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root/OpenMD/trunk/src/nonbonded/Electrostatic.cpp

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branches/development/src/nonbonded/Electrostatic.cpp (file contents), Revision 1750 by gezelter, Thu Jun 7 12:53:46 2012 UTC vs.
trunk/src/nonbonded/Electrostatic.cpp (file contents), Revision 1993 by gezelter, Tue Apr 29 17:32:31 2014 UTC

#	Line 35 | Line 35
35		*
36		* [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37		* [2]  Fennell & Gezelter, J. Chem. Phys. 124 234104 (2006).
38	<	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
38	>	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
39		* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
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 53 | Line 58
58		#include "io/Globals.hpp"
59		#include "nonbonded/SlaterIntegrals.hpp"
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
57	–
66		namespace OpenMD {
67
68		Electrostatic::Electrostatic(): name_("Electrostatic"), initialized_(false),
#	Line 62 | Line 70 | namespace OpenMD {
70		haveCutoffRadius_(false),
71		haveDampingAlpha_(false),
72		haveDielectric_(false),
73	<	haveElectroSpline_(false)
74	<	{}
73	>	haveElectroSplines_(false)
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 74 | Line 94 | namespace OpenMD {
94		summationMap_["SWITCHING_FUNCTION"] = esm_SWITCHING_FUNCTION;
95		summationMap_["SHIFTED_POTENTIAL"]  = esm_SHIFTED_POTENTIAL;
96		summationMap_["SHIFTED_FORCE"]      = esm_SHIFTED_FORCE;
97	+	summationMap_["TAYLOR_SHIFTED"]     = esm_TAYLOR_SHIFTED;
98		summationMap_["REACTION_FIELD"]     = esm_REACTION_FIELD;
99		summationMap_["EWALD_FULL"]         = esm_EWALD_FULL;
100		summationMap_["EWALD_PME"]          = esm_EWALD_PME;
#	Line 88 | Line 109 | namespace OpenMD {
109		// Charge-Dipole, assuming charges are measured in electrons, and
110		// dipoles are measured in debyes
111		pre12_ = 69.13373;
112	<	// Dipole-Dipole, assuming dipoles are measured in debyes
112	>	// Dipole-Dipole, assuming dipoles are measured in Debye
113		pre22_ = 14.39325;
114		// Charge-Quadrupole, assuming charges are measured in electrons, and
115		// quadrupoles are measured in 10^-26 esu cm^2
116	<	// This unit is also known affectionately as an esu centi-barn.
116	>	// This unit is also known affectionately as an esu centibarn.
117		pre14_ = 69.13373;
118	<
118	>	// Dipole-Quadrupole, assuming dipoles are measured in debyes and
119	>	// quadrupoles in esu centibarns:
120	>	pre24_ = 14.39325;
121	>	// Quadrupole-Quadrupole, assuming esu centibarns:
122	>	pre44_ = 14.39325;
123	>
124		// conversions for the simulation box dipole moment
125		chargeToC_ = 1.60217733e-19;
126		angstromToM_ = 1.0e-10;
127		debyeToCm_ = 3.33564095198e-30;
128
129	<	// number of points for electrostatic splines
129	>	// Default number of points for electrostatic splines
130		np_ = 100;
131
132		// variables to handle different summation methods for long-range
#	Line 108 | Line 134 | namespace OpenMD {
134		summationMethod_ = esm_HARD;
135		screeningMethod_ = UNDAMPED;
136		dielectric_ = 1.0;
111	–	one_third_ = 1.0 / 3.0;
137
138		// check the summation method:
139		if (simParams_->haveElectrostaticSummationMethod()) {
#	Line 124 | Line 149 | namespace OpenMD {
149		"Electrostatic::initialize: Unknown electrostaticSummationMethod.\n"
150		"\t(Input file specified %s .)\n"
151		"\telectrostaticSummationMethod must be one of: \"hard\",\n"
152	<	"\t\"shifted_potential\", \"shifted_force\", or \n"
153	<	"\t\"reaction_field\".\n", myMethod.c_str() );
152	>	"\t\"shifted_potential\", \"shifted_force\",\n"
153	>	"\t\"taylor_shifted\", or \"reaction_field\".\n",
154	>	myMethod.c_str() );
155		painCave.isFatal = 1;
156		simError();
157		}
#	Line 184 | 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;
193	<
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 206 | Line 231 | namespace OpenMD {
231		haveDampingAlpha_ = true;
232		}
233
234	<	// find all of the Electrostatic atom Types:
235	<	ForceField::AtomTypeContainer* atomTypes = forceField_->getAtomTypes();
236	<	ForceField::AtomTypeContainer::MapTypeIterator i;
237	<	AtomType* at;
238	<
239	<	for (at = atomTypes->beginType(i); at != NULL;
240	<	at = atomTypes->nextType(i)) {
241	<
242	<	if (at->isElectrostatic())
218	<	addType(at);
219	<	}
220	<
221	<	cutoffRadius2_ = cutoffRadius_ * cutoffRadius_;
222	<	rcuti_ = 1.0 / cutoffRadius_;
223	<	rcuti2_ = rcuti_ * rcuti_;
224	<	rcuti3_ = rcuti2_ * rcuti_;
225	<	rcuti4_ = rcuti2_ * rcuti2_;
234	>
235	>	Etypes.clear();
236	>	Etids.clear();
237	>	FQtypes.clear();
238	>	FQtids.clear();
239	>	ElectrostaticMap.clear();
240	>	Jij.clear();
241	>	nElectro_ = 0;
242	>	nFlucq_ = 0;
243
244	<	if (screeningMethod_ == DAMPED) {
245	<
229	<	alpha2_ = dampingAlpha_ * dampingAlpha_;
230	<	alpha4_ = alpha2_ * alpha2_;
231	<	alpha6_ = alpha4_ * alpha2_;
232	<	alpha8_ = alpha4_ * alpha4_;
233	<
234	<	constEXP_ = exp(-alpha2_ * cutoffRadius2_);
235	<	invRootPi_ = 0.56418958354775628695;
236	<	alphaPi_ = 2.0 * dampingAlpha_ * invRootPi_;
244	>	Etids.resize( forceField_->getNAtomType(), -1);
245	>	FQtids.resize( forceField_->getNAtomType(), -1);
246
247	<	c1c_ = erfc(dampingAlpha_ * cutoffRadius_) * rcuti_;
248	<	c2c_ = alphaPi_ * constEXP_ * rcuti_ + c1c_ * rcuti_;
249	<	c3c_ = 2.0 * alphaPi_ * alpha2_ + 3.0 * c2c_ * rcuti_;
250	<	c4c_ = 4.0 * alphaPi_ * alpha4_ + 5.0 * c3c_ * rcuti2_;
242	<	c5c_ = 8.0 * alphaPi_ * alpha6_ + 7.0 * c4c_ * rcuti2_;
243	<	c6c_ = 16.0 * alphaPi_ * alpha8_ + 9.0 * c5c_ * rcuti2_;
244	<	} else {
245	<	c1c_ = rcuti_;
246	<	c2c_ = c1c_ * rcuti_;
247	<	c3c_ = 3.0 * c2c_ * rcuti_;
248	<	c4c_ = 5.0 * c3c_ * rcuti2_;
249	<	c5c_ = 7.0 * c4c_ * rcuti2_;
250	<	c6c_ = 9.0 * c5c_ * rcuti2_;
247	>	set<AtomType*>::iterator at;
248	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
249	>	if ((*at)->isElectrostatic()) nElectro_++;
250	>	if ((*at)->isFluctuatingCharge()) nFlucq_++;
251		}
252	<
252	>
253	>	Jij.resize(nFlucq_);
254	>
255	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
256	>	if ((*at)->isElectrostatic()) addType(*at);
257	>	}
258	>
259		if (summationMethod_ == esm_REACTION_FIELD) {
260		preRF_ = (dielectric_ - 1.0) /
261	<	((2.0 * dielectric_ + 1.0) * cutoffRadius2_ * cutoffRadius_);
256	<	preRF2_ = 2.0 * preRF_;
261	>	((2.0 * dielectric_ + 1.0) * pow(cutoffRadius_,3) );
262		}
263
264	+	RealType b0c, b1c, b2c, b3c, b4c, b5c;
265	+	RealType db0c_1, db0c_2, db0c_3, db0c_4, db0c_5;
266	+	RealType a2, expTerm, invArootPi;
267	+
268	+	RealType r = cutoffRadius_;
269	+	RealType r2 = r * r;
270	+	RealType ric = 1.0 / r;
271	+	RealType ric2 = ric * ric;
272	+
273	+	if (screeningMethod_ == DAMPED) {
274	+	a2 = dampingAlpha_ * dampingAlpha_;
275	+	invArootPi = 1.0 / (dampingAlpha_ * sqrt(M_PI));
276	+	expTerm = exp(-a2 * r2);
277	+	// values of Smith's B_l functions at the cutoff radius:
278	+	b0c = erfc(dampingAlpha_ * r) / r;
279	+	b1c = (      b0c     + 2.0*a2     * expTerm * invArootPi) / r2;
280	+	b2c = (3.0 * b1c + pow(2.0*a2, 2) * expTerm * invArootPi) / r2;
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	+	// 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;
291	+	b1c = (      b0c) / r2;
292	+	b2c = (3.0 * b1c) / r2;
293	+	b3c = (5.0 * b2c) / r2;
294	+	b4c = (7.0 * b3c) / r2;
295	+	b5c = (9.0 * b4c) / r2;
296	+	selfMult1_ = 0.0;
297	+	selfMult2_ = 0.0;
298	+	selfMult4_ = 0.0;
299	+	}
300	+
301	+	// higher derivatives of B_0 at the cutoff radius:
302	+	db0c_1 = -r * b1c;
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;
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;
317	+	RealType db0_1, db0_2, db0_3, db0_4, db0_5;
318	+	RealType f, fc, f0;
319	+	RealType g, gc, g0, g1, g2, g3, g4;
320	+	RealType h, hc, h1, h2, h3, h4;
321	+	RealType s, sc, s2, s3, s4;
322	+	RealType t, tc, t3, t4;
323	+	RealType u, uc, u4;
324	+
325	+	// working variables for Taylor expansion:
326	+	RealType rmRc, rmRc2, rmRc3, rmRc4;
327	+
328	+	// Approximate using splines using a maximum of 0.1 Angstroms
329	+	// between points.
330	+	int nptest = int((cutoffRadius_ + 2.0) / 0.1);
331	+	np_ = (np_ > nptest) ? np_ : nptest;
332	+
333		// Add a 2 angstrom safety window to deal with cutoffGroups that
334		// have charged atoms longer than the cutoffRadius away from each
335	<	// other.  Splining may not be the best choice here.  Direct calls
336	<	// to erfc might be preferrable.
335	>	// other.  Splining is almost certainly the best choice here.
336	>	// Direct calls to erfc would be preferrable if it is a very fast
337	>	// implementation.
