /**
    * Topology 2 restraint gradient for end state bonded terms.
    */
   private final double[] rg2;
   /**
    * Topology 1 derivative of the coordinate gradient with respect to lambda.
    */
   private final double[] gl1;
   /**
    * Topology 2 derivative of the coordinate gradient with respect to lambda.
    */
   private final double[] gl2;
   /**
    * Topology 1 derivative of the coordinate gradient with respect to lambda for end state bonded
    * terms
    */
   private final double[] rgl1;
   /**
    * Topology 2 derivative of the coordinate gradient with respect to lambda for end state bonded
    * terms
    */
   private final double[] rgl2;
   /**
    * Topology 1 Potential.
    */
   private final CrystalPotential potential1;
   /**
    * Topology 2 Potential.
    */
   private final CrystalPotential potential2;
   /**
    * Topology 1 LambdaInterface.
    */
   private final LambdaInterface lambdaInterface1;
   /**
    * Topology 2 LambdaInterface.
    */
   private final LambdaInterface lambdaInterface2;
   /**
    * Topology 1 ForceFieldEnergy.
    */
   private final ForceFieldEnergy forceFieldEnergy1;
   /**
    * Topology 2 ForceFieldEnergy.
    */
   private final ForceFieldEnergy forceFieldEnergy2;
   /**
    * Number of active atoms in Topology 1.
    */
   private final int nActive1;
   /**
    * Number of active atoms in Topology 2.
    */
   private final int nActive2;
   /**
    * Array of active atoms in Topology 1.
    */
   private final Atom[] activeAtoms1;
   /**
    * Array of active atoms in Topology 2.
    */
   private final Atom[] activeAtoms2;
   /**
    * Flag is true if the atom is shared (not alchemical) for Topology 1.
    */
   private final boolean[] sharedAtoms1;
   /**
    * Flag is true if the atom is shared (not alchemical) for Topology 1.
    */
   private final boolean[] sharedAtoms2;
   /**
    * Will default to a power-1 PowerSwitch function.
    */
   private final UnivariateSwitchingFunction switchFunction;
   /**
    * Current potential energy of topology 1 (kcal/mol).
    */
   private double energy1 = 0;
   /**
    * Current potential energy of topology 2 (kcal/mol).
    */
   private double energy2 = 0;
   /**
    * ParallelTeam to execute the EnergyRegion.
    */
   private ParallelTeam parallelTeam;
   /**
    * Include a valence restraint energy for atoms being "disappeared."
    */
   private final boolean doValenceRestraint1;
   /**
    * Include a valence restraint energy for atoms being "disappeared."
    */
   private final boolean doValenceRestraint2;
   /**
    * Use System 1 Bonded Energy.
    */
   private final boolean useFirstSystemBondedEnergy;
   /**
    * End-state restraint energy of topology 1 (kcal/mol).
    */
   private double restraintEnergy1 = 0;
   /**
    * End-state restraint energy of topology 2 (kcal/mol).
    */
   private double restraintEnergy2 = 0;
   /**
    * dEdL of topology 1 (kcal/mol).
    */
   private double dEdL_1 = 0;
   /**
    * dEdL of topology 2 (kcal/mol).
    */
   private double dEdL_2 = 0;
   /**
    * End-state restraint dEdL of topology 1 (kcal/mol).
    */
   private double restraintdEdL_1 = 0;
   /**
    * End-state restraint dEdL of topology 2 (kcal/mol).
    */
   private double restraintdEdL_2 = 0;
   /**
    * d2EdL2 of topology 1 (kcal/mol).
    */
   private double d2EdL2_1 = 0;
   /**
    * d2EdL2 of topology 2 (kcal/mol).
    */
   private double d2EdL2_2 = 0;
   /**
    * End-state restraint d2EdL2 of topology 1 (kcal/mol).
    */
   private double restraintd2EdL2_1 = 0;
   /**
    * End-state restraint d2EdL2 of topology 2 (kcal/mol).
    */
   private double restraintd2EdL2_2 = 0;
   /**
    * Total energy of the dual topology, including lambda scaling.
    */
   private double totalEnergy = 0;
   /**
    * Current lambda value.
    */
   private double lambda = 1.0;
   /**
    * Value of the switching function at lambda.
    */
   private double f1L = 1.0;
   /**
    * Value of the switching function at (1-lambda).
    */
   private double f2L = 0.0;
   /**
    * First derivative with respect to lambda of the switching function.
    */
   private double dF1dL = 0.0;
   /**
    * First derivative with respect to (1-lambda) of the switching function.
    */
   private double dF2dL = 0.0;
   /**
    * Second derivative with respect to lambda of the switching function.
    */
   private double d2F1dL2 = 0.0;
   /**
    * Second derivative with respect to (1-lambda) of the switching function.
    */
   private double d2F2dL2 = 0.0;
   /**
    * Scaling array for shared and softcore atoms.
    */
   private double[] scaling = null;
   /**
    * State for calculating energies.
    */
   private STATE state = STATE.BOTH;
   /**
    * Symmetry operator to superimpose system 2 onto system 1
    */
   private SymOp[] symOp;
   /**
    * Symmetry operator to move system 2 back to original frame
    */
   private SymOp[] inverse;
   /**
    * Atom selection for each symmetry operator.
    */
   private final ArrayList<List<Integer>> symOpAtoms = new ArrayList<>();
   /**
    * Mask to determine which atoms a sym op will be applied.
    */
   private boolean[][] mask = null;
   /**
    * Utilize a provided SymOp
    */
   private boolean useSymOp = false;
 
   /**
    * Constructor for DualTopologyEnergy.
    *
    * @param topology1      a {@link ffx.potential.MolecularAssembly} object.
    * @param topology2      a {@link ffx.potential.MolecularAssembly} object.
    * @param switchFunction a {@link UnivariateSwitchingFunction} object.
    */
   public DualTopologyEnergy(
       MolecularAssembly topology1,
       MolecularAssembly topology2,
       UnivariateSwitchingFunction switchFunction) {
     forceFieldEnergy1 = topology1.getPotentialEnergy();
     forceFieldEnergy2 = topology2.getPotentialEnergy();
     potential1 = forceFieldEnergy1;
     potential2 = forceFieldEnergy2;
     lambdaInterface1 = forceFieldEnergy1;
     lambdaInterface2 = forceFieldEnergy2;
 
     /* Apom array for topology 1. */
     Atom[] atoms1 = topology1.getAtomArray();
     /* Atom array for topology 2. */
     Atom[] atoms2 = topology2.getAtomArray();
 
     ForceField forceField1 = topology1.getForceField();
     doValenceRestraint1 = forceField1.getBoolean("LAMBDA_VALENCE_RESTRAINTS", true);
     ForceField forceField2 = topology2.getForceField();
     doValenceRestraint2 = forceField2.getBoolean("LAMBDA_VALENCE_RESTRAINTS", true);
 
     useFirstSystemBondedEnergy = forceField2.getBoolean("USE_FIRST_SYSTEM_BONDED_ENERGY", false);
 
