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Comparing trunk/src/nonbonded/Electrostatic.cpp (file contents):
Revision 1895 by gezelter, Mon Jul 1 21:09:37 2013 UTC vs.
Revision 1981 by gezelter, Mon Apr 14 18:32:51 2014 UTC

# Line 40 | Line 40
40   * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41   */
42  
43 + #ifdef IS_MPI
44 + #include <mpi.h>
45 + #endif
46 +
47   #include <stdio.h>
48   #include <string.h>
49  
50   #include <cmath>
51 + #include <numeric>
52   #include "nonbonded/Electrostatic.hpp"
53   #include "utils/simError.h"
54   #include "types/NonBondedInteractionType.hpp"
# Line 55 | Line 60
60   #include "utils/PhysicalConstants.hpp"
61   #include "math/erfc.hpp"
62   #include "math/SquareMatrix.hpp"
63 + #include "primitives/Molecule.hpp"
64 + #include "flucq/FluctuatingChargeForces.hpp"
65  
66   namespace OpenMD {
67    
# Line 64 | Line 71 | namespace OpenMD {
71                                    haveDampingAlpha_(false),
72                                    haveDielectric_(false),
73                                    haveElectroSplines_(false)
74 <  {}
74 >  {
75 >    flucQ_ = new FluctuatingChargeForces(info_);
76 >  }
77    
78 +  void Electrostatic::setForceField(ForceField *ff) {
79 +    forceField_ = ff;
80 +    flucQ_->setForceField(forceField_);
81 +  }
82 +
83 +  void Electrostatic::setSimulatedAtomTypes(set<AtomType*> &simtypes) {
84 +    simTypes_ = simtypes;
85 +    flucQ_->setSimulatedAtomTypes(simTypes_);
86 +  }
87 +
88    void Electrostatic::initialize() {
89      
90      Globals* simParams_ = info_->getSimParams();
# Line 191 | Line 210 | namespace OpenMD {
210        simError();
211      }
212            
213 <    if (screeningMethod_ == DAMPED) {      
213 >    if (screeningMethod_ == DAMPED || summationMethod_ == esm_EWALD_FULL) {
214        if (!simParams_->haveDampingAlpha()) {
215          // first set a cutoff dependent alpha value
216          // we assume alpha depends linearly with rcut from 0 to 20.5 ang
217          dampingAlpha_ = 0.425 - cutoffRadius_* 0.02;
218 <        if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;
200 <        
218 >        if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;        
219          // throw warning
220          sprintf( painCave.errMsg,
221                   "Electrostatic::initialize: dampingAlpha was not specified in the\n"
# Line 213 | Line 231 | namespace OpenMD {
231        haveDampingAlpha_ = true;
232      }
233  
234 +
235      Etypes.clear();
236      Etids.clear();
237      FQtypes.clear();
# Line 262 | Line 281 | namespace OpenMD {
281        b3c = (5.0 * b2c + pow(2.0*a2, 3) * expTerm * invArootPi) / r2;
282        b4c = (7.0 * b3c + pow(2.0*a2, 4) * expTerm * invArootPi) / r2;
283        b5c = (9.0 * b4c + pow(2.0*a2, 5) * expTerm * invArootPi) / r2;
284 <      selfMult_ = b0c + a2 * invArootPi;
284 >      // Half the Smith self piece:
285 >      selfMult1_ = - a2 * invArootPi;
286 >      selfMult2_ = - 2.0 * a2 * a2 * invArootPi / 3.0;
287 >      selfMult4_ = - 4.0 * a2 * a2 * a2 * invArootPi / 5.0;
288      } else {
289        a2 = 0.0;
290        b0c = 1.0 / r;
# Line 271 | Line 293 | namespace OpenMD {
293        b3c = (5.0 * b2c) / r2;
294        b4c = (7.0 * b3c) / r2;
295        b5c = (9.0 * b4c) / r2;
296 <      selfMult_ = b0c;
296 >      selfMult1_ = 0.0;
297 >      selfMult2_ = 0.0;
298 >      selfMult4_ = 0.0;
299      }
300  
301      // higher derivatives of B_0 at the cutoff radius:
# Line 279 | Line 303 | namespace OpenMD {
303      db0c_2 =     -b1c + r2 * b2c;
