UFF.cpp

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 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *
 * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
 * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
 * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
 * [4] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 * [5] Kuang & Gezelter, Mol. Phys., 110, 691-701 (2012).
 * [6] Lamichhane, Gezelter & Newman, J. Chem. Phys. 141, 134109 (2014).
 * [7] Lamichhane, Newman & Gezelter, J. Chem. Phys. 141, 134110 (2014).
 * [8] Bhattarai, Newman & Gezelter, Phys. Rev. B 99, 094106 (2019).
 */
 
#include "forceFields/UFF.hpp"
 
namespace OpenMD {
  namespace UFF {
 
    RealType fastPower(RealType x, int y) {
      RealType temp;
      if( y == 0)
        return 1;
      temp = fastPower(x, y/2);
      if (y%2 == 0)
        return temp*temp;
      else {
        if(y > 0)
          return x*temp*temp;
        else
          return (temp*temp)/x;
      }
    }
    
    RealType calcBondRestLength(RealType bondOrder, const AtomType *at1,
                                const AtomType *at2) {
      assert(bondOrder > 0);
      assert(at1);
      assert(at2);
 
      UFFAdapter uff1 = UFFAdapter(at1);
      UFFAdapter uff2 = UFFAdapter(at2);
      
      RealType ri = uff1->getR1();
      RealType rj = uff2->getR1();
      // Precompute the equilibrium bond distance
      // From equation 3
      // this is the pauling correction:
      RealType rBO = -Params::lambda * (ri + rj) * log(bondOrder);
      
      // O'Keefe and Breese electronegativity correction:
      RealType Xi = uff1->getXi();
      RealType Xj = uff2->getXi();
      RealType rEN = ri * rj * (sqrt(Xi) - sqrt(Xj)) * (sqrt(Xi) - sqrt(Xj)) /
        (Xi * ri + Xj * rj);
      // NOTE: See http://towhee.sourceforge.net/forcefields/uff.html
      // There is a typo in the published paper
      RealType r0 = ri + rj + rBO - rEN;
      return r0;
    }
 
    RealType calcBondForceConstant(RealType restLength, const AtomType *at1,
                                   const AtomType *at2) {
      UFFAdapter uff1 = UFFAdapter(at1);
      UFFAdapter uff2 = UFFAdapter(at2);
      
      RealType kb = 2.0 * Params::G * uff1->getZ1() * uff2->getZ1() /
        (restLength * restLength * restLength);
      return kb;
    }
 
    RealType calcAngleForceConstant(RealType theta0, RealType bondOrder12,
                              RealType bondOrder23, const AtomType *at1,
                              const AtomType *at2,
                              const AtomType *at3) {
      UFFAdapter uff1 = UFFAdapter(at1);
      UFFAdapter uff2 = UFFAdapter(at2);
      UFFAdapter uff3 = UFFAdapter(at3);
 
      RealType cosTheta0 = cos(theta0);
      RealType r12 = calcBondRestLength(bondOrder12, at1, at2);
      RealType r23 = calcBondRestLength(bondOrder23, at2, at3);
      RealType r13 = sqrt(r12 * r12 + r23 * r23 - 2. * r12 * r23 * cosTheta0);
      RealType beta = 2. * Params::G / (r12 * r23);
      
      RealType preFactor = beta * uff1->getZ1() * uff3->getZ1() /
        fastPower(r13,5);
      RealType rTerm = r12 * r23;
      RealType innerBit =
        3. * rTerm * (1. - cosTheta0 * cosTheta0) - r13 * r13 * cosTheta0;
      RealType res = preFactor * rTerm * innerBit;
      return res;
    }
    
    void calcTorsionParams(RealType bondOrder23, int atNum2,
                           int atNum3,
                           RDKit::Atom::HybridizationType hyb2,
                           RDKit::Atom::HybridizationType hyb3,
                           const AtomType *at2,
                           const AtomType *at3,
                           bool endAtomIsSP2) {
      assert((hyb2 == RDKit::Atom::SP2 || hyb2 == RDKit::Atom::SP3) &&
             (hyb3 == RDKit::Atom::SP2 || hyb3 == RDKit::Atom::SP3));
 
      UFFAdapter uff2 = UFFAdapter(at2);
      UFFAdapter uff3 = UFFAdapter(at3);
 
      
      if (hyb2 == RDKit::Atom::SP3 && hyb3 == RDKit::Atom::SP3) {
        // general case:
        d_forceConstant = sqrt(uff2->getV1() * uff3->getV1());
        d_order = 3;
        d_cosTerm = -1;  // phi0=60
        
