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#include "primitives/Torsion.hpp"
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namespace oopse {
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Torsion::Torsion(Atom* atom1, Atom* atom2, Atom* atom3, Atom* atom4, TorsionType* tt)
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: atom1_(atom1), atom2_(atom2), atom3_(atom3), atom4_(atom4) {
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}
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void Torsion::calcForce() {
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Vector3d pos1 = atom1_->getPos();
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Vector3d pos2 = atom2_->getPos();
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Vector3d pos3 = atom3_->getPos();
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Vector3d pos4 = atom4_->getPos();
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Vector3d r12 = pos1 - pos2;
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Vector3d r23 = pos2 - pos3;
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Vector3d r34 = pos3 - pos4;
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// Calculate the cross products and distances
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Vector3d A = cross(r12,r23);
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double rA = A.length();
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Vector3d B = cross(r23,r34);
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double rB = B.length();
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Vector3d C = cross(r23,A);
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double rC = C.length();
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// Calculate the sin and cos
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double cos_phi = (A*B)/(rA*rB);
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double sin_phi = (C*B)/(rC*rB);
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double phi= -atan2(sin_phi,cos_phi);
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double firstDerivative;
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torsionType_->calcForce(phi, firstDerivative, potential_);
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Vector3d f1,f2,f3;
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// Normalize B
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rB = 1.0/rB;
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B *= rB;
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// Next, we want to calculate the forces. In order
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// to do that, we first need to figure out whether the
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// sin or cos form will be more stable. For this,
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// just look at the value of phi
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if (fabs(sin_phi) > 0.1) {
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// use the sin version to avoid 1/cos terms
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rA = 1.0/rA;
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A *= rA;
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Vector3d dcosdA = rA*(cos_phi*A-B);
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Vector3d dcosdB = rB*(cos_phi*B-A);
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K1 = K1/sin_phi;
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//simple form
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//f1 = K1 * cross(r23, dcosdA);
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//f3 = K1 * cross(r23, dcosdB);
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//f2 = K1 * ( cross(r34, dcosdB) - cross(r12, dcosdA));
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f1.x = K1*(r23.y*dcosdA.z - r23.z*dcosdA.y);
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f1.y = K1*(r23.z*dcosdA.x - r23.x*dcosdA.z);
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f1.z = K1*(r23.x*dcosdA.y - r23.y*dcosdA.x);
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f3.x = K1*(r23.z*dcosdB.y - r23.y*dcosdB.z);
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f3.y = K1*(r23.x*dcosdB.z - r23.z*dcosdB.x);
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f3.z = K1*(r23.y*dcosdB.x - r23.x*dcosdB.y);
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f2.x = K1*(r12.z*dcosdA.y - r12.y*dcosdA.z + r34.y*dcosdB.z - r34.z*dcosdB.y);
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f2.y = K1*(r12.x*dcosdA.z - r12.z*dcosdA.x + r34.z*dcosdB.x - r34.x*dcosdB.z);
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f2.z = K1*(r12.y*dcosdA.x - r12.x*dcosdA.y + r34.x*dcosdB.y - r34.y*dcosdB.x);
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} else {
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// This angle is closer to 0 or 180 than it is to
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// 90, so use the cos version to avoid 1/sin terms
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// Normalize C
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rC = 1.0/rC;
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C *= rC;
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Vector3d dsindC = rC*(sin_phi*C-B);
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Vector3d dsindB = rB*(sin_phi*B-C);
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K1 = -K1/cos_phi;
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f1.x = K1*((r23.y*r23.y + r23.z*r23.z)*dsindC.x - r23.x*r23.y*dsindC.y - r23.x*r23.z*dsindC.z);
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f1.y = K1*((r23.z*r23.z + r23.x*r23.x)*dsindC.y - r23.y*r23.z*dsindC.z - r23.y*r23.x*dsindC.x);
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f1.z = K1*((r23.x*r23.x + r23.y*r23.y)*dsindC.z - r23.z*r23.x*dsindC.x - r23.z*r23.y*dsindC.y);
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f3 = K1 *cross(dsindB,r23);
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f2.x = K1*(-(r23.y*r12.y + r23.z*r12.z)*dsindC.x + (2.0*r23.x*r12.y - r12.x*r23.y)*dsindC.y
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+ (2.0*r23.x*r12.z - r12.x*r23.z)*dsindC.z + dsindB.z*r34.y - dsindB.y*r34.z);
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f2.y = K1*(-(r23.z*r12.z + r23.x*r12.x)*dsindC.y + (2.0*r23.y*r12.z - r12.y*r23.z)*dsindC.z
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+ (2.0*r23.y*r12.x - r12.y*r23.x)*dsindC.x + dsindB.x*r34.z - dsindB.z*r34.x);
