// $Id$ // // Copyright (C) 2004-2013 Rational Discovery LLC // // @@ All Rights Reserved @@ // This file is part of the RDKit. // The contents are covered by the terms of the BSD license // which is included in the file license.txt, found at the root // of the RDKit source tree. // #include "AngleBend.h" #include "BondStretch.h" #include "Params.h" #include #include #include #include namespace ForceFields { namespace UFF { namespace Utils { double calcAngleForceConstant(double theta0, double bondOrder12,double bondOrder23, const AtomicParams *at1Params, const AtomicParams *at2Params, const AtomicParams *at3Params){ double cosTheta0=cos(theta0); double r12 = calcBondRestLength(bondOrder12,at1Params,at2Params); double r23 = calcBondRestLength(bondOrder23,at2Params,at3Params); double r13 = sqrt(r12*r12 + r23*r23 - 2.*r12*r23*cosTheta0); double beta = 2.*Params::G/(r12*r23); double preFactor = beta*at1Params->Z1*at3Params->Z1 / int_pow<5>(r13); double rTerm = r12*r23; double innerBit = 3.*rTerm*(1.-cosTheta0*cosTheta0) - r13*r13*cosTheta0; double res=preFactor*rTerm*innerBit; return res; } void calcAngleBendGrad(RDGeom::Point3D *r, double *dist, double **g, double &dE_dTheta, double &cosTheta, double &sinTheta) { // ------- // dTheta/dx is trickier: double dCos_dS[6] = { 1.0 / dist[0] * (r[1].x - cosTheta * r[0].x), 1.0 / dist[0] * (r[1].y - cosTheta * r[0].y), 1.0 / dist[0] * (r[1].z - cosTheta * r[0].z), 1.0 / dist[1] * (r[0].x - cosTheta * r[1].x), 1.0 / dist[1] * (r[0].y - cosTheta * r[1].y), 1.0 / dist[1] * (r[0].z - cosTheta * r[1].z) }; g[0][0] += dE_dTheta * dCos_dS[0] / (-sinTheta); g[0][1] += dE_dTheta * dCos_dS[1] / (-sinTheta); g[0][2] += dE_dTheta * dCos_dS[2] / (-sinTheta); g[1][0] += dE_dTheta * (-dCos_dS[0] - dCos_dS[3]) / (-sinTheta); g[1][1] += dE_dTheta * (-dCos_dS[1] - dCos_dS[4]) / (-sinTheta); g[1][2] += dE_dTheta * (-dCos_dS[2] - dCos_dS[5]) / (-sinTheta); g[2][0] += dE_dTheta * dCos_dS[3] / (-sinTheta); g[2][1] += dE_dTheta * dCos_dS[4] / (-sinTheta); g[2][2] += dE_dTheta * dCos_dS[5] / (-sinTheta); } } // end of namespace Utils AngleBendContrib::AngleBendContrib(ForceField *owner, unsigned int idx1,unsigned int idx2,unsigned int idx3, double bondOrder12,double bondOrder23, const AtomicParams *at1Params, const AtomicParams *at2Params, const AtomicParams *at3Params, unsigned int order){ PRECONDITION(owner,"bad owner"); PRECONDITION(at1Params,"bad params pointer"); PRECONDITION(at2Params,"bad params pointer"); PRECONDITION(at3Params,"bad params pointer"); PRECONDITION((idx1!=idx2&&idx2!=idx3&&idx1!=idx3),"degenerate points"); RANGE_CHECK(0,idx1,owner->positions().size()-1); RANGE_CHECK(0,idx2,owner->positions().size()-1); RANGE_CHECK(0,idx3,owner->positions().size()-1); // the following is a hack to get decent geometries // with 3- and 4-membered rings incorporating sp2 atoms double theta0 = at2Params->theta0; if (order >= 30) { switch (order) { case 30: theta0 = 150.0 / 180.0 * M_PI; break; case 35: theta0 = 60.0 / 180.0 * M_PI; break; case 40: theta0 = 135.0 / 180.0 * M_PI; break; case 45: theta0 = 90.0 / 180.0 * M_PI; break; } order = 0; } // end of the hack dp_forceField = owner; d_at1Idx = idx1; d_at2Idx = idx2; d_at3Idx = idx3; d_order = order; d_forceConstant = Utils::calcAngleForceConstant (theta0, bondOrder12,bondOrder23, at1Params,at2Params,at3Params); if(order==0){ double sinTheta0=sin(theta0); double cosTheta0=cos(theta0); d_C2 = 1./(4.*std::max(sinTheta0*sinTheta0,1e-8)); d_C1 = -4.*d_C2*cosTheta0; d_C0 = d_C2*(2.