double getDihedralRad(const Conformer &conf, unsigned int iAtomId,
unsigned int jAtomId, unsigned int kAtomId,
unsigned int lAtomId) {
const RDGeom::POINT3D_VECT &pos = conf.getPositions();
URANGE_CHECK(iAtomId, pos.size());
URANGE_CHECK(jAtomId, pos.size());
URANGE_CHECK(kAtomId, pos.size());
URANGE_CHECK(lAtomId, pos.size());
RDGeom::Point3D rIJ = pos[jAtomId] - pos[iAtomId];
double rIJSqLength = rIJ.lengthSq();
if (rIJSqLength <= 1.e-16)
throw ValueErrorException("atoms i and j have identical 3D coordinates");
RDGeom::Point3D rJK = pos[kAtomId] - pos[jAtomId];
double rJKSqLength = rJK.lengthSq();
if (rJKSqLength <= 1.e-16)
throw ValueErrorException("atoms j and k have identical 3D coordinates");
RDGeom::Point3D rKL = pos[lAtomId] - pos[kAtomId];
double rKLSqLength = rKL.lengthSq();
if (rKLSqLength <= 1.e-16)
throw ValueErrorException("atoms k and l have identical 3D coordinates");
RDGeom::Point3D nIJK = rIJ.crossProduct(rJK);
double nIJKSqLength = nIJK.lengthSq();
RDGeom::Point3D nJKL = rJK.crossProduct(rKL);
double nJKLSqLength = nJKL.lengthSq();
RDGeom::Point3D m = nIJK.crossProduct(rJK);
// we want a signed dihedral, that's why we use atan2 instead of acos
return -atan2(m.dotProduct(nJKL) / sqrt(nJKLSqLength * m.lengthSq()),
nIJK.dotProduct(nJKL) / sqrt(nIJKSqLength * nJKLSqLength));
}
void setDihedralRad(Conformer &conf, unsigned int iAtomId, unsigned int jAtomId,
unsigned int kAtomId, unsigned int lAtomId, double value) {
RDGeom::POINT3D_VECT &pos = conf.getPositions();
URANGE_CHECK(iAtomId, pos.size());
URANGE_CHECK(jAtomId, pos.size());
URANGE_CHECK(kAtomId, pos.size());
URANGE_CHECK(lAtomId, pos.size());
ROMol &mol = conf.getOwningMol();
Bond *bondIJ = mol.getBondBetweenAtoms(iAtomId, jAtomId);
if (!bondIJ) throw ValueErrorException("atoms i and j must be bonded");
Bond *bondJK = mol.getBondBetweenAtoms(jAtomId, kAtomId);
if (!bondJK) throw ValueErrorException("atoms j and k must be bonded");
Bond *bondKL = mol.getBondBetweenAtoms(kAtomId, lAtomId);
if (!bondKL) throw ValueErrorException("atoms k and l must be bonded");
if (queryIsBondInRing(bondJK))
throw ValueErrorException("bond (j,k) must not belong to a ring");
RDGeom::Point3D rIJ = pos[jAtomId] - pos[iAtomId];
double rIJSqLength = rIJ.lengthSq();
if (rIJSqLength <= 1.e-16)
throw ValueErrorException("atoms i and j have identical 3D coordinates");
RDGeom::Point3D rJK = pos[kAtomId] - pos[jAtomId];
double rJKSqLength = rJK.lengthSq();
if (rJKSqLength <= 1.e-16)
throw ValueErrorException("atoms j and k have identical 3D coordinates");
RDGeom::Point3D rKL = pos[lAtomId] - pos[kAtomId];
double rKLSqLength = rKL.lengthSq();
if (rKLSqLength <= 1.e-16)
throw ValueErrorException("atoms k and l have identical 3D coordinates");
