// ******************************************************************************
   //
   // 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.
  //
  // ******************************************************************************
  package ffx.potential.nonbonded.implicit;
  
  import static ffx.potential.nonbonded.VanDerWaalsForm.getCombinedEps;
  import static ffx.potential.nonbonded.VanDerWaalsForm.getCombinedRadius;
  import static org.apache.commons.math3.util.FastMath.PI;
  import static org.apache.commons.math3.util.FastMath.max;
  import static org.apache.commons.math3.util.FastMath.min;
  import static org.apache.commons.math3.util.FastMath.pow;
  import static org.apache.commons.math3.util.FastMath.sqrt;
  
  import edu.rit.pj.IntegerForLoop;
  import edu.rit.pj.ParallelRegion;
  import edu.rit.pj.reduction.SharedDouble;
  import ffx.crystal.Crystal;
  import ffx.numerics.atomic.AtomicDoubleArray3D;
  import ffx.potential.bonded.Atom;
  import ffx.potential.parameters.VDWType.EPSILON_RULE;
  import ffx.potential.parameters.VDWType.RADIUS_RULE;
  import ffx.potential.parameters.ForceField;
  import ffx.potential.parameters.VDWType;
  import java.util.logging.Level;
  import java.util.logging.Logger;
  
  /**
   * Parallel calculation of continuum dispersion energy via pairwise descreening.
   *
   * @author Michael J. Schnieders
   * @since 1.0
   */
  public class DispersionRegion extends ParallelRegion {
  
    /** The dispersion integral begins for each atom at: Rmin_ij + DISPERSION_OFFSET */
    public static final double DEFAULT_DISPERSION_OFFSET = 1.056;
    /** Each solute atom blocks dispersion interactions with solvent: Rmin + SOLUTE_OFFSET */
    public static final double DEFAULT_SOLUTE_OFFSET = 0.0;
  
    private static final Logger logger = Logger.getLogger(DispersionRegion.class.getName());
    /** The dispersion integral HCT overlap scale factor. */
    private static final double DEFAULT_DISP_OVERLAP_FACTOR = 0.75;
    /**
     * Conversion between solute-solvent dispersion enthalpy and solute-solvent dispersion free
     * energy.
     */
    private static final double SLEVY = 1.0;
    /** Number density of water (water per A^3). */
    private static final double AWATER = 0.033428;
    /** AMOEBA '03 Water oxygen epsilon. */
    private static final double EPSO = 0.1100;
    /** AMOEBA '03 Water hydrogen epsilon. */
    private static final double EPSH = 0.0135;
    /** AMOEBA '03 Water oxygen Rmin (A). */
    private static final double RMINO = 1.7025;
    /** AMOEBA '03 Water hydrogen Rmin (A). */
    private static final double RMINH = 1.3275;
    /** AMOEBA epsilon rule. */
    private static final EPSILON_RULE epsilonRule = VDWType.EPSILON_RULE.HHG;
    /** AMOEBA radius rule. */
    private static final RADIUS_RULE radiusRule = VDWType.RADIUS_RULE.CUBIC_MEAN;
  
    private final DispersionLoop[] dispersionLoop;
    private final SharedDouble sharedDispersion;
    /** An ordered array of atoms in the system. */
   protected Atom[] atoms;
   /** Periodic boundary conditions and symmetry. */
   private Crystal crystal;
   /** Flag to indicate if an atom should be included. */
   private boolean[] use = null;
   /** Neighbor lists for each atom and symmetry operator. */
   private int[][][] neighborLists;
   /** Cartesian coordinates of each atom. */
   private double[] x, y, z;
   /** GK cut-off distance squared. */
   private double cut2;
   /** Boolean flag to indicate GK will be scaled by the lambda state variable. */
   private boolean gradient = false;
   /** Gradient array for each thread. */
   private AtomicDoubleArray3D grad;
   /** Where the dispersion integral begins for each atom (A): Rmin + dispersionOffset */
   private double dispersionOffest;
   /**
    * Each solute atom blocks dispersion interactions with solvent with this radius (A): Rmin +
    * soluteOffset
    */
   private double soluteOffset;
   /** The dispersion integral HCT overlap scale factor (unitless). */
   private double dispersionOverlapFactor;
 