     // Check that all atoms that are not undergoing alchemy are common to both topologies.
     int shared1 = 0;
     int shared2 = 0;
     int activeCount1 = 0;
     int activeCount2 = 0;
     for (Atom a1 : atoms1) {
       if (a1.isActive()) {
         activeCount1++;
         if (!a1.applyLambda()) {
           shared1++;
         }
       }
     }
     for (Atom a2 : atoms2) {
       if (a2.isActive()) {
         activeCount2++;
         if (!a2.applyLambda()) {
           shared2++;
         }
       }
     }
     nActive1 = activeCount1;
     nActive2 = activeCount2;
     activeAtoms1 = new Atom[nActive1];
     activeAtoms2 = new Atom[nActive2];
     sharedAtoms1 = new boolean[nActive1];
     sharedAtoms2 = new boolean[nActive2];
     Arrays.fill(sharedAtoms1, true);
     Arrays.fill(sharedAtoms2, true);
     int index = 0;
     for (Atom a1 : atoms1) {
       if (a1.isActive()) {
         activeAtoms1[index] = a1;
         if (a1.applyLambda()) {
           // This atom is softcore with independent coordinates.
           sharedAtoms1[index] = false;
         }
         index++;
       }
     }
     index = 0;
     for (Atom a2 : atoms2) {
       if (a2.isActive()) {
         activeAtoms2[index] = a2;
         if (a2.applyLambda()) {
           // This atom is softcore with independent coordinates.
           sharedAtoms2[index] = false;
         }
         index++;
       }
     }
 
     assert (shared1 == shared2);
     nShared = shared1;
     /* Topology 1 number of softcore atoms. */
     int nSoftCore1 = nActive1 - nShared;
     /* Topology 2 number of softcore atoms. */
     int nSoftCore2 = nActive2 - nShared;
     /* Total number of softcore and shared atoms: nTotal = nShared + nSoftcore1 + nSoftcore2 */
     int nTotal = nShared + nSoftCore1 + nSoftCore2;
     nVariables = 3 * nTotal;
 
     // Allocate memory for coordinates and derivatives.
     x1 = new double[nActive1 * 3];
     x2 = new double[nActive2 * 3];
     g1 = new double[nActive1 * 3];
     g2 = new double[nActive2 * 3];
     rg1 = new double[nActive1 * 3];
     rg2 = new double[nActive2 * 3];
     gl1 = new double[nActive1 * 3];
     gl2 = new double[nActive2 * 3];
     rgl1 = new double[nActive1 * 3];
     rgl2 = new double[nActive2 * 3];
 
     // All variables are coordinates.
     index = 0;
     variableTypes = new VARIABLE_TYPE[nVariables];
     for (int i = 0; i < nTotal; i++) {
       variableTypes[index++] = VARIABLE_TYPE.X;
       variableTypes[index++] = VARIABLE_TYPE.Y;
       variableTypes[index++] = VARIABLE_TYPE.Z;
     }
 
     // Fill the mass array.
     int commonIndex = 0;
     int softcoreIndex = 3 * nShared;
     mass = new double[nVariables];
     for (int i = 0; i < nActive1; i++) {
       Atom a = activeAtoms1[i];
       double m = a.getMass();
       if (sharedAtoms1[i]) {
         mass[commonIndex++] = m;
         mass[commonIndex++] = m;
         mass[commonIndex++] = m;
       } else {
         mass[softcoreIndex++] = m;
         mass[softcoreIndex++] = m;
         mass[softcoreIndex++] = m;
       }
     }
     commonIndex = 0;
     for (int i = 0; i < nActive2; i++) {
       Atom a = activeAtoms2[i];
       double m = a.getMass();
       if (sharedAtoms2[i]) {
         for (int j = 0; j < 3; j++) {
           double massCommon = mass[commonIndex];
           massCommon = Math.max(massCommon, m);
           mass[commonIndex++] = massCommon;
         }
       } else {
         mass[softcoreIndex++] = m;
         mass[softcoreIndex++] = m;
         mass[softcoreIndex++] = m;
       }
     }
     energyRegion = new EnergyRegion();
     parallelTeam = new ParallelTeam(1);
 
     this.switchFunction = switchFunction;
     logger.info(format("\n Dual topology using switching function:\n  %s", switchFunction));
     logger.info(format(" Shared atoms: %d (1: %d of %d; 2: %d of %d)\n ", nShared, shared1, nActive1, shared2, nActive2));
     String symOpString = forceField2.getString("symop", null);
     if (symOpString != null) {
       readSymOp(symOpString);
     } else {
       // Both end-states will use the same crystal object.
       potential2.setCrystal(potential1.getCrystal());
       useSymOp = false;
       symOp = null;
       inverse = null;
     }
 
     // Check that all Dual-Topology atoms start with identical coordinates.
     int i1 = 0;
     int i2 = 0;
     // Not true if mapping atoms via symmetry operator.
     if (!useSymOp) {
       for (int i = 0; i < nShared; i++) {
         Atom a1 = atoms1[i1++];
         while (a1.applyLambda()) {
           a1 = atoms1[i1++];
         }
         Atom a2 = atoms2[i2++];
         while (a2.applyLambda()) {
           a2 = atoms2[i2++];
         }
         assert (a1.getX() == a2.getX());
         assert (a1.getY() == a2.getY());
         assert (a1.getZ() == a2.getZ());
         reconcileAtoms(a1, a2, Level.INFO);
       }
     }
   }
 