RDGeom::Point3D nIJK = rIJ.crossProduct(rJK);
double nIJKSqLength = nIJK.lengthSq();
RDGeom::Point3D nJKL = rJK.crossProduct(rKL);
double nJKLSqLength = nJKL.lengthSq();
RDGeom::Point3D m = nIJK.crossProduct(rJK);
// we only need to rotate by delta with respect to the current dihedral value
value -= -atan2(m.dotProduct(nJKL) / sqrt(nJKLSqLength * m.lengthSq()),
nIJK.dotProduct(nJKL) / sqrt(nIJKSqLength * nJKLSqLength));
// our rotation axis is the (j,k) bond
RDGeom::Point3D &rotAxisBegin = pos[jAtomId];
RDGeom::Point3D &rotAxisEnd = pos[kAtomId];
RDGeom::Point3D rotAxis = rotAxisEnd - rotAxisBegin;
rotAxis.normalize();
// get all atoms bonded to k and loop through them
std::list<unsigned int> alist;
_toBeMovedIdxList(mol, jAtomId, kAtomId, alist);
for (std::list<unsigned int>::iterator it = alist.begin(); it != alist.end();
++it) {
// translate atom so that it coincides with the origin of rotation
pos[*it] -= rotAxisBegin;
// rotate around our rotation axis
RDGeom::Transform3D rotByAngle;
rotByAngle.SetRotation(value, rotAxis);
rotByAngle.TransformPoint(pos[*it]);
// translate atom back
pos[*it] += rotAxisBegin;
}
}
double calculateCosY(const RDGeom::Point3D &iPoint,
const RDGeom::Point3D &jPoint, const RDGeom::Point3D &kPoint,
const RDGeom::Point3D &lPoint) {
RDGeom::Point3D rJI = iPoint - jPoint;
RDGeom::Point3D rJK = kPoint - jPoint;
RDGeom::Point3D rJL = lPoint - jPoint;
rJI /= rJI.length();
rJK /= rJK.length();
rJL /= rJL.length();
RDGeom::Point3D n = rJI.crossProduct(rJK);
n /= n.length();
return n.dotProduct(rJL);
}
double TorsionConstraintContrib::getEnergy(double *pos) const
{
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
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]);
RDGeom::Point3D r1 = p1 - p2;
RDGeom::Point3D r2 = p3 - p2;
RDGeom::Point3D r3 = p2 - p3;
RDGeom::Point3D r4 = p4 - p3;
RDGeom::Point3D t1 = r1.crossProduct(r2);
RDGeom::Point3D t2 = r3.crossProduct(r4);
double d1 = std::max(t1.length(), 0.0);
double d2 = std::max(t2.length(), 0.0);
t1 /= d1;
t2 /= d2;
double cosPhi = t1.dotProduct(t2);
RDGeom::Point3D n123 = (-r1).crossProduct(r2);
double n123SqLength = n123.lengthSq();
RDGeom::Point3D n234 = r2.crossProduct(r4);
double n234SqLength = n234.lengthSq();
RDGeom::Point3D m = n123.crossProduct(r2);
// we want a signed dihedral, that's why we use atan2 instead of acos
double dihedral = RAD2DEG * (-atan2(m.dotProduct(n234) / sqrt(n234SqLength * m.lengthSq()),
n123.dotProduct(n234) / sqrt(n123SqLength * n234SqLength)));
double ave = 0.5 * (d_minDihedralDeg + d_maxDihedralDeg);
dihedral += 360.0 * boost::math::round((ave - dihedral) / 360.0);
double dihedralTerm = 0.0;
if (dihedral < d_minDihedralDeg) {
dihedralTerm = dihedral - d_minDihedralDeg;
