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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 1922 by gezelter, Mon Aug 5 13:41:15 2013 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		*/
#	Line 44 | Line 44
44		#include <string.h>
45
46		#include <cmath>
47	+	#include <numeric>
48		#include "nonbonded/Electrostatic.hpp"
49		#include "utils/simError.h"
50		#include "types/NonBondedInteractionType.hpp"
#	Line 53 | Line 54
54		#include "io/Globals.hpp"
55		#include "nonbonded/SlaterIntegrals.hpp"
56		#include "utils/PhysicalConstants.hpp"
57	+	#include "math/erfc.hpp"
58	+	#include "math/SquareMatrix.hpp"
59	+	#include "primitives/Molecule.hpp"
60
61
62		namespace OpenMD {
#	Line 62 | Line 66 | namespace OpenMD {
66		haveCutoffRadius_(false),
67		haveDampingAlpha_(false),
68		haveDielectric_(false),
69	<	haveElectroSpline_(false)
69	>	haveElectroSplines_(false)
70		{}
71
72		void Electrostatic::initialize() {
#	Line 74 | Line 78 | namespace OpenMD {
78		summationMap_["SWITCHING_FUNCTION"] = esm_SWITCHING_FUNCTION;
79		summationMap_["SHIFTED_POTENTIAL"]  = esm_SHIFTED_POTENTIAL;
80		summationMap_["SHIFTED_FORCE"]      = esm_SHIFTED_FORCE;
81	+	summationMap_["TAYLOR_SHIFTED"]     = esm_TAYLOR_SHIFTED;
82		summationMap_["REACTION_FIELD"]     = esm_REACTION_FIELD;
83		summationMap_["EWALD_FULL"]         = esm_EWALD_FULL;
84		summationMap_["EWALD_PME"]          = esm_EWALD_PME;
#	Line 88 | Line 93 | namespace OpenMD {
93		// Charge-Dipole, assuming charges are measured in electrons, and
94		// dipoles are measured in debyes
95		pre12_ = 69.13373;
96	<	// Dipole-Dipole, assuming dipoles are measured in debyes
96	>	// Dipole-Dipole, assuming dipoles are measured in Debye
97		pre22_ = 14.39325;
98		// Charge-Quadrupole, assuming charges are measured in electrons, and
99		// quadrupoles are measured in 10^-26 esu cm^2
100	<	// This unit is also known affectionately as an esu centi-barn.
100	>	// This unit is also known affectionately as an esu centibarn.
101		pre14_ = 69.13373;
102	<
102	>	// Dipole-Quadrupole, assuming dipoles are measured in debyes and
103	>	// quadrupoles in esu centibarns:
104	>	pre24_ = 14.39325;
105	>	// Quadrupole-Quadrupole, assuming esu centibarns:
106	>	pre44_ = 14.39325;
107	>
108		// conversions for the simulation box dipole moment
109		chargeToC_ = 1.60217733e-19;
110		angstromToM_ = 1.0e-10;
111		debyeToCm_ = 3.33564095198e-30;
112
113	<	// number of points for electrostatic splines
113	>	// Default number of points for electrostatic splines
114		np_ = 100;
115
116		// variables to handle different summation methods for long-range
#	Line 108 | Line 118 | namespace OpenMD {
118		summationMethod_ = esm_HARD;
119		screeningMethod_ = UNDAMPED;
120		dielectric_ = 1.0;
111	–	one_third_ = 1.0 / 3.0;
121
122		// check the summation method:
123		if (simParams_->haveElectrostaticSummationMethod()) {
#	Line 124 | Line 133 | namespace OpenMD {
133		"Electrostatic::initialize: Unknown electrostaticSummationMethod.\n"
134		"\t(Input file specified %s .)\n"
135		"\telectrostaticSummationMethod must be one of: \"hard\",\n"
136	<	"\t\"shifted_potential\", \"shifted_force\", or \n"
137	<	"\t\"reaction_field\".\n", myMethod.c_str() );
136	>	"\t\"shifted_potential\", \"shifted_force\",\n"
137	>	"\t\"taylor_shifted\", or \"reaction_field\".\n",
138	>	myMethod.c_str() );
139		painCave.isFatal = 1;
140		simError();
141		}
#	Line 184 | Line 194 | namespace OpenMD {
194		simError();
195		}
196
197	<	if (screeningMethod_ == DAMPED) {
