text: /*----------------------------------------------------------------------
    PuReMD - Purdue ReaxFF Molecular Dynamics Program
    Website: https://www.cs.purdue.edu/puremd
  
    Copyright (2010) Purdue University
  
    Contributing authors:
    H. M. Aktulga, J. Fogarty, S. Pandit, A. Grama
    Corresponding author:
    Hasan Metin Aktulga, Michigan State University, hma@cse.msu.edu
  
    Please cite the related publication:
    H. M. Aktulga, J. C. Fogarty, S. A. Pandit, A. Y. Grama,
    "Parallel Reactive Molecular Dynamics: Numerical Methods and
    Algorithmic Techniques", Parallel Computing, 38 (4-5), 245-259
  
    This program is free software; you can redistribute it and/or
    modify it under the terms of the GNU General Public License as
    published by the Free Software Foundation; either version 2 of
    the License, or (at your option) any later version.
  
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
    See the GNU General Public License for more details:
    <http://www.gnu.org/licenses/>.
    ----------------------------------------------------------------------*/
  
  #include "pair_reaxc_omp.h"
  #include "thr_data.h"
  
  #include "reaxc_types.h"
  #include "reaxc_torsion_angles_omp.h"
  #include "reaxc_bond_orders_omp.h"
  #include "reaxc_list.h"
  #include "reaxc_tool_box.h"
  #include "reaxc_vector.h"
  
  #if defined(_OPENMP)
  #include <omp.h>
  #endif
  
  #define MIN_SINE 1e-10
  
  using namespace LAMMPS_NS;
  
  // Functions defined in reaxc_torsion_angles.cpp
  extern double Calculate_Omega(rvec, double, rvec, double, rvec, double, rvec, double,
                              three_body_interaction_data*, three_body_interaction_data*,
                              rvec, rvec, rvec, rvec, output_controls*);
  
  /* ---------------------------------------------------------------------- */
  
  void Torsion_AnglesOMP( reax_system *system, control_params *control,
                       simulation_data *data, storage *workspace,
                       reax_list **lists, output_controls *out_control )
  {
  #ifdef OMP_TIMING
    double endTimeBase, startTimeBase;
    startTimeBase = MPI_Wtime();
  #endif
  
    int natoms = system->n;
    reax_list *bonds = (*lists) + BONDS;
    reax_list *thb_intrs = (*lists) + THREE_BODIES;
    double p_tor2 = system->reax_param.gp.l[23];
    double p_tor3 = system->reax_param.gp.l[24];
    double p_tor4 = system->reax_param.gp.l[25];
    double p_cot2 = system->reax_param.gp.l[27];
    double total_Etor = 0;
    double total_Econ = 0;
    int  nthreads = control->nthreads;
  
  #if defined(_OPENMP)
  #pragma omp parallel default(shared) reduction(+: total_Etor, total_Econ)
  #endif
    {
    int i, j, k, l, pi, pj, pk, pl, pij, plk;
    int type_i, type_j, type_k, type_l;
    int start_j, end_j;
    int start_pj, end_pj, start_pk, end_pk;
    int num_frb_intrs = 0;
  
    double Delta_j, Delta_k;
    double r_ij, r_jk, r_kl, r_li;
    double BOA_ij, BOA_jk, BOA_kl;
  
    double exp_tor2_ij, exp_tor2_jk, exp_tor2_kl;
    double exp_tor1, exp_tor3_DjDk, exp_tor4_DjDk, exp_tor34_inv;
    double exp_cot2_jk, exp_cot2_ij, exp_cot2_kl;
    double fn10, f11_DjDk, dfn11, fn12;
    double theta_ijk, theta_jkl;
    double sin_ijk, sin_jkl;
    double cos_ijk, cos_jkl;
    double tan_ijk_i, tan_jkl_i;
    double omega, cos_omega, cos2omega, cos3omega;
    rvec dcos_omega_di, dcos_omega_dj, dcos_omega_dk, dcos_omega_dl;
    double CV, cmn, CEtors1, CEtors2, CEtors3, CEtors4;
    double CEtors5, CEtors6, CEtors7, CEtors8, CEtors9;
    double Cconj, CEconj1, CEconj2, CEconj3;
    double CEconj4, CEconj5, CEconj6;
    double e_tor, e_con;
    rvec dvec_li;
    rvec force, ext_press;
    ivec rel_box_jl;
    // rtensor total_rtensor, temp_rtensor;
    four_body_header *fbh;
    four_body_parameters *fbp;
    bond_data *pbond_ij, *pbond_jk, *pbond_kl;
    bond_order_data *bo_ij, *bo_jk, *bo_kl;
    three_body_interaction_data *p_ijk, *p_jkl;
  