}
else if (dihedral > d_maxDihedralDeg) {
dihedralTerm = dihedral - d_maxDihedralDeg;
}
double const c = 0.5 * DEG2RAD * DEG2RAD;
double res = c * d_forceConstant * dihedralTerm * dihedralTerm;
return res;
}
double calcOopChi(const RDGeom::Point3D &iPoint, const RDGeom::Point3D &jPoint,
const RDGeom::Point3D &kPoint,
const RDGeom::Point3D &lPoint) {
RDGeom::Point3D rJI = iPoint - jPoint;
RDGeom::Point3D rJK = kPoint - jPoint;
RDGeom::Point3D rJL = lPoint - jPoint;
rJI /= rJI.length();
rJK /= rJK.length();
rJL /= rJL.length();
RDGeom::Point3D n = rJI.crossProduct(rJK);
n /= n.length();
double sinChi = n.dotProduct(rJL);
clipToOne(sinChi);
return RAD2DEG * asin(sinChi);
}
TorsionConstraintContrib::TorsionConstraintContrib(ForceField *owner,
unsigned int idx1, unsigned int idx2, unsigned int idx3,
unsigned int idx4, bool relative, double minDihedralDeg,
double maxDihedralDeg, double forceConst)
{
PRECONDITION(owner,"bad owner");
const RDGeom::PointPtrVect &pos = owner->positions();
RANGE_CHECK(0, idx1, pos.size() - 1);
RANGE_CHECK(0, idx2, pos.size() - 1);
RANGE_CHECK(0, idx3, pos.size() - 1);
RANGE_CHECK(0, idx4, pos.size() - 1);
PRECONDITION((!(maxDihedralDeg < minDihedralDeg))
&& ((maxDihedralDeg - minDihedralDeg) < 360.0), "bad bounds");
double dihedral = 0.0;
if (relative) {
RDGeom::Point3D p1 = *((RDGeom::Point3D *)pos[idx1]);
RDGeom::Point3D p2 = *((RDGeom::Point3D *)pos[idx2]);
RDGeom::Point3D p3 = *((RDGeom::Point3D *)pos[idx3]);
RDGeom::Point3D p4 = *((RDGeom::Point3D *)pos[idx4]);
RDGeom::Point3D r12 = p2 - p1;
RDGeom::Point3D r23 = p3 - p2;
RDGeom::Point3D r34 = p4 - p3;
RDGeom::Point3D n123 = r12.crossProduct(r23);
double nIJKSqLength = n123.lengthSq();
RDGeom::Point3D n234 = r23.crossProduct(r34);
double nJKLSqLength = n234.lengthSq();
RDGeom::Point3D m = n123.crossProduct(r23);
// we want a signed dihedral, that's why we use atan2 instead of acos
dihedral = RAD2DEG
* (-atan2(m.dotProduct(n234) / sqrt(nJKLSqLength * m.lengthSq()),
n123.dotProduct(n234) / sqrt(nIJKSqLength * nJKLSqLength)));
}
dp_forceField = owner;
d_at1Idx = idx1;
d_at2Idx = idx2;
d_at3Idx = idx3;
d_at4Idx = idx4;
minDihedralDeg += dihedral;
maxDihedralDeg += dihedral;
_pretreatDihedrals(minDihedralDeg, maxDihedralDeg);
d_minDihedralDeg = minDihedralDeg;
d_maxDihedralDeg = maxDihedralDeg;
d_forceConstant = forceConst;
}
void InversionContrib::getGrad(double *pos, double *grad) const {
PRECONDITION(dp_forceField, "no owner");
PRECONDITION(pos, "bad vector");
PRECONDITION(grad, "bad vector");
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 *g1 = &(grad[3 * d_at1Idx]);
double *g2 = &(grad[3 * d_at2Idx]);
double *g3 = &(grad[3 * d_at3Idx]);
double *g4 = &(grad[3 * d_at4Idx]);
RDGeom::Point3D rJI = p1 - p2;