   /**
    * Temporary method to be used as a benchmark. Move to SymOp?
    *
    * @param symOpString String containing sym op.
    */
   private void readSymOp(String symOpString) {
     int numSymOps;
     try {
       String[] tokens = symOpString.split(" +");
       int numTokens = tokens.length;
       // Only need to move one system onto the other.
       if (numTokens == 12) {
         numSymOps = 1;
         symOp = new SymOp[numSymOps];
         inverse = new SymOp[numSymOps];
         // Assume applies to all atoms...
         symOpAtoms.add(parseAtomRanges("symmetryAtoms", "1-N", nActive2));
         // Twelve values makes 1 sym op. so assign to [0][0].
         symOp[0] = new SymOp(new double[][]{
             {parseDouble(tokens[0]), parseDouble(tokens[1]), parseDouble(tokens[2])},
             {parseDouble(tokens[3]), parseDouble(tokens[4]), parseDouble(tokens[5])},
             {parseDouble(tokens[6]), parseDouble(tokens[7]), parseDouble(tokens[8])}},
             new double[]{parseDouble(tokens[9]), parseDouble(tokens[10]), parseDouble(tokens[11])});
       } else if (numTokens % 14 == 0) {
         numSymOps = numTokens / 14;
         symOp = new SymOp[numSymOps];
         inverse = new SymOp[numSymOps];
         if (logger.isLoggable(Level.FINER)) {
           logger.finer(format(" Number of Tokens: %3d Number of Sym Ops: %2d", numTokens, numSymOps));
         }
         for (int i = 0; i < numSymOps; i++) {
           int j = i * 14;
           // Should be tokens[j] or tokens[j+1]?? Switches forward vs backward...
           symOpAtoms.add(parseAtomRanges("symmetryAtoms", tokens[j], nActive2));
           symOp[i] = new SymOp(new double[][]{
               {parseDouble(tokens[j + 2]), parseDouble(tokens[j + 3]), parseDouble(tokens[j + 4])},
               {parseDouble(tokens[j + 5]), parseDouble(tokens[j + 6]), parseDouble(tokens[j + 7])},
               {parseDouble(tokens[j + 8]), parseDouble(tokens[j + 9]), parseDouble(tokens[j + 10])}},
               new double[]{parseDouble(tokens[j + 11]), parseDouble(tokens[j + 12]), parseDouble(tokens[j + 13])});
         }
       } else {
         logger.warning(format(" Provided symmetry operator is formatted incorrectly. Should have 12 or 14 entries, but found %3d.", numTokens));
         return;
       }
       useSymOp = true;
       // Define mask(s) needed to apply sym ops.
       mask = new boolean[numSymOps][nActive2];
       // Mask(s) used locally to check symmetry operator overlap.
       boolean[][] sharedMask = new boolean[numSymOps][nShared];
       for (int i = 0; i < numSymOps; i++) {
         List<Integer> symAtoms = symOpAtoms.get(i);
         for (int atom : symAtoms) {
           if (sharedAtoms2[atom]) {
             mask[i][atom] = true;
           }
         }
         // TODO: Condense with loop above by replacing nActive2 with incremental index?
         int sharedIndex = 0;
         for (int j = 0; j < nActive2; j++) {
           if (sharedAtoms2[j]) {
             if (mask[i][j]) {
               sharedMask[i][sharedIndex] = true;
             }
             sharedIndex++;
           }
         }
       }
 
       // Get the coordinates for active atoms.
       potential1.getCoordinates(x1);
       potential2.getCoordinates(x2);
 
       // Collect coordinates for shared atoms (remove alchemical atoms from the superposition).
       double[] x1Shared = new double[nShared * 3];
       double[] x2Shared = new double[nShared * 3];
       int sharedIndex = 0;
       for (int i = 0; i < nActive1; i++) {
         if (sharedAtoms1[i]) {
           int index = i * 3;
           x1Shared[sharedIndex++] = x1[index];
           x1Shared[sharedIndex++] = x1[index + 1];
           x1Shared[sharedIndex++] = x1[index + 2];
         }
       }
       sharedIndex = 0;
       for (int i = 0; i < nActive2; i++) {
         if (sharedAtoms2[i]) {
           int index = i * 3;
           x2Shared[sharedIndex++] = x2[index];
           x2Shared[sharedIndex++] = x2[index + 1];
           x2Shared[sharedIndex++] = x2[index + 2];
         }
       }
 
       double origRMSD = rmsd(x1Shared, x2Shared, mass);
       logger.info("\n RMSD to topology 2 coordinates from input file:");
       logger.info(format(" RMSD: %12.3f A", origRMSD));
 
       // Get a fresh copy of the original coordinates.
       double[] origX1 = Arrays.copyOf(x1Shared, nShared * 3);
       double[] origX2 = Arrays.copyOf(x2Shared, nShared * 3);
 
       // Determine if first topology or second?
       // Explicitly written (as opposed to applySymOp()) since only applied to shared atoms.
       for (int i = 0; i < numSymOps; i++) {
         // Transpose == inverse for orthogonal matrices (value needed later).
         inverse[i] = invertSymOp(symOp[i]);
         // Apply symOp to appropriate coords (validity check).
         // Applied to topology 1 to generate approximate coordinates for topology 2.
         applyCartesianSymOp(origX1, origX1, symOp[i], sharedMask[i]);
         logger.info(format("\n SymOp %3d of %3d between topologies:\n Applied to atoms: %s\n %s\n Inverse SymOp:\n %s",
             i + 1, numSymOps, writeAtomRanges(symOpAtoms.get(i).stream().mapToInt(j -> j).toArray()), symOp[i].toString(), inverse[i].toString()));
       }
       double symOpRMSD = rmsd(origX1, origX2, mass);
       logger.info("\n RMSD to topology 2 coordinates via loaded symop:");
       logger.info(format(" RMSD: %12.3f A", symOpRMSD));
 
       // TODO: Validate 0th order check for alchemical atoms (i.e., not bonded between sym ops).
       logger.info("\n Checking alchemical atoms for system 1:");
       validateAlchemicalAtoms(nActive1, sharedAtoms1, activeAtoms1);
       logger.info(" Checking alchemical atoms for system 2:");
       validateAlchemicalAtoms(nActive2, sharedAtoms2, activeAtoms2);
 
       if (logger.isLoggable(Level.FINE)) {
         for (int i = 0; i < nShared; i++) {
           int i3 = i * 3;
           double rmsd = rmsd(new double[]{origX1[i3], origX1[i3 + 1], origX1[i3 + 2]}, new double[]{origX2[i3], origX2[i3 + 1], origX2[i3 + 2]}, new double[]{mass[i]});
           if (rmsd > 0.5) {
             logger.fine(format(" Shared atom %3d has a distance of %8.3f", i + 1, rmsd));
           }
         }
       }
     } catch (Exception ex) {
       logger.severe(" Error parsing SymOp for Dual Topology:\n (" + symOpString + ")" + Utilities.stackTraceToString(ex));
     }
   }
 
   /**
    * {@inheritDoc}
    *
    * <p>Returns true if both force field energies are zero at the ends, and the switching function's
    * first derivative is zero at the end bounds.
    */
   @Override
   public boolean dEdLZeroAtEnds() {
     if (!forceFieldEnergy1.dEdLZeroAtEnds() || !forceFieldEnergy2.dEdLZeroAtEnds()) {
       return false;
     }
     return (switchFunction.highestOrderZeroDerivativeAtZeroBound() > 0);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public boolean destroy() {
     boolean ffe1Destroy = forceFieldEnergy1.destroy();
     boolean ffe2Destroy = forceFieldEnergy2.destroy();
     try {
       if (parallelTeam != null) {
         parallelTeam.shutdown();
       }
       return ffe1Destroy && ffe2Destroy;
     } catch (Exception ex) {
       logger.warning(format(" Exception in shutting down DualTopologyEnergy: %s", ex));
       logger.info(Utilities.stackTraceToString(ex));
       return false;
     }
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double energy(double[] x) {
     return energy(x, false);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double energy(double[] x, boolean verbose) {
     try {
       energyRegion.setX(x);
       energyRegion.setVerbose(verbose);
       parallelTeam.execute(energyRegion);
     } catch (Exception ex) {
       throw new EnergyException(format(" Exception in calculating dual-topology energy: %s", ex));
     }
     return totalEnergy;
   }
 