   /**
    * DispersionRegion constructor.
    *
    * @param nt Number of threads.
    * @param atoms Atom array.
    * @param forceField ForceField in use.
    */
   public DispersionRegion(int nt, Atom[] atoms, ForceField forceField) {
     dispersionLoop = new DispersionLoop[nt];
     for (int i = 0; i < nt; i++) {
       dispersionLoop[i] = new DispersionLoop();
     }
     sharedDispersion = new SharedDouble();
 
     dispersionOffest = forceField.getDouble("DISPERSION_OFFSET", DEFAULT_DISPERSION_OFFSET);
     soluteOffset = forceField.getDouble("SOLUTE_OFFSET", DEFAULT_SOLUTE_OFFSET);
     dispersionOverlapFactor =
         forceField.getDouble("DISP_OVERLAP_FACTOR", DEFAULT_DISP_OVERLAP_FACTOR);
 
     allocate(atoms);
   }
 
   /**
    * Compute a Buffered-14-7 tail correction.
    *
    * @param r0 The separation distance where the intregal begins.
    * @param eps The mixed eps value.
    * @param rmin The mixed rmin value.
    * @return The tail correction.
    */
   private static double tailCorrection(double r0, double eps, double rmin) {
     if (r0 < rmin) {
       double r03 = r0 * r0 * r0;
       double rmin3 = rmin * rmin * rmin;
       return -eps * 4.0 * PI * (rmin3 - r03) / 3.0 - eps * PI * 18.0 * rmin3 / 11.0;
     } else {
       double ri2 = r0 * r0;
       double ri4 = ri2 * ri2;
       double ri7 = r0 * ri2 * ri4;
       double ri11 = ri7 * ri4;
       double rmin2 = rmin * rmin;
       double rmin4 = rmin2 * rmin2;
       double rmin7 = rmin * rmin2 * rmin4;
       return 2.0 * PI * eps * rmin7 * (2.0 * rmin7 - 11.0 * ri7) / (11.0 * ri11);
     }
   }
 
   /**
    * Allocate storage given the Atom array.
    *
    * @param atoms Atom array in use.
    */
   public void allocate(Atom[] atoms) {
     this.atoms = atoms;
   }
 
   /**
    * The dispersion integral begins offset from the vdW radius.
    *
    * @param dispersionOffest The dispersion integral offset.
    */
   public void setDispersionOffest(double dispersionOffest) {
     this.dispersionOffest = dispersionOffest;
   }
 
   /**
    * The dispersion integral begins offset from the vdW radius.
    *
    * @return the dispersion integral offset.
    */
   public double getDispersionOffset() {
     return dispersionOffest;
   }
 
   public double getDispersionOverlapFactor() {
     return dispersionOverlapFactor;
   }
 
   /**
    * Set the dispersion overlap HCT scale factor.
    *
    * @param dispersionOverlapFactor The dispersion integral HCT scale factor.
    */
   public void setDispersionOverlapFactor(double dispersionOverlapFactor) {
     this.dispersionOverlapFactor = dispersionOverlapFactor;
   }
 
   public double getEnergy() {
     return sharedDispersion.get();
   }
 
   public double getSoluteOffset() {
     return soluteOffset;
   }
 
   public void setSoluteOffset(double soluteOffset) {
     this.soluteOffset = soluteOffset;
   }
 
   /**
    * Initialize the DispersionRegion for energy calculation.
    *
    * @param atoms Atom array.
    * @param crystal Crystal for periodic boundary conditions.
    * @param use Flag to indicate an atom is to be used.
    * @param neighborLists Neighbor-list for each atom.
    * @param x X-coordinate array.
    * @param y Y-coordinate array.
    * @param z Z-coordinate array.
    * @param cut2 The cut-off distance squared.
    * @param gradient If true, compute the gradient.
    * @param grad Array to store the gradient.
    */
   public void init(
       Atom[] atoms,
       Crystal crystal,
       boolean[] use,
       int[][][] neighborLists,
       double[] x,
       double[] y,
       double[] z,
       double cut2,
       boolean gradient,
       AtomicDoubleArray3D grad) {
     this.atoms = atoms;
     this.crystal = crystal;
     this.use = use;
     this.neighborLists = neighborLists;
     this.x = x;
     this.y = y;
     this.z = z;
     this.cut2 = cut2;
     this.gradient = gradient;
     this.grad = grad;
   }
 