    // Virial tallying variables
    double delil[3], deljl[3], delkl[3];
    double eng_tmp, fi_tmp[3], fj_tmp[3], fk_tmp[3];
  
  #if defined(_OPENMP)
    int tid = omp_get_thread_num();
  #else
    int tid = 0;
  #endif
    long reductionOffset = (system->N * tid);
    class PairReaxCOMP *pair_reax_ptr;
    pair_reax_ptr = static_cast<class PairReaxCOMP*>(system->pair_ptr);
    class ThrData *thr = pair_reax_ptr->getFixOMP()->get_thr(tid);
  
  #if defined(_OPENMP)
  #pragma omp for schedule(static)
  #endif
    for (j = 0; j < system->N; ++j) {
      start_j = Start_Index(j, bonds);
      end_j = End_Index(j, bonds);
  
      for (pk = start_j; pk < end_j; ++pk) {
        bo_jk = &( bonds->select.bond_list[pk].bo_data );
        for (k = 0; k < nthreads; ++k)
          bo_jk->CdboReduction[k] = 0.;
      }
    }
  
  #if defined(_OPENMP)
  #pragma omp for schedule(dynamic,50)
  #endif
    for (j = 0; j < natoms; ++j) {
      type_j = system->my_atoms[j].type;
      Delta_j = workspace->Delta_boc[j];
      start_j = Start_Index(j, bonds);
      end_j = End_Index(j, bonds);
  
      for (pk = start_j; pk < end_j; ++pk) {
        pbond_jk = &( bonds->select.bond_list[pk] );
        k = pbond_jk->nbr;
        bo_jk = &( pbond_jk->bo_data );
        BOA_jk = bo_jk->BO - control->thb_cut;
  
        /* see if there are any 3-body interactions involving j&k
           where j is the central atom. Otherwise there is no point in
           trying to form a 4-body interaction out of this neighborhood */
        if (system->my_atoms[j].orig_id < system->my_atoms[k].orig_id &&
            bo_jk->BO > control->thb_cut/*0*/ && Num_Entries(pk, thb_intrs)) {
          pj = pbond_jk->sym_index; // pj points to j on k's list
  
          /* do the same check as above:
             are there any 3-body interactions involving k&j
             where k is the central atom */
          if (Num_Entries(pj, thb_intrs)) {
            type_k = system->my_atoms[k].type;
            Delta_k = workspace->Delta_boc[k];
            r_jk = pbond_jk->d;
  
            start_pk = Start_Index(pk, thb_intrs );
            end_pk = End_Index(pk, thb_intrs );
            start_pj = Start_Index(pj, thb_intrs );
            end_pj = End_Index(pj, thb_intrs );
  
            exp_tor2_jk = exp( -p_tor2 * BOA_jk );
            exp_cot2_jk = exp( -p_cot2 * SQR(BOA_jk - 1.5) );
            exp_tor3_DjDk = exp( -p_tor3 * (Delta_j + Delta_k) );
            exp_tor4_DjDk = exp( p_tor4  * (Delta_j + Delta_k) );
            exp_tor34_inv = 1.0 / (1.0 + exp_tor3_DjDk + exp_tor4_DjDk);
            f11_DjDk = (2.0 + exp_tor3_DjDk) * exp_tor34_inv;
  
  
            /* pick i up from j-k interaction where j is the central atom */
            for (pi = start_pk; pi < end_pk; ++pi) {
              p_ijk = &( thb_intrs->select.three_body_list[pi] );
              pij = p_ijk->pthb; // pij is pointer to i on j's bond_list
              pbond_ij = &( bonds->select.bond_list[pij] );
              bo_ij = &( pbond_ij->bo_data );
  
              if (bo_ij->BO > control->thb_cut/*0*/) {
                i = p_ijk->thb;
                type_i = system->my_atoms[i].type;
                r_ij = pbond_ij->d;
                BOA_ij = bo_ij->BO - control->thb_cut;
  
                theta_ijk = p_ijk->theta;
                sin_ijk = sin( theta_ijk );
                cos_ijk = cos( theta_ijk );
                //tan_ijk_i = 1. / tan( theta_ijk );
                if (sin_ijk >= 0 && sin_ijk <= MIN_SINE)
                  tan_ijk_i = cos_ijk / MIN_SINE;
                else if( sin_ijk <= 0 && sin_ijk >= -MIN_SINE )
                  tan_ijk_i = cos_ijk / -MIN_SINE;
                else tan_ijk_i = cos_ijk / sin_ijk;
  
                exp_tor2_ij = exp( -p_tor2 * BOA_ij );
                exp_cot2_ij = exp( -p_cot2 * SQR(BOA_ij -1.5) );
  
