dihedral_spherical.cpp
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dihedral_spherical.cpp
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	/* ----------------------------------------------------------------------
	LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
	http://lammps.sandia.gov, Sandia National Laboratories
	Steve Plimpton, sjplimp@sandia.gov

	Copyright (2003) Sandia Corporation. Under the terms of Contract
	DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
	certain rights in this software. This software is distributed under
	the GNU General Public License.

	See the README file in the top-level LAMMPS directory.
	------------------------------------------------------------------------- */

	/* ----------------------------------------------------------------------
	Contributing author: Andrew Jewett (Caltech)
	[ using code borrowed from Loukas D. Peristeras (Scienomics SARL)
	and Paul Crozier (SNL) ]
	------------------------------------------------------------------------- */

	#include <mpi.h>
	#include <cmath>
	#include <cstdlib>
	#include <cassert>
	#include "atom.h"
	#include "comm.h"
	#include "neighbor.h"
	#include "domain.h"
	#include "force.h"
	#include "pair.h"
	#include "update.h"
	#include "math_const.h"
	#include "math_extra.h"
	#include "memory.h"
	#include "error.h"
	#include "dihedral_spherical.h"

	using namespace std;
	using namespace LAMMPS_NS;
	using namespace MathConst;
	using namespace MathExtra;

	/* ---------------------------------------------------------------------- */

	DihedralSpherical::DihedralSpherical(LAMMPS *lmp) : Dihedral(lmp) {}

	/* ---------------------------------------------------------------------- */

	DihedralSpherical::~DihedralSpherical()
	{
	if (allocated && !copymode) {
	memory->destroy(setflag);
	memory->destroy(nterms);

	for (int i=1; i<= atom->ndihedraltypes; i++) {
	if ( Ccoeff[i] ) delete [] Ccoeff[i];
	if ( phi_mult[i] ) delete [] phi_mult[i];
	if ( phi_shift[i] ) delete [] phi_shift[i];
	if ( phi_offset[i] ) delete [] phi_offset[i];
	if ( theta1_mult[i] ) delete [] theta1_mult[i];
	if ( theta1_shift[i] ) delete [] theta1_shift[i];
	if ( theta1_offset[i] ) delete [] theta1_offset[i];
	if ( theta2_mult[i] ) delete [] theta2_mult[i];
	if ( theta2_shift[i] ) delete [] theta2_shift[i];
	if ( theta2_offset[i] ) delete [] theta2_offset[i];
	}
	delete [] Ccoeff;
	delete [] phi_mult;
	delete [] phi_shift;
	delete [] phi_offset;
	delete [] theta1_mult;
	delete [] theta1_shift;
	delete [] theta1_offset;
	delete [] theta2_mult;
	delete [] theta2_shift;
	delete [] theta2_offset;
	}
	}


	static void norm3safe(double *v) {
	double inv_scale = sqrt(v[0]v[0]+v[1]v[1]+v[2]*v[2]);
	double scale = 1.0;
	if (inv_scale > 0.0)
	scale = 1.0 / inv_scale;
	v[0] *= scale;
	v[1] *= scale;
	v[2] *= scale;
	}


	// --------------------------------------------
	// ------- Calculate the dihedral angle -------
	// --------------------------------------------
	static const int g_dim=3;

	static double Phi(double const *x1, //array holding x,y,z coords atom 1
	double const *x2, // : : : : 2
	double const *x3, // : : : : 3
	double const *x4, // : : : : 4
	Domain *domain, //<-periodic boundary information
	double *vb12, //<-preallocated vector will store x2-x1
	double *vb23, //<-preallocated vector will store x3-x2
	double *vb34, //<-preallocated vector will store x4-x3
	double *n123, //<-will store normal to plane x1,x2,x3
	double *n234) //<-will store normal to plane x2,x3,x4
	{

	for (int d=0; d < g_dim; ++d) {
	vb12[d] = x2[d] - x1[d]; // 1st bond
	vb23[d] = x3[d] - x2[d]; // 2nd bond
	vb34[d] = x4[d] - x3[d]; // 3rd bond
	}

	//Consider periodic boundary conditions:
	domain->minimum_image(vb12[0],vb12[1],vb12[2]);
	domain->minimum_image(vb23[0],vb23[1],vb23[2]);
	domain->minimum_image(vb34[0],vb34[1],vb34[2]);