304      db0c_3 =          3.0*r*b2c  - r2*r*b3c;
305      db0c_4 =          3.0*b2c  - 6.0*r2*b3c     + r2*r2*b4c;
306 <    db0c_5 =                    -15.0*r*b3c + 10.0*r2*r*b4c - r2*r2*r*b5c;
283 <    
306 >    db0c_5 =                    -15.0*r*b3c + 10.0*r2*r*b4c - r2*r2*r*b5c;  
307  
308 +    if (summationMethod_ != esm_EWALD_FULL) {
309 +      selfMult1_ -= b0c;
310 +      selfMult2_ += (db0c_2 + 2.0*db0c_1*ric) /  3.0;
311 +      selfMult4_ -= (db0c_4 + 4.0*db0c_3*ric) / 15.0;
312 +    }
313 +
314      // working variables for the splines:
315      RealType ri, ri2;
316      RealType b0, b1, b2, b3, b4, b5;
# Line 316 | Line 345 | namespace OpenMD {
345      vector<RealType> v21v, v22v;
346      vector<RealType> v31v, v32v;
347      vector<RealType> v41v, v42v, v43v;
319 –
320 –    /*
321 –    vector<RealType> dv01v;
322 –    vector<RealType> dv11v;
323 –    vector<RealType> dv21v, dv22v;
324 –    vector<RealType> dv31v, dv32v;
325 –    vector<RealType> dv41v, dv42v, dv43v;
326 –    */
348  
349      for (int i = 1; i < np_ + 1; i++) {
350        r = RealType(i) * dx;
# Line 488 | Line 509 | namespace OpenMD {
509  
510        case esm_SWITCHING_FUNCTION:
511        case esm_HARD:
512 +      case esm_EWALD_FULL:
513  
514          v01 = f;
515          v11 = g;
# Line 546 | Line 568 | namespace OpenMD {
568  
569          break;
570                  
549 –      case esm_EWALD_FULL:
571        case esm_EWALD_PME:
572        case esm_EWALD_SPME:
573        default :
# Line 575 | Line 596 | namespace OpenMD {
596        v41v.push_back(v41);
597        v42v.push_back(v42);
598        v43v.push_back(v43);
578 –      /*
579 –      dv01v.push_back(dv01);
580 –      dv11v.push_back(dv11);
581 –      dv21v.push_back(dv21);
582 –      dv22v.push_back(dv22);
583 –      dv31v.push_back(dv31);
584 –      dv32v.push_back(dv32);      
585 –      dv41v.push_back(dv41);
586 –      dv42v.push_back(dv42);
587 –      dv43v.push_back(dv43);
588 –      */
599      }
600  
601      // construct the spline structures and fill them with the values we've
# Line 609 | Line 619 | namespace OpenMD {
619      v42s->addPoints(rv, v42v);
620      v43s = new CubicSpline();
621      v43s->addPoints(rv, v43v);
612 –
613 –    /*
614 –    dv01s = new CubicSpline();
615 –    dv01s->addPoints(rv, dv01v);
616 –    dv11s = new CubicSpline();
617 –    dv11s->addPoints(rv, dv11v);
618 –    dv21s = new CubicSpline();
619 –    dv21s->addPoints(rv, dv21v);
620 –    dv22s = new CubicSpline();
621 –    dv22s->addPoints(rv, dv22v);
622 –    dv31s = new CubicSpline();
623 –    dv31s->addPoints(rv, dv31v);
624 –    dv32s = new CubicSpline();
625 –    dv32s->addPoints(rv, dv32v);
626 –    dv41s = new CubicSpline();
627 –    dv41s->addPoints(rv, dv41v);
628 –    dv42s = new CubicSpline();
629 –    dv42s->addPoints(rv, dv42v);
630 –    dv43s = new CubicSpline();
631 –    dv43s->addPoints(rv, dv43v);
632 –    */
622  
623      haveElectroSplines_ = true;
624  
# Line 704 | Line 693 | namespace OpenMD {
693        FQtids[atid] = fqtid;
694        Jij[fqtid].resize(nFlucq_);
695  
696 <      // Now, iterate over all known fluctuating and add to the coulomb integral map:
696 >      // Now, iterate over all known fluctuating and add to the
697 >      // coulomb integral map:
698        
699        std::set<int>::iterator it;
700        for( it = FQtypes.begin(); it != FQtypes.end(); ++it) {    
# Line 790 | Line 780 | namespace OpenMD {
780      // Excluded potential that is still computed for fluctuating charges