338
339	<	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
340	<	RealType rval;
341	<	vector<RealType> rvals;
342	<	vector<RealType> yvals;
343	<	for (int i = 0; i < np_; i++) {
344	<	rval = RealType(i) * dx;
345	<	rvals.push_back(rval);
346	<	yvals.push_back(erfc(dampingAlpha_ * rval));
339	>	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_);
340	>
341	>	// Storage vectors for the computed functions
342	>	vector<RealType> rv;
343	>	vector<RealType> v01v;
344	>	vector<RealType> v11v;
345	>	vector<RealType> v21v, v22v;
346	>	vector<RealType> v31v, v32v;
347	>	vector<RealType> v41v, v42v, v43v;
348	>
349	>	for (int i = 1; i < np_ + 1; i++) {
350	>	r = RealType(i) * dx;
351	>	rv.push_back(r);
352	>
353	>	ri = 1.0 / r;
354	>	ri2 = ri * ri;
355	>
356	>	r2 = r * r;
357	>	expTerm = exp(-a2 * r2);
358	>
359	>	// Taylor expansion factors (no need for factorials this way):
360	>	rmRc = r - cutoffRadius_;
361	>	rmRc2 = rmRc  * rmRc / 2.0;
362	>	rmRc3 = rmRc2 * rmRc / 3.0;
363	>	rmRc4 = rmRc3 * rmRc / 4.0;
364	>
365	>	// values of Smith's B_l functions at r:
366	>	if (screeningMethod_ == DAMPED) {
367	>	b0 = erfc(dampingAlpha_ * r) * ri;
368	>	b1 = (      b0 +     2.0*a2     * expTerm * invArootPi) * ri2;
369	>	b2 = (3.0 * b1 + pow(2.0*a2, 2) * expTerm * invArootPi) * ri2;
370	>	b3 = (5.0 * b2 + pow(2.0*a2, 3) * expTerm * invArootPi) * ri2;
371	>	b4 = (7.0 * b3 + pow(2.0*a2, 4) * expTerm * invArootPi) * ri2;
372	>	b5 = (9.0 * b4 + pow(2.0*a2, 5) * expTerm * invArootPi) * ri2;
373	>	} else {
374	>	b0 = ri;
375	>	b1 = (      b0) * ri2;
376	>	b2 = (3.0 * b1) * ri2;
377	>	b3 = (5.0 * b2) * ri2;
378	>	b4 = (7.0 * b3) * ri2;
379	>	b5 = (9.0 * b4) * ri2;
380	>	}
381	>
382	>	// higher derivatives of B_0 at r:
383	>	db0_1 = -r * b1;
384	>	db0_2 =     -b1 + r2 * b2;
385	>	db0_3 =          3.0*r*b2   - r2*r*b3;
386	>	db0_4 =          3.0*b2   - 6.0*r2*b3     + r2*r2*b4;
387	>	db0_5 =                    -15.0*r*b3 + 10.0*r2*r*b4 - r2*r2*r*b5;
388	>
389	>	f = b0;
390	>	fc = b0c;
391	>	f0 = f - fc - rmRc*db0c_1;
392	>
393	>	g = db0_1;
394	>	gc = db0c_1;
395	>	g0 = g - gc;
396	>	g1 = g0 - rmRc *db0c_2;
397	>	g2 = g1 - rmRc2*db0c_3;
398	>	g3 = g2 - rmRc3*db0c_4;
399	>	g4 = g3 - rmRc4*db0c_5;
400	>
401	>	h = db0_2;
402	>	hc = db0c_2;
403	>	h1 = h - hc;
404	>	h2 = h1 - rmRc *db0c_3;
405	>	h3 = h2 - rmRc2*db0c_4;
406	>	h4 = h3 - rmRc3*db0c_5;
407	>
408	>	s = db0_3;
409	>	sc = db0c_3;
410	>	s2 = s - sc;
411	>	s3 = s2 - rmRc *db0c_4;
412	>	s4 = s3 - rmRc2*db0c_5;
413	>
414	>	t = db0_4;
415	>	tc = db0c_4;
416	>	t3 = t - tc;
417	>	t4 = t3 - rmRc *db0c_5;
418	>
419	>	u = db0_5;
420	>	uc = db0c_5;
421	>	u4 = u - uc;
422	>
423	>	// in what follows below, the various v functions are used for
424	>	// potentials and torques, while the w functions show up in the
425	>	// forces.
426	>
427	>	switch (summationMethod_) {
428	>	case esm_SHIFTED_FORCE:
429	>
430	>	v01 = f - fc - rmRc*gc;
431	>	v11 = g - gc - rmRc*hc;
432	>	v21 = g*ri - gc*ric - rmRc*(hc - gc*ric)*ric;
433	>	v22 = h - g*ri - (hc - gc*ric) - rmRc*(sc - (hc - gc*ric)*ric);
434	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric - rmRc*(sc-2.0*(hc-gc*ric)*ric)*ric;
435	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric)
436	>	- rmRc*(tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
437	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2
438	>	- rmRc*(sc - 3.0*(hc-gc*ric)*ric)*ric2;
439	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric
440	>	- rmRc*(tc - (4.0*sc - 9.0*(hc - gc*ric)*ric)*ric)*ric;
441	>
442	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
443	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric)
444	>	- rmRc*(uc-3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
445	>
446	>	dv01 = g - gc;
447	>	dv11 = h - hc;
448	>	dv21 = (h - g*ri)*ri - (hc - gc*ric)*ric;
449	>	dv22 = (s - (h - g*ri)*ri) - (sc - (hc - gc*ric)*ric);
450	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri - (sc - 2.0*(hc-gc*ric)*ric)*ric;
451	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri)
452	>	- (tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
453	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2 - (sc - 3.0*(hc - gc*ric)*ric)*ric2;
454	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri
455	>	- (tc - (4.0*sc - 9.0*(hc-gc*ric)*ric)*ric)*ric;
456	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri)
457	>	- (uc - 3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
458	>
459	>	break;
460	>
461	>	case esm_TAYLOR_SHIFTED:
462	>
463	>	v01 = f0;
464	>	v11 = g1;
465	>	v21 = g2 * ri;
466	>	v22 = h2 - v21;
467	>	v31 = (h3 - g3 * ri) * ri;
468	>	v32 = s3 - 3.0*v31;
469	>	v41 = (h4 - g4 * ri) * ri2;
470	>	v42 = s4 * ri - 3.0*v41;
471	>	v43 = t4 - 6.0*v42 - 3.0*v41;
472	>
473	>	dv01 = g0;
474	>	dv11 = h1;
475	>	dv21 = (h2 - g2*ri)*ri;
476	>	dv22 = (s2 - (h2 - g2*ri)*ri);
477	>	dv31 = (s3 - 2.0*(h3-g3*ri)*ri)*ri;
478	>	dv32 = (t3 - 3.0*(s3-2.0*(h3-g3*ri)*ri)*ri);
479	>	dv41 = (s4 - 3.0*(h4 - g4*ri)*ri)*ri2;
480	>	dv42 = (t4 - (4.0*s4 - 9.0*(h4-g4*ri)*ri)*ri)*ri;
481	>	dv43 = (u4 - 3.0*(2.0*t4 - (7.0*s4 - 15.0*(h4 - g4*ri)*ri)*ri)*ri);
482	>
483	>	break;
484	>
485	>	case esm_SHIFTED_POTENTIAL:
486	>
487	>	v01 = f - fc;
488	>	v11 = g - gc;
489	>	v21 = g*ri - gc*ric;
490	>	v22 = h - g*ri - (hc - gc*ric);
491	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
492	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
493	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
494	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
495	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
496	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
497	>
498	>	dv01 = g;
499	>	dv11 = h;
500	>	dv21 = (h - g*ri)*ri;
501	>	dv22 = (s - (h - g*ri)*ri);
502	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
503	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
504	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
505	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
506	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
507	>
508	>	break;
509	>
510	>	case esm_SWITCHING_FUNCTION:
511	>	case esm_HARD:
512	>	case esm_EWALD_FULL:
513	>
514	>	v01 = f;
515	>	v11 = g;
516	>	v21 = g*ri;
517	>	v22 = h - g*ri;
518	>	v31 = (h-g*ri)*ri;
519	>	v32 = (s - 3.0*(h-g*ri)*ri);
520	>	v41 = (h - g*ri)*ri2;
521	>	v42 = (s-3.0*(h-g*ri)*ri)*ri;
522	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri);
523	>
524	>	dv01 = g;
525	>	dv11 = h;
526	>	dv21 = (h - g*ri)*ri;
527	>	dv22 = (s - (h - g*ri)*ri);
528	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
529	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
530	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
531	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
532	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
533	>
534	>	break;
535	>
536	>	case esm_REACTION_FIELD:
537	>
538	>	// following DL_POLY's lead for shifting the image charge potential:
539	>	f = b0 + preRF_ * r2;
540	>	fc = b0c + preRF_ * cutoffRadius_ * cutoffRadius_;
541	>
542	>	g = db0_1 + preRF_ * 2.0 * r;
543	>	gc = db0c_1 + preRF_ * 2.0 * cutoffRadius_;
544	>
545	>	h = db0_2 + preRF_ * 2.0;
546	>	hc = db0c_2 + preRF_ * 2.0;
547	>
548	>	v01 = f - fc;
549	>	v11 = g - gc;
550	>	v21 = g*ri - gc*ric;
551	>	v22 = h - g*ri - (hc - gc*ric);
552	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
553	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
554	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
555	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
556	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
557	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
558	>
559	>	dv01 = g;
560	>	dv11 = h;
561	>	dv21 = (h - g*ri)*ri;
562	>	dv22 = (s - (h - g*ri)*ri);
563	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
564	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
565	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
566	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
567	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
568	>
569	>	break;
570	>
571	>	case esm_EWALD_PME:
572	>	case esm_EWALD_SPME:
573	>	default :
574	>	map<string, ElectrostaticSummationMethod>::iterator i;
575	>	std::string meth;
576	>	for (i = summationMap_.begin(); i != summationMap_.end(); ++i) {
577	>	if ((*i).second == summationMethod_) meth = (*i).first;
578	>	}
579	>	sprintf( painCave.errMsg,
580	>	"Electrostatic::initialize: electrostaticSummationMethod %s \n"
581	>	"\thas not been implemented yet. Please select one of:\n"
582	>	"\t\"hard\", \"shifted_potential\", or \"shifted_force\"\n",
583	>	meth.c_str() );
584	>	painCave.isFatal = 1;
585	>	simError();
586	>	break;
587	>	}
588	>
589	>	// Add these computed values to the storage vectors for spline creation:
590	>	v01v.push_back(v01);
591	>	v11v.push_back(v11);
592	>	v21v.push_back(v21);
593	>	v22v.push_back(v22);
594	>	v31v.push_back(v31);
595	>	v32v.push_back(v32);
596	>	v41v.push_back(v41);
597	>	v42v.push_back(v42);
598	>	v43v.push_back(v43);
599		}
273	–	erfcSpline_ = new CubicSpline();
274	–	erfcSpline_->addPoints(rvals, yvals);
275	–	haveElectroSpline_ = true;
600
601	+	// construct the spline structures and fill them with the values we've
602	+	// computed:
603	+
604	+	v01s = new CubicSpline();
605	+	v01s->addPoints(rv, v01v);
606	+	v11s = new CubicSpline();
607	+	v11s->addPoints(rv, v11v);
608	+	v21s = new CubicSpline();
609	+	v21s->addPoints(rv, v21v);
610	+	v22s = new CubicSpline();
611	+	v22s->addPoints(rv, v22v);
612	+	v31s = new CubicSpline();
613	+	v31s->addPoints(rv, v31v);
614	+	v32s = new CubicSpline();
615	+	v32s->addPoints(rv, v32v);
616	+	v41s = new CubicSpline();
617	+	v41s->addPoints(rv, v41v);
618	+	v42s = new CubicSpline();
619	+	v42s->addPoints(rv, v42v);
620	+	v43s = new CubicSpline();
621	+	v43s->addPoints(rv, v43v);
622	+
623	+	haveElectroSplines_ = true;
624	+
625		initialized_ = true;
626		}
627
628		void Electrostatic::addType(AtomType* atomType){
629	<
629	>
630		ElectrostaticAtomData electrostaticAtomData;
631		electrostaticAtomData.is_Charge = false;
632		electrostaticAtomData.is_Dipole = false;
285	–	electrostaticAtomData.is_SplitDipole = false;
633		electrostaticAtomData.is_Quadrupole = false;
634		electrostaticAtomData.is_Fluctuating = false;
635
#	Line 297 | Line 644 | namespace OpenMD {
644		if (ma.isMultipole()) {
645		if (ma.isDipole()) {
646		electrostaticAtomData.is_Dipole = true;
647	<	electrostaticAtomData.dipole_moment = ma.getDipoleMoment();
647	>	electrostaticAtomData.dipole = ma.getDipole();
648		}
302	–	if (ma.isSplitDipole()) {
303	–	electrostaticAtomData.is_SplitDipole = true;
304	–	electrostaticAtomData.split_dipole_distance = ma.getSplitDipoleDistance();
305	–	}
649		if (ma.isQuadrupole()) {
307	–	// Quadrupoles in OpenMD are set as the diagonal elements
308	–	// of the diagonalized traceless quadrupole moment tensor.