  
                /* pick l up from j-k interaction where k is the central atom */
                for (pl = start_pj; pl < end_pj; ++pl) {
                  p_jkl = &( thb_intrs->select.three_body_list[pl] );
                  l = p_jkl->thb;
                  plk = p_jkl->pthb; //pointer to l on k's bond_list!
                  pbond_kl = &( bonds->select.bond_list[plk] );
                  bo_kl = &( pbond_kl->bo_data );
                  type_l = system->my_atoms[l].type;
                  fbh = &(system->reax_param.fbp[type_i][type_j]
                          [type_k][type_l]);
                  fbp = &(system->reax_param.fbp[type_i][type_j]
                          [type_k][type_l].prm[0]);
  
                  if (i != l && fbh->cnt &&
                      bo_kl->BO > control->thb_cut/*0*/ &&
                      bo_ij->BO * bo_jk->BO * bo_kl->BO > control->thb_cut/*0*/) {
                    ++num_frb_intrs;
                    //fprintf(stderr,
                    //      "%5d: %6d %6d %6d %6d\n", num_frb_intrs,
                    //      system->my_atoms[i].orig_id,system->my_atoms[j].orig_id,
                    //      system->my_atoms[k].orig_id,system->my_atoms[l].orig_id);
  
                    r_kl = pbond_kl->d;
                    BOA_kl = bo_kl->BO - control->thb_cut;
  
                    theta_jkl = p_jkl->theta;
                    sin_jkl = sin( theta_jkl );
                    cos_jkl = cos( theta_jkl );
                    //tan_jkl_i = 1. / tan( theta_jkl );
                    if (sin_jkl >= 0 && sin_jkl <= MIN_SINE)
                      tan_jkl_i = cos_jkl / MIN_SINE;
                    else if( sin_jkl <= 0 && sin_jkl >= -MIN_SINE )
                      tan_jkl_i = cos_jkl / -MIN_SINE;
                    else tan_jkl_i = cos_jkl /sin_jkl;
  
                    rvec_ScaledSum( dvec_li, 1., system->my_atoms[i].x,
                                    -1., system->my_atoms[l].x );
                    r_li = rvec_Norm( dvec_li );
  
  
                    /* omega and its derivative */
                    omega = Calculate_Omega( pbond_ij->dvec, r_ij,
                                             pbond_jk->dvec, r_jk,
                                             pbond_kl->dvec, r_kl,
                                             dvec_li, r_li,
                                             p_ijk, p_jkl,
                                             dcos_omega_di, dcos_omega_dj,
                                             dcos_omega_dk, dcos_omega_dl,
                                             out_control );
  
                    cos_omega = cos( omega );
                    cos2omega = cos( 2. * omega );
                    cos3omega = cos( 3. * omega );
                    /* end omega calculations */
  
                    /* torsion energy */
                    exp_tor1 = exp( fbp->p_tor1 *
                                    SQR(2.0 - bo_jk->BO_pi - f11_DjDk) );
                    exp_tor2_kl = exp( -p_tor2 * BOA_kl );
                    exp_cot2_kl = exp( -p_cot2 * SQR(BOA_kl - 1.5) );
                    fn10 = (1.0 - exp_tor2_ij) * (1.0 - exp_tor2_jk) *
                      (1.0 - exp_tor2_kl);
  
                    CV = 0.5 * ( fbp->V1 * (1.0 + cos_omega) +
                                 fbp->V2 * exp_tor1 * (1.0 - cos2omega) +
                                 fbp->V3 * (1.0 + cos3omega) );
  
                    total_Etor += e_tor = fn10 * sin_ijk * sin_jkl * CV;
  
                    dfn11 = (-p_tor3 * exp_tor3_DjDk +
                             (p_tor3 * exp_tor3_DjDk - p_tor4 * exp_tor4_DjDk) *
                             (2.0 + exp_tor3_DjDk) * exp_tor34_inv) *
                      exp_tor34_inv;
  
                    CEtors1 = sin_ijk * sin_jkl * CV;
  
                    CEtors2 = -fn10 * 2.0 * fbp->p_tor1 * fbp->V2 * exp_tor1 *
                      (2.0 - bo_jk->BO_pi - f11_DjDk) * (1.0 - SQR(cos_omega)) *
                      sin_ijk * sin_jkl;
                    CEtors3 = CEtors2 * dfn11;
  