781      excluded_Pot= 0.0;
782  
793 –
783      // some variables we'll need independent of electrostatic type:
784  
785      ri = 1.0 /  *(idat.rij);
# Line 911 | Line 900 | namespace OpenMD {
900          Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
901                          + rdQbr * rhat * (dv22 - 2.0*v22or));
902      }
903 <    
903 >        
904 >
905      if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
906        J = Jij[FQtids[idat.atid1]][FQtids[idat.atid2]];
907      }    
908 <    
908 >
909      if (a_is_Charge) {    
910        
911        if (b_is_Charge) {
912          pref =  pre11_ * *(idat.electroMult);      
913          U  += C_a * C_b * pref * v01;
914          F  += C_a * C_b * pref * dv01 * rhat;
915 <        
915 >
916          // If this is an excluded pair, there are still indirect
917          // interactions via the reaction field we must worry about:
918  
# Line 931 | Line 921 | namespace OpenMD {
921            indirect_Pot += rfContrib;
922            indirect_F   += rfContrib * 2.0 * ri * rhat;
923          }
924 <        
924 >
925          // Fluctuating charge forces are handled via Coulomb integrals
926          // for excluded pairs (i.e. those connected via bonds) and
927          // with the standard charge-charge interaction otherwise.
928  
929 <        if (idat.excluded) {          
929 >        if (idat.excluded) {
930            if (a_is_Fluctuating || b_is_Fluctuating) {
931              coulInt = J->getValueAt( *(idat.rij) );
932 <            if (a_is_Fluctuating)  dUdCa += coulInt * C_b;
933 <            if (b_is_Fluctuating)  dUdCb += coulInt * C_a;
934 <            excluded_Pot += C_a * C_b * coulInt;
945 <          }          
932 >            if (a_is_Fluctuating) dUdCa += C_b * coulInt;
933 >            if (b_is_Fluctuating) dUdCb += C_a * coulInt;          
934 >          }
935          } else {
936            if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
937 <          if (a_is_Fluctuating) dUdCb += C_a * pref * v01;
938 <        }
937 >          if (b_is_Fluctuating) dUdCb += C_a * pref * v01;
938 >        }              
939        }
940  
941        if (b_is_Dipole) {
# Line 1012 | Line 1001 | namespace OpenMD {
1001          F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
1002          Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
1003          Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
1015 –
1004          // Even if we excluded this pair from direct interactions, we
1005          // still have the reaction-field-mediated dipole-dipole
1006          // interaction:
# Line 1072 | Line 1060 | namespace OpenMD {
1060          trQaQb = QaQb.trace();
1061          rQaQb = rhat * QaQb;
1062          QaQbr = QaQb * rhat;
1063 <        QaxQb = cross(Q_a, Q_b);
1063 >        QaxQb = mCross(Q_a, Q_b);
1064          rQaQbr = dot(rQa, Qbr);
1065          rQaxQbr = cross(rQa, Qbr);
1066          
# Line 1103 | Line 1091 | namespace OpenMD {
1091          //             + 4.0 * cross(rhat, QbQar)
1092  
1093          Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1106 –
1107 –        //  cerr << " tsum = " << Ta + Tb - cross(  *(idat.d) , F ) << "\n";
1094        }
1095      }
1096  
# Line 1156 | Line 1142 | namespace OpenMD {
1142      // logicals
1143      bool i_is_Charge = data.is_Charge;
1144      bool i_is_Dipole = data.is_Dipole;
1145 +    bool i_is_Quadrupole = data.is_Quadrupole;
1146      bool i_is_Fluctuating = data.is_Fluctuating;
1147      RealType C_a = data.fixedCharge;  