RDGeom::Point3D rJK = p3 - p2;
RDGeom::Point3D rJL = p4 - p2;
double dJI = rJI.length();
double dJK = rJK.length();
double dJL = rJL.length();
if (isDoubleZero(dJI) || isDoubleZero(dJK) || isDoubleZero(dJL)) {
return;
}
rJI /= dJI;
rJK /= dJK;
rJL /= dJL;
RDGeom::Point3D n = (-rJI).crossProduct(rJK);
n /= n.length();
double cosY = n.dotProduct(rJL);
double sinYSq = 1.0 - cosY * cosY;
double sinY = std::max(((sinYSq > 0.0) ? sqrt(sinYSq) : 0.0), 1.0e-8);
double cosTheta = rJI.dotProduct(rJK);
double sinThetaSq = std::max(1.0 - cosTheta * cosTheta, 1.0e-8);
double sinTheta = std::max(((sinThetaSq > 0.0) ? sqrt(sinThetaSq) : 0.0), 1.0e-8);
// sin(2 * W) = 2 * sin(W) * cos(W) = 2 * cos(Y) * sin(Y)
double dE_dW = -d_forceConstant
* (d_C1 * cosY - 4.0 * d_C2 * cosY * sinY);
RDGeom::Point3D t1 = rJL.crossProduct(rJK);
RDGeom::Point3D t2 = rJI.crossProduct(rJL);
RDGeom::Point3D t3 = rJK.crossProduct(rJI);
double term1 = sinY * sinTheta;
double term2 = cosY / (sinY * sinThetaSq);
double tg1[3] = { (t1.x / term1 - (rJI.x - rJK.x * cosTheta) * term2) / dJI,
(t1.y / term1 - (rJI.y - rJK.y * cosTheta) * term2) / dJI,
(t1.z / term1 - (rJI.z - rJK.z * cosTheta) * term2) / dJI };
double tg3[3] = { (t2.x / term1 - (rJK.x - rJI.x * cosTheta) * term2) / dJK,
(t2.y / term1 - (rJK.y - rJI.y * cosTheta) * term2) / dJK,
(t2.z / term1 - (rJK.z - rJI.z * cosTheta) * term2) / dJK };
double tg4[3] = { (t3.x / term1 - rJL.x * cosY / sinY) / dJL,
(t3.y / term1 - rJL.y * cosY / sinY) / dJL,
(t3.z / term1 - rJL.z * cosY / sinY) / dJL };
for (unsigned int i = 0; i < 3; ++i) {
g1[i] += dE_dW * tg1[i];
g2[i] += -dE_dW * (tg1[i] + tg3[i] + tg4[i]);
g3[i] += dE_dW * tg3[i];
g4[i] += dE_dW * tg4[i];
}
}
void OopBendContrib::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 *g1 = &(grad[3 * d_at1Idx]);
double *g2 = &(grad[3 * d_at2Idx]);
double *g3 = &(grad[3 * d_at3Idx]);
double *g4 = &(grad[3 * d_at4Idx]);
RDGeom::Point3D rJI = iPoint - jPoint;
RDGeom::Point3D rJK = kPoint - jPoint;
RDGeom::Point3D rJL = lPoint - jPoint;
double dJI = rJI.length();
double dJK = rJK.length();
double dJL = rJL.length();
if (isDoubleZero(dJI) || isDoubleZero(dJK) || isDoubleZero(dJL)) {
return;
}
rJI /= dJI;
rJK /= dJK;
rJL /= dJL;
RDGeom::Point3D n = (-rJI).crossProduct(rJK);
n /= n.length();
double const c2 = MDYNE_A_TO_KCAL_MOL * DEG2RAD * DEG2RAD;
double sinChi = rJL.dotProduct(n);
clipToOne(sinChi);
double cosChiSq = 1.0 - sinChi * sinChi;
double cosChi = std::max(((cosChiSq > 0.0) ? sqrt(cosChiSq) : 0.0), 1.0e-8);
double chi = RAD2DEG * asin(sinChi);
double cosTheta = rJI.dotProduct(rJK);
clipToOne(cosTheta);
double sinThetaSq = std::max(1.0 - cosTheta * cosTheta, 1.0e-8);
double sinTheta =