*cosTheta0*cosTheta0 + 1.); } } double AngleBendContrib::getEnergy(double *pos) const { PRECONDITION(dp_forceField,"no owner"); PRECONDITION(pos,"bad vector"); double dist1=dp_forceField->distance(d_at1Idx,d_at2Idx,pos); double dist2=dp_forceField->distance(d_at2Idx,d_at3Idx,pos); RDGeom::Point3D p1(pos[3*d_at1Idx], pos[3*d_at1Idx+1], pos[3*d_at1Idx+2]); RDGeom::Point3D p2(pos[3*d_at2Idx], pos[3*d_at2Idx+1], pos[3*d_at2Idx+2]); RDGeom::Point3D p3(pos[3*d_at3Idx], pos[3*d_at3Idx+1], pos[3*d_at3Idx+2]); RDGeom::Point3D p12=p1-p2; RDGeom::Point3D p32=p3-p2; double cosTheta = p12.dotProduct(p32)/(dist1*dist2); clipToOne(cosTheta); // we need sin^2(theta) to get cos(2*theta), so compute that: double sinThetaSq = 1.-cosTheta*cosTheta; double angleTerm = getEnergyTerm(cosTheta,sinThetaSq); double res = d_forceConstant*angleTerm; return res; } void AngleBendContrib::getGrad(double *pos,double *grad) const { PRECONDITION(dp_forceField,"no owner"); PRECONDITION(pos,"bad vector"); PRECONDITION(grad,"bad vector"); double dist[2] = { dp_forceField->distance(d_at1Idx, d_at2Idx, pos), dp_forceField->distance(d_at2Idx, d_at3Idx, pos) }; RDGeom::Point3D p1(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1], pos[3 * d_at1Idx + 2]); RDGeom::Point3D p2(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1], pos[3 * d_at2Idx + 2]); RDGeom::Point3D p3(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1], pos[3 * d_at3Idx + 2]); double *g[3] = { &(grad[3 * d_at1Idx]), &(grad[3 * d_at2Idx]), &(grad[3 * d_at3Idx]) }; RDGeom::Point3D r[2] = { (p1 - p2) / dist[0], (p3 - p2) / dist[1] }; double cosTheta = r[0].dotProduct(r[1]); clipToOne(cosTheta); double sinThetaSq = 1.0 - cosTheta * cosTheta; double sinTheta = std::max(((sinThetaSq > 0.0) ? sqrt(sinThetaSq) : 0.0), 1.0e-8); //std::cerr << "GRAD: " << cosTheta << " (" << acos(cosTheta)<< "), "; //std::cerr << sinTheta << " (" << asin(sinTheta)<< ")" << std::endl; // use the chain rule: // dE/dx = dE/dTheta * dTheta/dx // dE/dTheta is independent of cartesians: double dE_dTheta=getThetaDeriv(cosTheta,sinTheta); Utils::calcAngleBendGrad(r, dist, g, dE_dTheta, cosTheta, sinTheta); } double AngleBendContrib::getEnergyTerm(double cosTheta,double sinThetaSq) const { PRECONDITION(d_order==0||d_order==1||d_order==2||d_order==3||d_order==4,"bad order"); // cos(2x) = cos^2(x) - sin^2(x); double cos2Theta = cosTheta*cosTheta - sinThetaSq; double res=0.0; if(d_order==0){ res=d_C0 + d_C1*cosTheta + d_C2*cos2Theta; } else { switch(d_order){ case 1: res=-cosTheta; break; case 2: res=cos2Theta; break; case 3: // cos(3x) = cos^3(x) - 3*cos(x)*sin^2(x) res = cosTheta*(cosTheta*cosTheta-3.*sinThetaSq); break; case 4: // cos(4x) = cos^4(x) - 6*cos^2(x)*sin^2(x)+sin^4(x) res = int_pow<4>(cosTheta) - 6.*cosTheta*cosTheta*sinThetaSq + sinThetaSq*sinThetaSq; break; } res = 1.-res; res /= (double)(d_order*d_order); } return res; } double AngleBendContrib::getThetaDeriv(double cosTheta,double sinTheta) const { PRECONDITION(d_order==0||d_order==1||d_order==2||d_order==3||d_order==4,"bad order"); double dE_dTheta=0.0; double sin2Theta = 2.*sinTheta*cosTheta; if(d_order==0){ dE_dTheta = -1.*d_forceConstant*(d_C1*sinTheta + 2.*d_C2*sin2Theta); } else { // E = k/n^2 [1-cos(n theta)] // dE = - k/n^2 * d cos(n theta) // these all use: // d cos(ax) = -a sin(ax) switch(d_order){ case 1: dE_dTheta = -sinTheta; break; case 2: // sin(2*x) = 2*cos(x)*sin(x) dE_dTheta = sin2Theta; break; case 3: // sin(3*x) = 3*sin(x) - 4*sin^3(x) dE_dTheta = sinTheta*(3.-4.*sinTheta*sinTheta); break; case 4: // sin(4*x) = cos(x)*(4*sin(x) - 8*sin^3(x)) dE_dTheta = cosTheta*sinTheta*(4.-8.*sinTheta*sinTheta); break; } dE_dTheta *= d_forceConstant/(double)(d_order); } return dE_dTheta; } } }