   /** {@inheritDoc} */
   @Override
   public void run() {
     try {
       int nAtoms = atoms.length;
       execute(0, nAtoms - 1, dispersionLoop[getThreadIndex()]);
     } catch (Exception e) {
       String message =
           "Fatal exception computing Dispersion energy in thread " + getThreadIndex() + "\n";
       logger.log(Level.SEVERE, message, e);
     }
   }
 
   /** {@inheritDoc} */
   @Override
   public void start() {
     sharedDispersion.set(0.0);
   }
 
   /**
    * Compute Dispersion energy for a range of atoms via pairwise descreening.
    *
    * @since 1.0
    */
   private class DispersionLoop extends IntegerForLoop {
 
     private final double[] dx_local;
     private double edisp;
     private double r, r2, r3;
     private double xr, yr, zr;
     private int threadID;
 
     DispersionLoop() {
       dx_local = new double[3];
     }
 
     @Override
     public void finish() {
       sharedDispersion.addAndGet(edisp);
     }
 
     @Override
     public void run(int lb, int ub) {
       for (int i = lb; i <= ub; i++) {
         if (!use[i]) {
           continue;
         }
 
         //  Compute the limit of atom alone in solvent.
         VDWType type = atoms[i].getVDWType();
         double epsi = type.wellDepth;
         double rmini = type.radius / 2.0;
         double cDisp = 0.0;
         if (rmini > 0.0 && epsi > 0.0) {
           double emixo = getCombinedEps(EPSO, epsi, RMINO, rmini, epsilonRule);
           double rmixo = getCombinedRadius(RMINO, rmini, radiusRule);
           // Start of integration of dispersion for atom i with water oxygen.
           double riO = rmixo / 2.0 + dispersionOffest;
           cDisp = tailCorrection(riO, emixo, rmixo);
           double emixh = getCombinedEps(EPSH, epsi, RMINH, rmini, epsilonRule);
           double rmixh = getCombinedRadius(RMINH, rmini, radiusRule);
           // Start of integration of dispersion for atom i with water hydrogen.
           double riH = rmixh / 2.0 + dispersionOffest;
           cDisp += 2.0 * tailCorrection(riH, emixh, rmixh);
           cDisp = SLEVY * AWATER * cDisp;
         }
 
         edisp += cDisp;
 
         // Now descreen over neighbors.
         double sum = 0.0;
         final double xi = x[i];
         final double yi = y[i];
         final double zi = z[i];
         int[] list = neighborLists[0][i];
         for (int k : list) {
           if (!use[k] || i == k) {
             continue;
           }
           if (atoms[k].getVDWType().radius > 0.0) {
             dx_local[0] = xi - x[k];
             dx_local[1] = yi - y[k];
             dx_local[2] = zi - z[k];
             r2 = crystal.image(dx_local);
             if (r2 > cut2) {
               continue;
             }
             xr = dx_local[0];
             yr = dx_local[1];
             zr = dx_local[2];
             r = sqrt(r2);
             r3 = r * r2;
             // Atom i descreened by atom k.
             sum += removeSoluteDispersion(i, k);
             // Flip the sign on {xr, yr, zr};
             xr = -xr;
             yr = -yr;
             zr = -zr;
             // Atom k descreened by atom i.
             sum += removeSoluteDispersion(k, i);
           }
         }
         // Subtract descreening.
         edisp -= SLEVY * AWATER * sum;
       }
     }
 
     @Override
     public void start() {
       threadID = getThreadIndex();
       edisp = 0;
     }
 
     /**
      * Remove solute dispersion between atom i and solvent due to blocking of solveny by atom k.
      *
      * @param i Atom i index.
      * @param k Atom k index.
      * @return Reduction of dispersion.
      */
     private double removeSoluteDispersion(int i, int k) {
 
       // Van der Waals parameters for atom i.
       VDWType type = atoms[i].getVDWType();
       double epsi = type.wellDepth;
       double rmini = type.radius / 2.0;
 
       // Van der Waals radius for atom k.
       double rmink = atoms[k].getVDWType().radius / 2.0;
 
       // Parameters for atom i with water oxygen.
       double emixo = getCombinedEps(EPSO, epsi, RMINO, rmini, epsilonRule);
       double rmixo = getCombinedRadius(RMINO, rmini, radiusRule);
       // Start of integration of dispersion for atom i with water oxygen.
       double riO = rmixo / 2.0 + dispersionOffest;
       double nO = 1.0;
 
