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t_tensors.cpp
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#include <iostream>
#include <cmath>
#include <stdio.h>
#include <string>
#include <cstring>
#include <iomanip>
#include <time.h>
#include <numeric>
#include <stdlib.h>
#include "./math_module.hpp"
// Default parameters
#define nCols 3 // Number of columns
#define d_min 0.5 // Minimum separation
#define d_max 1.5 // Maximum separation
#define mu1_mag 1.0 // Dipole moment of molecule 1
#define mu2_mag 1.0 // Dipole moment of molecule 2
#define quad1_mag 1.0 // Quadrupole moment of molecule 1
#define quad2_mag 1.0 // Quadrupole moment of molecule 2
int main()
{
double r12_mag, c1, c2, c12, v12t, v12e, h;
double* g = new double[nCols];
double* h1 = new double[nCols];
double* h2 = new double[nCols];
double* e1 = new double[nCols];
double* e2 = new double[nCols];
double* mu1 = new double[nCols];
double* mu2 = new double[nCols];
double* t1t = new double[nCols];
double* t1tt1e = new double[nCols];
double* t2tt2e = new double[nCols];
double* t2t = new double[nCols];
double* t1e = new double[nCols];
double* t2e = new double[nCols];
double* f12t = new double[nCols];
double* f12e = new double[nCols];
double* f12tf12e= new double[nCols];
double* r12 = new double[nCols];
double* r12_hat = new double[nCols];
double* cross = new double[nCols];
double** gg = allocate2DArray(nCols,nCols);
double** tt2 = allocate2DArray(nCols,nCols);
double** quad1 = allocate2DArray(nCols,nCols);
double** quad2 = allocate2DArray(nCols,nCols);
double** ident = allocate2DArray(nCols,nCols);
double*** tt3 = allocate3DArray(nCols,nCols,nCols);
double*** ggg = allocate3DArray(nCols,nCols,nCols);
double**** tt4 = allocate4DArray(nCols,nCols,nCols,nCols);
double***** tt5 = allocate5DArray(nCols,nCols,nCols,nCols,nCols);
std::cout << '\n';
std::cout <<"T-tensor" << '\n';
std::cout <<"Calculation of electrostatic interactions between linear molecules" << '\n';
std::cout <<"using T-tensors and Euler angles" << '\n';
std::cout << '\n';
// Write out parameters
printf( "Min separation d_min %15.6f \n", d_min);
printf( "Max separation d_max %15.6f \n", d_max);
printf( "Dipole moment of molecule %15.6f \n", mu1_mag);
printf( "Dipole moment of molecule %15.6f \n", mu2_mag);
printf( "Quadrupole moment of molecule %15.6f \n", quad1_mag);
printf( "Quadrupole moment of molecule %15.6f \n", quad2_mag);
std::cout << '\n';
random_vector(e1);
random_vector(e2);
// Place atom 2 at origin and atom 1 in a random direction within desired distance range
random_vector(r12_hat);
r12_mag = (double) rand()/RAND_MAX;
r12_mag = d_min + (d_max-d_min)*r12_mag; // Magnitude of r12