309	–	// The column vectors of the unitary matrix that diagonalizes
310	–	// the quadrupole moment tensor become the eFrame (or the
311	–	// electrostatic version of the body-fixed frame.
650		electrostaticAtomData.is_Quadrupole = true;
651	<	electrostaticAtomData.quadrupole_moments = ma.getQuadrupoleMoments();
651	>	electrostaticAtomData.quadrupole = ma.getQuadrupole();
652		}
653		}
654
#	Line 324 | Line 662 | namespace OpenMD {
662		electrostaticAtomData.slaterZeta = fqa.getSlaterZeta();
663		}
664
665	<	pair<map<int,AtomType*>::iterator,bool> ret;
666	<	ret = ElectrostaticList.insert( pair<int,AtomType*>(atomType->getIdent(),
667	<	atomType) );
665	>	int atid = atomType->getIdent();
666	>	int etid = Etypes.size();
667	>	int fqtid = FQtypes.size();
668	>
669	>	pair<set<int>::iterator,bool> ret;
670	>	ret = Etypes.insert( atid );
671		if (ret.second == false) {
672		sprintf( painCave.errMsg,
673		"Electrostatic already had a previous entry with ident %d\n",
674	<	atomType->getIdent() );
674	>	atid);
675		painCave.severity = OPENMD_INFO;
676		painCave.isFatal = 0;
677		simError();
678		}
679
680	<	ElectrostaticMap[atomType] = electrostaticAtomData;
680	>	Etids[ atid ] = etid;
681	>	ElectrostaticMap.push_back(electrostaticAtomData);
682
683	<	// Now, iterate over all known types and add to the mixing map:
684	<
685	<	map<AtomType*, ElectrostaticAtomData>::iterator it;
686	<	for( it = ElectrostaticMap.begin(); it != ElectrostaticMap.end(); ++it) {
687	<	AtomType* atype2 = (*it).first;
688	<	ElectrostaticAtomData eaData2 = (*it).second;
689	<	if (eaData2.is_Fluctuating && electrostaticAtomData.is_Fluctuating) {
690	<
683	>	if (electrostaticAtomData.is_Fluctuating) {
684	>	ret = FQtypes.insert( atid );
685	>	if (ret.second == false) {
686	>	sprintf( painCave.errMsg,
687	>	"Electrostatic already had a previous fluctuating charge entry with ident %d\n",
688	>	atid );
689	>	painCave.severity = OPENMD_INFO;
690	>	painCave.isFatal = 0;
691	>	simError();
692	>	}
693	>	FQtids[atid] = fqtid;
694	>	Jij[fqtid].resize(nFlucq_);
695	>
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) {
701	>	int etid2 = Etids[ (*it) ];
702	>	int fqtid2 = FQtids[ (*it) ];
703	>	ElectrostaticAtomData eaData2 = ElectrostaticMap[ etid2 ];
704		RealType a = electrostaticAtomData.slaterZeta;
705		RealType b = eaData2.slaterZeta;
706		int m = electrostaticAtomData.slaterN;
707		int n = eaData2.slaterN;
708	<
708	>
709		// Create the spline of the coulombic integral for s-type
710		// Slater orbitals.  Add a 2 angstrom safety window to deal
711		// with cutoffGroups that have charged atoms longer than the
712		// cutoffRadius away from each other.
713	<
713	>
714		RealType rval;
715		RealType dr = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
716		vector<RealType> rvals;
717	<	vector<RealType> J1vals;
718	<	vector<RealType> J2vals;
719	<	for (int i = 0; i < np_; i++) {
717	>	vector<RealType> Jvals;
718	>	// don't start at i = 0, as rval = 0 is undefined for the
719	>	// slater overlap integrals.
720	>	for (int i = 1; i < np_+1; i++) {
721		rval = RealType(i) * dr;
722		rvals.push_back(rval);
723	<	J1vals.push_back(electrostaticAtomData.hardness * sSTOCoulInt( a, b, m, n, rval * PhysicalConstants::angstromsToBohr ) );
724	<	// may not be necessary if Slater coulomb integral is symmetric
725	<	J2vals.push_back(eaData2.hardness *  sSTOCoulInt( b, a, n, m, rval * PhysicalConstants::angstromsToBohr ) );
723	>	Jvals.push_back(sSTOCoulInt( a, b, m, n, rval *
724	>	PhysicalConstants::angstromToBohr ) *
725	>	PhysicalConstants::hartreeToKcal );
726		}
371	–
372	–	CubicSpline* J1 = new CubicSpline();
373	–	J1->addPoints(rvals, J1vals);
374	–	CubicSpline* J2 = new CubicSpline();
375	–	J2->addPoints(rvals, J2vals);
727
728	<	pair<AtomType*, AtomType*> key1, key2;
729	<	key1 = make_pair(atomType, atype2);
730	<	key2 = make_pair(atype2, atomType);
731	<
732	<	Jij[key1] = J1;
733	<	Jij[key2] = J2;
734	<	}
384	<	}
385	<
728	>	CubicSpline* J = new CubicSpline();
729	>	J->addPoints(rvals, Jvals);
730	>	Jij[fqtid][fqtid2] = J;
731	>	Jij[fqtid2].resize( nFlucq_ );
732	>	Jij[fqtid2][fqtid] = J;
733	>	}
734	>	}
735		return;
736		}
737
738		void Electrostatic::setCutoffRadius( RealType rCut ) {
739		cutoffRadius_ = rCut;
391	–	rrf_ = cutoffRadius_;
740		haveCutoffRadius_ = true;
741		}
742
395	–	void Electrostatic::setSwitchingRadius( RealType rSwitch ) {
396	–	rt_ = rSwitch;
397	–	}
743		void Electrostatic::setElectrostaticSummationMethod( ElectrostaticSummationMethod esm ) {
744		summationMethod_ = esm;
745		}
#	Line 412 | Line 757 | namespace OpenMD {
757
758		void Electrostatic::calcForce(InteractionData &idat) {
759
415	–	// utility variables.  Should clean these up and use the Vector3d and
416	–	// Mat3x3d to replace as many as we can in future versions:
417	–
418	–	RealType q_i, q_j, mu_i, mu_j, d_i, d_j;
419	–	RealType qxx_i, qyy_i, qzz_i;
420	–	RealType qxx_j, qyy_j, qzz_j;
421	–	RealType cx_i, cy_i, cz_i;
422	–	RealType cx_j, cy_j, cz_j;
423	–	RealType cx2, cy2, cz2;
424	–	RealType ct_i, ct_j, ct_ij, a1;
425	–	RealType riji, ri, ri2, ri3, ri4;
426	–	RealType pref, vterm, epot, dudr;
427	–	RealType vpair(0.0);
428	–	RealType scale, sc2;
429	–	RealType pot_term, preVal, rfVal;
430	–	RealType c2ri, c3ri, c4rij, cti3, ctj3, ctidotj;
431	–	RealType preSw, preSwSc;
432	–	RealType c1, c2, c3, c4;
433	–	RealType erfcVal(1.0), derfcVal(0.0);
434	–	RealType BigR;
435	–	RealType two(2.0), three(3.0);
436	–
437	–	Vector3d Q_i, Q_j;
438	–	Vector3d ux_i, uy_i, uz_i;
439	–	Vector3d ux_j, uy_j, uz_j;
440	–	Vector3d dudux_i, duduy_i, duduz_i;
441	–	Vector3d dudux_j, duduy_j, duduz_j;
442	–	Vector3d rhatdot2, rhatc4;
443	–	Vector3d dVdr;
444	–
445	–	// variables for indirect (reaction field) interactions for excluded pairs:
446	–	RealType indirect_Pot(0.0);
447	–	RealType indirect_vpair(0.0);
448	–	Vector3d indirect_dVdr(V3Zero);
449	–	Vector3d indirect_duduz_i(V3Zero), indirect_duduz_j(V3Zero);
450	–
451	–	RealType coulInt, vFluc1(0.0), vFluc2(0.0);
452	–	pair<RealType, RealType> res;
453	–
454	–	// splines for coulomb integrals
455	–	CubicSpline* J1;
456	–	CubicSpline* J2;
457	–
760		if (!initialized_) initialize();
761
762	<	ElectrostaticAtomData data1 = ElectrostaticMap[idat.atypes.first];
763	<	ElectrostaticAtomData data2 = ElectrostaticMap[idat.atypes.second];
762	>	data1 = ElectrostaticMap[Etids[idat.atid1]];
763	>	data2 = ElectrostaticMap[Etids[idat.atid2]];
764	>
765	>	U = 0.0;  // Potential
766	>	F.zero();  // Force
767	>	Ta.zero(); // Torque on site a
768	>	Tb.zero(); // Torque on site b
769	>	Ea.zero(); // Electric field at site a
770	>	Eb.zero(); // Electric field at site b
771	>	Pa = 0.0;  // Site potential at site a
772	>	Pb = 0.0;  // Site potential at site b
773	>	dUdCa = 0.0; // fluctuating charge force at site a
774	>	dUdCb = 0.0; // fluctuating charge force at site a
775
776	<	// some variables we'll need independent of electrostatic type:
776	>	// Indirect interactions mediated by the reaction field.
777	>	indirect_Pot = 0.0;   // Potential
778	>	indirect_F.zero();    // Force
779	>	indirect_Ta.zero();   // Torque on site a
780	>	indirect_Tb.zero();   // Torque on site b
781
782	<	riji = 1.0 /  *(idat.rij) ;
783	<	Vector3d rhat =  *(idat.d)   * riji;
782	>	// Excluded potential that is still computed for fluctuating charges
783	>	excluded_Pot= 0.0;
784
785	+	// some variables we'll need independent of electrostatic type:
786	+
787	+	ri = 1.0 /  *(idat.rij);
788	+	rhat =  *(idat.d)  * ri;
789	+
790		// logicals
791
792	<	bool i_is_Charge = data1.is_Charge;
793	<	bool i_is_Dipole = data1.is_Dipole;
794	<	bool i_is_SplitDipole = data1.is_SplitDipole;
795	<	bool i_is_Quadrupole = data1.is_Quadrupole;
474	<	bool i_is_Fluctuating = data1.is_Fluctuating;
792	>	a_is_Charge = data1.is_Charge;
793	>	a_is_Dipole = data1.is_Dipole;
794	>	a_is_Quadrupole = data1.is_Quadrupole;
795	>	a_is_Fluctuating = data1.is_Fluctuating;
796
797	<	bool j_is_Charge = data2.is_Charge;
798	<	bool j_is_Dipole = data2.is_Dipole;
799	<	bool j_is_SplitDipole = data2.is_SplitDipole;
800	<	bool j_is_Quadrupole = data2.is_Quadrupole;
801	<	bool j_is_Fluctuating = data2.is_Fluctuating;
797	>	b_is_Charge = data2.is_Charge;
798	>	b_is_Dipole = data2.is_Dipole;
799	>	b_is_Quadrupole = data2.is_Quadrupole;
800	>	b_is_Fluctuating = data2.is_Fluctuating;
801	>
802	>	// Obtain all of the required radial function values from the
803	>	// spline structures:
804
805	<	if (i_is_Charge) {
806	<	q_i = data1.fixedCharge;
805	>	// needed for fields (and forces):
806	>	if (a_is_Charge || b_is_Charge) {
807	>	v01s->getValueAndDerivativeAt( *(idat.rij), v01, dv01);
808	>	}
809	>	if (a_is_Dipole || b_is_Dipole) {
810	>	v11s->getValueAndDerivativeAt( *(idat.rij), v11, dv11);
811	>	v11or = ri * v11;
812	>	}
813	>	if (a_is_Quadrupole || b_is_Quadrupole ||  (a_is_Dipole && b_is_Dipole)) {
814	>	v21s->getValueAndDerivativeAt( *(idat.rij), v21, dv21);
815	>	v22s->getValueAndDerivativeAt( *(idat.rij), v22, dv22);
816	>	v22or = ri * v22;
817	>	}
818
819	<	if (i_is_Fluctuating) {
820	<	q_i += *(idat.flucQ1);
819	>	// needed for potentials (and forces and torques):
820	>	if ((a_is_Dipole && b_is_Quadrupole) ||
821	>	(b_is_Dipole && a_is_Quadrupole)) {
822	>	v31s->getValueAndDerivativeAt( *(idat.rij), v31, dv31);
823	>	v32s->getValueAndDerivativeAt( *(idat.rij), v32, dv32);
824	>	v31or = v31 * ri;
825	>	v32or = v32 * ri;
826	>	}
827	>	if (a_is_Quadrupole && b_is_Quadrupole) {
828	>	v41s->getValueAndDerivativeAt( *(idat.rij), v41, dv41);
829	>	v42s->getValueAndDerivativeAt( *(idat.rij), v42, dv42);
830	>	v43s->getValueAndDerivativeAt( *(idat.rij), v43, dv43);
831	>	v42or = v42 * ri;
832	>	v43or = v43 * ri;
833	>	}
834	>
835	>	// calculate the single-site contributions (fields, etc).