1148 <    RealType self, preVal, DadDa;
1149 <    
1148 >    RealType self(0.0), preVal, DdD, trQ, trQQ;
1149 >
1150 >    if (i_is_Dipole) {
1151 >      DdD = data.dipole.lengthSquare();
1152 >    }
1153 >        
1154      if (i_is_Fluctuating) {
1155        C_a += *(sdat.flucQ);
1156 <      // dVdFQ is really a force, so this is negative the derivative
1157 <      *(sdat.dVdFQ) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1158 <      (*(sdat.excludedPot))[ELECTROSTATIC_FAMILY] += (*sdat.flucQ) *
1159 <        (*(sdat.flucQ) * data.hardness * 0.5 + data.electronegativity);
1156 >
1157 >      flucQ_->getSelfInteraction(sdat.atid, *(sdat.flucQ),  
1158 >                                 (*(sdat.excludedPot))[ELECTROSTATIC_FAMILY],
1159 >                                 *(sdat.flucQfrc) );
1160 >
1161      }
1162  
1163      switch (summationMethod_) {
# Line 1180 | Line 1172 | namespace OpenMD {
1172        }
1173  
1174        if (i_is_Dipole) {
1175 <        DadDa = data.dipole.lengthSquare();
1184 <        (*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DadDa;
1175 >        (*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DdD;
1176        }
1177        
1178        break;
1179        
1180      case esm_SHIFTED_FORCE:
1181      case esm_SHIFTED_POTENTIAL:
1182 <      if (i_is_Charge) {
1183 <        self = - selfMult_ * C_a * (C_a + *(sdat.skippedCharge)) * pre11_;
1184 <        (*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1182 >    case esm_TAYLOR_SHIFTED:
1183 >    case esm_EWALD_FULL:
1184 >      if (i_is_Charge)
1185 >        self += selfMult1_ * pre11_ * C_a * (C_a + *(sdat.skippedCharge));      
1186 >      if (i_is_Dipole)
1187 >        self += selfMult2_ * pre22_ * DdD;      
1188 >      if (i_is_Quadrupole) {
1189 >        trQ = data.quadrupole.trace();
1190 >        trQQ = (data.quadrupole * data.quadrupole).trace();
1191 >        self += selfMult4_ * pre44_ * (2.0*trQQ + trQ*trQ);
1192 >        if (i_is_Charge)
1193 >          self -= selfMult2_ * pre14_ * 2.0 * C_a * trQ;
1194        }
1195 +      (*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;      
1196        break;
1197      default:
1198        break;
# Line 1204 | Line 1205 | namespace OpenMD {
1205      // 12 angstroms seems to be a reasonably good guess for most
1206      // cases.
1207      return 12.0;
1208 +  }
1209 +
1210 +
1211 +  void Electrostatic::ReciprocalSpaceSum(RealType& pot) {
1212 +    
1213 +    RealType kPot = 0.0;
1214 +    RealType kVir = 0.0;
1215 +    
1216 +    const RealType mPoleConverter = 0.20819434; // converts from the
1217 +                                                // internal units of
1218 +                                                // Debye (for dipoles)
1219 +                                                // or Debye-angstroms
1220 +                                                // (for quadrupoles) to
1221 +                                                // electron angstroms or
1222 +                                                // electron-angstroms^2
1223 +    
1224 +    const RealType eConverter = 332.0637778; // convert the
1225 +                                             // Charge-Charge
1226 +                                             // electrostatic
1227 +                                             // interactions into kcal /
1228 +                                             // mol assuming distances
1229 +                                             // are measured in
1230 +                                             // angstroms.