197	>	if (screeningMethod_ == DAMPED || summationMethod_ == esm_EWALD_FULL) {
198		if (!simParams_->haveDampingAlpha()) {
199		// first set a cutoff dependent alpha value
200		// we assume alpha depends linearly with rcut from 0 to 20.5 ang
201		dampingAlpha_ = 0.425 - cutoffRadius_* 0.02;
202	<	if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;
193	<
202	>	if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;
203		// throw warning
204		sprintf( painCave.errMsg,
205		"Electrostatic::initialize: dampingAlpha was not specified in the\n"
#	Line 206 | Line 215 | namespace OpenMD {
215		haveDampingAlpha_ = true;
216		}
217
209	–	// find all of the Electrostatic atom Types:
210	–	ForceField::AtomTypeContainer* atomTypes = forceField_->getAtomTypes();
211	–	ForceField::AtomTypeContainer::MapTypeIterator i;
212	–	AtomType* at;
213	–
214	–	for (at = atomTypes->beginType(i); at != NULL;
215	–	at = atomTypes->nextType(i)) {
216	–
217	–	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_;
218
219	<	if (screeningMethod_ == DAMPED) {
220	<
221	<	alpha2_ = dampingAlpha_ * dampingAlpha_;
222	<	alpha4_ = alpha2_ * alpha2_;
223	<	alpha6_ = alpha4_ * alpha2_;
224	<	alpha8_ = alpha4_ * alpha4_;
225	<
226	<	constEXP_ = exp(-alpha2_ * cutoffRadius2_);
235	<	invRootPi_ = 0.56418958354775628695;
236	<	alphaPi_ = 2.0 * dampingAlpha_ * invRootPi_;
219	>	Etypes.clear();
220	>	Etids.clear();
221	>	FQtypes.clear();
222	>	FQtids.clear();
223	>	ElectrostaticMap.clear();
224	>	Jij.clear();
225	>	nElectro_ = 0;
226	>	nFlucq_ = 0;
227
228	<	c1c_ = erfc(dampingAlpha_ * cutoffRadius_) * rcuti_;
229	<	c2c_ = alphaPi_ * constEXP_ * rcuti_ + c1c_ * rcuti_;
230	<	c3c_ = 2.0 * alphaPi_ * alpha2_ + 3.0 * c2c_ * rcuti_;
231	<	c4c_ = 4.0 * alphaPi_ * alpha4_ + 5.0 * c3c_ * rcuti2_;
232	<	c5c_ = 8.0 * alphaPi_ * alpha6_ + 7.0 * c4c_ * rcuti2_;
233	<	c6c_ = 16.0 * alphaPi_ * alpha8_ + 9.0 * c5c_ * rcuti2_;
234	<	} 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_;
228	>	Etids.resize( forceField_->getNAtomType(), -1);
229	>	FQtids.resize( forceField_->getNAtomType(), -1);
230	>
231	>	set<AtomType*>::iterator at;
232	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
233	>	if ((*at)->isElectrostatic()) nElectro_++;
234	>	if ((*at)->isFluctuatingCharge()) nFlucq_++;
235		}
236	<
236	>
237	>	Jij.resize(nFlucq_);
238	>
239	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
240	>	if ((*at)->isElectrostatic()) addType(*at);
241	>	}
242	>
243		if (summationMethod_ == esm_REACTION_FIELD) {
244		preRF_ = (dielectric_ - 1.0) /
245	<	((2.0 * dielectric_ + 1.0) * cutoffRadius2_ * cutoffRadius_);
256	<	preRF2_ = 2.0 * preRF_;
245	>	((2.0 * dielectric_ + 1.0) * pow(cutoffRadius_,3) );
246		}
247
248	+	RealType b0c, b1c, b2c, b3c, b4c, b5c;
249	+	RealType db0c_1, db0c_2, db0c_3, db0c_4, db0c_5;
250	+	RealType a2, expTerm, invArootPi;
251	+
252	+	RealType r = cutoffRadius_;
253	+	RealType r2 = r * r;
254	+	RealType ric = 1.0 / r;
255	+	RealType ric2 = ric * ric;
256	+
257	+	if (screeningMethod_ == DAMPED) {
258	+	a2 = dampingAlpha_ * dampingAlpha_;
259	+	invArootPi = 1.0 / (dampingAlpha_ * sqrt(M_PI));
260	+	expTerm = exp(-a2 * r2);
261	+	// values of Smith's B_l functions at the cutoff radius:
262	+	b0c = erfc(dampingAlpha_ * r) / r;
263	+	b1c = (      b0c     + 2.0*a2     * expTerm * invArootPi) / r2;
264	+	b2c = (3.0 * b1c + pow(2.0*a2, 2) * expTerm * invArootPi) / r2;
265	+	b3c = (5.0 * b2c + pow(2.0*a2, 3) * expTerm * invArootPi) / r2;