       // Parameters for atom i with water hydrogen.
       double emixh = getCombinedEps(EPSH, epsi, RMINH, rmini, epsilonRule);
       double rmixh = getCombinedRadius(RMINH, rmini, radiusRule);
       // Start of integration of dispersion for atom i with water oxygen.
       double riH = rmixh / 2.0 + dispersionOffest;
       double nH = 2.0;
 
       // Atom k blocks the interaction of atom i with solvent.
       double sk = (rmink + soluteOffset) * dispersionOverlapFactor;
       return interact(i, k, nO, riO, sk, rmixo, emixo) + interact(i, k, nH, riH, sk, rmixh, emixh);
     }
 
     /**
      * Solvent dispersion blocking of atom i by atom k.
      *
      * @param i Index of atom i.
      * @param k Index of atom k.
      * @param factor Apply this factor to the interaction.
      * @param ri Start of the dispersion integral.
      * @param sk Size of the solvent blocking atom.
      * @param rmix Combined Rmin for atom i and solvent atom.
      * @param emix Combined Eps for atom i and solvent atom.
      * @return Contribution of atom k to removing dispersion.
      */
     private double interact(
         int i, int k, double factor, double ri, double sk, double rmix, double emix) {
       double sum = 0.0;
       // Nothing to do if the integral begins beyond r + sk (i.e. atom k does not exclude solvent)
       if (ri < r + sk) {
         // Zero out the derivative contribution of atom k.
         double de = 0.0;
         double sk2 = sk * sk;
         // Compute the maximum of 1) the beginning of the integral and 2) closest edge of atom K.
         double iStart = max(ri, r - sk);
         // Use this as the lower limit for integrating the constant eps value below Rmin.
         double lik = iStart;
         // Interaction with water from lik to Rmin; nothing to do if the lower limit is greater than
         // Rmin.
         if (lik < rmix) {
           double lik2 = lik * lik;
           double lik3 = lik2 * lik;
           double lik4 = lik3 * lik;
           // Upper limit is the minimum of Rmin and the farthest edge of atom K.
           double uik = min(r + sk, rmix);
           double uik2 = uik * uik;
           double uik3 = uik2 * uik;
           double uik4 = uik3 * uik;
           sum = integralBeforeRMin(emix, r, r2, sk2, lik2, lik3, lik4, uik2, uik3, uik4);
           if (gradient) {
             de =
                 integralBeforeRminDerivative(
                     ri, emix, rmix, r, r2, r3, sk, sk2, lik, lik2, lik3, uik, uik2, uik3);
           }
         }
         // Upper limit the variable part of Uwca always the farthest edge of atom K.
         double uik = r + sk;
         // Interaction with water beyond Rmin, from lik to uik = r + sk.
         if (uik > rmix) {
           // Start the integral at the max of 1) iStart and 2) Rmin.
           lik = max(iStart, rmix);
           double lik2 = lik * lik;
           double lik3 = lik2 * lik;
           double lik4 = lik3 * lik;
           double lik5 = lik4 * lik;
           double lik6 = lik5 * lik;
           double lik10 = lik5 * lik5;
           double lik11 = lik10 * lik;
           double lik12 = lik11 * lik;
           double uik2 = uik * uik;
           double uik3 = uik2 * uik;
           double uik4 = uik3 * uik;
           double uik5 = uik4 * uik;
           double uik10 = uik5 * uik5;
           double uik11 = uik10 * uik;
           double uik12 = uik11 * uik;
           double rmix7 = pow(rmix, 7);
           sum +=
               integratlAfterRmin(
                   emix, rmix7, r, r2, sk2, lik, lik2, lik3, lik4, lik5, lik10, lik11, lik12, uik,
                   uik2, uik3, uik4, uik5, uik10, uik11, uik12);
           if (gradient) {
             double lik13 = lik12 * lik;
             double uik6 = uik5 * uik;
             double uik13 = uik12 * uik;
             de +=
                 integratlAfterRminDerivative(
                     ri, emix, rmix, rmix7, iStart, r, r2, r3, sk, sk2, lik, lik2, lik3, lik5, lik6,
                     lik12, lik13, uik, uik2, uik3, uik6, uik13);
           }
         }
         // Increment the individual dispersion gradient components.
         if (gradient) {
           de = -de / r * factor * SLEVY * AWATER;
           double dedx = de * xr;
           double dedy = de * yr;
           double dedz = de * zr;
           grad.add(threadID, i, dedx, dedy, dedz);
           grad.sub(threadID, k, dedx, dedy, dedz);
         }
       }
       return factor * sum;
     }
 