1231 +
1232 +    Mat3x3d hmat = info_->getSnapshotManager()->getCurrentSnapshot()->getHmat();
1233 +    Vector3d box = hmat.diagonals();
1234 +    RealType boxMax = box.max();
1235 +    
1236 +    //int kMax = int(2.0 * M_PI / (pow(dampingAlpha_,2)*cutoffRadius_ * boxMax) );
1237 +    int kMax = 7;
1238 +    int kSqMax = kMax*kMax + 2;
1239 +    
1240 +    int kLimit = kMax+1;
1241 +    int kLim2 = 2*kMax+1;
1242 +    int kSqLim = kSqMax;
1243 +    
1244 +    vector<RealType> AK(kSqLim+1, 0.0);
1245 +    RealType xcl = 2.0 * M_PI / box.x();
1246 +    RealType ycl = 2.0 * M_PI / box.y();
1247 +    RealType zcl = 2.0 * M_PI / box.z();
1248 +    RealType rcl = 2.0 * M_PI / boxMax;
1249 +    RealType rvol = 2.0 * M_PI /(box.x() * box.y() * box.z());
1250 +    
1251 +    if(dampingAlpha_ < 1.0e-12) return;
1252 +    
1253 +    RealType ralph = -0.25/pow(dampingAlpha_,2);
1254 +    
1255 +    // Calculate and store exponential factors  
1256 +    
1257 +    vector<vector<RealType> > elc;
1258 +    vector<vector<RealType> > emc;
1259 +    vector<vector<RealType> > enc;
1260 +    vector<vector<RealType> > els;
1261 +    vector<vector<RealType> > ems;
1262 +    vector<vector<RealType> > ens;
1263 +    
1264 +    int nMax = info_->getNAtoms();
1265 +    
1266 +    elc.resize(kLimit+1);
1267 +    emc.resize(kLimit+1);
1268 +    enc.resize(kLimit+1);
1269 +    els.resize(kLimit+1);
1270 +    ems.resize(kLimit+1);
1271 +    ens.resize(kLimit+1);
1272 +
1273 +    for (int j = 0; j < kLimit+1; j++) {
1274 +      elc[j].resize(nMax);
1275 +      emc[j].resize(nMax);
1276 +      enc[j].resize(nMax);
1277 +      els[j].resize(nMax);
1278 +      ems[j].resize(nMax);
1279 +      ens[j].resize(nMax);
1280 +    }
1281 +    
1282 +    Vector3d t( 2.0 * M_PI );
1283 +    t.Vdiv(t, box);
1284 +
1285 +    SimInfo::MoleculeIterator mi;
1286 +    Molecule::AtomIterator ai;
1287 +    int i;
1288 +    Vector3d r;
1289 +    Vector3d tt;
1290 +    
1291 +    for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1292 +         mol = info_->nextMolecule(mi)) {
1293 +      for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1294 +          atom = mol->nextAtom(ai)) {  
1295 +        
1296 +        i = atom->getLocalIndex();
1297 +        r = atom->getPos();
1298 +        info_->getSnapshotManager()->getCurrentSnapshot()->wrapVector(r);
1299 +        
1300 +        tt.Vmul(t, r);
1301 +
1302 +        elc[1][i] = 1.0;
1303 +        emc[1][i] = 1.0;
1304 +        enc[1][i] = 1.0;
1305 +        els[1][i] = 0.0;
1306 +        ems[1][i] = 0.0;
1307 +        ens[1][i] = 0.0;
1308 +
1309 +        elc[2][i] = cos(tt.x());
1310 +        emc[2][i] = cos(tt.y());
1311 +        enc[2][i] = cos(tt.z());
1312 +        els[2][i] = sin(tt.x());
1313 +        ems[2][i] = sin(tt.y());
1314 +        ens[2][i] = sin(tt.z());
1315 +        
1316 +        for(int l = 3; l <= kLimit; l++) {
1317 +          elc[l][i]=elc[l-1][i]*elc[2][i]-els[l-1][i]*els[2][i];
1318 +          emc[l][i]=emc[l-1][i]*emc[2][i]-ems[l-1][i]*ems[2][i];
1319 +          enc[l][i]=enc[l-1][i]*enc[2][i]-ens[l-1][i]*ens[2][i];
1320 +          els[l][i]=els[l-1][i]*elc[2][i]+elc[l-1][i]*els[2][i];
1321 +          ems[l][i]=ems[l-1][i]*emc[2][i]+emc[l-1][i]*ems[2][i];