	//--- Compute the normal to the planes formed by atoms 1,2,3 and 2,3,4 ---

	cross3(vb23, vb12, n123); // <- n123=vb23 x vb12
	cross3(vb23, vb34, n234); // <- n234=vb23 x vb34

	norm3safe(n123);
	norm3safe(n234);

	double cos_phi = -dot3(n123, n234);

	if (cos_phi > 1.0)
	cos_phi = 1.0;
	else if (cos_phi < -1.0)
	cos_phi = -1.0;

	double phi = acos(cos_phi);

	if (dot3(n123, vb34) > 0.0) {
	phi = -phi; //(Note: Negative dihedral angles are possible only in 3-D.)
	phi += MY_2PI; //<- This insure phi is always in the range 0 to 2*PI
	}
	return phi;
	} // DihedralSpherical::Phi()



	/* ---------------------------------------------------------------------- */

	void DihedralSpherical::compute(int eflag, int vflag)
	{
	int i1,i2,i3,i4,n,type;
	double edihedral,f1[3],f2[3],f3[3],f4[3];

	double **x = atom->x;
	double **f = atom->f;

	int **dihedrallist = neighbor->dihedrallist;
	int ndihedrallist = neighbor->ndihedrallist;
	int nlocal = atom->nlocal;
	int newton_bond = force->newton_bond;

	// The dihedral angle "phi" is the angle between n123 and n234
	// the planes defined by atoms i1,i2,i3, and i2,i3,i4.
	//
	// Definitions of vectors: vb12, vb23, vb34, perp12on23
	// proj12on23, perp43on32, proj43on32
	//
	// Note: The positions of the 4 atoms are labeled x[i1], x[i2], x[i3], x[i4]
	// (which are also vectors)
	//
	// proj12on23 proj34on23
	// ---------> ----------->
	//
	//
	//
	// x[i2] x[i3]
	// . __@----------vb23-------->@ .
	// /\|\ /\| \ \|
	// \| / \ \|
	// \| / \ \|
	// perp12on23 / \ \|
	// \| / \ perp34on23
	// \| vb12 \ \|
	// \| / vb34 \|
	// \| / \ \|
	// \| / \ \|
	// \| / \ \|
	// @ \ \|
	// _\\| \\|/
	// x[i1] @
	//
	// x[i4]
	//

	double vb12[g_dim]; // displacement vector from atom i1 towards atom i2
	// vb12[d] = x[i2][d] - x[i1][d] (for d=0,1,2)
	double vb23[g_dim]; // displacement vector from atom i2 towards atom i3
	// vb23[d] = x[i3][d] - x[i2][d] (for d=0,1,2)
	double vb34[g_dim]; // displacement vector from atom i3 towards atom i4
	// vb34[d] = x[i4][d] - x[i3][d] (for d=0,1,2)

	// n123 & n234: These two unit vectors are normal to the planes
	// defined by atoms 1,2,3 and 2,3,4.
	double n123[g_dim]; //n123=vb23 x vb12 / \|vb23 x vb12\| ("x" is cross product)
	double n234[g_dim]; //n234=vb23 x vb34 / \|vb23 x vb34\| ("x" is cross product)

	// The next 4 vectors are needed to calculate dphi_dx = d phi / dx
	double proj12on23[g_dim];
	// proj12on23[d] = (vb23[d]/\|vb23\|) * dot3(vb12,vb23)/\|vb12\|*\|vb23\|
	double proj34on23[g_dim];
	// proj34on23[d] = (vb34[d]/\|vb23\|) * dot3(vb34,vb23)/\|vb34\|*\|vb23\|
	double perp12on23[g_dim];
	// perp12on23[d] = v12[d] - proj12on23[d]
	double perp34on23[g_dim];
	// perp34on23[d] = v34[d] - proj34on23[d]

	edihedral = 0.0;
	if (eflag \|\| vflag) ev_setup(eflag,vflag);
	else evflag = 0;


	for (n = 0; n < ndihedrallist; n++) {

	i1 = dihedrallist[n][0];
	i2 = dihedrallist[n][1];
	i3 = dihedrallist[n][2];
	i4 = dihedrallist[n][3];
	type = dihedrallist[n][4];

	// ------ Step 1: Compute the dihedral angle "phi" ------
	//

	// Phi() calculates the dihedral angle.
	// This function also calculates the vectors:
	// vb12, vb23, vb34, n123, and n234, which we will need later.


	double phi = Phi(x[i1], x[i2], x[i3], x[i4], domain,
	vb12, vb23, vb34, n123, n234);

	// Step 2: Compute the gradients of phi, theta1, theta2 with atom position:


	// ===================== Step2a) phi dependence: ========================
	//
	// Gradient variables:
	//
	// dphi_dx1, dphi_dx2, dphi_dx3, dphi_dx4 are the gradients of phi with
	// respect to the atomic positions of atoms i1, i2, i3, i4, respectively.
	// As an example, consider dphi_dx1. The d'th element is:
	double dphi_dx1[g_dim]; // d phi
	double dphi_dx2[g_dim]; // dphi_dx1[d] = ---------- (partial derivatives)
	double dphi_dx3[g_dim]; // d x[i1][d]
	double dphi_dx4[g_dim]; //where d=0,1,2 corresponds to x,y,z (g_dim==3)

	double dot123 = dot3(vb12, vb23);
	double dot234 = dot3(vb23, vb34);

	double L23sqr = dot3(vb23, vb23);
	double L23 = sqrt(L23sqr); // (central bond length)

	double inv_L23sqr = 0.0;
	double inv_L23 = 0.0;
	if (L23sqr != 0.0) {
	inv_L23sqr = 1.0 / L23sqr;
	inv_L23 = 1.0 / L23;
	}

	double neg_inv_L23 = -inv_L23;
	double dot123_over_L23sqr = dot123 * inv_L23sqr;
	double dot234_over_L23sqr = dot234 * inv_L23sqr;

	for (int d=0; d < g_dim; ++d) {
	// See figure above for a visual definitions of these vectors:
	proj12on23[d] = vb23[d] * dot123_over_L23sqr;
	proj34on23[d] = vb23[d] * dot234_over_L23sqr;
	perp12on23[d] = vb12[d] - proj12on23[d];
	perp34on23[d] = vb34[d] - proj34on23[d];
	}

	// --- Compute the gradient vectors dphi/dx1 and dphi/dx4: ---

	// These two gradients point in the direction of n123 and n234,
	// and are scaled by the distances of atoms 1 and 4 from the central axis.
	// Distance of atom 1 to central axis:
	double perp12on23_len = sqrt(dot3(perp12on23, perp12on23));
	// Distance of atom 4 to central axis:
	double perp34on23_len = sqrt(dot3(perp34on23, perp34on23));

	double inv_perp12on23 = 0.0;
	if (perp12on23_len != 0.0) inv_perp12on23 = 1.0 / perp12on23_len;
	double inv_perp34on23 = 0.0;
	if (perp34on23_len != 0.0) inv_perp34on23 = 1.0 / perp34on23_len;

	for (int d=0; d < g_dim; ++d) {
	dphi_dx1[d] = n123[d] * inv_perp12on23;
	dphi_dx4[d] = n234[d] * inv_perp34on23;
	}

	// --- Compute the gradient vectors dphi/dx2 and dphi/dx3: ---
	//
	// This is more tricky because atoms 2 and 3 are shared by both planes
	// 123 and 234 (the angle between which defines "phi"). Moving either
	// one of these atoms effects both the 123 and 234 planes
	// Both the 123 and 234 planes intersect with the plane perpendicular to the
	// central bond axis (vb23). The two lines where these intersections occur
	// will shift when you move either atom 2 or atom 3. The angle between
	// these lines is the dihedral angle, phi. We can define four quantities:
	// dphi123_dx2 is the change in "phi" due to the movement of the 123 plane
	// ...as a result of moving atom 2.
	// dphi234_dx2 is the change in "phi" due to the movement of the 234 plane
	// ...as a result of moving atom 2.
	// dphi123_dx3 is the change in "phi" due to the movement of the 123 plane
	// ...as a result of moving atom 3.
	// dphi234_dx3 is the change in "phi" due to the movement of the 234 plane
	// ...as a result of moving atom 3.

	double proj12on23_len = dot123 * inv_L23;
	double proj34on23_len = dot234 * inv_L23;
	// Interpretation:
	//The magnitude of "proj12on23_len" is the length of the proj12on23 vector.
	//The sign is positive if it points in the same direction as the central
	//bond (vb23). Otherwise it is negative. The same goes for "proj34on23".
	//(In the example figure in the comment above, both variables are positive.)