     /**
      * Integrate over the constant portion of the WCA disperion interaction Uwca(x) = eps; x < rmin.
      *
      * @param eps The well depth.
      * @param rij The separation between the current atom and solvent blocking atom.
      * @param rij2 The separation squared.
      * @param rho2 The scaled size of the solvent blocking atom squared.
      * @param lik2 The beginning of the integral squared.
      * @param lik3 The beginning of the integral to the third.
      * @param lik4 The beginning of the integral to the fourth.
      * @param uik2 The end of the integral squared.
      * @param uik3 The end of the integral to the third.
      * @param uik4 The end of the integral to the fourth.
      * @return The integral.
      */
     private double integralBeforeRMin(
         double eps,
         double rij,
         double rij2,
         double rho2,
         double lik2,
         double lik3,
         double lik4,
         double uik2,
         double uik3,
         double uik4) {
       return -eps
           * (4.0
           * PI
           * (3.0 * (lik4 - uik4) - 8.0 * rij * (lik3 - uik3) + 6.0 * (rij2 - rho2) * (lik2 - uik2))
           / (48.0 * rij));
     }
 
     /**
      * Derivative of the integral over the constant portion of the WCA disperion interaction Uwca(x)
      * = eps; x < rmin.
      *
      * @param ri The beginning of the integral.
      * @param eps The well depth.
      * @param rmin The Rmin value.
      * @param rij The separation between the current atom and solvent blocking atom.
      * @param rij2 The separation squared.
      * @param rij3 The separation to the third.
      * @param rho The scaled size of the solvent blocking atom.
      * @param rho2 The scaled size of the solvent blocking atom squared.
      * @param lik The beginning of the integral.
      * @param lik2 The beginning of the integral squared.
      * @param lik3 The beginning of the integral to the third.
      * @param uik The end of the integral.
      * @param uik2 The end of the integral squared.
      * @param uik3 The end of the integral to the third.
      * @return The derivative of the integral.
      */
     private double integralBeforeRminDerivative(
         double ri,
         double eps,
         double rmin,
         double rij,
         double rij2,
         double rij3,
         double rho,
         double rho2,
         double lik,
         double lik2,
         double lik3,
         double uik,
         double uik2,
         double uik3) {
       double dl;
       if (ri > rij - rho) {
         dl = (-lik2 + 2.0 * rij2 + 2.0 * rho2) * lik2;
       } else {
         dl =
             (-lik3 + 4.0 * lik2 * rij - 6.0 * lik * rij2 + 2.0 * lik * rho2 + 4.0 * rij3
                 - 4.0 * rij * rho2)
                 * lik;
       }
       double du;
       if (rij + rho > rmin) {
         du = -(-uik2 + 2.0 * rij2 + 2.0 * rho2) * uik2;
       } else {
         du =
             -(-uik3 + 4.0 * uik2 * rij - 6.0 * uik * rij2 + 2.0 * uik * rho2 + 4.0 * rij3
                 - 4.0 * rij * rho2)
                 * uik;
       }
       return -eps * PI * (dl + du) / (4.0 * rij2);
     }
 