1322 +          ens[l][i]=ens[l-1][i]*enc[2][i]+enc[l-1][i]*ens[2][i];
1323 +        }
1324 +      }
1325 +    }
1326 +    
1327 +    // Calculate and store AK coefficients:
1328 +    
1329 +    RealType eksq = 1.0;
1330 +    RealType expf = 0.0;
1331 +    if (ralph < 0.0) expf = exp(ralph*rcl*rcl);
1332 +    for (i = 1; i <= kSqLim; i++) {
1333 +      RealType rksq = float(i)*rcl*rcl;
1334 +      eksq = expf*eksq;
1335 +      AK[i] = eConverter * eksq/rksq;
1336 +    }
1337 +    
1338 +    /*
1339 +     * Loop over all k vectors k = 2 pi (ll/Lx, mm/Ly, nn/Lz)
1340 +     * the values of ll, mm and nn are selected so that the symmetry of
1341 +     * reciprocal lattice is taken into account i.e. the following
1342 +     * rules apply.
1343 +     *
1344 +     * ll ranges over the values 0 to kMax only.
1345 +     *
1346 +     * mm ranges over 0 to kMax when ll=0 and over
1347 +     *            -kMax to kMax otherwise.
1348 +     * nn ranges over 1 to kMax when ll=mm=0 and over
1349 +     *            -kMax to kMax otherwise.
1350 +     *
1351 +     * Hence the result of the summation must be doubled at the end.    
1352 +     */
1353 +    
1354 +    std::vector<RealType> clm(nMax, 0.0);
1355 +    std::vector<RealType> slm(nMax, 0.0);
1356 +    std::vector<RealType> ckr(nMax, 0.0);
1357 +    std::vector<RealType> skr(nMax, 0.0);
1358 +    std::vector<RealType> ckc(nMax, 0.0);
1359 +    std::vector<RealType> cks(nMax, 0.0);
1360 +    std::vector<RealType> dkc(nMax, 0.0);
1361 +    std::vector<RealType> dks(nMax, 0.0);
1362 +    std::vector<RealType> qkc(nMax, 0.0);
1363 +    std::vector<RealType> qks(nMax, 0.0);
1364 +    std::vector<Vector3d> dxk(nMax, V3Zero);
1365 +    std::vector<Vector3d> qxk(nMax, V3Zero);
1366 +    RealType rl, rm, rn;
1367 +    Vector3d kVec;
1368 +    Vector3d Qk;
1369 +    Mat3x3d k2;
1370 +    RealType ckcs, ckss, dkcs, dkss, qkcs, qkss;
1371 +    int atid;
1372 +    ElectrostaticAtomData data;
1373 +    RealType C, dk, qk;
1374 +    Vector3d D;
1375 +    Mat3x3d  Q;
1376 +
1377 +    int mMin = kLimit;
1378 +    int nMin = kLimit + 1;
1379 +    for (int l = 1; l <= kLimit; l++) {
1380 +      int ll = l - 1;
1381 +      rl = xcl * float(ll);
1382 +      for (int mmm = mMin; mmm <= kLim2; mmm++) {
1383 +        int mm = mmm - kLimit;
1384 +        int m = abs(mm) + 1;
1385 +        rm = ycl * float(mm);
1386 +        // Set temporary products of exponential terms
1387 +        for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1388 +             mol = info_->nextMolecule(mi)) {
1389 +          for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1390 +              atom = mol->nextAtom(ai)) {
1391 +            
1392 +            i = atom->getLocalIndex();
1393 +            if(mm < 0) {
1394 +              clm[i]=elc[l][i]*emc[m][i]+els[l][i]*ems[m][i];
1395 +              slm[i]=els[l][i]*emc[m][i]-ems[m][i]*elc[l][i];
1396 +            } else {
1397 +              clm[i]=elc[l][i]*emc[m][i]-els[l][i]*ems[m][i];
1398 +              slm[i]=els[l][i]*emc[m][i]+ems[m][i]*elc[l][i];
1399 +            }
1400 +          }
1401 +        }
1402 +        for (int nnn = nMin; nnn <= kLim2; nnn++) {
1403 +          int nn = nnn - kLimit;          
1404 +          int n = abs(nn) + 1;