	// The following 8 lines of code are used to calculate the gradient of phi
	// with respect to the two "middle" atom positions (x[i2] and x[i3]).
	// For an explanation of the formula used below, download the file
	// "dihedral_table_2011-8-02.tar.gz" at the bottom of this post:
	// http://lammps.sandia.gov/threads/msg22233.html
	// Unpack it and go to this subdirectory:
	// "supporting_information/doc/gradient_formula_explanation/"
	double dphi123_dx2_coef = neg_inv_L23 * (L23 + proj12on23_len);
	double dphi234_dx2_coef = inv_L23 * proj34on23_len;

	double dphi234_dx3_coef = neg_inv_L23 * (L23 + proj34on23_len);
	double dphi123_dx3_coef = inv_L23 * proj12on23_len;

	for (int d=0; d < g_dim; ++d) {
	// Recall that the n123 and n234 plane normal vectors are proportional to
	// the dphi/dx1 and dphi/dx2 gradients vectors
	// It turns out we can save slightly more CPU cycles by expressing
	// dphi/dx2 and dphi/dx3 as linear combinations of dphi/dx1 and dphi/dx2
	// which we computed already (instead of n123 & n234).
	dphi_dx2[d] = dphi123_dx2_coefdphi_dx1[d] + dphi234_dx2_coefdphi_dx4[d];
	dphi_dx3[d] = dphi123_dx3_coefdphi_dx1[d] + dphi234_dx3_coefdphi_dx4[d];
	}


	// ============= Step2b) theta1 and theta2 dependence: =============

	// --- Compute the gradient vectors dtheta1/dx1 and dtheta2/dx4: ---

	// These two gradients point in the direction of n123 and n234,
	// and are scaled by the distances of atoms 1 and 4 from the central axis.
	// Distance of atom 1 to central axis:
	double dth1_dx1[g_dim]; // d theta1 (partial
	double dth1_dx2[g_dim]; // dth1_dx1[d] = ---------- derivative)
	double dth1_dx3[g_dim]; // d x[i1][d]
	//Note dth1_dx4 = 0

	//Note dth2_dx1 = 0
	double dth2_dx2[g_dim]; // d theta2 (partial
	double dth2_dx3[g_dim]; // dth2_dx1[d] = ---------- derivative)
	double dth2_dx4[g_dim]; // d x[i1][d]
	//where d=0,1,2 corresponds to x,y,z (g_dim==3)

	double L12sqr = dot3(vb12, vb12);
	double L12 = sqrt(L12sqr);
	double L34sqr = dot3(vb34, vb34);
	double L34 = sqrt(L34sqr);
	double inv_L12sqr = 0.0;
	double inv_L12 = 0.0;
	double inv_L34sqr = 0.0;
	double inv_L34 = 0.0;
	if (L12sqr != 0.0) {
	inv_L12sqr = 1.0 / L12sqr;
	inv_L12 = 1.0 / L12;
	}
	if (L34sqr != 0.0) {
	inv_L34sqr = 1.0 / L34sqr;
	inv_L34 = 1.0 / L34;
	}

	// The next 2 vectors are needed for calculating dth1_dx = d theta1 / d x
	double proj23on12[g_dim];
	// proj23on12[d] = (vb12[d]/\|vb12\|) * dot3(vb23,vb12)/\|vb23\|*\|vb12\|
	double perp23on12[g_dim];
	// perp23on12[d] = v23[d] - proj23on12[d]

	// The next 2 vectors are needed for calculating dth2_dx = d theta2 / d x
	double proj23on34[g_dim];
	// proj23on34[d] = (vb23[d]/\|vb34\|) * dot3(vb23,vb34)/\|vb23\|*\|vb34\|
	double perp23on34[g_dim];
	// perp23on34[d] = v23[d] - proj23on34[d]

	double dot123_over_L12sqr = dot123 * inv_L12sqr;
	double dot234_over_L34sqr = dot234 * inv_L34sqr;

	/* __ .
	* proj23on12 .\ .
	* . . proj23on34
	* . .
	* . .
	* x[i2] . _./ x[i3]
	* __@----------vb23-------->@
	* /\| / \ \
	* / theta1 theta2 \
	* / <-' `-> \
	* / \
	* / \
	* vb12 \
	* / vb34
	* / \
	* / \
	* / \
	* @ \
	* _\\|
	* x[i1] @
	*
	* x[i4]
	*/

	for (int d=0; d < g_dim; ++d) {
	// See figure above for a visual definitions of these vectors:
	proj23on12[d] = vb12[d] * dot123_over_L12sqr;
	proj23on34[d] = vb34[d] * dot234_over_L34sqr;
	perp23on12[d] = vb23[d] - proj23on12[d];
	perp23on34[d] = vb23[d] - proj23on34[d];
	}

	double perp23on12_len = sqrt(dot3(perp23on12, perp23on12));
	double perp23on34_len = sqrt(dot3(perp23on34, perp23on34));