836	>
837	>	if (a_is_Charge) {
838	>	C_a = data1.fixedCharge;
839	>
840	>	if (a_is_Fluctuating) {
841	>	C_a += *(idat.flucQ1);
842		}
843
844		if (idat.excluded) {
845	<	*(idat.skippedCharge2) += q_i;
845	>	*(idat.skippedCharge2) += C_a;
846	>	} else {
847	>	// only do the field and site potentials if we're not excluded:
848	>	Eb -= C_a *  pre11_ * dv01 * rhat;
849	>	Pb += C_a *  pre11_ * v01;
850		}
851		}
852	<
853	<	if (i_is_Dipole) {
854	<	mu_i = data1.dipole_moment;
855	<	uz_i = idat.eFrame1->getColumn(2);
856	<
857	<	ct_i = dot(uz_i, rhat);
858	<
859	<	if (i_is_SplitDipole)
860	<	d_i = data1.split_dipole_distance;
502	<
503	<	duduz_i = V3Zero;
504	<	}
505	<
506	<	if (i_is_Quadrupole) {
507	<	Q_i = data1.quadrupole_moments;
508	<	qxx_i = Q_i.x();
509	<	qyy_i = Q_i.y();
510	<	qzz_i = Q_i.z();
511	<
512	<	ux_i = idat.eFrame1->getColumn(0);
513	<	uy_i = idat.eFrame1->getColumn(1);
514	<	uz_i = idat.eFrame1->getColumn(2);
852	>
853	>	if (a_is_Dipole) {
854	>	D_a = *(idat.dipole1);
855	>	rdDa = dot(rhat, D_a);
856	>	rxDa = cross(rhat, D_a);
857	>	if (!idat.excluded) {
858	>	Eb -=  pre12_ * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
859	>	Pb +=  pre12_ * v11 * rdDa;
860	>	}
861
516	–	cx_i = dot(ux_i, rhat);
517	–	cy_i = dot(uy_i, rhat);
518	–	cz_i = dot(uz_i, rhat);
519	–
520	–	dudux_i = V3Zero;
521	–	duduy_i = V3Zero;
522	–	duduz_i = V3Zero;
862		}
863	<
864	<	if (j_is_Charge) {
865	<	q_j = data2.fixedCharge;
866	<
867	<	if (j_is_Fluctuating)
868	<	q_j += *(idat.flucQ2);
869	<
870	<	if (idat.excluded) {
871	<	*(idat.skippedCharge1) += q_j;
863	>
864	>	if (a_is_Quadrupole) {
865	>	Q_a = *(idat.quadrupole1);
866	>	trQa =  Q_a.trace();
867	>	Qar =   Q_a * rhat;
868	>	rQa = rhat * Q_a;
869	>	rdQar = dot(rhat, Qar);
870	>	rxQar = cross(rhat, Qar);
871	>	if (!idat.excluded) {
872	>	Eb -= pre14_ * (trQa * rhat * dv21 + 2.0 * Qar * v22or
873	>	+ rdQar * rhat * (dv22 - 2.0*v22or));
874	>	Pb += pre14_ * (v21 * trQa + v22 * rdQar);
875		}
876		}
877	<
878	<
879	<	if (j_is_Dipole) {
538	<	mu_j = data2.dipole_moment;
539	<	uz_j = idat.eFrame2->getColumn(2);
877	>
878	>	if (b_is_Charge) {
879	>	C_b = data2.fixedCharge;
880
881	<	ct_j = dot(uz_j, rhat);
882	<
543	<	if (j_is_SplitDipole)
544	<	d_j = data2.split_dipole_distance;
881	>	if (b_is_Fluctuating)
882	>	C_b += *(idat.flucQ2);
883
884	<	duduz_j = V3Zero;
884	>	if (idat.excluded) {
885	>	*(idat.skippedCharge1) += C_b;
886	>	} else {
887	>	// only do the field if we're not excluded:
888	>	Ea += C_b *  pre11_ * dv01 * rhat;
889	>	Pa += C_b *  pre11_ * v01;
890	>
891	>	}
892		}
893
894	<	if (j_is_Quadrupole) {
895	<	Q_j = data2.quadrupole_moments;
896	<	qxx_j = Q_j.x();
897	<	qyy_j = Q_j.y();
898	<	qzz_j = Q_j.z();
899	<
900	<	ux_j = idat.eFrame2->getColumn(0);
901	<	uy_j = idat.eFrame2->getColumn(1);
557	<	uz_j = idat.eFrame2->getColumn(2);
558	<
559	<	cx_j = dot(ux_j, rhat);
560	<	cy_j = dot(uy_j, rhat);
561	<	cz_j = dot(uz_j, rhat);
562	<
563	<	dudux_j = V3Zero;
564	<	duduy_j = V3Zero;
565	<	duduz_j = V3Zero;
894	>	if (b_is_Dipole) {
895	>	D_b = *(idat.dipole2);
896	>	rdDb = dot(rhat, D_b);
897	>	rxDb = cross(rhat, D_b);
898	>	if (!idat.excluded) {
899	>	Ea += pre12_ * ((dv11-v11or) * rdDb * rhat + v11or * D_b);
900	>	Pa += pre12_ * v11 * rdDb;
901	>	}
902		}
903
904	<	if (i_is_Fluctuating && j_is_Fluctuating) {
905	<	J1 = Jij[idat.atypes];
906	<	J2 = Jij[make_pair(idat.atypes.second, idat.atypes.first)];
904	>	if (b_is_Quadrupole) {
905	>	Q_b = *(idat.quadrupole2);
906	>	trQb =  Q_b.trace();
907	>	Qbr =   Q_b * rhat;
908	>	rQb = rhat * Q_b;
909	>	rdQbr = dot(rhat, Qbr);
910	>	rxQbr = cross(rhat, Qbr);
911	>	if (!idat.excluded) {
912	>	Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
913	>	+ rdQbr * rhat * (dv22 - 2.0*v22or));
914	>	Pa += pre14_ * (v21 * trQb + v22 * rdQbr);
915	>	}
916		}
917	+
918
919	<	epot = 0.0;
920	<	dVdr = V3Zero;
921	<
922	<	if (i_is_Charge) {
919	>	if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
920	>	J = Jij[FQtids[idat.atid1]][FQtids[idat.atid2]];
921	>	}
922	>
923	>	if (a_is_Charge) {
924
925	<	if (j_is_Charge) {
926	<	if (screeningMethod_ == DAMPED) {
927	<	// assemble the damping variables
928	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
582	<	//erfcVal = res.first;
583	<	//derfcVal = res.second;
925	>	if (b_is_Charge) {
926	>	pref =  pre11_ * *(idat.electroMult);
927	>	U  += C_a * C_b * pref * v01;
928	>	F  += C_a * C_b * pref * dv01 * rhat;
929
930	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
931	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
930	>	// If this is an excluded pair, there are still indirect
931	>	// interactions via the reaction field we must worry about:
932
933	<	c1 = erfcVal * riji;
934	<	c2 = (-derfcVal + c1) * riji;
935	<	} else {
936	<	c1 = riji;
592	<	c2 = c1 * riji;
933	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
934	>	rfContrib = preRF_ * pref * C_a * C_b * *(idat.r2);
935	>	indirect_Pot += rfContrib;
936	>	indirect_F   += rfContrib * 2.0 * ri * rhat;
937		}
938
939	<	preVal =  *(idat.electroMult) * pre11_;
940	<
941	<	if (summationMethod_ == esm_SHIFTED_POTENTIAL) {
598	<	vterm = preVal * (c1 - c1c_);
599	<	dudr  = - *(idat.sw)  * preVal * c2;
939	>	// Fluctuating charge forces are handled via Coulomb integrals
940	>	// for excluded pairs (i.e. those connected via bonds) and
941	>	// with the standard charge-charge interaction otherwise.
942
943	<	} else if (summationMethod_ == esm_SHIFTED_FORCE)  {
944	<	vterm = preVal * ( c1 - c1c_ + c2c_*( *(idat.rij)  - cutoffRadius_) );
945	<	dudr  =  *(idat.sw)  * preVal * (c2c_ - c2);
943	>	if (idat.excluded) {
944	>	if (a_is_Fluctuating || b_is_Fluctuating) {
945	>	coulInt = J->getValueAt( *(idat.rij) );
946	>	if (a_is_Fluctuating) dUdCa += C_b * coulInt;
947	>	if (b_is_Fluctuating) dUdCb += C_a * coulInt;
948	>	}
949	>	} else {
950	>	if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
951	>	if (b_is_Fluctuating) dUdCb += C_a * pref * v01;
952	>	}
953	>	}
954
955	<	} else if (summationMethod_ == esm_REACTION_FIELD) {
956	<	rfVal = preRF_ *  *(idat.rij)  *  *(idat.rij);
955	>	if (b_is_Dipole) {
956	>	pref =  pre12_ * *(idat.electroMult);
957	>	U  += C_a * pref * v11 * rdDb;
958	>	F  += C_a * pref * ((dv11 - v11or) * rdDb * rhat + v11or * D_b);
959	>	Tb += C_a * pref * v11 * rxDb;
960
961	<	vterm = preVal * ( riji + rfVal );
609	<	dudr  =  *(idat.sw)  * preVal * ( 2.0 * rfVal - riji ) * riji;
610	<
611	<	// if this is an excluded pair, there are still indirect
612	<	// interactions via the reaction field we must worry about:
961	>	if (a_is_Fluctuating) dUdCa += pref * v11 * rdDb;
962
963	<	if (idat.excluded) {
964	<	indirect_vpair += preVal * rfVal;
965	<	indirect_Pot += *(idat.sw) * preVal * rfVal;
617	<	indirect_dVdr += *(idat.sw)  * preVal * two * rfVal  * riji * rhat;
618	<	}
619	<
620	<	} else {
963	>	// Even if we excluded this pair from direct interactions, we
964	>	// still have the reaction-field-mediated charge-dipole
965	>	// interaction:
966
967	<	vterm = preVal * riji * erfcVal;
968	<	dudr  = -  *(idat.sw)  * preVal * c2;
969	<
967	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
968	>	rfContrib = C_a * pref * preRF_ * 2.0 * *(idat.rij);
969	>	indirect_Pot += rfContrib * rdDb;
970	>	indirect_F   += rfContrib * D_b / (*idat.rij);
971	>	indirect_Tb  += C_a * pref * preRF_ * rxDb;
972		}
973	<
627	<	vpair += vterm * q_i * q_j;
628	<	epot +=  *(idat.sw)  * vterm * q_i * q_j;
629	<	dVdr += dudr * rhat * q_i * q_j;
973	>	}
974
975	<	if (i_is_Fluctuating) {
976	<	if (idat.excluded) {
977	<	// vFluc1 is the difference between the direct coulomb integral
978	<	// and the normal 1/r-like  interaction between point charges.