std::max(((sinThetaSq > 0.0) ? sqrt(sinThetaSq) : 0.0), 1.0e-8);
double dE_dChi = RAD2DEG * c2 * d_koop * chi;
RDGeom::Point3D t1 = rJL.crossProduct(rJK);
RDGeom::Point3D t2 = rJI.crossProduct(rJL);
RDGeom::Point3D t3 = rJK.crossProduct(rJI);
double term1 = cosChi * sinTheta;
double term2 = sinChi / (cosChi * sinThetaSq);
double tg1[3] = {(t1.x / term1 - (rJI.x - rJK.x * cosTheta) * term2) / dJI,
(t1.y / term1 - (rJI.y - rJK.y * cosTheta) * term2) / dJI,
(t1.z / term1 - (rJI.z - rJK.z * cosTheta) * term2) / dJI};
double tg3[3] = {(t2.x / term1 - (rJK.x - rJI.x * cosTheta) * term2) / dJK,
(t2.y / term1 - (rJK.y - rJI.y * cosTheta) * term2) / dJK,
(t2.z / term1 - (rJK.z - rJI.z * cosTheta) * term2) / dJK};
double tg4[3] = {(t3.x / term1 - rJL.x * sinChi / cosChi) / dJL,
(t3.y / term1 - rJL.y * sinChi / cosChi) / dJL,
(t3.z / term1 - rJL.z * sinChi / cosChi) / dJL};
for (unsigned int i = 0; i < 3; ++i) {
g1[i] += dE_dChi * tg1[i];
g2[i] += -dE_dChi * (tg1[i] + tg3[i] + tg4[i]);
g3[i] += dE_dChi * tg3[i];
g4[i] += dE_dChi * tg4[i];
}
}
void TorsionConstraintContrib::getGrad(double *pos, double *grad) const
{
PRECONDITION(dp_forceField,"no owner");
PRECONDITION(pos,"bad vector");
PRECONDITION(grad,"bad vector");
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 *g[4] = {
&(grad[3 * d_at1Idx]),
&(grad[3 * d_at2Idx]),
&(grad[3 * d_at3Idx]),
&(grad[3 * d_at4Idx])
};
RDGeom::Point3D r[4] = {
p1 - p2,
p3 - p2,
p2 - p3,
p4 - p3
};
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]);
double sinPhiSq = 1.0 - cosPhi * cosPhi;
double sinPhi = ((sinPhiSq > 0.0) ? sqrt(sinPhiSq) : 0.0);
// dE/dPhi is independent of cartesians:
RDGeom::Point3D n123 = (-r[0]).crossProduct(r[1]);
double n123SqLength = n123.lengthSq();
RDGeom::Point3D n234 = r[1].crossProduct(r[3]);
double n234SqLength = n234.lengthSq();
RDGeom::Point3D m = n123.crossProduct(r[1]);
// we want a signed dihedral, that's why we use atan2 instead of acos
double dihedral = RAD2DEG * (-atan2(m.dotProduct(n234) / sqrt(n234SqLength * m.lengthSq()),
n123.dotProduct(n234) / sqrt(n123SqLength * n234SqLength)));
//double dihedral = RAD2DEG * acos(cosPhi);
double ave = 0.5 * (d_minDihedralDeg + d_maxDihedralDeg);
dihedral += 360.0 * boost::math::round((ave - dihedral) / 360.0);
double dihedralTerm = 0.0;
if (dihedral < d_minDihedralDeg) {
dihedralTerm = dihedral - d_minDihedralDeg;
}
else if (dihedral > d_maxDihedralDeg) {
dihedralTerm = dihedral - d_maxDihedralDeg;
}
double dE_dPhi = DEG2RAD * d_forceConstant * dihedralTerm;
// FIX: use a tolerance here
// this is hacky, but it's per the
// recommendation from Niketic and Rasmussen:
double sinTerm = -dE_dPhi * (isDoubleZero(sinPhi)
? (1.0 / cosPhi) : (1.0 / sinPhi));
Utils::calcTorsionGrad(r, t, d, g, sinTerm, cosPhi);
}