	double inv_perp23on12 = 0.0;
	if (perp23on12_len != 0.0) inv_perp23on12 = 1.0 / perp23on12_len;
	double inv_perp23on34 = 0.0;
	if (perp23on34_len != 0.0) inv_perp23on34 = 1.0 / perp23on34_len;

	double coeff_dth1_dx1 = -inv_perp23on12 * inv_L12;
	double coeff_dth1_dx3 = inv_perp12on23 * inv_L23;
	double coeff_dth2_dx2 = -inv_perp34on23 * inv_L23;
	double coeff_dth2_dx4 = inv_perp23on34 * inv_L34;

	for (int d=0; d < g_dim; ++d) {
	dth1_dx1[d] = perp23on12[d] * coeff_dth1_dx1;
	dth1_dx3[d] = perp12on23[d] * coeff_dth1_dx3;
	dth1_dx2[d] = -(dth1_dx1[d] + dth1_dx3[d]);
	//dtheta1_dx4 = 0

	//dtheta2_dx1 = 0
	dth2_dx2[d] = perp34on23[d] * coeff_dth2_dx2;
	dth2_dx4[d] = perp23on34[d] * coeff_dth2_dx4;
	dth2_dx3[d] = -(dth2_dx2[d] + dth2_dx4[d]);
	}

	double ct1 = -dot123 * inv_L12 * inv_L23;
	if (ct1 < -1.0) ct1 = -1.0;
	else if (ct1 > 1.0) ct1 = 1.0;
	double theta1 = acos(ct1);
	double ct2 = -dot234 * inv_L23 * inv_L34;
	if (ct2 < -1.0) ct2 = -1.0;
	else if (ct2 > 1.0) ct2 = 1.0;
	double theta2 = acos(ct2);

	// - Step 3: Calculate the energy and force in the phi & theta1/2 directions

	double u=0.0; // u = energy
	double m_du_dth1 = 0.0; // m_du_dth1 = -du / d theta1
	double m_du_dth2 = 0.0; // m_du_dth2 = -du / d theta2
	double m_du_dphi = 0.0; // m_du_dphi = -du / d phi

	u = CalcGeneralizedForces(type,
	phi, theta1, theta2,
	&m_du_dth1, &m_du_dth2, &m_du_dphi);

	if (eflag) edihedral = u;

	// ----- Step 4: Calculate the force direction in real space -----

	// chain rule:
	// d U d U d phi d U d theta1 d U d theta2
	// -f = ----- = ----- * ----- + -------------- + ----------------
	// d x d phi d x d theta1 d X d theta2 d X
	for(int d=0; d < g_dim; ++d) {
	f1[d] = m_du_dphidphi_dx1[d]+m_du_dth1dth1_dx1[d];
	//note: dth2_dx1[d]=0
	f2[d] = m_du_dphidphi_dx2[d]+m_du_dth1dth1_dx2[d]+m_du_dth2*dth2_dx2[d];
	f3[d] = m_du_dphidphi_dx3[d]+m_du_dth1dth1_dx3[d]+m_du_dth2*dth2_dx3[d];
	f4[d] = m_du_dphidphi_dx4[d] + m_du_dth2dth2_dx4[d];
	//note: dth1_dx4[d] = 0
	}

	// apply force to each of 4 atoms

	if (newton_bond \|\| i1 < nlocal) {
	f[i1][0] += f1[0];
	f[i1][1] += f1[1];
	f[i1][2] += f1[2];
	}

	if (newton_bond \|\| i2 < nlocal) {
	f[i2][0] += f2[0];
	f[i2][1] += f2[1];
	f[i2][2] += f2[2];
	}

	if (newton_bond \|\| i3 < nlocal) {
	f[i3][0] += f3[0];
	f[i3][1] += f3[1];
	f[i3][2] += f3[2];
	}

	if (newton_bond \|\| i4 < nlocal) {
	f[i4][0] += f4[0];
	f[i4][1] += f4[1];
	f[i4][2] += f4[2];
	}

	if (evflag)
	ev_tally(i1,i2,i3,i4,
	nlocal,newton_bond,edihedral,
	f1,f3,f4,
	vb12[0],vb12[1],vb12[2],
	vb23[0],vb23[1],vb23[2],
	vb34[0],vb34[1],vb34[2]);
	}
	} // void DihedralSpherical::compute()






	// --- CalcGeneralizedForces() ---
	// --- Calculate the energy as a function of theta1, theta2, and phi ---
	// --- as well as its derivatives (with respect to theta1, theta2, and phi) ---



