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// $Id$
//
// Copyright (C) 2004-2006 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 "TorsionAngle.h"
#include "Params.h"
#include <math.h>
#include <ForceField/ForceField.h>
#include <RDGeneral/Invariant.h>
namespace ForceFields {
namespace UFF {
namespace Utils {
double calculateCosTorsion(const RDGeom::Point3D &p1, const RDGeom::Point3D &p2,
const RDGeom::Point3D &p3,
const RDGeom::Point3D &p4) {
RDGeom::Point3D r1 = p1 - p2, r2 = p3 - p2, r3 = p2 - p3, r4 = p4 - p3;
RDGeom::Point3D t1 = r1.crossProduct(r2);
RDGeom::Point3D t2 = r3.crossProduct(r4);
double d1 = t1.length(), d2 = t2.length();
double cosPhi = t1.dotProduct(t2) / (d1 * d2);
clipToOne(cosPhi);
return cosPhi;
}
// used locally
bool isInGroup6(int num) {
return (num == 8 || num == 16 || num == 34 || num == 52 || num == 84);
}
// used locally, implement equation 17 of the UFF paper.
double equation17(double bondOrder23, const AtomicParams *at2Params,
const AtomicParams *at3Params) {
return 5. * sqrt(at2Params->U1 * at3Params->U1) *
(1. + 4.18 * log(bondOrder23));
}
void calcTorsionGrad(RDGeom::Point3D *r, RDGeom::Point3D *t, double *d,
double **g, double &sinTerm, double &cosPhi) {
// -------
// dTheta/dx is trickier:
double dCos_dT[6] = {1.0 / d[0] * (t[1].x - cosPhi * t[0].x),
1.0 / d[0] * (t[1].y - cosPhi * t[0].y),
1.0 / d[0] * (t[1].z - cosPhi * t[0].z),
1.0 / d[1] * (t[0].x - cosPhi * t[1].x),
1.0 / d[1] * (t[0].y - cosPhi * t[1].y),
1.0 / d[1] * (t[0].z - cosPhi * t[1].z)};
g[0][0] += sinTerm * (dCos_dT[2] * r[1].y - dCos_dT[1] * r[1].z);
g[0][1] += sinTerm * (dCos_dT[0] * r[1].z - dCos_dT[2] * r[1].x);
g[0][2] += sinTerm * (dCos_dT[1] * r[1].x - dCos_dT[0] * r[1].y);
g[1][0] += sinTerm *
(dCos_dT[1] * (r[1].z - r[0].z) + dCos_dT[2] * (r[0].y - r[1].y) +
dCos_dT[4] * (-r[3].z) + dCos_dT[5] * (r[3].y));
g[1][1] += sinTerm *
(dCos_dT[0] * (r[0].z - r[1].z) + dCos_dT[2] * (r[1].x - r[0].x) +
dCos_dT[3] * (r[3].z) + dCos_dT[5] * (-r[3].x));
g[1][2] += sinTerm *
(dCos_dT[0] * (r[1].y - r[0].y) + dCos_dT[1] * (r[0].x - r[1].x) +
dCos_dT[3] * (-r[3].y) + dCos_dT[4] * (r[3].x));
g[2][0] += sinTerm *
(dCos_dT[1] * (r[0].z) + dCos_dT[2] * (-r[0].y) +
dCos_dT[4] * (r[3].z - r[2].z) + dCos_dT[5] * (r[2].y - r[3].y));
g[2][1] += sinTerm *
(dCos_dT[0] * (-r[0].z) + dCos_dT[2] * (r[0].x) +
dCos_dT[3] * (r[2].z - r[3].z) + dCos_dT[5] * (r[3].x - r[2].x));
g[2][2] += sinTerm *
(dCos_dT[0] * (r[0].y) + dCos_dT[1] * (-r[0].x) +
dCos_dT[3] * (r[3].y - r[2].y) + dCos_dT[4] * (r[2].x - r[3].x));
g[3][0] += sinTerm * (dCos_dT[4] * r[2].z - dCos_dT[5] * r[2].y);
g[3][1] += sinTerm * (dCos_dT[5] * r[2].x - dCos_dT[3] * r[2].z);
g[3][2] += sinTerm * (dCos_dT[3] * r[2].y - dCos_dT[4] * r[2].x);
}
}
TorsionAngleContrib::TorsionAngleContrib(