   /**
    * {@inheritDoc}
    *
    * <p>The coordinate and gradient arrays are unpacked/packed based on the dual topology.
    */
   @Override
   public double energyAndGradient(double[] x, double[] g) {
     return energyAndGradient(x, g, false);
   }
 
   /**
    * {@inheritDoc}
    *
    * <p>The coordinate and gradient arrays are unpacked/packed based on the dual topology.
    */
   @Override
   public double energyAndGradient(double[] x, double[] g, boolean verbose) {
     assert Arrays.stream(x).allMatch(Double::isFinite);
     try {
       energyRegion.setX(x);
       energyRegion.setG(g);
       energyRegion.setVerbose(verbose);
       parallelTeam.execute(energyRegion);
     } catch (Exception ex) {
       throw new EnergyException(format(" Exception in calculating dual-topology energy: %s", ex));
     }
     return totalEnergy;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getAcceleration(double[] acceleration) {
     if (acceleration == null || acceleration.length < nVariables) {
       acceleration = new double[nVariables];
     }
     int indexCommon = 0;
     int indexUnique = nShared * 3;
     double[] accel = new double[3];
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       atom.getAcceleration(accel);
       if (sharedAtoms1[i]) {
         acceleration[indexCommon++] = accel[0];
         acceleration[indexCommon++] = accel[1];
         acceleration[indexCommon++] = accel[2];
       } else {
         acceleration[indexUnique++] = accel[0];
         acceleration[indexUnique++] = accel[1];
         acceleration[indexUnique++] = accel[2];
       }
     }
     for (int i = 0; i < nActive2; i++) {
       if (!sharedAtoms2[i]) {
         Atom atom = activeAtoms2[i];
         atom.getAcceleration(accel);
         acceleration[indexUnique++] = accel[0];
         acceleration[indexUnique++] = accel[1];
         acceleration[indexUnique++] = accel[2];
       }
     }
 
     return acceleration;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getCoordinates(double[] x) {
     if (x == null) {
       x = new double[nVariables];
     }
     int indexCommon = 0;
     int indexUnique = nShared * 3;
     for (int i = 0; i < nActive1; i++) {
       Atom a = activeAtoms1[i];
       if (sharedAtoms1[i]) {
         x[indexCommon++] = a.getX();
         x[indexCommon++] = a.getY();
         x[indexCommon++] = a.getZ();
       } else {
         x[indexUnique++] = a.getX();
         x[indexUnique++] = a.getY();
         x[indexUnique++] = a.getZ();
       }
     }
     for (int i = 0; i < nActive2; i++) {
       if (!sharedAtoms2[i]) {
         Atom a = activeAtoms2[i];
         x[indexUnique++] = a.getX();
         x[indexUnique++] = a.getY();
         x[indexUnique++] = a.getZ();
       }
     }
     return x;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public Crystal getCrystal() {
     // TODO: Handle the case where each system has a unique crystal instance (e.g., different space groups).
     if (useSymOp && logger.isLoggable(Level.FINE)) {
       logger.fine(" Get method only returned first crystal.");
     }
     return potential1.getCrystal();
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setCrystal(Crystal crystal) {
     // TODO: Handle the case where each system has a unique crystal instance (e.g., different space groups).
     if (useSymOp && logger.isLoggable(Level.FINE)) {
       logger.fine(" Both systems set to the same crystal.");
     }
     potential1.setCrystal(crystal);
     potential2.setCrystal(crystal);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public STATE getEnergyTermState() {
     return state;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setEnergyTermState(STATE state) {
     this.state = state;
     potential1.setEnergyTermState(state);
     potential2.setEnergyTermState(state);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double getLambda() {
     return lambda;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setLambda(double lambda) {
     if (lambda <= 1.0 && lambda >= 0.0) {
       this.lambda = lambda;
       double oneMinusLambda = 1.0 - lambda;
       lambdaInterface1.setLambda(lambda);
       lambdaInterface2.setLambda(oneMinusLambda);
 
       f1L = switchFunction.valueAt(lambda);
       dF1dL = switchFunction.firstDerivative(lambda);
       d2F1dL2 = switchFunction.secondDerivative(lambda);
 
       f2L = switchFunction.valueAt(oneMinusLambda);
       dF2dL = -1.0 * switchFunction.firstDerivative(oneMinusLambda);
       d2F2dL2 = switchFunction.secondDerivative(oneMinusLambda);
     } else {
       String message = format("Lambda value %8.3f is not in the range [0..1].", lambda);
       throw new IllegalArgumentException(message);
     }
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getMass() {
     return mass;
   }
 
   /**
    * Returns the number of shared variables (3 * number of shared atoms).
    *
    * @return An int
    */
   public int getNumSharedVariables() {
     return 3 * nShared;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public int getNumberOfVariables() {
     return nVariables;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getPreviousAcceleration(double[] previousAcceleration) {
     if (previousAcceleration == null || previousAcceleration.length < nVariables) {
       previousAcceleration = new double[nVariables];
     }
     int indexCommon = 0;
     int indexUnique = nShared * 3;
     double[] prev = new double[3];
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       atom.getPreviousAcceleration(prev);
       if (sharedAtoms1[i]) {
         previousAcceleration[indexCommon++] = prev[0];
         previousAcceleration[indexCommon++] = prev[1];
         previousAcceleration[indexCommon++] = prev[2];
       } else {
         previousAcceleration[indexUnique++] = prev[0];
         previousAcceleration[indexUnique++] = prev[1];
         previousAcceleration[indexUnique++] = prev[2];
       }
     }
     for (int i = 0; i < nActive2; i++) {
       Atom atom = activeAtoms2[i];
       if (!sharedAtoms2[i]) {
         atom.getPreviousAcceleration(prev);
         previousAcceleration[indexUnique++] = prev[0];
         previousAcceleration[indexUnique++] = prev[1];
         previousAcceleration[indexUnique++] = prev[2];
       }
     }
 
     return previousAcceleration;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getScaling() {
     return scaling;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setScaling(double[] scaling) {
     this.scaling = scaling;
   }
 
   /**
    * Returns the switching function used by this DualTopologyEnergy; presently, switching functions
    * are immutable, and cannot be changed once a DualTopologyEnergy is constructed.
    *
    * @return The switching function.
    */
   public UnivariateSwitchingFunction getSwitch() {
     return switchFunction;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double getTotalEnergy() {
     return totalEnergy;
   }
 