     /**
      * @param eps The well depth.
      * @param rmin7 The rmin value to the seventh.
      * @param rij The separation between the current atom and solvent blocking atom.
      * @param rij2 The separation squared.
      * @param rho2 The scaled size of the solvent blocking atom squared.
      * @param lik The beginning of the integral.
      * @param lik2 The beginning of the integral squared.
      * @param lik3 The beginning of the integral to the third.
      * @param lik4 The beginning of the integral to the fourth.
      * @param lik5 The beginning of the integral to the fifth.
      * @param lik10 The beginning of the integral to the tenth.
      * @param lik11 The beginning of the integral to the eleventh.
      * @param lik12 The beginning of the integral to the twelfth.
      * @param uik The end of the integral.
      * @param uik2 The end of the integral squared.
      * @param uik3 The end of the integral to the third.
      * @param uik4 The end of the integral to the fourth.
      * @param uik5 The end of the integral to the fifth.
      * @param uik10 The end of the integral to the tenth.
      * @param uik11 The end of the integral to the eleventh.
      * @param uik12 The end of the integral to the twelfth.
      * @return The value of the integral.
      */
     private double integratlAfterRmin(
         double eps,
         double rmin7,
         double rij,
         double rij2,
         double rho2,
         double lik,
         double lik2,
         double lik3,
         double lik4,
         double lik5,
         double lik10,
         double lik11,
         double lik12,
         double uik,
         double uik2,
         double uik3,
         double uik4,
         double uik5,
         double uik10,
         double uik11,
         double uik12) {
       double er7 = eps * rmin7;
       double term = (15.0 * uik * lik * rij * (uik4 - lik4)
           - 10.0 * uik2 * lik2 * (uik3 - lik3)
           + 6.0 * (rho2 - rij2) * (uik5 - lik5)) / (120.0 * rij * lik5 * uik5);
       double term2 = (120.0 * uik * lik * rij * (uik11 - lik11)
           - 66.0 * uik2 * lik2 * (uik10 - lik10)
           + 55.0 * (rho2 - rij2) * (uik12 - lik12)) / (2640.0 * rij * lik12 * uik12);
       double idisp = -2.0 * er7 * term;
       double irep = er7 * rmin7 * term2;
       return 4.0 * PI * (irep + idisp);
     }
 
     /**
      * @param ri The beginning of the integral.
      * @param eps The eps value.
      * @param rmin The rmin value to the seventh.
      * @param rmin7 The rmin value to the seventh.
      * @param rij The separation between the current atom and solvent blocking atom.
      * @param rij2 The separation squared.
      * @param rij3 The separation cubed.
      * @param rho The scaled size of the solvent blocking atom.
      * @param rho2 The scaled size of the solvent blocking atom squared.
      * @param lik The beginning of the integral.
      * @param lik2 The beginning of the integral squared.
      * @param lik3 The beginning of the integral to the third.
      * @param lik5 The beginning of the integral to the fifth.
      * @param lik6 The beginning of the integral to the sixth.
      * @param lik12 The beginning of the integral to the twelfth.
      * @param lik13 The beginning of the integral to the thirteenth.
      * @param uik The end of the integral.
      * @param uik2 The end of the integral squared.
      * @param uik3 The end of the integral to the third.
      * @param uik6 The end of the integral to the sixth.
      * @param uik13 The end of the integral to the thirteenth.
      * @return The value of the integral derivative.
      */
     private double integratlAfterRminDerivative(
         double ri,
         double eps,
         double rmin,
         double rmin7,
         double rmax,
         double rij,
         double rij2,
         double rij3,
         double rho,
         double rho2,
         double lik,
         double lik2,
         double lik3,
         double lik5,
         double lik6,
         double lik12,
         double lik13,
         double uik,
         double uik2,
         double uik3,
         double uik6,
         double uik13) {
       double er7 = eps * rmin7;
       double lowerTerm = lik2 * rij + rij3 - rij * rho2;
       double upperTerm = uik2 * rij + rij3 - rij * rho2;
 
       double dl;
       if (ri > rij - rho || rmax < rmin) {
         dl = -(-5.0 * lik2 + 3.0 * rij2 + 3.0 * rho2) / lik5;
       } else {
         dl = (5.0 * lik3 - 33.0 * lik * rij2 - 3.0 * lik * rho2 + 15.0 * lowerTerm) / lik6;
       }
       double du = -(5.0 * uik3 - 33.0 * uik * rij2 - 3.0 * uik * rho2 + 15.0 * upperTerm) / uik6;
       double de = -2.0 * PI * er7 * (dl + du) / (15.0 * rij2);
 
       if (ri > rij - rho || rmax < rmin) {
         dl = -(-6.0 * lik2 + 5.0 * rij2 + 5.0 * rho2) / lik12;
       } else {
         dl = (6.0 * lik3 - 125.0 * lik * rij2 - 5.0 * lik * rho2 + 60.0 * lowerTerm) / lik13;
       }
       du = -(6.0 * uik3 - 125.0 * uik * rij2 - 5.0 * uik * rho2 + 60.0 * upperTerm) / uik13;
       de += PI * er7 * rmin7 * (dl + du) / (60.0 * rij2);
 
       return de;
     }
   }
 }