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f2.z = K1*(-(r23.x*r12.x + r23.y*r12.y)*dsindC.z + (2.0*r23.z*r12.x - r12.z*r23.x)*dsindC.x
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+(2.0*r23.z*r12.y - r12.z*r23.y)*dsindC.y + dsindB.y*r34.x - dsindB.x*r34.y);
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}
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atom1_->addFrc(f1);
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atom2_->addFrc(f2 - f1);
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atom3_->addFrc(f3 - f2);
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atom4_->addFrc(-f3);
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}
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double K=0; // energy
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double K1=0; // force
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// get the dihedral information
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int multiplicity = value->multiplicity;
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// Loop through the multiple parameter sets for this
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// bond. We will only loop more than once if this
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// has multiple parameter sets from Charmm22
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for (int mult_num=0; mult_num<multiplicity; mult_num++)
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{
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/* get angle information */
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double k = value->values[mult_num].k * scale;
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double delta = value->values[mult_num].delta;
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int n = value->values[mult_num].n;
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// Calculate the energy
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if (n)
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{
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// Periodicity is greater than 0, so use cos form
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K += k*(1+cos(n*phi + delta));
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K1 += -n*k*sin(n*phi + delta);
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}
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else
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{
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// Periodicity is 0, so just use the harmonic form
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double diff = phi-delta;
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if (diff < -PI) diff += TWOPI;
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else if (diff > PI) diff -= TWOPI;
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K += k*diff*diff;
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K1 += 2.0*k*diff;
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}
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} /* for multiplicity */
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void Torsion::calc_forces(){
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/**********************************************************************
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*
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* initialize vectors
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*
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***********************************************************************/
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vect r_ab; /* the vector whose origin is a and end is b */
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vect r_cb; /* the vector whose origin is c and end is b */
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vect r_cd; /* the vector whose origin is c and end is b */
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vect r_cr1; /* the cross product of r_ab and r_cb */
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vect r_cr2; /* the cross product of r_cb and r_cd */
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double r_cr1_x2; /* the components of r_cr1 squared */
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double r_cr1_y2;
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double r_cr1_z2;
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double r_cr2_x2; /* the components of r_cr2 squared */
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double r_cr2_y2;
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double r_cr2_z2;
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double r_cr1_sqr; /* the length of r_cr1 squared */
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double r_cr2_sqr; /* the length of r_cr2 squared */
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double r_cr1_r_cr2; /* the length of r_cr1 * length of r_cr2 */
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Vector3d aR, bR, cR, dR;
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Vector3d aF, bF, cF, dF;
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aR = c_p_a->getPos();
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bR = c_p_b->getPos();
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cR = c_p_c->getPos();
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dR = c_p_d->getPos();
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r_ab.x = bR[0] - aR[0];
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r_ab.y = bR[1] - aR[1];
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r_ab.z = bR[2] - aR[2];
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r_ab.length = sqrt((r_ab.x * r_ab.x + r_ab.y * r_ab.y + r_ab.z * r_ab.z));
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r_cb.x = bR[0] - cR[0];
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r_cb.y = bR[1] - cR[1];
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r_cb.z = bR[2] - cR[2];
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r_cb.length = sqrt((r_cb.x * r_cb.x + r_cb.y * r_cb.y + r_cb.z * r_cb.z));
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r_cd.x = dR[0] - cR[0];
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r_cd.y = dR[1] - cR[1];
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r_cd.z = dR[2] - cR[2];
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r_cd.length = sqrt((r_cd.x * r_cd.x + r_cd.y * r_cd.y + r_cd.z * r_cd.z));
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r_cr1.x = r_ab.y * r_cb.z - r_cb.y * r_ab.z;