   @Override
   public List<Potential> getUnderlyingPotentials() {
     List<Potential> under = new ArrayList<>(2);
     under.add(forceFieldEnergy1);
     under.add(forceFieldEnergy2);
     under.addAll(forceFieldEnergy1.getUnderlyingPotentials());
     under.addAll(forceFieldEnergy2.getUnderlyingPotentials());
     return under;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public VARIABLE_TYPE[] getVariableTypes() {
     return variableTypes;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double[] getVelocity(double[] velocity) {
     if (velocity == null || velocity.length < nVariables) {
       velocity = new double[nVariables];
     }
     int indexCommon = 0;
     int indexUnique = nShared * 3;
     double[] vel = new double[3];
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       atom.getVelocity(vel);
       if (sharedAtoms1[i]) {
         velocity[indexCommon++] = vel[0];
         velocity[indexCommon++] = vel[1];
         velocity[indexCommon++] = vel[2];
       } else {
         velocity[indexUnique++] = vel[0];
         velocity[indexUnique++] = vel[1];
         velocity[indexUnique++] = vel[2];
       }
     }
     for (int i = 0; i < nActive2; i++) {
       if (!sharedAtoms2[i]) {
         Atom atom = activeAtoms2[i];
         atom.getVelocity(vel);
         velocity[indexUnique++] = vel[0];
         velocity[indexUnique++] = vel[1];
         velocity[indexUnique++] = vel[2];
       }
     }
 
     return velocity;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double getd2EdL2() {
     double e1 =
         f1L * d2EdL2_1
             + 2.0 * dF1dL * dEdL_1
             + d2F1dL2 * energy1
             + f2L * restraintd2EdL2_1
             + 2.0 * dF2dL * restraintdEdL_1
             + d2F2dL2 * restraintEnergy1;
     double e2;
     if (!useFirstSystemBondedEnergy) {
       e2 = f2L * d2EdL2_2
           + 2.0 * dF2dL * dEdL_2
           + d2F2dL2 * energy2
           + f1L * restraintd2EdL2_2
           + 2.0 * dF1dL * restraintdEdL_2
           + d2F1dL2 * restraintEnergy2;
     } else {
       e2 = f2L * d2EdL2_2
           + 2.0 * dF2dL * dEdL_2
           + d2F2dL2 * energy2
           - f2L * restraintd2EdL2_2
           - 2.0 * dF2dL * restraintdEdL_2
           - d2F2dL2 * restraintEnergy2;
     }
     return e1 + e2;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public double getdEdL() {
     // Subtraction is implicit, as dEdL_2 and dF2dL are both multiplied by
     // negative 1 when set.
     double e1 = f1L * dEdL_1 + dF1dL * energy1 + f2L * restraintdEdL_1 + dF2dL * restraintEnergy1;
     double e2;
     if (!useFirstSystemBondedEnergy) {
       e2 = f2L * dEdL_2 + dF2dL * energy2 + f1L * restraintdEdL_2 + dF1dL * restraintEnergy2;
     } else {
       e2 = f2L * dEdL_2 + dF2dL * energy2 - f2L * restraintdEdL_2 - dF2dL * restraintEnergy2;
     }
     return e1 + e2;
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void getdEdXdL(double[] g) {
     if (g == null) {
       g = new double[nVariables];
     }
 
     int index = 0;
     int indexCommon = 0;
     int indexUnique = nShared * 3;
     // Coordinate Gradient from Topology 1.
     for (int i = 0; i < nActive1; i++) {
       if (sharedAtoms1[i]) {
         g[indexCommon++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
         g[indexCommon++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
         g[indexCommon++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
       } else {
         g[indexUnique++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
         g[indexUnique++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
         g[indexUnique++] =
             f1L * gl1[index] + dF1dL * g1[index] + f2L * rgl1[index] + dF2dL * rg1[index++];
       }
     }
 
     // Coordinate Gradient from Topology 2.
     if (!useFirstSystemBondedEnergy) {
       index = 0;
       indexCommon = 0;
       for (int i = 0; i < nActive2; i++) {
         if (sharedAtoms2[i]) {
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
         } else {
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] - f1L * rgl2[index]
               + dF1dL * rg2[index++]);
         }
       }
     } else {
       index = 0;
       indexCommon = 0;
       for (int i = 0; i < nActive2; i++) {
         if (sharedAtoms2[i]) {
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
           g[indexCommon++] += (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
         } else {
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
           g[indexUnique++] = (-f2L * gl2[index] + dF2dL * g2[index] + f2L * rgl2[index]
               - dF2dL * rg2[index++]);
         }
       }
 
     }
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setAcceleration(double[] acceleration) {
     double[] accel = new double[3];
     int indexCommon = 0;
     int indexUnique = 3 * nShared;
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       if (sharedAtoms1[i]) {
         accel[0] = acceleration[indexCommon++];
         accel[1] = acceleration[indexCommon++];
         accel[2] = acceleration[indexCommon++];
       } else {
         accel[0] = acceleration[indexUnique++];
         accel[1] = acceleration[indexUnique++];
         accel[2] = acceleration[indexUnique++];
       }
       atom.setAcceleration(accel);
     }
     indexCommon = 0;
     for (int i = 0; i < nActive2; i++) {
       Atom atom = activeAtoms2[i];
       if (sharedAtoms2[i]) {
         accel[0] = acceleration[indexCommon++];
         accel[1] = acceleration[indexCommon++];
         accel[2] = acceleration[indexCommon++];
       } else {
         accel[0] = acceleration[indexUnique++];
         accel[1] = acceleration[indexUnique++];
         accel[2] = acceleration[indexUnique++];
       }
       atom.setAcceleration(accel);
     }
   }
 
   /**
    * setParallel.
    *
    * @param parallel a boolean.
    */
   public void setParallel(boolean parallel) {
     if (parallelTeam != null) {
       try {
         parallelTeam.shutdown();
       } catch (Exception e) {
         logger.severe(format(" Exception in shutting down old ParallelTeam for DualTopologyEnergy: %s", e));
       }
     }
     parallelTeam = parallel ? new ParallelTeam(2) : new ParallelTeam(1);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setPreviousAcceleration(double[] previousAcceleration) {
     double[] prev = new double[3];
     int indexCommon = 0;
     int indexUnique = 3 * nShared;
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       if (sharedAtoms1[i]) {
         prev[0] = previousAcceleration[indexCommon++];
         prev[1] = previousAcceleration[indexCommon++];
         prev[2] = previousAcceleration[indexCommon++];
       } else {
         prev[0] = previousAcceleration[indexUnique++];
         prev[1] = previousAcceleration[indexUnique++];
         prev[2] = previousAcceleration[indexUnique++];
       }
       atom.setPreviousAcceleration(prev);
     }
     indexCommon = 0;
     for (int i = 0; i < nActive2; i++) {
       Atom atom = activeAtoms2[i];
       if (sharedAtoms2[i]) {
         prev[0] = previousAcceleration[indexCommon++];
         prev[1] = previousAcceleration[indexCommon++];
         prev[2] = previousAcceleration[indexCommon++];
       } else {
         prev[0] = previousAcceleration[indexUnique++];
         prev[1] = previousAcceleration[indexUnique++];
         prev[2] = previousAcceleration[indexUnique++];
       }
       atom.setPreviousAcceleration(prev);
     }
   }
 