scalar1DArrayMultip(nCols,r12_mag,r12_hat,r12); // Within desired range of origin
c1 = dotProduct2D(nCols,e1,r12_hat); // Cosine of angle between e1 and r12
c2 = dotProduct2D(nCols,e2,r12_hat); // Cosine of angle between e2 and r12
c12 = dotProduct2D(nCols,e1,e2); // Cosine of angle between e1 and e2
printf("%s %25.6f %10.6f %10.6f\n", "Displacement r12", r12[0],r12[1],r12[2]);
printf("%s %25.6f %10.6f %10.6f\n", "Orientation e1", e1[0], e1[1], e1[2]);
printf("%s %25.6f %10.6f %10.6f\n", "Orientation e2", e2[0], e2[1], e2[2]);
std::cout << '\n';
// Dipole vectors in space-fixed frame
scalar1DArrayMultip(nCols,mu1_mag,e1,mu1);
scalar1DArrayMultip(nCols,mu2_mag,e2,mu2);
// Quadrupole tensors in space-fixed frame (traceless)
outer2D(nCols,e1,e1,quad1);
scalar2DArrayMultip(nCols,nCols,1.5,quad1,quad1);
identMatrix(nCols,nCols,ident);
scalar2DArrayMultip(nCols,nCols,0.5,ident,ident);
subtract2DArrays(nCols,nCols,quad1,ident,quad1);
scalar2DArrayMultip(nCols,nCols,quad1_mag,quad1,quad1);
outer2D(nCols,e2,e2,quad2);
scalar2DArrayMultip(nCols,nCols,1.5,quad2,quad2);
identMatrix(nCols,nCols,ident);
scalar2DArrayMultip(nCols,nCols,0.5,ident,ident);
subtract2DArrays(nCols,nCols,quad2,ident,quad2);
scalar2DArrayMultip(nCols,nCols,quad2_mag,quad2,quad2);
// The T tensors of each rank: T2, T3, T4, T5
t2_tensor (r12_hat, pow(r12_mag,3),tt2);
t3_tensor (r12_hat, pow(r12_mag,4),tt3);
t4_tensor (r12_hat, pow(r12_mag,5),tt4);
t5_tensor (r12_hat, pow(r12_mag,6),tt5);
// Heading
printf("%66s %40s %40s \n", ".....Result from T tensor", ".....Result from Euler angles",".........Difference");
std::cout << '\n';
std::cout << "Dipole-dipole" << '\n';
// Calculate the dipole-dipole energy
contract_ij_j(tt2, mu2,g); // Contract T2 with dipole 2
v12t = -1 * contract_i_i (nCols, mu1, g ); // Contract result with dipole 1
v12e = (mu1_mag*mu2_mag/pow(r12_mag,3)) * ( c12 - 3.0 * c1 * c2 ); // Compare result from angles
printf ("Energy %59.6f %40.6f %40.6f \n", v12t, v12e, v12t-v12e);
// Calculate the dipole-dipole force
contract_ijk_k(tt3, mu2,gg); // Contract T3 with dipole 2
contract_ij_j (gg , mu1,f12t); // Contract result with dipole 1
scalar1DArrayMultip(nCols,-1,f12t,f12t);
double* f12e1 = new double[nCols];
scalar1DArrayMultip(nCols,(c12-5.0*c1*c2),r12_hat,f12e);
scalar1DArrayMultip(nCols,c2,e1,f12e1);
sum1DArrays(nCols,f12e1,f12e,f12e);
scalar1DArrayMultip(nCols,c1,e2,f12e1);
sum1DArrays(nCols,f12e,f12e1,f12e);
scalar1DArrayMultip(nCols,(3.0*mu1_mag*mu2_mag/pow(r12_mag,4)),f12e,f12e); // Compare result from angles
subtract1DArrays(nCols, f12t, f12e,f12tf12e);