                    CEtors4 = CEtors1 * p_tor2 * exp_tor2_ij *
                      (1.0 - exp_tor2_jk) * (1.0 - exp_tor2_kl);
                    CEtors5 = CEtors1 * p_tor2 *
                      (1.0 - exp_tor2_ij) * exp_tor2_jk * (1.0 - exp_tor2_kl);
                    CEtors6 = CEtors1 * p_tor2 *
                      (1.0 - exp_tor2_ij) * (1.0 - exp_tor2_jk) * exp_tor2_kl;
  
                    cmn = -fn10 * CV;
                    CEtors7 = cmn * sin_jkl * tan_ijk_i;
                    CEtors8 = cmn * sin_ijk * tan_jkl_i;
  
                    CEtors9 = fn10 * sin_ijk * sin_jkl *
                      (0.5 * fbp->V1 - 2.0 * fbp->V2 * exp_tor1 * cos_omega +
                       1.5 * fbp->V3 * (cos2omega + 2.0 * SQR(cos_omega)));
                    /* end  of torsion energy */
  
  
                    /* 4-body conjugation energy */
                    fn12 = exp_cot2_ij * exp_cot2_jk * exp_cot2_kl;
                    //data->my_en.e_con += e_con =
                    total_Econ += e_con =
                      fbp->p_cot1 * fn12 *
                      (1.0 + (SQR(cos_omega) - 1.0) * sin_ijk * sin_jkl);
  
                    Cconj = -2.0 * fn12 * fbp->p_cot1 * p_cot2 *
                      (1.0 + (SQR(cos_omega) - 1.0) * sin_ijk * sin_jkl);
  
                    CEconj1 = Cconj * (BOA_ij - 1.5e0);
                    CEconj2 = Cconj * (BOA_jk - 1.5e0);
                    CEconj3 = Cconj * (BOA_kl - 1.5e0);
  
                    CEconj4 = -fbp->p_cot1 * fn12 *
                      (SQR(cos_omega) - 1.0) * sin_jkl * tan_ijk_i;
                    CEconj5 = -fbp->p_cot1 * fn12 *
                      (SQR(cos_omega) - 1.0) * sin_ijk * tan_jkl_i;
                    CEconj6 = 2.0 * fbp->p_cot1 * fn12 *
                      cos_omega * sin_ijk * sin_jkl;
                    /* end 4-body conjugation energy */
  
                    /* FORCES */
                    bo_jk->Cdbopi += CEtors2;
                    workspace->CdDelta[j] += CEtors3;
                    //workspace->CdDelta[k] += CEtors3;
                    workspace->CdDeltaReduction[reductionOffset+k] += CEtors3;
                    bo_ij->Cdbo += (CEtors4 + CEconj1);
                    bo_jk->Cdbo += (CEtors5 + CEconj2);
                    //bo_kl->Cdbo += (CEtors6 + CEconj3);
                    bo_kl->CdboReduction[tid] += (CEtors6 + CEconj3);
  
                    if (control->virial == 0) {
                      /* dcos_theta_ijk */
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors7 + CEconj4, p_ijk->dcos_dj );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+i],
                                      CEtors7 + CEconj4, p_ijk->dcos_dk );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+k],
                                      CEtors7 + CEconj4, p_ijk->dcos_di );
  
                      /* dcos_theta_jkl */
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors8 + CEconj5, p_jkl->dcos_di );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+k],
                                      CEtors8 + CEconj5, p_jkl->dcos_dj );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+l],
                                      CEtors8 + CEconj5, p_jkl->dcos_dk );
  
                      /* dcos_omega */
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors9 + CEconj6, dcos_omega_dj );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+i],
                                      CEtors9 + CEconj6, dcos_omega_di );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+k],
                                      CEtors9 + CEconj6, dcos_omega_dk );
                      rvec_ScaledAdd( workspace->forceReduction[reductionOffset+l],
                                      CEtors9 + CEconj6, dcos_omega_dl );
                    }
                    else {
                      ivec_Sum(rel_box_jl, pbond_jk->rel_box, pbond_kl->rel_box);
  