ForceField *owner, unsigned int idx1, unsigned int idx2, unsigned int idx3,
unsigned int idx4, double bondOrder23, int atNum2, int atNum3,
RDKit::Atom::HybridizationType hyb2, RDKit::Atom::HybridizationType hyb3,
const AtomicParams *at2Params, const AtomicParams *at3Params,
bool endAtomIsSP2) {
PRECONDITION(owner, "bad owner");
PRECONDITION(at2Params, "bad params pointer");
PRECONDITION(at3Params, "bad params pointer");
PRECONDITION((idx1 != idx2 && idx1 != idx3 && idx1 != idx4 && idx2 != idx3 &&
idx2 != idx4 && idx3 != idx4),
"degenerate points");
URANGE_CHECK(idx1, owner->positions().size());
URANGE_CHECK(idx2, owner->positions().size());
URANGE_CHECK(idx3, owner->positions().size());
URANGE_CHECK(idx4, owner->positions().size());
dp_forceField = owner;
d_at1Idx = idx1;
d_at2Idx = idx2;
d_at3Idx = idx3;
d_at4Idx = idx4;
calcTorsionParams(bondOrder23, atNum2, atNum3, hyb2, hyb3, at2Params,
at3Params, endAtomIsSP2);
}
void TorsionAngleContrib::calcTorsionParams(double bondOrder23, int atNum2,
int atNum3,
RDKit::Atom::HybridizationType hyb2,
RDKit::Atom::HybridizationType hyb3,
const AtomicParams *at2Params,
const AtomicParams *at3Params,
bool endAtomIsSP2) {
PRECONDITION((hyb2 == RDKit::Atom::SP2 || hyb2 == RDKit::Atom::SP3) &&
(hyb3 == RDKit::Atom::SP2 || hyb3 == RDKit::Atom::SP3),
"bad hybridizations");
if (hyb2 == RDKit::Atom::SP3 && hyb3 == RDKit::Atom::SP3) {
// general case:
d_forceConstant = sqrt(at2Params->V1 * at3Params->V1);
d_order = 3;
d_cosTerm = -1; // phi0=60
// special case for single bonds between group 6 elements:
if (bondOrder23 == 1.0 && Utils::isInGroup6(atNum2) &&
Utils::isInGroup6(atNum3)) {
double 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 = Utils::equation17(bondOrder23, at2Params, at3Params);
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 && Utils::isInGroup6(atNum2) &&
!Utils::isInGroup6(atNum3)) ||
(hyb3 == RDKit::Atom::SP3 && Utils::isInGroup6(atNum3) &&
!Utils::isInGroup6(atNum2))) {
d_forceConstant = Utils::equation17(bondOrder23, at2Params, at3Params);
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;
}
}
}
}
double TorsionAngleContrib::getEnergy(double *pos) const {
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
PRECONDITION(d_order == 2 || d_order == 3 || d_order == 6, "bad order");
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 p4(pos[3 * d_at4Idx], pos[3 * d_at4Idx + 1],
pos[3 * d_at4Idx + 2]);
double cosPhi = Utils::calculateCosTorsion(p1, p2, p3, p4);
double sinPhiSq = 1 - cosPhi * cosPhi;
// E(phi) = V/2 * (1 - cos(n*phi_0)*cos(n*phi))
double cosNPhi = 0.0;
switch (d_order) {
case 2:
cosNPhi = cosPhi * cosPhi - sinPhiSq;
break;
case 3:
// cos(3x) = cos^3(x) - 3*cos(x)*sin^2(x)
cosNPhi = cosPhi * (cosPhi * cosPhi - 3. * sinPhiSq);
break;
case 6:
// cos(6x) = 1 - 32*sin^6(x) + 48*sin^4(x) - 18*sin^2(x)