printf("Force %37.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f\n", f12t[0],f12t[1],f12t[2], f12e[0], f12e[1],f12e[2], f12tf12e[0],f12tf12e[1],f12tf12e[2]);
delete [] f12e1;
// Calculate the dipole-dipole torques
zeroVec(3,g);
contract_ij_j(tt2, mu2,g); // Contract T2 with dipole 2
scalar1DArrayMultip(nCols,-1,g,g);
crossProduct(mu1, g,t1t); // Cross-product result with dipole 1
scalar1DArrayMultip(nCols,-1,t1t,t1t);
scalar1DArrayMultip(nCols,3.*c2,r12_hat,g);
subtract1DArrays(nCols,e2,g,g); // Compare result from angles
crossProduct(e1, g,cross);
scalar1DArrayMultip(nCols,-(mu1_mag*mu2_mag/pow(r12_mag,3)),cross,t1e);
subtract1DArrays(nCols, t1t, t1e,t1tt1e);
printf("Torque on 1 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t1t[0], t1t[1],t1t[2], t1e[0], t1e[1],t1e[2], t1tt1e[0], t1tt1e[1],t1tt1e[2]);
zeroVec(3,g);
contract_ij_j ( tt2, mu1,g ); // Contract T2 with dipole 1
scalar1DArrayMultip(nCols,-1,g,g);
crossProduct ( mu2, g,t2t ); // Cross-product result with dipole 2
scalar1DArrayMultip(nCols,-1,t2t,t2t);
scalar1DArrayMultip(nCols,3.*c1,r12_hat,g);
subtract1DArrays(nCols,e1,g,g); // Compare result from angles
crossProduct(e2, g,cross);
scalar1DArrayMultip(nCols,-(mu1_mag*mu2_mag/pow(r12_mag,3)),cross,t2e);
subtract1DArrays(nCols, t1t, t1e,t2tt2e);
printf("Torque on 2 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t2t[0], t2t[1],t2t[2], t2e[0], t2e[1],t2e[2], t2tt2e[0], t2tt2e[1],t2tt2e[2]);
std::cout << '\n' ;
std::cout << "Dipole-quadrupole" << '\n';
// Calculate the dipole-quadrupole energy
zeroVec(3,g);
contract_ijk_jk(tt3, quad2,g); // Contract T3 with quadrupole 2
v12t = -(1.0/3.0) *contract_i_i (nCols,mu1, g); // Contract result with dipole 1
v12e = (1.5*mu1_mag*quad2_mag/pow(r12_mag,4)) * ( c1*(1.0-5.0*c2*c2) + 2.0*c2*c12 );
printf ("Energy %59.6f %40.6f %40.2f \n", v12t, v12e, v12t-v12e);
// Calculate the dipole-quadrupole force
zeroMatrix(3,3,gg);
contract_ijkl_kl (tt4, quad2,gg); // Contract T4 with quadrupole 2
zeroVec(3,f12t);
contract_ij_j ( gg, mu1,f12t);
scalar1DArrayMultip(nCols,-(1.0/3.0),f12t,f12t); // Contract result with dipole 1
scalar1DArrayMultip(nCols,(35.0*c1*pow(c2,2)-10.0*c2*c12-5.0*c1),r12_hat,f12e);
scalar1DArrayMultip(nCols,(1.0 - 5.0*pow(c2,2)),e1,h1);
scalar1DArrayMultip(nCols,(2.0*c12-10.0*c1*c2),e2,h2);
sum1DArrays(nCols,h1,f12e,f12e);
sum1DArrays(nCols,h2,f12e,f12e); // Compare result from angles
scalar1DArrayMultip(nCols,-(1.5*mu1_mag*quad2_mag/pow(r12_mag,5)),f12e,f12e); // Compare result from angles
subtract1DArrays(nCols, f12t, f12e,f12tf12e);
printf("Force %37.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", f12t[0],f12t[1],f12t[2], f12e[0], f12e[1],f12e[2], f12tf12e[0],f12tf12e[1],f12tf12e[2]);
// Calculate the dipole-quadrupole torques