	// The code above above is sufficiently general that it can work with any
	// any function of the angles theta1, theta2, and phi. However the
	// function below calculates the energy and force according to this specific
	// formula:
	//
	// E(\theta_1,\theta_2,\phi) =
	// \sum_{i=1}^N C_i \Theta_{1i}(\theta_1) \Theta_{2i}(\theta_2) \Phi_i(\phi)
	// where:
	// \Theta_{1i}(\theta_1) = cos((\theta_1-a_i)K_i) + u_i
	// \Theta_{2i}(\theta_2) = cos((\theta_2-b_i)L_i) + v_i
	// \Phi_i(\phi) = cos((\phi - c_i)M_i) + w_i




	double DihedralSpherical::
	CalcGeneralizedForces(int type,
	double phi,
	double theta1,
	double theta2,
	double *m_du_dth1,
	double *m_du_dth2,
	double *m_du_dphi)
	{
	double energy = 0.0;
	assert(m_du_dphi && m_du_dphi && m_du_dphi);
	*m_du_dphi = 0.0;
	*m_du_dth1 = 0.0;
	*m_du_dth2 = 0.0;

	int i = type;
	for (int j = 0; j < nterms[i]; j++) {

	// (It's common that some terms in an expansion have phi_multi[i][j]=0.
	// When this happens, perhaps it will speed up the calculation to avoid
	// unnecessary calls to the cos() and sin() functions. Check this below)
	// I also check whether theta1_mult[i][j] and theta2_mult[i][j] are 0.
	double cp = 1.0;
	double sp = 0.0;
	if (phi_mult[i][j] != 0.0) {
	double p = phi_mult[i][j] * (phi - phi_shift[i][j]);
	cp = cos(p);
	sp = sin(p);
	}

	double ct1 = 1.0;
	double st1 = 0.0;
	if (theta1_mult[i][j] != 0.0) {
	double t1 = theta1_mult[i][j]*(theta1 - theta1_shift[i][j]);
	ct1 = cos(t1);
	st1 = sin(t1);
	}

	double ct2 = 1.0;
	double st2 = 0.0;
	if (theta2_mult[i][j] != 0.0) {
	double t2 = theta2_mult[i][j]*(theta2 - theta2_shift[i][j]);
	ct2 = cos(t2);
	st2 = sin(t2);
	}

	energy += Ccoeff[i][j] * (phi_offset[i][j] - cp) *
	(theta1_offset[i][j] - ct1) *
	(theta2_offset[i][j] - ct2);

	// Forces:
	m_du_dphi += -Ccoeff[i][j] sp * phi_mult[i][j] *
	(theta1_offset[i][j] - ct1) *
	(theta2_offset[i][j] - ct2);

	m_du_dth1 += -Ccoeff[i][j] (phi_offset[i][j] - cp) *
	st1 * theta1_mult[i][j] *
	(theta2_offset[i][j] - ct2);

	m_du_dth2 += -Ccoeff[i][j] (phi_offset[i][j] - cp) *
	(theta1_offset[i][j] - ct1) *
	st2 * theta2_mult[i][j];


	// Things to consider later:
	// To speed up the computation, one could try to simplify the expansion:
	// IE by factoring out common terms, and precomputing trig functions once:
	// cos(Ktheta1), sin(Ktheta1),
	// cos(Ltheta2), sin(Ltheta2), and
	// cos(Mphi), sin(Mphi)
	// Also: For integer K,L,M, the trig functions cos(Mphi) and sin(Mphi)
	// can be calculated more efficiently using polynomials of
	// cos(phi) and sin(phi)

	} //for (int j = 0; j < nterms[i]; j++) {

	return energy;

	} //CalcGeneralizedForces()







	void DihedralSpherical::allocate()
	{
	allocated = 1;
	int n = atom->ndihedraltypes;

	memory->create(nterms,n+1,"dihedral:nterms");

	Ccoeff = new double * [n+1];
	phi_mult = new double * [n+1];
	phi_shift = new double * [n+1];
	phi_offset = new double * [n+1];
	theta1_mult = new double * [n+1];
	theta1_shift = new double * [n+1];
	theta1_offset = new double * [n+1];
	theta2_mult = new double * [n+1];
	theta2_shift = new double * [n+1];
	theta2_offset = new double * [n+1];
	for (int i = 1; i <= n; i++) {
	Ccoeff[i] = NULL;
	phi_mult[i] = NULL;
	phi_shift[i] = NULL;
	phi_offset[i] = NULL;
	theta1_mult[i] = NULL;
	theta1_shift[i] = NULL;
	theta1_offset[i] = NULL;
	theta2_mult[i] = NULL;
	theta2_shift[i] = NULL;
	theta2_offset[i] = NULL;
	}

	memory->create(setflag,n+1,"dihedral:setflag");
	for (int i = 1; i <= n; i++) setflag[i] = 0;
	}