979	<	coulInt = J1->getValueAt( *(idat.rij) );
980	<	vFluc1 = coulInt - (*(idat.sw) * vterm);
637	<	} else {
638	<	vFluc1 = 0.0;
639	<	}
640	<	*(idat.dVdFQ1) += ( *(idat.sw) * vterm + vFluc1 ) * q_j;
641	<	}
975	>	if (b_is_Quadrupole) {
976	>	pref = pre14_ * *(idat.electroMult);
977	>	U  +=  C_a * pref * (v21 * trQb + v22 * rdQbr);
978	>	F  +=  C_a * pref * (trQb * dv21 * rhat + 2.0 * Qbr * v22or);
979	>	F  +=  C_a * pref * rdQbr * rhat * (dv22 - 2.0*v22or);
980	>	Tb +=  C_a * pref * 2.0 * rxQbr * v22;
981
982	<	if (j_is_Fluctuating) {
644	<	if (idat.excluded) {
645	<	// vFluc2 is the difference between the direct coulomb integral
646	<	// and the normal 1/r-like  interaction between point charges.
647	<	coulInt = J2->getValueAt( *(idat.rij) );
648	<	vFluc2 = coulInt - (*(idat.sw) * vterm);
649	<	} else {
650	<	vFluc2 = 0.0;
651	<	}
652	<	*(idat.dVdFQ2) += ( *(idat.sw) * vterm + vFluc2 ) * q_i;
653	<	}
654	<
655	<
982	>	if (a_is_Fluctuating) dUdCa += pref * (v21 * trQb + v22 * rdQbr);
983		}
984	+	}
985
986	<	if (j_is_Dipole) {
659	<	// pref is used by all the possible methods
660	<	pref =  *(idat.electroMult) * pre12_ * q_i * mu_j;
661	<	preSw =  *(idat.sw)  * pref;
986	>	if (a_is_Dipole) {
987
988	<	if (summationMethod_ == esm_REACTION_FIELD) {
989	<	ri2 = riji * riji;
665	<	ri3 = ri2 * riji;
666	<
667	<	vterm = - pref * ct_j * ( ri2 - preRF2_ *  *(idat.rij)  );
668	<	vpair += vterm;
669	<	epot +=  *(idat.sw)  * vterm;
988	>	if (b_is_Charge) {
989	>	pref = pre12_ * *(idat.electroMult);
990
991	<	dVdr +=  -preSw * (ri3 * (uz_j - three * ct_j * rhat) - preRF2_*uz_j);
992	<	duduz_j += -preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
991	>	U  -= C_b * pref * v11 * rdDa;
992	>	F  -= C_b * pref * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
993	>	Ta -= C_b * pref * v11 * rxDa;
994
995	<	// Even if we excluded this pair from direct interactions,
675	<	// we still have the reaction-field-mediated charge-dipole
676	<	// interaction:
995	>	if (b_is_Fluctuating) dUdCb -= pref * v11 * rdDa;
996
997	<	if (idat.excluded) {
998	<	indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij);
999	<	indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij);
1000	<	indirect_dVdr += preSw * preRF2_ * uz_j;
1001	<	indirect_duduz_j += preSw * rhat * preRF2_ *  *(idat.rij);
1002	<	}
1003	<
1004	<	} else {
686	<	// determine the inverse r used if we have split dipoles
687	<	if (j_is_SplitDipole) {
688	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
689	<	ri = 1.0 / BigR;
690	<	scale =  *(idat.rij)  * ri;
691	<	} else {
692	<	ri = riji;
693	<	scale = 1.0;
694	<	}
695	<
696	<	sc2 = scale * scale;
697	<
698	<	if (screeningMethod_ == DAMPED) {
699	<	// assemble the damping variables
700	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
701	<	//erfcVal = res.first;
702	<	//derfcVal = res.second;
703	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
704	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
705	<	c1 = erfcVal * ri;
706	<	c2 = (-derfcVal + c1) * ri;
707	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
708	<	} else {
709	<	c1 = ri;
710	<	c2 = c1 * ri;
711	<	c3 = 3.0 * c2 * ri;
712	<	}
713	<
714	<	c2ri = c2 * ri;
715	<
716	<	// calculate the potential
717	<	pot_term =  scale * c2;
718	<	vterm = -pref * ct_j * pot_term;
719	<	vpair += vterm;
720	<	epot +=  *(idat.sw)  * vterm;
721	<
722	<	// calculate derivatives for forces and torques
723	<
724	<	dVdr += -preSw * (uz_j * c2ri - ct_j * rhat * sc2 * c3);
725	<	duduz_j += -preSw * pot_term * rhat;
726	<
997	>	// Even if we excluded this pair from direct interactions,
998	>	// we still have the reaction-field-mediated charge-dipole
999	>	// interaction:
1000	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
1001	>	rfContrib = C_b * pref * preRF_ * 2.0 * *(idat.rij);
1002	>	indirect_Pot -= rfContrib * rdDa;
1003	>	indirect_F   -= rfContrib * D_a / (*idat.rij);
1004	>	indirect_Ta  -= C_b * pref * preRF_ * rxDa;
1005		}
728	–	if (i_is_Fluctuating) {
729	–	*(idat.dVdFQ1) += ( *(idat.sw) * vterm ) / q_i;
730	–	}
1006		}
1007
1008	<	if (j_is_Quadrupole) {
1009	<	// first precalculate some necessary variables
1010	<	cx2 = cx_j * cx_j;
1011	<	cy2 = cy_j * cy_j;
737	<	cz2 = cz_j * cz_j;
738	<	pref =   *(idat.electroMult) * pre14_ * q_i * one_third_;
739	<
740	<	if (screeningMethod_ == DAMPED) {
741	<	// assemble the damping variables
742	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
743	<	//erfcVal = res.first;
744	<	//derfcVal = res.second;
745	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
746	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
747	<	c1 = erfcVal * riji;
748	<	c2 = (-derfcVal + c1) * riji;
749	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
750	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
751	<	} else {
752	<	c1 = riji;
753	<	c2 = c1 * riji;
754	<	c3 = 3.0 * c2 * riji;
755	<	c4 = 5.0 * c3 * riji * riji;
756	<	}
1008	>	if (b_is_Dipole) {
1009	>	pref = pre22_ * *(idat.electroMult);
1010	>	DadDb = dot(D_a, D_b);
1011	>	DaxDb = cross(D_a, D_b);
1012
1013	<	// precompute variables for convenience
1014	<	preSw =  *(idat.sw)  * pref;
1015	<	c2ri = c2 * riji;
1016	<	c3ri = c3 * riji;
1017	<	c4rij = c4 *  *(idat.rij) ;
1018	<	rhatdot2 = two * rhat * c3;
1019	<	rhatc4 = rhat * c4rij;
1020	<
1021	<	// calculate the potential
1022	<	pot_term = ( qxx_j * (cx2*c3 - c2ri) +
1023	<	qyy_j * (cy2*c3 - c2ri) +
1024	<	qzz_j * (cz2*c3 - c2ri) );
1025	<	vterm = pref * pot_term;
771	<	vpair += vterm;
772	<	epot +=  *(idat.sw)  * vterm;
773	<
774	<	// calculate derivatives for the forces and torques
775	<
776	<	dVdr += -preSw * ( qxx_j* (cx2*rhatc4 - (two*cx_j*ux_j + rhat)*c3ri) +
777	<	qyy_j* (cy2*rhatc4 - (two*cy_j*uy_j + rhat)*c3ri) +
778	<	qzz_j* (cz2*rhatc4 - (two*cz_j*uz_j + rhat)*c3ri));
779	<
780	<	dudux_j += preSw * qxx_j * cx_j * rhatdot2;
781	<	duduy_j += preSw * qyy_j * cy_j * rhatdot2;
782	<	duduz_j += preSw * qzz_j * cz_j * rhatdot2;
783	<	if (i_is_Fluctuating) {
784	<	*(idat.dVdFQ1) += ( *(idat.sw) * vterm ) / q_i;
1013	>	U  -= pref * (DadDb * v21 + rdDa * rdDb * v22);
1014	>	F  -= pref * (dv21 * DadDb * rhat + v22or * (rdDb * D_a + rdDa * D_b));
1015	>	F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
1016	>	Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
1017	>	Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
1018	>	// Even if we excluded this pair from direct interactions, we
1019	>	// still have the reaction-field-mediated dipole-dipole
1020	>	// interaction:
1021	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
1022	>	rfContrib = -pref * preRF_ * 2.0;
1023	>	indirect_Pot += rfContrib * DadDb;
1024	>	indirect_Ta  += rfContrib * DaxDb;
1025	>	indirect_Tb  -= rfContrib * DaxDb;
1026		}
1027	+	}
1028
1029	+	if (b_is_Quadrupole) {
1030	+	pref = pre24_ * *(idat.electroMult);
1031	+	DadQb = D_a * Q_b;
1032	+	DadQbr = dot(D_a, Qbr);
1033	+	DaxQbr = cross(D_a, Qbr);
1034	+
1035	+	U  -= pref * ((trQb*rdDa + 2.0*DadQbr)*v31 + rdDa*rdQbr*v32);
1036	+	F  -= pref * (trQb*D_a + 2.0*DadQb) * v31or;
1037	+	F  -= pref * (trQb*rdDa + 2.0*DadQbr) * (dv31-v31or) * rhat;
1038	+	F  -= pref * (D_a*rdQbr + 2.0*rdDa*rQb) * v32or;
1039	+	F  -= pref * (rdDa * rdQbr * rhat * (dv32-3.0*v32or));
1040	+	Ta += pref * ((-trQb*rxDa + 2.0 * DaxQbr)*v31 - rxDa*rdQbr*v32);
1041	+	Tb += pref * ((2.0*cross(DadQb, rhat) - 2.0*DaxQbr)*v31
1042	+	- 2.0*rdDa*rxQbr*v32);
1043		}
1044		}
789	–
790	–	if (i_is_Dipole) {
1045
1046	<	if (j_is_Charge) {
1047	<	// variables used by all the methods
1048	<	pref =  *(idat.electroMult) * pre12_ * q_j * mu_i;
1049	<	preSw =  *(idat.sw)  * pref;
1046	>	if (a_is_Quadrupole) {
1047	>	if (b_is_Charge) {
1048	>	pref = pre14_ * *(idat.electroMult);
1049	>	U  += C_b * pref * (v21 * trQa + v22 * rdQar);
1050	>	F  += C_b * pref * (trQa * rhat * dv21 + 2.0 * Qar * v22or);
1051	>	F  += C_b * pref * rdQar * rhat * (dv22 - 2.0*v22or);
1052	>	Ta += C_b * pref * 2.0 * rxQar * v22;
1053
1054	<	if (summationMethod_ == esm_REACTION_FIELD) {
1054	>	if (b_is_Fluctuating) dUdCb += pref * (v21 * trQa + v22 * rdQar);
1055	>	}
1056	>	if (b_is_Dipole) {
1057	>	pref = pre24_ * *(idat.electroMult);
1058	>	DbdQa = D_b * Q_a;
1059	>	DbdQar = dot(D_b, Qar);
1060	>	DbxQar = cross(D_b, Qar);
1061
1062	<	ri2 = riji * riji;
1063	<	ri3 = ri2 * riji;
1062	>	U  += pref * ((trQa*rdDb + 2.0*DbdQar)*v31 + rdDb*rdQar*v32);
1063	>	F  += pref * (trQa*D_b + 2.0*DbdQa) * v31or;
1064	>	F  += pref * (trQa*rdDb + 2.0*DbdQar) * (dv31-v31or) * rhat;
1065	>	F  += pref * (D_b*rdQar + 2.0*rdDb*rQa) * v32or;
1066	>	F  += pref * (rdDb * rdQar * rhat * (dv32-3.0*v32or));
1067	>	Ta += pref * ((-2.0*cross(DbdQa, rhat) + 2.0*DbxQar)*v31
1068	>	+ 2.0*rdDb*rxQar*v32);
1069	>	Tb += pref * ((trQa*rxDb - 2.0 * DbxQar)*v31 + rxDb*rdQar*v32);
1070	>	}
1071	>	if (b_is_Quadrupole) {
1072	>	pref = pre44_ * *(idat.electroMult);  // yes
1073	>	QaQb = Q_a * Q_b;
1074	>	trQaQb = QaQb.trace();
1075	>	rQaQb = rhat * QaQb;
1076	>	QaQbr = QaQb * rhat;
1077	>	QaxQb = mCross(Q_a, Q_b);
1078	>	rQaQbr = dot(rQa, Qbr);
1079	>	rQaxQbr = cross(rQa, Qbr);
1080	>
1081	>	U  += pref * (trQa * trQb + 2.0 * trQaQb) * v41;
1082	>	U  += pref * (trQa * rdQbr + trQb * rdQar  + 4.0 * rQaQbr) * v42;
1083	>	U  += pref * (rdQar * rdQbr) * v43;
1084