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r_cr1.y = r_ab.z * r_cb.x - r_cb.z * r_ab.x;
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r_cr1.z = r_ab.x * r_cb.y - r_cb.x * r_ab.y;
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r_cr1_x2 = r_cr1.x * r_cr1.x;
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r_cr1_y2 = r_cr1.y * r_cr1.y;
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r_cr1_z2 = r_cr1.z * r_cr1.z;
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r_cr1_sqr = r_cr1_x2 + r_cr1_y2 + r_cr1_z2;
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r_cr1.length = sqrt(r_cr1_sqr);
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r_cr2.x = r_cb.y * r_cd.z - r_cd.y * r_cb.z;
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r_cr2.y = r_cb.z * r_cd.x - r_cd.z * r_cb.x;
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r_cr2.z = r_cb.x * r_cd.y - r_cd.x * r_cb.y;
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r_cr2_x2 = r_cr2.x * r_cr2.x;
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r_cr2_y2 = r_cr2.y * r_cr2.y;
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r_cr2_z2 = r_cr2.z * r_cr2.z;
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r_cr2_sqr = r_cr2_x2 + r_cr2_y2 + r_cr2_z2;
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r_cr2.length = sqrt(r_cr2_sqr);
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r_cr1_r_cr2 = r_cr1.length * r_cr2.length;
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//Vector3d pos1 = atom1_->getPos();
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//Vector3d pos2 = atom2_->getPos();
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//Vector3d pos3 = atom3_->getPos();
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//Vector3d pos4 = atom4_->getPos();
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//Vector3d r12 = pos2 - pos1;
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//Vector3d r32 = pos2 - pos3;
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//Vector3d r34 = pos4 - pos3;
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//A = cross(r12, r32);
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//B = cross(r32, r34);
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//rA = A.length();
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//rB = B.length();
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/**********************************************************************
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*
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* dot product and angle calculations
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*
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***********************************************************************/
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double cr1_dot_cr2; /* the dot product of the cr1 and cr2 vectors */
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double cos_phi; /* the cosine of the torsion angle */
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cr1_dot_cr2 = r_cr1.x * r_cr2.x + r_cr1.y * r_cr2.y + r_cr1.z * r_cr2.z;
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cos_phi = cr1_dot_cr2 / r_cr1_r_cr2;
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/* adjust for the granularity of the numbers for angles near 0 or pi */
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if(cos_phi > 1.0) cos_phi = 1.0;
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if(cos_phi < -1.0) cos_phi = -1.0;
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//cos_phi = dot (A, B) / (rA * rB);
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//if (cos_phi > 1.0) {
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// cos_phi = 1.0;
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//}
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//if (cos_phi < -1.0) {
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// cos_phi = -1.0;
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//}
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/********************************************************************
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*
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* This next section calculates derivatives needed for the force
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* calculation
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*
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********************************************************************/
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/* the derivatives of cos phi with respect to the x, y,
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and z components of vectors cr1 and cr2. */
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double d_cos_dx_cr1;
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double d_cos_dy_cr1;
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double d_cos_dz_cr1;
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double d_cos_dx_cr2;
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double d_cos_dy_cr2;
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double d_cos_dz_cr2;
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d_cos_dx_cr1 = r_cr2.x / r_cr1_r_cr2 - (cos_phi * r_cr1.x) / r_cr1_sqr;
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d_cos_dy_cr1 = r_cr2.y / r_cr1_r_cr2 - (cos_phi * r_cr1.y) / r_cr1_sqr;
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d_cos_dz_cr1 = r_cr2.z / r_cr1_r_cr2 - (cos_phi * r_cr1.z) / r_cr1_sqr;
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d_cos_dx_cr2 = r_cr1.x / r_cr1_r_cr2 - (cos_phi * r_cr2.x) / r_cr2_sqr;
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d_cos_dy_cr2 = r_cr1.y / r_cr1_r_cr2 - (cos_phi * r_cr2.y) / r_cr2_sqr;
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d_cos_dz_cr2 = r_cr1.z / r_cr1_r_cr2 - (cos_phi * r_cr2.z) / r_cr2_sqr;
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//Vector3d dcosdA = B /(rA * rB) - cos_phi /(rA * rA) * A;
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//Vector3d dcosdA = 1.0 /rA * (B.normalize() - cos_phi * A.normalize());
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//Vector3d dcosdB = 1.0 /rB * (A.normalize() - cos_phi * B.normalize());
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/***********************************************************************
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*
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* Calculate the actual forces and place them in the atoms.