                      /* dcos_theta_ijk */
                      rvec_Scale( force, CEtors7 + CEconj4, p_ijk->dcos_dk );
                      rvec_Add( workspace->forceReduction[reductionOffset+i], force );
                      rvec_iMultiply( ext_press, pbond_ij->rel_box, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors7 + CEconj4, p_ijk->dcos_dj );
  
                      rvec_Scale( force, CEtors7 + CEconj4, p_ijk->dcos_di );
                      rvec_Add( workspace->forceReduction[reductionOffset+k], force );
                      rvec_iMultiply( ext_press, pbond_jk->rel_box, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      /* dcos_theta_jkl */
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors8 + CEconj5, p_jkl->dcos_di );
  
                      rvec_Scale( force, CEtors8 + CEconj5, p_jkl->dcos_dj );
                      rvec_Add( workspace->forceReduction[reductionOffset+k], force );
                      rvec_iMultiply( ext_press, pbond_jk->rel_box, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      rvec_Scale( force, CEtors8 + CEconj5, p_jkl->dcos_dk );
                      rvec_Add( workspace->forceReduction[reductionOffset+l], force );
                      rvec_iMultiply( ext_press, rel_box_jl, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      /* dcos_omega */
                      rvec_Scale( force, CEtors9 + CEconj6, dcos_omega_di );
                      rvec_Add( workspace->forceReduction[reductionOffset+i], force );
                      rvec_iMultiply( ext_press, pbond_ij->rel_box, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      rvec_ScaledAdd( workspace->f[j],
                                      CEtors9 + CEconj6, dcos_omega_dj );
  
                      rvec_Scale( force, CEtors9 + CEconj6, dcos_omega_dk );
                      rvec_Add( workspace->forceReduction[reductionOffset+k], force );
                      rvec_iMultiply( ext_press, pbond_jk->rel_box, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
  
                      rvec_Scale( force, CEtors9 + CEconj6, dcos_omega_dl );
                      rvec_Add( workspace->forceReduction[reductionOffset+i], force );
                      rvec_iMultiply( ext_press, rel_box_jl, force );
                      rvec_Add( workspace->my_ext_pressReduction[tid], ext_press );
                    }
  
                    /* tally into per-atom virials */
                    if (system->pair_ptr->vflag_atom || system->pair_ptr->evflag) {
  
                      // acquire vectors
                      rvec_ScaledSum( delil, 1., system->my_atoms[l].x,
                                            -1., system->my_atoms[i].x );
                      rvec_ScaledSum( deljl, 1., system->my_atoms[l].x,
                                            -1., system->my_atoms[j].x );
                      rvec_ScaledSum( delkl, 1., system->my_atoms[l].x,
                                            -1., system->my_atoms[k].x );
                      // dcos_theta_ijk
                      rvec_Scale( fi_tmp, CEtors7 + CEconj4, p_ijk->dcos_dk );
                      rvec_Scale( fj_tmp, CEtors7 + CEconj4, p_ijk->dcos_dj );
                      rvec_Scale( fk_tmp, CEtors7 + CEconj4, p_ijk->dcos_di );
  
                      // dcos_theta_jkl
                      rvec_ScaledAdd( fj_tmp, CEtors8 + CEconj5, p_jkl->dcos_di );
                      rvec_ScaledAdd( fk_tmp, CEtors8 + CEconj5, p_jkl->dcos_dj );
  
                      // dcos_omega
                      rvec_ScaledAdd( fi_tmp, CEtors9 + CEconj6, dcos_omega_di );
                      rvec_ScaledAdd( fj_tmp, CEtors9 + CEconj6, dcos_omega_dj );
                      rvec_ScaledAdd( fk_tmp, CEtors9 + CEconj6, dcos_omega_dk );
  
                      // tally
                      eng_tmp = e_tor + e_con;
  
                      if (system->pair_ptr->evflag)
                        pair_reax_ptr->ev_tally_thr_proxy(system->pair_ptr, j, k, system->n, 1,
                                                          eng_tmp, 0.0, 0.0, 0.0, 0.0, 0.0, thr);
  
                      // NEED TO MAKE AN OMP VERSION OF THIS CALL!
                      if (system->pair_ptr->vflag_atom)
                        system->pair_ptr->v_tally4(i, j, k, l, fi_tmp, fj_tmp, fk_tmp,
                                                   delil, deljl, delkl );
                    }
  
                  } // pl check ends
                } // pl loop ends
              } // pi check ends
            } // pi loop ends
          } // k-j neighbor check ends
        } // j<k && j-k neighbor check ends
      } // pk loop ends
    } // j loop
  
   } // end omp parallel
  
    data->my_en.e_tor = total_Etor;
    data->my_en.e_con = total_Econ;
  
  #ifdef OMP_TIMING
    endTimeBase = MPI_Wtime();
    ompTimingData[COMPUTETORSIONANGLESBOINDEX] += (endTimeBase-startTimeBase);
  #endif
  }
  