1085	<	vterm = pref * ct_i * ( ri2 - preRF2_ *  *(idat.rij)  );
1086	<	vpair += vterm;
1087	<	epot +=  *(idat.sw)  * vterm;
805	<
806	<	dVdr += preSw * (ri3 * (uz_i - three * ct_i * rhat) - preRF2_ * uz_i);
807	<
808	<	duduz_i += preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
1085	>	F  += pref * rhat * (trQa * trQb + 2.0 * trQaQb)*dv41;
1086	>	F  += pref*rhat*(trQa*rdQbr + trQb*rdQar + 4.0*rQaQbr)*(dv42-2.0*v42or);
1087	>	F  += pref * rhat * (rdQar * rdQbr)*(dv43 - 4.0*v43or);
1088
1089	<	// Even if we excluded this pair from direct interactions,
1090	<	// we still have the reaction-field-mediated charge-dipole
1091	<	// interaction:
1089	>	F  += pref * 2.0 * (trQb*rQa + trQa*rQb) * v42or;
1090	>	F  += pref * 4.0 * (rQaQb + QaQbr) * v42or;
1091	>	F  += pref * 2.0 * (rQa*rdQbr + rdQar*rQb) * v43or;
1092
1093	<	if (idat.excluded) {
1094	<	indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij);
1095	<	indirect_Pot += -preSw * ct_i * preRF2_ * *(idat.rij);
1096	<	indirect_dVdr += -preSw * preRF2_ * uz_i;
1097	<	indirect_duduz_i += -preSw * rhat * preRF2_ *  *(idat.rij);
819	<	}
820	<
821	<	} else {
822	<
823	<	// determine inverse r if we are using split dipoles
824	<	if (i_is_SplitDipole) {
825	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
826	<	ri = 1.0 / BigR;
827	<	scale =  *(idat.rij)  * ri;
828	<	} else {
829	<	ri = riji;
830	<	scale = 1.0;
831	<	}
832	<
833	<	sc2 = scale * scale;
834	<
835	<	if (screeningMethod_ == DAMPED) {
836	<	// assemble the damping variables
837	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
838	<	//erfcVal = res.first;
839	<	//derfcVal = res.second;
840	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
841	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
842	<	c1 = erfcVal * ri;
843	<	c2 = (-derfcVal + c1) * ri;
844	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
845	<	} else {
846	<	c1 = ri;
847	<	c2 = c1 * ri;
848	<	c3 = 3.0 * c2 * ri;
849	<	}
850	<
851	<	c2ri = c2 * ri;
852	<
853	<	// calculate the potential
854	<	pot_term = c2 * scale;
855	<	vterm = pref * ct_i * pot_term;
856	<	vpair += vterm;
857	<	epot +=  *(idat.sw)  * vterm;
1093	>	Ta += pref * (- 4.0 * QaxQb * v41);
1094	>	Ta += pref * (- 2.0 * trQb * cross(rQa, rhat)
1095	>	+ 4.0 * cross(rhat, QaQbr)
1096	>	- 4.0 * rQaxQbr) * v42;
1097	>	Ta += pref * 2.0 * cross(rhat,Qar) * rdQbr * v43;
1098
859	–	// calculate derivatives for the forces and torques
860	–	dVdr += preSw * (uz_i * c2ri - ct_i * rhat * sc2 * c3);
861	–	duduz_i += preSw * pot_term * rhat;
862	–	}
1099
1100	<	if (j_is_Fluctuating) {
1101	<	*(idat.dVdFQ2) += ( *(idat.sw) * vterm ) / q_j;
1102	<	}
1100	>	Tb += pref * (+ 4.0 * QaxQb * v41);
1101	>	Tb += pref * (- 2.0 * trQa * cross(rQb, rhat)
1102	>	- 4.0 * cross(rQaQb, rhat)
1103	>	+ 4.0 * rQaxQbr) * v42;
1104	>	// Possible replacement for line 2 above:
1105	>	//             + 4.0 * cross(rhat, QbQar)
1106
1107	+	Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1108		}
1109	+	}
1110
1111	<	if (j_is_Dipole) {
1112	<	// variables used by all methods
1113	<	ct_ij = dot(uz_i, uz_j);
873	<
874	<	pref =  *(idat.electroMult) * pre22_ * mu_i * mu_j;
875	<	preSw =  *(idat.sw)  * pref;
876	<
877	<	if (summationMethod_ == esm_REACTION_FIELD) {
878	<	ri2 = riji * riji;
879	<	ri3 = ri2 * riji;
880	<	ri4 = ri2 * ri2;
881	<
882	<	vterm = pref * ( ri3 * (ct_ij - 3.0 * ct_i * ct_j) -
883	<	preRF2_ * ct_ij );
884	<	vpair += vterm;
885	<	epot +=  *(idat.sw)  * vterm;
886	<
887	<	a1 = 5.0 * ct_i * ct_j - ct_ij;
888	<
889	<	dVdr += preSw * three * ri4 * (a1 * rhat - ct_i * uz_j - ct_j * uz_i);
890	<
891	<	duduz_i += preSw * (ri3 * (uz_j - three * ct_j * rhat) - preRF2_*uz_j);
892	<	duduz_j += preSw * (ri3 * (uz_i - three * ct_i * rhat) - preRF2_*uz_i);
893	<
894	<	if (idat.excluded) {
895	<	indirect_vpair +=  - pref * preRF2_ * ct_ij;
896	<	indirect_Pot +=    - preSw * preRF2_ * ct_ij;
897	<	indirect_duduz_i += -preSw * preRF2_ * uz_j;
898	<	indirect_duduz_j += -preSw * preRF2_ * uz_i;
899	<	}
900	<
901	<	} else {
902	<
903	<	if (i_is_SplitDipole) {
904	<	if (j_is_SplitDipole) {
905	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i + 0.25 * d_j * d_j);
906	<	} else {
907	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
908	<	}
909	<	ri = 1.0 / BigR;
910	<	scale =  *(idat.rij)  * ri;
911	<	} else {
912	<	if (j_is_SplitDipole) {
913	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
914	<	ri = 1.0 / BigR;
915	<	scale =  *(idat.rij)  * ri;
916	<	} else {
917	<	ri = riji;
918	<	scale = 1.0;
919	<	}
920	<	}
921	<	if (screeningMethod_ == DAMPED) {
922	<	// assemble damping variables
923	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
924	<	//erfcVal = res.first;
925	<	//derfcVal = res.second;
926	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
927	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
928	<	c1 = erfcVal * ri;
929	<	c2 = (-derfcVal + c1) * ri;
930	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
931	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * ri * ri;
932	<	} else {
933	<	c1 = ri;
934	<	c2 = c1 * ri;
935	<	c3 = 3.0 * c2 * ri;
936	<	c4 = 5.0 * c3 * ri * ri;
937	<	}
938	<
939	<	// precompute variables for convenience
940	<	sc2 = scale * scale;
941	<	cti3 = ct_i * sc2 * c3;
942	<	ctj3 = ct_j * sc2 * c3;
943	<	ctidotj = ct_i * ct_j * sc2;
944	<	preSwSc = preSw * scale;
945	<	c2ri = c2 * ri;
946	<	c3ri = c3 * ri;
947	<	c4rij = c4 *  *(idat.rij) ;
948	<
949	<	// calculate the potential
950	<	pot_term = (ct_ij * c2ri - ctidotj * c3);
951	<	vterm = pref * pot_term;
952	<	vpair += vterm;
953	<	epot +=  *(idat.sw)  * vterm;
954	<
955	<	// calculate derivatives for the forces and torques
956	<	dVdr += preSwSc * ( ctidotj * rhat * c4rij  -
957	<	(ct_i*uz_j + ct_j*uz_i + ct_ij*rhat) * c3ri);
958	<
959	<	duduz_i += preSw * (uz_j * c2ri - ctj3 * rhat);
960	<	duduz_j += preSw * (uz_i * c2ri - cti3 * rhat);
961	<	}
962	<	}
1111	>	if (idat.doElectricField) {
1112	>	*(idat.eField1) += Ea * *(idat.electroMult);
1113	>	*(idat.eField2) += Eb * *(idat.electroMult);
1114		}
1115
1116	<	if (i_is_Quadrupole) {
1117	<	if (j_is_Charge) {
1118	<	// precompute some necessary variables
968	<	cx2 = cx_i * cx_i;
969	<	cy2 = cy_i * cy_i;
970	<	cz2 = cz_i * cz_i;
971	<
972	<	pref =  *(idat.electroMult) * pre14_ * q_j * one_third_;
973	<
974	<	if (screeningMethod_ == DAMPED) {
975	<	// assemble the damping variables
976	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
977	<	//erfcVal = res.first;
978	<	//derfcVal = res.second;
979	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
980	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
981	<	c1 = erfcVal * riji;
982	<	c2 = (-derfcVal + c1) * riji;
983	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
984	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
985	<	} else {
986	<	c1 = riji;
987	<	c2 = c1 * riji;
988	<	c3 = 3.0 * c2 * riji;
989	<	c4 = 5.0 * c3 * riji * riji;
990	<	}
991	<
992	<	// precompute some variables for convenience
993	<	preSw =  *(idat.sw)  * pref;
994	<	c2ri = c2 * riji;
995	<	c3ri = c3 * riji;
996	<	c4rij = c4 *  *(idat.rij) ;
997	<	rhatdot2 = two * rhat * c3;
998	<	rhatc4 = rhat * c4rij;
999	<
1000	<	// calculate the potential
1001	<	pot_term = ( qxx_i * (cx2 * c3 - c2ri) +
1002	<	qyy_i * (cy2 * c3 - c2ri) +
1003	<	qzz_i * (cz2 * c3 - c2ri) );
1004	<
1005	<	vterm = pref * pot_term;
1006	<	vpair += vterm;
1007	<	epot +=  *(idat.sw)  * vterm;
1008	<
1009	<	// calculate the derivatives for the forces and torques
1010	<
1011	<	dVdr += -preSw * (qxx_i* (cx2*rhatc4 - (two*cx_i*ux_i + rhat)*c3ri) +
1012	<	qyy_i* (cy2*rhatc4 - (two*cy_i*uy_i + rhat)*c3ri) +
1013	<	qzz_i* (cz2*rhatc4 - (two*cz_i*uz_i + rhat)*c3ri));
1014	<
1015	<	dudux_i += preSw * qxx_i * cx_i *  rhatdot2;
1016	<	duduy_i += preSw * qyy_i * cy_i *  rhatdot2;
1017	<	duduz_i += preSw * qzz_i * cz_i *  rhatdot2;
1018	<
1019	<	if (j_is_Fluctuating) {
1020	<	*(idat.dVdFQ2) += ( *(idat.sw) * vterm ) / q_j;
1021	<	}
1022	<
1023	<	}
1116	>	if (idat.doSitePotential) {
1117	>	*(idat.sPot1) += Pa * *(idat.electroMult);
1118	>	*(idat.sPot2) += Pb * *(idat.electroMult);
1119		}
1120
1121	+	if (a_is_Fluctuating) *(idat.dVdFQ1) += dUdCa * *(idat.sw);
1122	+	if (b_is_Fluctuating) *(idat.dVdFQ2) += dUdCb * *(idat.sw);
1123
1124		if (!idat.excluded) {
1028	–	*(idat.vpair) += vpair;
1029	–	(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot;
1030	–	*(idat.f1) += dVdr;
1125
1126	<	if (i_is_Dipole || i_is_Quadrupole)
1127	<	*(idat.t1) -= cross(uz_i, duduz_i);
1128	<	if (i_is_Quadrupole) {
1035	<	*(idat.t1) -= cross(ux_i, dudux_i);
1036	<	*(idat.t1) -= cross(uy_i, duduy_i);
1037	<	}
1126	>	*(idat.vpair) += U;
1127	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += U * *(idat.sw);
1128	>	*(idat.f1) += F * *(idat.sw);
1129
1130	<	if (j_is_Dipole || j_is_Quadrupole)
1131	<	*(idat.t2) -= cross(uz_j, duduz_j);
1041	<	if (j_is_Quadrupole) {
1042	<	*(idat.t2) -= cross(uz_j, dudux_j);
1043	<	*(idat.t2) -= cross(uz_j, duduy_j);
1044	<	}
1130	>	if (a_is_Dipole || a_is_Quadrupole)
1131	>	*(idat.t1) += Ta * *(idat.sw);
1132
1133	+	if (b_is_Dipole || b_is_Quadrupole)
1134	+	*(idat.t2) += Tb * *(idat.sw);
1135	+
1136		} else {
1137
1138		// only accumulate the forces and torques resulting from the
1139		// indirect reaction field terms.