	/* ----------------------------------------------------------------------
	set coeffs for one type
	------------------------------------------------------------------------- */

	void DihedralSpherical::coeff(int narg, char **arg)
	{
	if (narg < 4) error->all(FLERR,"Incorrect args for dihedral coefficients");
	if (!allocated) allocate();

	int ilo,ihi;
	force->bounds(FLERR,arg[0],atom->ndihedraltypes,ilo,ihi);

	int nterms_one = force->inumeric(FLERR,arg[1]);

	if (nterms_one < 1)
	error->all(FLERR,"Incorrect number of terms arg for dihedral coefficients");

	if (2+10*nterms_one < narg)
	error->all(FLERR,"Incorrect number of arguments for dihedral coefficients");

	int count = 0;
	for (int i = ilo; i <= ihi; i++) {
	nterms[i] = nterms_one;
	Ccoeff[i] = new double [nterms_one];
	phi_mult[i] = new double [nterms_one];
	phi_shift[i] = new double [nterms_one];
	phi_offset[i] = new double [nterms_one];
	theta1_mult[i] = new double [nterms_one];
	theta1_shift[i] = new double [nterms_one];
	theta1_offset[i] = new double [nterms_one];
	theta2_mult[i] = new double [nterms_one];
	theta2_shift[i] = new double [nterms_one];
	theta2_offset[i] = new double [nterms_one];
	for (int j = 0; j < nterms_one; j++) {
	int offset = 1+10*j;
	Ccoeff[i][j] = force->numeric(FLERR,arg[offset+1]);
	phi_mult[i][j] = force->numeric(FLERR,arg[offset+2]);
	phi_shift[i][j] = force->numeric(FLERR,arg[offset+3]) * MY_PI/180.0;
	phi_offset[i][j] = force->numeric(FLERR,arg[offset+4]);
	theta1_mult[i][j] = force->numeric(FLERR,arg[offset+5]);
	theta1_shift[i][j] = force->numeric(FLERR,arg[offset+6]) * MY_PI/180.0;
	theta1_offset[i][j] = force->numeric(FLERR,arg[offset+7]);
	theta2_mult[i][j] = force->numeric(FLERR,arg[offset+8]);
	theta2_shift[i][j] = force->numeric(FLERR,arg[offset+9]) * MY_PI/180.0;
	theta2_offset[i][j] = force->numeric(FLERR,arg[offset+10]);
	}
	setflag[i] = 1;
	count++;
	}

	if (count == 0) error->all(FLERR,"Incorrect args for dihedral coefficients");
	}

	/* ----------------------------------------------------------------------
	proc 0 writes out coeffs to restart file
	------------------------------------------------------------------------- */

	void DihedralSpherical::write_restart(FILE *fp)
	{

	fwrite(&nterms[1],sizeof(int),atom->ndihedraltypes,fp);
	for(int i = 1; i <= atom->ndihedraltypes; i++) {
	fwrite(Ccoeff[i],sizeof(double),nterms[i],fp);
	fwrite(phi_mult[i],sizeof(double),nterms[i],fp);
	fwrite(phi_shift[i],sizeof(double),nterms[i],fp);
	fwrite(phi_offset[i],sizeof(double),nterms[i],fp);
	fwrite(theta1_mult[i],sizeof(double),nterms[i],fp);
	fwrite(theta1_shift[i],sizeof(double),nterms[i],fp);
	fwrite(theta1_offset[i],sizeof(double),nterms[i],fp);
	fwrite(theta2_mult[i],sizeof(double),nterms[i],fp);
	fwrite(theta2_shift[i],sizeof(double),nterms[i],fp);
	fwrite(theta2_offset[i],sizeof(double),nterms[i],fp);
	}

	}

	/* ----------------------------------------------------------------------
	proc 0 reads coeffs from restart file, bcasts them
	------------------------------------------------------------------------- */

	void DihedralSpherical::read_restart(FILE *fp)
	{
	allocate();

	if (comm->me == 0)
	fread(&nterms[1],sizeof(int),atom->ndihedraltypes,fp);

	MPI_Bcast(&nterms[1],atom->ndihedraltypes,MPI_INT,0,world);