1405 +          rn = zcl * float(nn);
1406 +          // Test on magnitude of k vector:
1407 +          int kk=ll*ll + mm*mm + nn*nn;
1408 +          if(kk <= kSqLim) {
1409 +            kVec = Vector3d(rl, rm, rn);
1410 +            k2 = outProduct(kVec, kVec);
1411 +            // Calculate exp(ikr) terms
1412 +            for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1413 +                 mol = info_->nextMolecule(mi)) {
1414 +              for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1415 +                  atom = mol->nextAtom(ai)) {
1416 +                i = atom->getLocalIndex();
1417 +                
1418 +                if (nn < 0) {
1419 +                  ckr[i]=clm[i]*enc[n][i]+slm[i]*ens[n][i];
1420 +                  skr[i]=slm[i]*enc[n][i]-clm[i]*ens[n][i];
1421 +
1422 +                } else {
1423 +                  ckr[i]=clm[i]*enc[n][i]-slm[i]*ens[n][i];
1424 +                  skr[i]=slm[i]*enc[n][i]+clm[i]*ens[n][i];
1425 +                }
1426 +              }
1427 +            }
1428 +            
1429 +            // Calculate scalar and vector products for each site:
1430 +            
1431 +            for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1432 +                 mol = info_->nextMolecule(mi)) {
1433 +              for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1434 +                  atom = mol->nextAtom(ai)) {
1435 +                i = atom->getLocalIndex();
1436 +                int atid = atom->getAtomType()->getIdent();
1437 +                data = ElectrostaticMap[Etids[atid]];
1438 +                              
1439 +                if (data.is_Charge) {
1440 +                  C = data.fixedCharge;
1441 +                  if (atom->isFluctuatingCharge()) C += atom->getFlucQPos();
1442 +                  ckc[i] = C * ckr[i];
1443 +                  cks[i] = C * skr[i];
1444 +                }
1445 +                
1446 +                if (data.is_Dipole) {
1447 +                  D = atom->getDipole() * mPoleConverter;
1448 +                  dk = dot(D, kVec);
1449 +                  dxk[i] = cross(D, kVec);
1450 +                  dkc[i] = dk * ckr[i];
1451 +                  dks[i] = dk * skr[i];
1452 +                }
1453 +                if (data.is_Quadrupole) {
1454 +                  Q = atom->getQuadrupole() * mPoleConverter;
1455 +                  Qk = Q * kVec;                  
1456 +                  qk = dot(kVec, Qk);
1457 +                  qxk[i] = -cross(kVec, Qk);
1458 +                  qkc[i] = qk * ckr[i];
1459 +                  qks[i] = qk * skr[i];
1460 +                }              
1461 +              }
1462 +            }
1463 +
1464 +            // calculate vector sums
1465 +            
1466 +            ckcs = std::accumulate(ckc.begin(),ckc.end(),0.0);
1467 +            ckss = std::accumulate(cks.begin(),cks.end(),0.0);
1468 +            dkcs = std::accumulate(dkc.begin(),dkc.end(),0.0);
1469 +            dkss = std::accumulate(dks.begin(),dks.end(),0.0);
1470 +            qkcs = std::accumulate(qkc.begin(),qkc.end(),0.0);
1471 +            qkss = std::accumulate(qks.begin(),qks.end(),0.0);
1472 +            
1473 + #ifdef IS_MPI
1474 +            MPI_Allreduce(MPI_IN_PLACE, &ckcs, 1, MPI_REALTYPE,