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*
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***********************************************************************/
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double force; /*the force scaling factor */
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force = torsion_force(cos_phi);
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aF[0] = force * (d_cos_dy_cr1 * r_cb.z - d_cos_dz_cr1 * r_cb.y);
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aF[1] = force * (d_cos_dz_cr1 * r_cb.x - d_cos_dx_cr1 * r_cb.z);
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aF[2] = force * (d_cos_dx_cr1 * r_cb.y - d_cos_dy_cr1 * r_cb.x);
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bF[0] = force * ( d_cos_dy_cr1 * (r_ab.z - r_cb.z)
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- d_cos_dy_cr2 * r_cd.z
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+ d_cos_dz_cr1 * (r_cb.y - r_ab.y)
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+ d_cos_dz_cr2 * r_cd.y);
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bF[1] = force * ( d_cos_dx_cr1 * (r_cb.z - r_ab.z)
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+ d_cos_dx_cr2 * r_cd.z
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+ d_cos_dz_cr1 * (r_ab.x - r_cb.x)
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- d_cos_dz_cr2 * r_cd.x);
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bF[2] = force * ( d_cos_dx_cr1 * (r_ab.y - r_cb.y)
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- d_cos_dx_cr2 * r_cd.y
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+ d_cos_dy_cr1 * (r_cb.x - r_ab.x)
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+ d_cos_dy_cr2 * r_cd.x);
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cF[0] = force * (- d_cos_dy_cr1 * r_ab.z
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- d_cos_dy_cr2 * (r_cb.z - r_cd.z)
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+ d_cos_dz_cr1 * r_ab.y
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- d_cos_dz_cr2 * (r_cd.y - r_cb.y));
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cF[1] = force * ( d_cos_dx_cr1 * r_ab.z
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- d_cos_dx_cr2 * (r_cd.z - r_cb.z)
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- d_cos_dz_cr1 * r_ab.x
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- d_cos_dz_cr2 * (r_cb.x - r_cd.x));
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cF[2] = force * (- d_cos_dx_cr1 * r_ab.y
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- d_cos_dx_cr2 * (r_cb.y - r_cd.y)
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+ d_cos_dy_cr1 * r_ab.x
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- d_cos_dy_cr2 * (r_cd.x - r_cb.x));
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dF[0] = force * (d_cos_dy_cr2 * r_cb.z - d_cos_dz_cr2 * r_cb.y);
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dF[1] = force * (d_cos_dz_cr2 * r_cb.x - d_cos_dx_cr2 * r_cb.z);
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dF[2] = force * (d_cos_dx_cr2 * r_cb.y - d_cos_dy_cr2 * r_cb.x);
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c_p_a->addFrc(aF);
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c_p_b->addFrc(bF);
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c_p_c->addFrc(cF);
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c_p_d->addFrc(dF);
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//double firstDerivative;
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//bondType_->calcForce(cos_phi, firstDerivative, potential_);
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//f1 = force * cross (dcosdA, r32);
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//f2 =
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//f3 =
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//f4 = force * cross(dcosdB, r32);
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//atom1_->addFrc(f1);
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//atom2_->addFrc(f2);
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//atom3_->addFrc(f3);
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//atom4_->addFrc(f4);
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}
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}
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