   /**
    * Sets the printOnFailure flag; if override is true, over-rides any existing property. Essentially
    * sets the default value of printOnFailure for an algorithm. For example, rotamer optimization
    * will generally run into force field issues in the normal course of execution as it tries
    * unphysical self and pair configurations, so the algorithm should not print out a large number of
    * error PDBs.
    *
    * @param onFail   To set
    * @param override Override properties
    */
   public void setPrintOnFailure(boolean onFail, boolean override) {
     forceFieldEnergy1.setPrintOnFailure(onFail, override);
     forceFieldEnergy2.setPrintOnFailure(onFail, override);
   }
 
   /**
    * {@inheritDoc}
    */
   @Override
   public void setVelocity(double[] velocity) {
     double[] vel = new double[3];
     int indexCommon = 0;
     int indexUnique = 3 * nShared;
     for (int i = 0; i < nActive1; i++) {
       Atom atom = activeAtoms1[i];
       if (sharedAtoms1[i]) {
         vel[0] = velocity[indexCommon++];
         vel[1] = velocity[indexCommon++];
         vel[2] = velocity[indexCommon++];
       } else {
         vel[0] = velocity[indexUnique++];
         vel[1] = velocity[indexUnique++];
         vel[2] = velocity[indexUnique++];
       }
       atom.setVelocity(vel);
     }
 
     indexCommon = 0;
     for (int i = 0; i < nActive2; i++) {
       Atom atom = activeAtoms2[i];
       if (sharedAtoms2[i]) {
         vel[0] = velocity[indexCommon++];
         vel[1] = velocity[indexCommon++];
         vel[2] = velocity[indexCommon++];
       } else {
         vel[0] = velocity[indexUnique++];
         vel[1] = velocity[indexUnique++];
         vel[2] = velocity[indexUnique++];
       }
       atom.setVelocity(vel);
     }
   }
 
   /**
    * Moves two shared atoms together if there is a small discrepancy (such as that caused by the
    * mutator script).
    *
    * @param a1      Atom from topology 1
    * @param a2      Atom from topology 2
    * @param warnlev Logging level to use when warning about small movements
    */
   private void reconcileAtoms(Atom a1, Atom a2, Level warnlev) {
     double dist = 0;
     double[] xyz1 = a1.getXYZ(null);
     double[] xyz2 = a2.getXYZ(null);
     double[] xyzAv = new double[3];
     for (int i = 0; i < 3; i++) {
       double dx = xyz1[i] - xyz2[i];
       dist += (dx * dx);
       xyzAv[i] = xyz1[i] + (0.5 * dx);
     }
 
     // Square of the maximum distance permissible between two shared atoms.
     double maxDist2 = 0.09;
 
     /*
      Square of the minimum distance between shared atoms which will cause a
      warning. Intended to cover anything larger than a rounding error.
     */
     double minDistWarn2 = 0.00001;
 
     if (dist > maxDist2) {
       logger.log(
           Level.SEVERE,
           format(
               " Distance between atoms %s " + "and %s is %7.4f >> maximum allowed %7.4f",
               a1, a2, sqrt(dist), sqrt(maxDist2)));
     } else if (dist > minDistWarn2) {
       logger.log(
           warnlev,
           format(
               " Distance between atoms %s " + "and %s is %7.4f; moving atoms together.",
               a1, a2, sqrt(dist)));
       a1.setXYZ(xyzAv);
       a2.setXYZ(xyzAv);
     } else if (dist > 0) {
       // Silently move them together; probably just a rounding error.
       a1.setXYZ(xyzAv);
       a2.setXYZ(xyzAv);
     }
   }
 
   private void packGradient(double[] x, double[] g) {
     if (g == null) {
       g = new double[nVariables];
     }
     int indexCommon = 0;
     int indexUnique = nShared * 3;
 
     // Coordinate Gradient from Topology 1.
     int index = 0;
     for (int i = 0; i < nActive1; i++) {
       if (sharedAtoms1[i]) {
         g[indexCommon++] = f1L * g1[index] + f2L * rg1[index++];
         g[indexCommon++] = f1L * g1[index] + f2L * rg1[index++];
         g[indexCommon++] = f1L * g1[index] + f2L * rg1[index++];
       } else {
         g[indexUnique++] = f1L * g1[index] + f2L * rg1[index++];
         g[indexUnique++] = f1L * g1[index] + f2L * rg1[index++];
         g[indexUnique++] = f1L * g1[index] + f2L * rg1[index++];
       }
     }
 
     if (!useFirstSystemBondedEnergy) {
       // Coordinate Gradient from Topology 2.
       indexCommon = 0;
       index = 0;
       for (int i = 0; i < nActive2; i++) {
         if (sharedAtoms2[i]) {
           g[indexCommon++] += f2L * g2[index] + f1L * rg2[index++];
           g[indexCommon++] += f2L * g2[index] + f1L * rg2[index++];
           g[indexCommon++] += f2L * g2[index] + f1L * rg2[index++];
         } else {
           g[indexUnique++] = f2L * g2[index] + f1L * rg2[index++];
           g[indexUnique++] = f2L * g2[index] + f1L * rg2[index++];
           g[indexUnique++] = f2L * g2[index] + f1L * rg2[index++];
         }
       }
     } else {
       // Coordinate Gradient from Topology 2.
       indexCommon = 0;
       index = 0;
       for (int i = 0; i < nActive2; i++) {
         if (sharedAtoms2[i]) {
           g[indexCommon++] += f2L * g2[index] - f2L * rg2[index++];
           g[indexCommon++] += f2L * g2[index] - f2L * rg2[index++];
           g[indexCommon++] += f2L * g2[index] - f2L * rg2[index++];
         } else {
           g[indexUnique++] = f2L * g2[index] - f2L * rg2[index++];
           g[indexUnique++] = f2L * g2[index] - f2L * rg2[index++];
           g[indexUnique++] = f2L * g2[index] - f2L * rg2[index++];
         }
       }
     }
 
     scaleCoordinatesAndGradient(x, g);
   }
 
   private void unpackCoordinates(double[] x) {
 
     // Unscale the coordinates.
     unscaleCoordinates(x);
 
     int index = 0;
     int indexCommon = 0;
     int indexUnique = 3 * nShared;
     for (int i = 0; i < nActive1; i++) {
       if (sharedAtoms1[i]) {
         x1[index++] = x[indexCommon++];
         x1[index++] = x[indexCommon++];
         x1[index++] = x[indexCommon++];
       } else {
         x1[index++] = x[indexUnique++];
         x1[index++] = x[indexUnique++];
         x1[index++] = x[indexUnique++];
       }
     }
 
     index = 0;
     indexCommon = 0;
     for (int i = 0; i < nActive2; i++) {
       if (sharedAtoms2[i]) {
         x2[index++] = x[indexCommon++];
         x2[index++] = x[indexCommon++];
         x2[index++] = x[indexCommon++];
       } else {
         x2[index++] = x[indexUnique++];
         x2[index++] = x[indexUnique++];
         x2[index++] = x[indexUnique++];
       }
     }
   }
 