double* g1 = new double[nCols];
zeroVec(3,g);
contract_ijk_jk( tt3, quad2,g);
scalar1DArrayMultip(nCols,-(1.0/3.0),g,g); // Contract T3 with quadrupole 2
crossProduct (mu1, g,t1t);
scalar1DArrayMultip(nCols,-1.,t1t,t1t); // Cross-product result with dipole 1
scalar1DArrayMultip(nCols,(1.0-5.0*pow(c2,2)),r12_hat,g);
scalar1DArrayMultip(nCols, 2.0*c2, e2,g1);
sum1DArrays(nCols,g,g1,g); // Compare result from angles
crossProduct(e1, g,cross);
scalar1DArrayMultip(nCols,-(1.5*mu1_mag*quad2_mag/pow(r12_mag,4)),cross,t1e);
subtract1DArrays(nCols, t1t, t1e,t1tt1e);
printf("Torque on 1 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t1t[0], t1t[1],t1t[2], t1e[0], t1e[1],t1e[2], t1tt1e[0], t1tt1e[1],t1tt1e[2]);
double* skg = new double[nCols];
double** gg1 = allocate2DArray(nCols,nCols);
zeroMatrix(3,3,gg);
contract_ijk_k(tt3, mu1,gg);
scalar2DArrayMultip(nCols,nCols,-(1.0/3.0),gg,gg); // Contract T3 with dipole 1
contract_ik_jk (quad2,gg,gg1); // Contract result with quadrupole 2
skew(gg1,skg);
scalar1DArrayMultip(nCols,-2.0,skg,t2t); // Contract with Levi-Civita symbol
scalar1DArrayMultip(nCols,(c12-5.0*c1*c2),r12_hat,g);
scalar1DArrayMultip(nCols,c2, e1,g1);
sum1DArrays(nCols,g,g1,g); // Compare result from angles
crossProduct(e2,g,cross);
scalar1DArrayMultip(nCols,-(3.0*mu1_mag*quad2_mag/pow(r12_mag,4)),cross,t2e);
subtract1DArrays(nCols, t1t, t1e,t2tt2e);
printf("Torque on 2 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t2t[0], t2t[1],t2t[2], t2e[0], t2e[1],t2e[2], t2tt2e[0], t2tt2e[1],t2tt2e[2]);
delete [] g1;
std::cout << '\n' ;
std::cout << "Quadrupole-dipole" << '\n';
// Calculate the quadrupole-dipole energy
zeroVec(3,g);
contract_ijk_jk(tt3, quad1,g); // Contract T3 with quadrupole 1
v12t = (1.0/3.0) *contract_i_i (nCols,g,mu2); // Contract result with dipole 2
v12e = -(1.5*quad1_mag*mu2_mag/pow(r12_mag,4)) * (c2*(1.0-5.0*c1*c1) + 2.0*c1*c12);
printf ("Energy %59.6f %40.6f %40.2f \n", v12t, v12e, v12t-v12e);
// Calculate the quadrupole-dipole force
zeroMatrix(3,3,gg);
contract_ijkl_kl(tt4, quad1,gg); // Contract T4 with quadrupole 1
zeroVec(3,g1);
contract_ij_j(gg, mu2,g1);
scalar1DArrayMultip(nCols,(1.0/3.0),g1,f12t); // Contract result with dipole 2
scalar1DArrayMultip(nCols,(35.0*c2*pow(c1,2)-10.0*c1*c12-5.0*c2),r12_hat,f12e);
scalar1DArrayMultip(nCols,(1.0 - 5.0*pow(c1,2)),e2,h1);
scalar1DArrayMultip(nCols,(2.0*c12-10.0*c1*c2),e1,h2);
sum1DArrays(nCols,h1,f12e,f12e);
sum1DArrays(nCols,h2,f12e,f12e);
scalar1DArrayMultip(nCols,(1.5*mu1_mag*quad2_mag/pow(r12_mag,5)),f12e,f12e); // Compare result from angles
subtract1DArrays(nCols, f12t, f12e,f12tf12e);