        // special case for single bonds between group 6 elements:
        if (bondOrder23 == 1.0 && isInGroup6(atNum2) &&
            isInGroup6(atNum3)) {
          RealType V2 = 6.8, V3 = 6.8;
          if (atNum2 == 8) {
            V2 = 2.0;
          }
          if (atNum3 == 8) {
            V3 = 2.0;
          }
          d_forceConstant = sqrt(V2 * V3);
          d_order = 2;
          d_cosTerm = -1;  // phi0=90
        }
      } else if (hyb2 == RDKit::Atom::SP2 && hyb3 == RDKit::Atom::SP2) {
        d_forceConstant = equation17(bondOrder23, at2, at3);
        d_order = 2;
        // FIX: is this angle term right?
        d_cosTerm = 1.0;  // phi0= 180
      } else {
        // SP2 - SP3,  this is, by default, independent of atom type in UFF:
        d_forceConstant = 1.0;
        d_order = 6;
        d_cosTerm = 1.0;  // phi0 = 0
        if (bondOrder23 == 1.0) {
          // special case between group 6 sp3 and non-group 6 sp2:
          if ((hyb2 == RDKit::Atom::SP3 && isInGroup6(atNum2) &&
               !isInGroup6(atNum3)) ||
              (hyb3 == RDKit::Atom::SP3 && isInGroup6(atNum3) &&
               !isInGroup6(atNum2))) {
            d_forceConstant = equation17(bondOrder23, at2, at3);
            d_order = 2;
            d_cosTerm = -1;  // phi0 = 90;
          }
          
          // special case for sp3 - sp2 - sp2
          // (i.e. the sp2 has another sp2 neighbor, like propene)
          else if (endAtomIsSP2) {
            d_forceConstant = 2.0;
            d_order = 3;
            d_cosTerm = -1;  // phi0 = 180;
          }
        }
      }
    }
 
    bool isInGroup6(int num) {
      return (num == 8 || num == 16 || num == 34 || num == 52 || num == 84);
    }
    
    // implements equation 17 of the UFF paper.
    RealType equation17(RealType bondOrder23, const AtomType *at2,
                        const AtomType *at3) {
      UFFAdapter uff2 = UFFAdapter(at2);
      UFFAdapter uff3 = UFFAdapter(at3);
 
      return 5. * sqrt(uff2->getU1() * uff3->getU1()) *
        (1. + 4.18 * log(bondOrder23));
    }
    
    RealType calculateCosY(const Vector3d &iPoint,
                           const Vector3d &jPoint,
                           const Vector3d &kPoint,
                           const Vector3d &lPoint) {
      Vector3d rJI = iPoint - jPoint;
      Vector3d rJK = kPoint - jPoint;
      Vector3d rJL = lPoint - jPoint;
      rJI /= rJI.length();
      rJK /= rJK.length();
      rJL /= rJL.length();
      
      Vector3d n = rJI.crossProduct(rJK);
      n /= n.length();
      
      return n.dotProduct(rJL);
    }
    
    calcInversionCoefficientsAndForceConstant(int at2AtomicNum,
                                              bool isCBoundToO) {
      RealType res = 0.0;
      RealType C0 = 0.0;
      RealType C1 = 0.0;
      RealType C2 = 0.0;
      // if the central atom is sp2 carbon, nitrogen or oxygen
      if ((at2AtomicNum == 6) || (at2AtomicNum == 7) || (at2AtomicNum == 8)) {
        C0 = 1.0;
        C1 = -1.0;
        C2 = 0.0;
        res = (isCBoundToO ? 50.0 : 6.0);
      } else {
        // group 5 elements are not clearly explained in the UFF paper
        // the following code was inspired by MCCCS Towhee's ffuff.F
        RealType w0 = M_PI / 180.0;
        switch (at2AtomicNum) {
          // if the central atom is phosphorous
        case 15:
          w0 *= 84.4339;
          break;
          
          // if the central atom is arsenic
        case 33:
          w0 *= 86.9735;
          break;
          
          // if the central atom is antimonium
        case 51:
          w0 *= 87.7047;
          break;
          
          // if the central atom is bismuth
        case 83:
          w0 *= 90.0;
          break;
        }
        C2 = 1.0;
        C1 = -4.0 * cos(w0);
        C0 = -(C1 * cos(w0) + C2 * cos(2.0 * w0));
        res = 22.0 / (C0 + C1 + C2);
      }
      res /= 3.0;
      
      return boost::make_tuple(res, C0, C1, C2);
    }
    
    RealType calcNonbondedMinimum(const AtomType *at1,
                                  const AtomType *at2) {
      UFFAdapter uff1 = UFFAdapter(at1);
      UFFAdapter uff2 = UFFAdapter(at2);
 
      return sqrt(uff1->getX1() * uff2->getX1());
    }
    
    RealType calcNonbondedDepth(const AtomType *at1,
                                const AtomType *at2) {
      UFFAdapter uff1 = UFFAdapter(at1);
      UFFAdapter uff2 = UFFAdapter(at2);
      
      return sqrt(uff1->getD1() * uff2->getD1());
    }
  }
}