cosNPhi =
1 + sinPhiSq * (-32. * sinPhiSq * sinPhiSq + 48. * sinPhiSq - 18.);
break;
}
double res = d_forceConstant / 2.0 * (1. - d_cosTerm * cosNPhi);
// std::cout << " torsion(" << d_at1Idx << "," << d_at2Idx << "," << d_at3Idx
// << "," << d_at4Idx << "): " << cosPhi << "(" << acos(cosPhi) << ")" << " ->
// " << res << std::endl;
// if(d_at2Idx==5&&d_at3Idx==6) std::cerr << " torsion(" << d_at1Idx << "," <<
// d_at2Idx << "," << d_at3Idx << "," << d_at4Idx << "): " << cosPhi << "(" <<
// acos(cosPhi) << ")" << " -> " << res << std::endl;
return res;
}
void TorsionAngleContrib::getGrad(double *pos, double *grad) const {
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
PRECONDITION(grad, "bad vector");
RDGeom::Point3D iPoint(pos[3 * d_at1Idx], pos[3 * d_at1Idx + 1],
pos[3 * d_at1Idx + 2]);
RDGeom::Point3D jPoint(pos[3 * d_at2Idx], pos[3 * d_at2Idx + 1],
pos[3 * d_at2Idx + 2]);
RDGeom::Point3D kPoint(pos[3 * d_at3Idx], pos[3 * d_at3Idx + 1],
pos[3 * d_at3Idx + 2]);
RDGeom::Point3D lPoint(pos[3 * d_at4Idx], pos[3 * d_at4Idx + 1],
pos[3 * d_at4Idx + 2]);
double *g[4] = {&(grad[3 * d_at1Idx]), &(grad[3 * d_at2Idx]),
&(grad[3 * d_at3Idx]), &(grad[3 * d_at4Idx])};
RDGeom::Point3D r[4] = {iPoint - jPoint, kPoint - jPoint, jPoint - kPoint,
lPoint - kPoint};
RDGeom::Point3D t[2] = {r[0].crossProduct(r[1]), r[2].crossProduct(r[3])};
double d[2] = {t[0].length(), t[1].length()};
if (isDoubleZero(d[0]) || isDoubleZero(d[1])) {
return;
}
t[0] /= d[0];
t[1] /= d[1];
double cosPhi = t[0].dotProduct(t[1]);
clipToOne(cosPhi);
double sinPhiSq = 1.0 - cosPhi * cosPhi;
double sinPhi = ((sinPhiSq > 0.0) ? sqrt(sinPhiSq) : 0.0);
// dE/dPhi is independent of cartesians:
double dE_dPhi = getThetaDeriv(cosPhi, sinPhi);
#if 0
if(dE_dPhi!=dE_dPhi){
std::cout << "\tNaN in Torsion("<<d_at1Idx<<","<<d_at2Idx<<","<<d_at3Idx<<","<<d_at4Idx<<")"<< std::endl;
std::cout << "sin: " << sinPhi << std::endl;
std::cout << "cos: " << cosPhi << std::endl;
}
#endif
double sinTerm =
dE_dPhi * (isDoubleZero(sinPhi) ? (1.0 / cosPhi) : (1.0 / sinPhi));
Utils::calcTorsionGrad(r, t, d, g, sinTerm, cosPhi);
}
double TorsionAngleContrib::getThetaDeriv(double cosTheta,
double sinTheta) const {
PRECONDITION(d_order == 2 || d_order == 3 || d_order == 6, "bad order");
double sinThetaSq = sinTheta * sinTheta;
// cos(6x) = 1 - 32*sin^6(x) + 48*sin^4(x) - 18*sin^2(x)
double res = 0.0;
switch (d_order) {
case 2:
res = 2 * sinTheta * cosTheta;
break;
case 3:
// sin(3*x) = 3*sin(x) - 4*sin^3(x)
res = sinTheta * (3 - 4 * sinThetaSq);
break;
case 6:
// sin(6x) = cos(x) * [ 32*sin^5(x) - 32*sin^3(x) + 6*sin(x) ]
res = cosTheta * sinTheta * (32 * sinThetaSq * (sinThetaSq - 1) + 6);
break;
}
res *= d_forceConstant / 2.0 * d_cosTerm * -1 * d_order;
return res;
}
}
}
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