	// allocate
	for (int i=1; i<=atom->ndihedraltypes; i++) {
	Ccoeff[i] = new double [nterms[i]];
	phi_mult[i] = new double [nterms[i]];
	phi_shift[i] = new double [nterms[i]];
	phi_offset[i] = new double [nterms[i]];
	theta1_mult[i] = new double [nterms[i]];
	theta1_shift[i] = new double [nterms[i]];
	theta1_offset[i] = new double [nterms[i]];
	theta2_mult[i] = new double [nterms[i]];
	theta2_shift[i] = new double [nterms[i]];
	theta2_offset[i] = new double [nterms[i]];
	}

	if (comm->me == 0) {
	for (int i=1; i<=atom->ndihedraltypes; i++) {
	fread(Ccoeff[i],sizeof(double),nterms[i],fp);
	fread(phi_mult[i],sizeof(double),nterms[i],fp);
	fread(phi_shift[i],sizeof(double),nterms[i],fp);
	fread(phi_offset[i],sizeof(double),nterms[i],fp);
	fread(theta1_mult[i],sizeof(double),nterms[i],fp);
	fread(theta1_shift[i],sizeof(double),nterms[i],fp);
	fread(theta1_offset[i],sizeof(double),nterms[i],fp);
	fread(theta2_mult[i],sizeof(double),nterms[i],fp);
	fread(theta2_shift[i],sizeof(double),nterms[i],fp);
	fread(theta2_offset[i],sizeof(double),nterms[i],fp);
	}
	}

	for (int i=1; i<=atom->ndihedraltypes; i++) {
	MPI_Bcast(Ccoeff[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(phi_mult[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(phi_shift[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(phi_offset[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta1_mult[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta1_shift[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta1_offset[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta2_mult[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta2_shift[i],nterms[i],MPI_DOUBLE,0,world);
	MPI_Bcast(theta2_offset[i],nterms[i],MPI_DOUBLE,0,world);
	}

	for (int i = 1; i <= atom->ndihedraltypes; i++) setflag[i] = 1;
	}




	/* ----------------------------------------------------------------------
	proc 0 writes to data file
	------------------------------------------------------------------------- */

	void DihedralSpherical::write_data(FILE *fp)
	{
	for (int i = 1; i <= atom->ndihedraltypes; i++) {
	fprintf(fp,"%d %d ", i , nterms[i]);
	for (int j = 0; j < nterms[i]; j++) {
	fprintf(fp, "%g %g %g %g %g %g %g %g %g ",
	phi_mult[i][j], phi_shift[i][j], phi_offset[i][j],
	theta1_mult[i][j], theta1_shift[i][j], theta1_offset[i][j],
	theta2_mult[i][j], theta2_shift[i][j], theta2_offset[i][j]);
	}
	fprintf(fp,"\n");
	}
	}






	// Not needed?
	// single() calculates the dihedral-angle energy of atoms i1, i2, i3, i4.
	//double DihedralSpherical::single(int type, int i1, int i2, int i3, int i4)
	//{
	// //variables we will need
	// double vb12[g_dim];
	// double vb23[g_dim];
	// double vb34[g_dim];
	//
	// // Some functions calculate numbers we don't care about. Store in variables:
	// double n123[g_dim]; // (will be ignored)
	// double n234[g_dim]; // (will be ignored)
	// double m_du_dth1; // (will be ignored)
	// double m_du_dth2; // (will be ignored)
	// double m_du_dphi; // (will be ignored)
	//
	// double **x = atom->x;
	//
	// // Calculate the 4-body angle: phi
	// double phi = Phi(x[i1], x[i2], x[i3], x[i4], domain,
	// vb12, vb23, vb34, n123, n234);
	//
	// // Calculate the 3-body angles: theta1 and theta2
	// double L12 = sqrt(dot3(vb12, vb12));
	// double L23 = sqrt(dot3(vb23, vb23));
	// double L34 = sqrt(dot3(vb34, vb34));
	//
	// double ct1 = -dot3(vb12, vb23) / (L12 * L23);
	// if (ct1 < -1.0) ct1 = -1.0;
	// else if (ct1 > 1.0) ct1 = 1.0;
	// double theta1 = acos(ct1);
	//
	// double ct2 = -dot3(vb23, vb34) / (L23 * L34);
	// if (ct2 < -1.0) ct2 = -1.0;
	// else if (ct2 > 1.0) ct2 = 1.0;
	// double theta2 = acos(ct2);
	//
	// double u = CalcGeneralizedForces(type,
	// phi, theta1, theta2,
	// &m_du_dth1, &m_du_dth2, &m_du_dphi);
	// return u;
	//}

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