   /**
    * Reload the common atomic masses. Intended for quad-topology dual force field corrections, where
    * common atoms may have slightly different masses; this was found to be the case between AMOEBA
    * 2013 and AMBER99SB carbons.
    *
    * @param secondTopology Load from second topology
    */
   void reloadCommonMasses(boolean secondTopology) {
     int commonIndex = 0;
     if (secondTopology) {
       for (int i = 0; i < nActive2; i++) {
         Atom a = activeAtoms2[i];
         double m = a.getMass();
         if (sharedAtoms2[i]) {
           mass[commonIndex++] = m;
           mass[commonIndex++] = m;
           mass[commonIndex++] = m;
         }
       }
     } else {
       for (int i = 0; i < nActive1; i++) {
         Atom a = activeAtoms1[i];
         double m = a.getMass();
         if (sharedAtoms1[i]) {
           mass[commonIndex++] = m;
           mass[commonIndex++] = m;
           mass[commonIndex++] = m;
         }
       }
     }
   }
 
   /**
    * Bonded terms for alchemical atoms are used to prevent them from being unconstrained.
    * These restraints have the potential to interact with symmetry operators applied in dual-topology simulations.
    *
    * @param nActive     Number of active atoms (shared and alchemical) in simulation for this system.
    * @param sharedAtoms Mask to determined which atoms are shared vs alchemical.
    * @param activeAtoms Active atoms for this simulation.
    */
   private void validateAlchemicalAtoms(int nActive, boolean[] sharedAtoms, Atom[] activeAtoms) {
     int numSymOps = symOpAtoms.size();
     // Loop through atoms in simulation.
     for (int i = 0; i < nActive; i++) {
       // Determine if this atom is alchemical.
       if (!sharedAtoms[i]) {
         Atom alchAtom = activeAtoms[i];
         int symOpForAlchemicalAtom = -1;
         for (int j = 0; j < numSymOps; j++) {
           List<Integer> symOpAtomGroup = symOpAtoms.get(j);
           if (symOpAtomGroup.contains(i)) {
             symOpForAlchemicalAtom = j;
             break;
           }
         }
 
         StringBuilder sb = new StringBuilder();
         sb.append(format("\n Alchemical atom %s\n Symmetry group %s:\n", alchAtom, symOpForAlchemicalAtom + 1));
         List<Integer> symOpAtomGroup = symOpAtoms.get(symOpForAlchemicalAtom);
         for (Integer j : symOpAtomGroup) {
           if (j == i) {
             continue;
           }
           sb.append(format("  %d %s\n", j + 1, activeAtoms[j]));
         }
         sb.append(format("\n 1-2, 1-3 or 1-4 atoms in other symmetry groups:\n"));
 
         // Collect atoms that are 1-2, 1-3 or 1-4 to the alchemical atom.
         ArrayList<Integer> bondedAtoms = new ArrayList<>();
         addUniqueBondedIndices(bondedAtoms, alchAtom.get12List());
         addUniqueBondedIndices(bondedAtoms, alchAtom.get13List());
         addUniqueBondedIndices(bondedAtoms, alchAtom.get14List());
         // Loop through atoms bonded to alchemical atom to determine if they're part of
         // a different SymOp group.
         boolean conflict = false;
         for (int j = 0; j < numSymOps; j++) {
           // If the bonded atom is in the same symmetry group as the alchemical atom, then there is no conflict.
           if (j == symOpForAlchemicalAtom) {
             continue;
           }
           symOpAtomGroup = symOpAtoms.get(j);
           for (Integer integer : bondedAtoms) {
             if (symOpAtomGroup.contains(integer)) {
               conflict = true;
               sb.append(format("  %d %s uses symmetry group %2d.\n", integer + 1, activeAtoms[integer], j + 1));
             }
           }
         }
         if (conflict) {
           logger.info(sb.toString());
         }
       }
     }
   }
 
   /**
    * Take list of aggregated unique indices based on input list of bonded atoms..
    *
    * @param uniqueIndices List of unique indices of bonded atoms.
    * @param bondedAtoms   Atoms that are bonded to the atom of interest.
    */
   private void addUniqueBondedIndices(ArrayList<Integer> uniqueIndices, List<Atom> bondedAtoms) {
     // Loop through bonded atoms
     for (Atom a : bondedAtoms) {
       int index = a.getIndex() - 1;
       // Determine if bonded atom's index is already in unique list.
       if (!uniqueIndices.contains(index)) {
         // Add to list if it is not already included.
         uniqueIndices.add(index);
       }
     }
   }
 
   private class EnergyRegion extends ParallelRegion {
 
     private final Energy1Section e1sect;
     private final Energy2Section e2sect;
     private double[] x;
     private double[] g;
     private boolean gradient = false;
     private boolean verbose = false;
 
     EnergyRegion() {
       e1sect = new Energy1Section();
       e2sect = new Energy2Section();
     }
 
     @Override
     public void finish() {
       // Apply the dual-topology scaling for the total energy.
       if (!useFirstSystemBondedEnergy) {
         totalEnergy =
             f1L * energy1 + f2L * restraintEnergy1 + f2L * energy2 + f1L * restraintEnergy2;
       } else {
         totalEnergy =
             f1L * energy1 + f2L * restraintEnergy1 + f2L * energy2 - f2L * restraintEnergy2;
       }
 
       if (gradient) {
         packGradient(x, g);
       } else {
         scaleCoordinates(x);
       }
 
       if (verbose) {
         logger.info(format(" Total dual-topology energy: %12.4f", totalEnergy));
       }
       setVerbose(false);
       setGradient(false);
     }
 
     @Override
     public void run() throws Exception {
       execute(e1sect, e2sect);
     }
 
     public void setG(double[] g) {
       this.g = g;
       setGradient(true);
     }
 
     public void setGradient(boolean grad) {
       this.gradient = grad;
       e1sect.setGradient(grad);
       e2sect.setGradient(grad);
     }
 
     public void setVerbose(boolean verb) {
       this.verbose = verb;
       e1sect.setVerbose(verb);
       e2sect.setVerbose(verb);
     }
 
     public void setX(double[] x) {
       this.x = x;
     }
 
     @Override
     public void start() {
       unpackCoordinates(x);
     }
   }
 
   private class Energy1Section extends ParallelSection {
 
     private boolean gradient = false;
     private boolean verbose = false;
 