1475 +                          MPI_SUM, MPI_COMM_WORLD);
1476 +            MPI_Allreduce(MPI_IN_PLACE, &ckss, 1, MPI_REALTYPE,
1477 +                          MPI_SUM, MPI_COMM_WORLD);
1478 +            MPI_Allreduce(MPI_IN_PLACE, &dkcs, 1, MPI_REALTYPE,
1479 +                          MPI_SUM, MPI_COMM_WORLD);
1480 +            MPI_Allreduce(MPI_IN_PLACE, &dkss, 1, MPI_REALTYPE,
1481 +                          MPI_SUM, MPI_COMM_WORLD);
1482 +            MPI_Allreduce(MPI_IN_PLACE, &qkcs, 1, MPI_REALTYPE,
1483 +                          MPI_SUM, MPI_COMM_WORLD);
1484 +            MPI_Allreduce(MPI_IN_PLACE, &qkss, 1, MPI_REALTYPE,
1485 +                          MPI_SUM, MPI_COMM_WORLD);
1486 + #endif        
1487 +            
1488 +            // Accumulate potential energy and virial contribution:
1489 +
1490 +            kPot += 2.0 * rvol * AK[kk]*((ckss+dkcs-qkss)*(ckss+dkcs-qkss)
1491 +                                         + (ckcs-dkss-qkcs)*(ckcs-dkss-qkcs));
1492 +
1493 +            kVir += 2.0 * rvol  * AK[kk]*(ckcs*ckcs+ckss*ckss
1494 +                                          +4.0*(ckss*dkcs-ckcs*dkss)
1495 +                                          +3.0*(dkcs*dkcs+dkss*dkss)
1496 +                                          -6.0*(ckss*qkss+ckcs*qkcs)
1497 +                                          +8.0*(dkss*qkcs-dkcs*qkss)
1498 +                                          +5.0*(qkss*qkss+qkcs*qkcs));
1499 +            
1500 +            // Calculate force and torque for each site:
1501 +            
1502 +            for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1503 +                 mol = info_->nextMolecule(mi)) {
1504 +              for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1505 +                  atom = mol->nextAtom(ai)) {
1506 +                
1507 +                i = atom->getLocalIndex();
1508 +                atid = atom->getAtomType()->getIdent();
1509 +                data = ElectrostaticMap[Etids[atid]];
1510 +
1511 +                RealType qfrc = AK[kk]*((cks[i]+dkc[i]-qks[i])*(ckcs-dkss-qkcs)
1512 +                                     - (ckc[i]-dks[i]-qkc[i])*(ckss+dkcs-qkss));
1513 +                RealType qtrq1 = AK[kk]*(skr[i]*(ckcs-dkss-qkcs)
1514 +                                         -ckr[i]*(ckss+dkcs-qkss));
1515 +                RealType qtrq2 = 2.0*AK[kk]*(ckr[i]*(ckcs-dkss-qkcs)
1516 +                                            +skr[i]*(ckss+dkcs-qkss));
1517 +              
1518 +                atom->addFrc( 4.0 * rvol * qfrc * kVec );
1519 +
1520 +                if (atom->isFluctuatingCharge()) {
1521 +                  atom->addFlucQFrc( - 2.0 * rvol * qtrq2 );
1522 +                }
1523 +                  
1524 +                if (data.is_Dipole) {
1525 +                  atom->addTrq( 4.0 * rvol * qtrq1 * dxk[i] );
1526 +                }
1527 +                if (data.is_Quadrupole) {
1528 +                  atom->addTrq( 4.0 * rvol * qtrq2 * qxk[i] );
1529 +                }
1530 +              }
1531 +            }
1532 +          }
1533 +        }
1534 +        nMin = 1;
1535 +      }
1536 +      mMin = 1;
1537 +    }
1538 +    pot += kPot;  
1539    }
1540   }

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