1140
1141	<	*(idat.vpair) += indirect_vpair;
1142	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot;
1143	<	*(idat.f1) += indirect_dVdr;
1141	>	*(idat.vpair) += indirect_Pot;
1142	>	(*(idat.excludedPot))[ELECTROSTATIC_FAMILY] +=  excluded_Pot;
1143	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += *(idat.sw) * indirect_Pot;
1144	>	*(idat.f1) += *(idat.sw) * indirect_F;
1145
1146	<	if (i_is_Dipole)
1147	<	*(idat.t1) -= cross(uz_i, indirect_duduz_i);
1148	<	if (j_is_Dipole)
1149	<	*(idat.t2) -= cross(uz_j, indirect_duduz_j);
1146	>	if (a_is_Dipole || a_is_Quadrupole)
1147	>	*(idat.t1) += *(idat.sw) * indirect_Ta;
1148	>
1149	>	if (b_is_Dipole || b_is_Quadrupole)
1150	>	*(idat.t2) += *(idat.sw) * indirect_Tb;
1151		}
1060	–
1152		return;
1153	<	}
1153	>	}
1154
1155		void Electrostatic::calcSelfCorrection(SelfData &sdat) {
1156	<	RealType mu1, preVal, self;
1156	>
1157		if (!initialized_) initialize();
1158
1159	<	ElectrostaticAtomData data = ElectrostaticMap[sdat.atype];
1160	<
1159	>	ElectrostaticAtomData data = ElectrostaticMap[Etids[sdat.atid]];
1160	>
1161		// logicals
1162		bool i_is_Charge = data.is_Charge;
1163		bool i_is_Dipole = data.is_Dipole;
1164	+	bool i_is_Quadrupole = data.is_Quadrupole;
1165		bool i_is_Fluctuating = data.is_Fluctuating;
1166	<	RealType chg1 = data.fixedCharge;
1167	<
1166	>	RealType C_a = data.fixedCharge;
1167	>	RealType self(0.0), preVal, DdD, trQ, trQQ;
1168	>
1169	>	if (i_is_Dipole) {
1170	>	DdD = data.dipole.lengthSquare();
1171	>	}
1172	>
1173		if (i_is_Fluctuating) {
1174	<	chg1 += *(sdat.flucQ);
1175	<	// dVdFQ is really a force, so this is negative the derivative
1176	<	*(sdat.dVdFQ) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1174	>	C_a += *(sdat.flucQ);
1175	>
1176	>	flucQ_->getSelfInteraction(sdat.atid, *(sdat.flucQ),
1177	>	(*(sdat.excludedPot))[ELECTROSTATIC_FAMILY],
1178	>	*(sdat.flucQfrc) );
1179	>
1180		}
1181
1182	<	if (summationMethod_ == esm_REACTION_FIELD) {
1183	<	if (i_is_Dipole) {
1184	<	mu1 = data.dipole_moment;
1185	<	preVal = pre22_ * preRF2_ * mu1 * mu1;
1186	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal;
1187	<
1188	<	// The self-correction term adds into the reaction field vector
1189	<	Vector3d uz_i = sdat.eFrame->getColumn(2);
1190	<	Vector3d ei = preVal * uz_i;
1182	>	switch (summationMethod_) {
1183	>	case esm_REACTION_FIELD:
1184	>
1185	>	if (i_is_Charge) {
1186	>	// Self potential [see Wang and Hermans, "Reaction Field
1187	>	// Molecular Dynamics Simulation with Friedman’s Image Charge
1188	>	// Method," J. Phys. Chem. 99, 12001-12007 (1995).]
1189	>	preVal = pre11_ * preRF_ * C_a * C_a;
1190	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal / cutoffRadius_;
1191	>	}
1192
1193	<	// This looks very wrong.  A vector crossed with itself is zero.
1194	<	*(sdat.t) -= cross(uz_i, ei);
1193	>	if (i_is_Dipole) {
1194	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DdD;
1195		}
1196	<	} else if (summationMethod_ == esm_SHIFTED_FORCE || summationMethod_ == esm_SHIFTED_POTENTIAL) {
1197	<	if (i_is_Charge) {
1198	<	if (screeningMethod_ == DAMPED) {
1199	<	self = - 0.5 * (c1c_ + alphaPi_) * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_;
1200	<	} else {
1201	<	self = - 0.5 * rcuti_ * chg1 * (chg1 +  *(sdat.skippedCharge)) * pre11_;
1202	<	}
1203	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1196	>
1197	>	break;
1198	>
1199	>	case esm_SHIFTED_FORCE:
1200	>	case esm_SHIFTED_POTENTIAL:
1201	>	case esm_TAYLOR_SHIFTED:
1202	>	case esm_EWALD_FULL:
1203	>	if (i_is_Charge)
1204	>	self += selfMult1_ * pre11_ * C_a * (C_a + *(sdat.skippedCharge));
1205	>	if (i_is_Dipole)
1206	>	self += selfMult2_ * pre22_ * DdD;
1207	>	if (i_is_Quadrupole) {
1208	>	trQ = data.quadrupole.trace();
1209	>	trQQ = (data.quadrupole * data.quadrupole).trace();
1210	>	self += selfMult4_ * pre44_ * (2.0*trQQ + trQ*trQ);
1211	>	if (i_is_Charge)
1212	>	self -= selfMult2_ * pre14_ * 2.0 * C_a * trQ;
1213		}
1214	+	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1215	+	break;
1216	+	default:
1217	+	break;
1218		}
1219		}
1220	<
1220	>
1221		RealType Electrostatic::getSuggestedCutoffRadius(pair<AtomType*, AtomType*> atypes) {
1222		// This seems to work moderately well as a default.  There's no
1223		// inherent scale for 1/r interactions that we can standardize.
1224		// 12 angstroms seems to be a reasonably good guess for most
1225		// cases.
1226		return 12.0;
1227	+	}
1228	+
1229	+
1230	+	void Electrostatic::ReciprocalSpaceSum(RealType& pot) {
1231	+
1232	+	RealType kPot = 0.0;
1233	+	RealType kVir = 0.0;
1234	+
1235	+	const RealType mPoleConverter = 0.20819434; // converts from the
1236	+	// internal units of
1237	+	// Debye (for dipoles)
1238	+	// or Debye-angstroms
1239	+	// (for quadrupoles) to
1240	+	// electron angstroms or
1241	+	// electron-angstroms^2
1242	+
1243	+	const RealType eConverter = 332.0637778; // convert the
1244	+	// Charge-Charge
1245	+	// electrostatic
1246	+	// interactions into kcal /
1247	+	// mol assuming distances
1248	+	// are measured in
1249	+	// angstroms.
1250	+
1251	+	Mat3x3d hmat = info_->getSnapshotManager()->getCurrentSnapshot()->getHmat();
1252	+	Vector3d box = hmat.diagonals();
1253	+	RealType boxMax = box.max();
1254	+
1255	+	//int kMax = int(2.0 * M_PI / (pow(dampingAlpha_,2)*cutoffRadius_ * boxMax) );
1256	+	int kMax = 7;
1257	+	int kSqMax = kMax*kMax + 2;
1258	+
1259	+	int kLimit = kMax+1;
1260	+	int kLim2 = 2*kMax+1;
1261	+	int kSqLim = kSqMax;
1262	+
1263	+	vector<RealType> AK(kSqLim+1, 0.0);
1264	+	RealType xcl = 2.0 * M_PI / box.x();
1265	+	RealType ycl = 2.0 * M_PI / box.y();
1266	+	RealType zcl = 2.0 * M_PI / box.z();
1267	+	RealType rcl = 2.0 * M_PI / boxMax;
1268	+	RealType rvol = 2.0 * M_PI /(box.x() * box.y() * box.z());
1269	+
1270	+	if(dampingAlpha_ < 1.0e-12) return;
1271	+
1272	+	RealType ralph = -0.25/pow(dampingAlpha_,2);
1273	+
1274	+	// Calculate and store exponential factors
1275	+
1276	+	vector<vector<RealType> > elc;
1277	+	vector<vector<RealType> > emc;
1278	+	vector<vector<RealType> > enc;
1279	+	vector<vector<RealType> > els;
1280	+	vector<vector<RealType> > ems;
1281	+	vector<vector<RealType> > ens;
1282	+
1283	+	int nMax = info_->getNAtoms();
1284	+
1285	+	elc.resize(kLimit+1);
1286	+	emc.resize(kLimit+1);
1287	+	enc.resize(kLimit+1);
1288	+	els.resize(kLimit+1);
1289	+	ems.resize(kLimit+1);
1290	+	ens.resize(kLimit+1);
1291	+
1292	+	for (int j = 0; j < kLimit+1; j++) {
1293	+	elc[j].resize(nMax);
1294	+	emc[j].resize(nMax);
1295	+	enc[j].resize(nMax);
1296	+	els[j].resize(nMax);
1297	+	ems[j].resize(nMax);
1298	+	ens[j].resize(nMax);
1299	+	}
1300	+
1301	+	Vector3d t( 2.0 * M_PI );
1302	+	t.Vdiv(t, box);
1303	+
1304	+	SimInfo::MoleculeIterator mi;
1305	+	Molecule::AtomIterator ai;
1306	+	int i;
1307	+	Vector3d r;
1308	+	Vector3d tt;
1309	+
1310	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1311	+	mol = info_->nextMolecule(mi)) {
1312	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1313	+	atom = mol->nextAtom(ai)) {
1314	+
1315	+	i = atom->getLocalIndex();
1316	+	r = atom->getPos();
1317	+	info_->getSnapshotManager()->getCurrentSnapshot()->wrapVector(r);
1318	+
1319	+	tt.Vmul(t, r);
1320	+
1321	+	elc[1][i] = 1.0;
1322	+	emc[1][i] = 1.0;
1323	+	enc[1][i] = 1.0;
1324	+	els[1][i] = 0.0;
1325	+	ems[1][i] = 0.0;
1326	+	ens[1][i] = 0.0;
1327	+
1328	+	elc[2][i] = cos(tt.x());
1329	+	emc[2][i] = cos(tt.y());
1330	+	enc[2][i] = cos(tt.z());
1331	+	els[2][i] = sin(tt.x());
1332	+	ems[2][i] = sin(tt.y());
1333	+	ens[2][i] = sin(tt.z());
1334	+
1335	+	for(int l = 3; l <= kLimit; l++) {
1336	+	elc[l][i]=elc[l-1][i]*elc[2][i]-els[l-1][i]*els[2][i];
1337	+	emc[l][i]=emc[l-1][i]*emc[2][i]-ems[l-1][i]*ems[2][i];
1338	+	enc[l][i]=enc[l-1][i]*enc[2][i]-ens[l-1][i]*ens[2][i];
1339	+	els[l][i]=els[l-1][i]*elc[2][i]+elc[l-1][i]*els[2][i];
1340	+	ems[l][i]=ems[l-1][i]*emc[2][i]+emc[l-1][i]*ems[2][i];
1341	+	ens[l][i]=ens[l-1][i]*enc[2][i]+enc[l-1][i]*ens[2][i];
1342	+	}
1343	+	}
1344	+	}
1345	+
1346	+	// Calculate and store AK coefficients:
1347	+
1348	+	RealType eksq = 1.0;
1349	+	RealType expf = 0.0;
1350	+	if (ralph < 0.0) expf = exp(ralph*rcl*rcl);
1351	+	for (i = 1; i <= kSqLim; i++) {
1352	+	RealType rksq = float(i)*rcl*rcl;
1353	+	eksq = expf*eksq;
1354	+	AK[i] = eConverter * eksq/rksq;
1355	+	}
1356	+
1357	+	/*
1358	+	* Loop over all k vectors k = 2 pi (ll/Lx, mm/Ly, nn/Lz)
1359	+	* the values of ll, mm and nn are selected so that the symmetry of
1360	+	* reciprocal lattice is taken into account i.e. the following
1361	+	* rules apply.