     @Override
     public void run() {
       if (gradient) {
         fill(gl1, 0.0);
         fill(rgl1, 0.0);
         energy1 = potential1.energyAndGradient(x1, g1, verbose);
         dEdL_1 = lambdaInterface1.getdEdL();
         d2EdL2_1 = lambdaInterface1.getd2EdL2();
         lambdaInterface1.getdEdXdL(gl1);
         if (doValenceRestraint1) {
           if (verbose) {
             logger.info(" Calculating lambda bonded terms for topology 1");
           }
           forceFieldEnergy1.setLambdaBondedTerms(true, useFirstSystemBondedEnergy);
           if (forceFieldEnergy1 instanceof OpenMMEnergy openMMEnergy) {
             // Use FFX to calculate the energy and gradient for the restraints.
             restraintEnergy1 = openMMEnergy.energyAndGradientFFX(x1, rg1, verbose);
           } else {
             restraintEnergy1 = forceFieldEnergy1.energyAndGradient(x1, rg1, verbose);
           }
           restraintdEdL_1 = forceFieldEnergy1.getdEdL();
           restraintd2EdL2_1 = forceFieldEnergy1.getd2EdL2();
           forceFieldEnergy1.getdEdXdL(rgl1);
           forceFieldEnergy1.setLambdaBondedTerms(false, false);
         } else {
           restraintEnergy1 = 0.0;
           restraintdEdL_1 = 0.0;
           restraintd2EdL2_1 = 0.0;
         }
         if (logger.isLoggable(Level.FINE)) {
           logger.fine(format(" Topology 1 Energy & Restraints: %15.8f %15.8f\n", f1L * energy1, f2L * restraintEnergy1));
           logger.fine(format(" Topology 1:    %15.8f * (%.2f)", energy1, f1L));
           logger.fine(format(" T1 Restraints: %15.8f * (%.2f)", restraintEnergy1, f2L));
         }
       } else {
         energy1 = potential1.energy(x1, verbose);
         if (doValenceRestraint1) {
           if (verbose) {
             logger.info(" Calculating lambda bonded terms for topology 1");
           }
           forceFieldEnergy1.setLambdaBondedTerms(true, useFirstSystemBondedEnergy);
           if (forceFieldEnergy1 instanceof OpenMMEnergy openMMEnergy) {
             // Use FFX to calculate the energy and gradient for the restraints.
             restraintEnergy1 = openMMEnergy.energyFFX(x1, verbose);
           } else {
             restraintEnergy1 = potential1.energy(x1, verbose);
           }
           forceFieldEnergy1.setLambdaBondedTerms(false, false);
         } else {
           restraintEnergy1 = 0.0;
         }
         if (logger.isLoggable(Level.FINE)) {
           logger.fine(format(" Topology 1 Energy & Restraints: %15.8f %15.8f\n", f1L * energy1, f2L * restraintEnergy1));
         }
       }
     }
 
     public void setGradient(boolean grad) {
       this.gradient = grad;
     }
 
     public void setVerbose(boolean verb) {
       this.verbose = verb;
     }
   }
 
   private class Energy2Section extends ParallelSection {
 
     private boolean gradient = false;
     private boolean verbose = false;
 
     @Override
     public void run() {
       // Number of symmetry operators to be applied to the system.
       int numSymOps = 0;
       if (useSymOp) {
         numSymOps = symOpAtoms.size();
         for (int i = 0; i < numSymOps; i++) {
           // Apply sym ops to system 1 coords (duplicate of x1) to get x2.
           applyCartesianSymOp(x2, x2, symOp[i], mask[i]);
         }
       }
 
       if (gradient) {
         fill(gl2, 0.0);
         fill(rgl2, 0.0);
 
         // Compute the energy and gradient of topology 2.
         energy2 = potential2.energyAndGradient(x2, g2, verbose);
         dEdL_2 = -lambdaInterface2.getdEdL();
         d2EdL2_2 = lambdaInterface2.getd2EdL2();
         lambdaInterface2.getdEdXdL(gl2);
         if (useSymOp) {
           // Rotate the gradient back for appropriate atoms.
           for (int i = 0; i < numSymOps; i++) {
             applyCartesianSymRot(g2, g2, inverse[i], mask[i]);
             applyCartesianSymRot(gl2, gl2, inverse[i], mask[i]);
           }
         }
         if (doValenceRestraint2) {
           if (verbose) {
             logger.info(" Calculating lambda bonded terms for topology 2");
           }
           forceFieldEnergy2.setLambdaBondedTerms(true, useFirstSystemBondedEnergy);
           if (forceFieldEnergy2 instanceof OpenMMEnergy openMMEnergy) {
             // Use FFX to calculate the energy and gradient for the restraints.
             restraintEnergy2 = openMMEnergy.energyAndGradientFFX(x2, rg2, verbose);
           } else {
             restraintEnergy2 = forceFieldEnergy2.energyAndGradient(x2, rg2, verbose);
           }
           restraintdEdL_2 = -forceFieldEnergy2.getdEdL();
           restraintd2EdL2_2 = forceFieldEnergy2.getd2EdL2();
           forceFieldEnergy2.getdEdXdL(rgl2);
           if (useSymOp) {
             // Rotate the gradient back for appropriate atoms.
             for (int i = 0; i < numSymOps; i++) {
               applyCartesianSymRot(rg2, rg2, inverse[i], mask[i]);
               applyCartesianSymRot(rgl2, rgl2, inverse[i], mask[i]);
             }
           }
           forceFieldEnergy2.setLambdaBondedTerms(false, false);
         } else {
           restraintEnergy2 = 0.0;
           restraintdEdL_2 = 0.0;
           restraintd2EdL2_2 = 0.0;
         }
         if (logger.isLoggable(Level.FINE)) {
           logger.fine(format(" Topology 2 Energy & Restraints: %15.8f %15.8f", f2L * energy2, f1L * restraintEnergy2));
           logger.fine(format(" Topology 2:    %15.8f * (%.2f)", energy2, f2L));
           logger.fine(format(" T2 Restraints: %15.8f * (%.2f)", restraintEnergy2, f1L));
         }
       } else {
         energy2 = potential2.energy(x2, verbose);
         if (doValenceRestraint2) {
           if (verbose) {
             logger.info(" Calculating lambda bonded terms for topology 2");
           }
           forceFieldEnergy2.setLambdaBondedTerms(true, useFirstSystemBondedEnergy);
           if (forceFieldEnergy2 instanceof OpenMMEnergy openMMEnergy) {
             // Use FFX to calculate the energy and gradient for the restraints.
             restraintEnergy2 = openMMEnergy.energyFFX(x2, verbose);
           } else {
             restraintEnergy2 = potential2.energy(x2, verbose);
           }
           forceFieldEnergy2.setLambdaBondedTerms(false, false);
         } else {
           restraintEnergy2 = 0.0;
         }
         if (logger.isLoggable(Level.FINE)) {
           logger.fine(format(" Topology 2 Energy & Restraints: %15.8f %15.8f", f2L * energy2, f1L * restraintEnergy2));
         }
       }
     }
 
     public void setGradient(boolean grad) {
       this.gradient = grad;
     }
 
     public void setVerbose(boolean verb) {
       this.verbose = verb;
     }
   }
 }