printf("Force %37.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", f12t[0],f12t[1],f12t[2], f12e[0], f12e[1],f12e[2], f12tf12e[0],f12tf12e[1],f12tf12e[2]);
// Calculate the quadrupole-dipole torques
zeroMatrix(3,3,gg);
contract_ijk_k(tt3, mu2,gg);
scalar2DArrayMultip(nCols,nCols,(1.0/3.0),gg,gg); // Contract T3 with dipole 2
zeroMatrix(3,3,gg1);
contract_ik_jk(quad1,gg,gg1); // Contract result with quadrupole 1
skew(gg1,skg);
scalar1DArrayMultip(nCols,-2.0,skg, t1t); // Contract with Levi-Civita symbol
scalar1DArrayMultip(nCols,(c12-5.0*c1*c2),r12_hat,g);
scalar1DArrayMultip(nCols,c1,e2,g1);
sum1DArrays(nCols,g,g1,g); // Compare result from angles
crossProduct(e1,g,cross);
scalar1DArrayMultip(nCols,3.0*quad1_mag*mu2_mag/pow(r12_mag,4),cross,t1e);
subtract1DArrays(nCols, t1t, t1e,t1tt1e);
printf("Torque on 1 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t1t[0], t1t[1],t1t[2], t1e[0], t1e[1],t1e[2], t1tt1e[0], t1tt1e[1],t1tt1e[2]);
zeroVec(3,g);
contract_ijk_jk(tt3,quad1,g);
scalar1DArrayMultip(nCols,(1.0/3.0),g,g); // Contract T3 with quadrupole 1
crossProduct(mu2,g,cross);
scalar1DArrayMultip(nCols,-1,cross,t2t); // Cross product result with dipole 2
scalar1DArrayMultip(nCols,(1.0-5.0*pow(c1,2)),r12_hat,g);
scalar1DArrayMultip(nCols,2.0*c1,e1,g1);
sum1DArrays(nCols,g1,g,g); // Compare result from angles
crossProduct(e2,g,cross);
scalar1DArrayMultip(nCols,(1.5*quad1_mag*mu2_mag/pow(r12_mag,4)),cross,t2e);
subtract1DArrays(nCols, t2t, t2e,t2tt2e);
printf("Torque on 2 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t2t[0], t2t[1],t2t[2], t2e[0], t2e[1],t2e[2], t2tt2e[0], t2tt2e[1],t2tt2e[2]);
std::cout << '\n' ;
std::cout << "Quadrupole-quadrupole" << '\n';
// Calculate the quadrupole-quadrupole energy
zeroMatrix(3,3,gg);
contract_ijkl_kl(tt4,quad2,gg); // Contract T4 with quadrupole 2
v12t = (1.0/9.0) * contract_ij_ij (quad1,gg); // Contract result with quadrupole 1
v12e = (0.75*quad1_mag*quad2_mag/pow(r12_mag,5)) * (1.0 - 5.0*pow(c1,2) - 5.0*pow(c2,2) + 2.0*pow(c12,2) + 35.0*pow((c1*c2),2) - 20.0*c1*c2*c12 ); // Compare result from angles
printf ("Energy %59.6f %40.6f %40.2f \n", v12t, v12e, v12t-v12e);
// Calculate the quadrupole-quadrupole force
contract_ijklm_lm(tt5,quad2,ggg); // Contract T5 with quadrupole 2
zeroVec(3,g);
contract_ijk_jk(ggg,quad1,g);
scalar1DArrayMultip(nCols,(1.0/9.0),g,f12t); // Contract result with quadrupole 1
scalar1DArrayMultip(nCols,(5.0 - 35.0*pow(c1,2) - 35.0*pow(c2,2) + 10.0*pow(c12,2) + 315.0*pow((c1*c2),2) - 140.0*c1*c2*c12),r12_hat,f12e);
scalar1DArrayMultip(nCols,(10.0*c1 - 70.0*c1*pow(c2,2) + 20.0*c2*c12),e1,h1);
scalar1DArrayMultip(nCols,(10.0*c2 - 70.0*c2*pow(c1,2) + 20.0*c1*c12),e2,h2);
sum1DArrays(nCols, h1,f12e,f12e);