1362	+	*
1363	+	* ll ranges over the values 0 to kMax only.
1364	+	*
1365	+	* mm ranges over 0 to kMax when ll=0 and over
1366	+	*            -kMax to kMax otherwise.
1367	+	* nn ranges over 1 to kMax when ll=mm=0 and over
1368	+	*            -kMax to kMax otherwise.
1369	+	*
1370	+	* Hence the result of the summation must be doubled at the end.
1371	+	*/
1372	+
1373	+	std::vector<RealType> clm(nMax, 0.0);
1374	+	std::vector<RealType> slm(nMax, 0.0);
1375	+	std::vector<RealType> ckr(nMax, 0.0);
1376	+	std::vector<RealType> skr(nMax, 0.0);
1377	+	std::vector<RealType> ckc(nMax, 0.0);
1378	+	std::vector<RealType> cks(nMax, 0.0);
1379	+	std::vector<RealType> dkc(nMax, 0.0);
1380	+	std::vector<RealType> dks(nMax, 0.0);
1381	+	std::vector<RealType> qkc(nMax, 0.0);
1382	+	std::vector<RealType> qks(nMax, 0.0);
1383	+	std::vector<Vector3d> dxk(nMax, V3Zero);
1384	+	std::vector<Vector3d> qxk(nMax, V3Zero);
1385	+	RealType rl, rm, rn;
1386	+	Vector3d kVec;
1387	+	Vector3d Qk;
1388	+	Mat3x3d k2;
1389	+	RealType ckcs, ckss, dkcs, dkss, qkcs, qkss;
1390	+	int atid;
1391	+	ElectrostaticAtomData data;
1392	+	RealType C, dk, qk;
1393	+	Vector3d D;
1394	+	Mat3x3d  Q;
1395	+
1396	+	int mMin = kLimit;
1397	+	int nMin = kLimit + 1;
1398	+	for (int l = 1; l <= kLimit; l++) {
1399	+	int ll = l - 1;
1400	+	rl = xcl * float(ll);
1401	+	for (int mmm = mMin; mmm <= kLim2; mmm++) {
1402	+	int mm = mmm - kLimit;
1403	+	int m = abs(mm) + 1;
1404	+	rm = ycl * float(mm);
1405	+	// Set temporary products of exponential terms
1406	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1407	+	mol = info_->nextMolecule(mi)) {
1408	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1409	+	atom = mol->nextAtom(ai)) {
1410	+
1411	+	i = atom->getLocalIndex();
1412	+	if(mm < 0) {
1413	+	clm[i]=elc[l][i]*emc[m][i]+els[l][i]*ems[m][i];
1414	+	slm[i]=els[l][i]*emc[m][i]-ems[m][i]*elc[l][i];
1415	+	} else {
1416	+	clm[i]=elc[l][i]*emc[m][i]-els[l][i]*ems[m][i];
1417	+	slm[i]=els[l][i]*emc[m][i]+ems[m][i]*elc[l][i];
1418	+	}
1419	+	}
1420	+	}
1421	+	for (int nnn = nMin; nnn <= kLim2; nnn++) {
1422	+	int nn = nnn - kLimit;
1423	+	int n = abs(nn) + 1;
1424	+	rn = zcl * float(nn);
1425	+	// Test on magnitude of k vector:
1426	+	int kk=ll*ll + mm*mm + nn*nn;
1427	+	if(kk <= kSqLim) {
1428	+	kVec = Vector3d(rl, rm, rn);
1429	+	k2 = outProduct(kVec, kVec);
1430	+	// Calculate exp(ikr) terms
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	+
1437	+	if (nn < 0) {
1438	+	ckr[i]=clm[i]*enc[n][i]+slm[i]*ens[n][i];
1439	+	skr[i]=slm[i]*enc[n][i]-clm[i]*ens[n][i];
1440	+
1441	+	} else {
1442	+	ckr[i]=clm[i]*enc[n][i]-slm[i]*ens[n][i];
1443	+	skr[i]=slm[i]*enc[n][i]+clm[i]*ens[n][i];
1444	+	}
1445	+	}
1446	+	}
1447	+
1448	+	// Calculate scalar and vector products for each site:
1449	+
1450	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1451	+	mol = info_->nextMolecule(mi)) {
1452	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1453	+	atom = mol->nextAtom(ai)) {
1454	+	i = atom->getLocalIndex();
1455	+	int atid = atom->getAtomType()->getIdent();
1456	+	data = ElectrostaticMap[Etids[atid]];
1457	+
1458	+	if (data.is_Charge) {
1459	+	C = data.fixedCharge;
1460	+	if (atom->isFluctuatingCharge()) C += atom->getFlucQPos();
1461	+	ckc[i] = C * ckr[i];
1462	+	cks[i] = C * skr[i];
1463	+	}
1464	+
1465	+	if (data.is_Dipole) {
1466	+	D = atom->getDipole() * mPoleConverter;
1467	+	dk = dot(D, kVec);
1468	+	dxk[i] = cross(D, kVec);
1469	+	dkc[i] = dk * ckr[i];
1470	+	dks[i] = dk * skr[i];
1471	+	}
1472	+	if (data.is_Quadrupole) {
1473	+	Q = atom->getQuadrupole() * mPoleConverter;
1474	+	Qk = Q * kVec;
1475	+	qk = dot(kVec, Qk);
1476	+	qxk[i] = -cross(kVec, Qk);
1477	+	qkc[i] = qk * ckr[i];
1478	+	qks[i] = qk * skr[i];
1479	+	}
1480	+	}
1481	+	}
1482	+
1483	+	// calculate vector sums
1484	+
1485	+	ckcs = std::accumulate(ckc.begin(),ckc.end(),0.0);
1486	+	ckss = std::accumulate(cks.begin(),cks.end(),0.0);
1487	+	dkcs = std::accumulate(dkc.begin(),dkc.end(),0.0);
1488	+	dkss = std::accumulate(dks.begin(),dks.end(),0.0);
1489	+	qkcs = std::accumulate(qkc.begin(),qkc.end(),0.0);
1490	+	qkss = std::accumulate(qks.begin(),qks.end(),0.0);
1491	+
1492	+	#ifdef IS_MPI
1493	+	MPI_Allreduce(MPI_IN_PLACE, &ckcs, 1, MPI_REALTYPE,
1494	+	MPI_SUM, MPI_COMM_WORLD);
1495	+	MPI_Allreduce(MPI_IN_PLACE, &ckss, 1, MPI_REALTYPE,
1496	+	MPI_SUM, MPI_COMM_WORLD);
1497	+	MPI_Allreduce(MPI_IN_PLACE, &dkcs, 1, MPI_REALTYPE,
1498	+	MPI_SUM, MPI_COMM_WORLD);
1499	+	MPI_Allreduce(MPI_IN_PLACE, &dkss, 1, MPI_REALTYPE,
1500	+	MPI_SUM, MPI_COMM_WORLD);
1501	+	MPI_Allreduce(MPI_IN_PLACE, &qkcs, 1, MPI_REALTYPE,
1502	+	MPI_SUM, MPI_COMM_WORLD);
1503	+	MPI_Allreduce(MPI_IN_PLACE, &qkss, 1, MPI_REALTYPE,
1504	+	MPI_SUM, MPI_COMM_WORLD);
1505	+	#endif
1506	+
1507	+	// Accumulate potential energy and virial contribution:
1508	+
1509	+	kPot += 2.0 * rvol * AK[kk]*((ckss+dkcs-qkss)*(ckss+dkcs-qkss)
1510	+	+ (ckcs-dkss-qkcs)*(ckcs-dkss-qkcs));
1511	+
1512	+	kVir += 2.0 * rvol  * AK[kk]*(ckcs*ckcs+ckss*ckss
1513	+	+4.0*(ckss*dkcs-ckcs*dkss)
1514	+	+3.0*(dkcs*dkcs+dkss*dkss)
1515	+	-6.0*(ckss*qkss+ckcs*qkcs)
1516	+	+8.0*(dkss*qkcs-dkcs*qkss)
1517	+	+5.0*(qkss*qkss+qkcs*qkcs));
1518	+
1519	+	// Calculate force and torque for each site:
1520	+
1521	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1522	+	mol = info_->nextMolecule(mi)) {
1523	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1524	+	atom = mol->nextAtom(ai)) {
1525	+
1526	+	i = atom->getLocalIndex();
1527	+	atid = atom->getAtomType()->getIdent();
1528	+	data = ElectrostaticMap[Etids[atid]];
1529	+
1530	+	RealType qfrc = AK[kk]*((cks[i]+dkc[i]-qks[i])*(ckcs-dkss-qkcs)
1531	+	- (ckc[i]-dks[i]-qkc[i])*(ckss+dkcs-qkss));
1532	+	RealType qtrq1 = AK[kk]*(skr[i]*(ckcs-dkss-qkcs)
1533	+	-ckr[i]*(ckss+dkcs-qkss));
1534	+	RealType qtrq2 = 2.0*AK[kk]*(ckr[i]*(ckcs-dkss-qkcs)
1535	+	+skr[i]*(ckss+dkcs-qkss));
1536	+
1537	+	atom->addFrc( 4.0 * rvol * qfrc * kVec );
1538	+
1539	+	if (atom->isFluctuatingCharge()) {
1540	+	atom->addFlucQFrc( - 2.0 * rvol * qtrq2 );
1541	+	}
1542	+
1543	+	if (data.is_Dipole) {
1544	+	atom->addTrq( 4.0 * rvol * qtrq1 * dxk[i] );
1545	+	}
1546	+	if (data.is_Quadrupole) {
1547	+	atom->addTrq( 4.0 * rvol * qtrq2 * qxk[i] );
1548	+	}
1549	+	}
1550	+	}
1551	+	}
1552	+	}
1553	+	nMin = 1;
1554	+	}
1555	+	mMin = 1;
1556	+	}
1557	+	pot += kPot;
1558		}
1559		}

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