sum1DArrays(nCols, h2,f12e,f12e);
scalar1DArrayMultip(nCols,(0.75*quad1_mag*quad2_mag/pow(r12_mag,6)),f12e,f12e); // Compare result from angles
subtract1DArrays(nCols, f12t, f12e,f12tf12e);
printf("Force %37.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", f12t[0],f12t[1],f12t[2], f12e[0], f12e[1],f12e[2], f12tf12e[0],f12tf12e[1],f12tf12e[2]);
// Calculate the quadrupole-quadrupole torques
zeroMatrix(3,3,gg);
contract_ijkl_kl(tt4,quad2,gg);
scalar2DArrayMultip(nCols,nCols,(1.0/9.0),gg,gg); // Contract T4 with quadrupole 2
zeroMatrix(3,3,gg1);
contract_ik_jk(quad1, gg,gg1); // Contract result with quadrupole 1
skew(gg1,skg);
scalar1DArrayMultip(nCols,-2.0,skg,t1t); // Contract with Levi-Civita symbol
scalar1DArrayMultip(nCols,(2.5*(c1*(7.0*pow(c2,2)-1.0)-2.0*c2*c12)), r12_hat,g);
scalar1DArrayMultip(nCols,(5.0*c1*c2-c12), e2,g1);
subtract1DArrays(nCols,g,g1,g); // Compare result from angles
crossProduct(e1,g,cross);
scalar1DArrayMultip(nCols,-(3.0*quad1_mag*quad2_mag/pow(r12_mag,5)),cross,t1e );
subtract1DArrays(nCols, t1t, t1e,t1tt1e);
printf("Torque on 1 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t1t[0], t1t[1],t1t[2], t1e[0], t1e[1],t1e[2], t1tt1e[0], t1tt1e[1],t1tt1e[2]);
zeroMatrix(3,3,gg);
contract_ijkl_kl(tt4,quad1,gg);
scalar2DArrayMultip(nCols,nCols,(1.0/9.0),gg,gg); // Contract T4 with quadrupole 1
zeroMatrix(3,3,gg1);
contract_ik_jk(quad2, gg,gg1); // Contract result with quadrupole 2
skew(gg1,skg);
scalar1DArrayMultip(nCols,-2.0,skg,t2t); // Contract with Levi-Civita symbol
scalar1DArrayMultip(nCols,2.5*(c2*(7.0*pow(c1,2)-1.0)-2.0*c1*c12),r12_hat, g);
scalar1DArrayMultip(nCols,(5.0*c1*c2-c12),e1,g1);
subtract1DArrays(nCols,g,g1,g); // Compare result from angles
crossProduct(e2,g,cross);
scalar1DArrayMultip(nCols,-(3.0*quad1_mag*quad2_mag/pow(r12_mag,5)),cross,t2e);
subtract1DArrays(nCols, t2t, t2e, t2tt2e);
printf("Torque on 2 %32.6f %10.6f %10.6f %18.6f %10.6f %10.6f %18.6f %10.6f %10.6f \n", t2t[0], t2t[1],t2t[2], t2e[0], t2e[1],t2e[2], t2tt2e[0], t2tt2e[1],t2tt2e[2]);
delete [] g;
delete [] g1;
delete [] h1;
delete [] h2;
delete [] e1;
delete [] e2;
delete [] mu1;
delete [] mu2;
delete [] t1t;
delete [] skg;
delete [] t1tt1e;
delete [] t2tt2e;
delete [] t2t;
delete [] t1e;
delete [] t2e;
delete [] f12t;
delete [] f12e;
delete [] f12tf12e;
delete [] r12;
delete [] r12_hat;
delete [] cross;
free2DArray(nCols,gg);
free2DArray(nCols,gg1);
free2DArray(nCols,tt2);
free2DArray(nCols,quad1);
free2DArray(nCols,quad2);
free2DArray(nCols,ident);
free3DArray(nCols,nCols,tt3);
free3DArray(nCols,nCols,ggg);
free4DArray(nCols,nCols,nCols,tt4);
free5DArray(nCols,nCols,nCols,nCols,tt5);
return 0;
}