266	+	b4c = (7.0 * b3c + pow(2.0*a2, 4) * expTerm * invArootPi) / r2;
267	+	b5c = (9.0 * b4c + pow(2.0*a2, 5) * expTerm * invArootPi) / r2;
268	+	// Half the Smith self piece:
269	+	selfMult1_ = - a2 * invArootPi;
270	+	selfMult2_ = - 2.0 * a2 * a2 * invArootPi / 3.0;
271	+	selfMult4_ = - 4.0 * a2 * a2 * a2 * invArootPi / 5.0;
272	+	} else {
273	+	a2 = 0.0;
274	+	b0c = 1.0 / r;
275	+	b1c = (      b0c) / r2;
276	+	b2c = (3.0 * b1c) / r2;
277	+	b3c = (5.0 * b2c) / r2;
278	+	b4c = (7.0 * b3c) / r2;
279	+	b5c = (9.0 * b4c) / r2;
280	+	selfMult1_ = 0.0;
281	+	selfMult2_ = 0.0;
282	+	selfMult4_ = 0.0;
283	+	}
284	+
285	+	// higher derivatives of B_0 at the cutoff radius:
286	+	db0c_1 = -r * b1c;
287	+	db0c_2 =     -b1c + r2 * b2c;
288	+	db0c_3 =          3.0*r*b2c  - r2*r*b3c;
289	+	db0c_4 =          3.0*b2c  - 6.0*r2*b3c     + r2*r2*b4c;
290	+	db0c_5 =                    -15.0*r*b3c + 10.0*r2*r*b4c - r2*r2*r*b5c;
291	+
292	+	if (summationMethod_ != esm_EWALD_FULL) {
293	+	selfMult1_ -= b0c;
294	+	selfMult2_ += (db0c_2 + 2.0*db0c_1*ric) /  3.0;
295	+	selfMult4_ -= (db0c_4 + 4.0*db0c_3*ric) / 15.0;
296	+	}
297	+
298	+	// working variables for the splines:
299	+	RealType ri, ri2;
300	+	RealType b0, b1, b2, b3, b4, b5;
301	+	RealType db0_1, db0_2, db0_3, db0_4, db0_5;
302	+	RealType f, fc, f0;
303	+	RealType g, gc, g0, g1, g2, g3, g4;
304	+	RealType h, hc, h1, h2, h3, h4;
305	+	RealType s, sc, s2, s3, s4;
306	+	RealType t, tc, t3, t4;
307	+	RealType u, uc, u4;
308	+
309	+	// working variables for Taylor expansion:
310	+	RealType rmRc, rmRc2, rmRc3, rmRc4;
311	+
312	+	// Approximate using splines using a maximum of 0.1 Angstroms
313	+	// between points.
314	+	int nptest = int((cutoffRadius_ + 2.0) / 0.1);
315	+	np_ = (np_ > nptest) ? np_ : nptest;
316	+
317		// Add a 2 angstrom safety window to deal with cutoffGroups that
318		// have charged atoms longer than the cutoffRadius away from each
319	<	// other.  Splining may not be the best choice here.  Direct calls
320	<	// to erfc might be preferrable.
319	>	// other.  Splining is almost certainly the best choice here.
320	>	// Direct calls to erfc would be preferrable if it is a very fast
321	>	// implementation.
322
323	<	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
324	<	RealType rval;
325	<	vector<RealType> rvals;
326	<	vector<RealType> yvals;
327	<	for (int i = 0; i < np_; i++) {
328	<	rval = RealType(i) * dx;
329	<	rvals.push_back(rval);
330	<	yvals.push_back(erfc(dampingAlpha_ * rval));
323	>	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_);
324	>
325	>	// Storage vectors for the computed functions
326	>	vector<RealType> rv;
327	>	vector<RealType> v01v;
328	>	vector<RealType> v11v;
329	>	vector<RealType> v21v, v22v;
330	>	vector<RealType> v31v, v32v;
331	>	vector<RealType> v41v, v42v, v43v;
332	>
333	>	for (int i = 1; i < np_ + 1; i++) {
334	>	r = RealType(i) * dx;
335	>	rv.push_back(r);
336	>
337	>	ri = 1.0 / r;
338	>	ri2 = ri * ri;
339	>
340	>	r2 = r * r;
341	>	expTerm = exp(-a2 * r2);
342	>
343	>	// Taylor expansion factors (no need for factorials this way):
344	>	rmRc = r - cutoffRadius_;
345	>	rmRc2 = rmRc  * rmRc / 2.0;
346	>	rmRc3 = rmRc2 * rmRc / 3.0;
347	>	rmRc4 = rmRc3 * rmRc / 4.0;
348	>
349	>	// values of Smith's B_l functions at r:
350	>	if (screeningMethod_ == DAMPED) {
351	>	b0 = erfc(dampingAlpha_ * r) * ri;
352	>	b1 = (      b0 +     2.0*a2     * expTerm * invArootPi) * ri2;
353	>	b2 = (3.0 * b1 + pow(2.0*a2, 2) * expTerm * invArootPi) * ri2;
354	>	b3 = (5.0 * b2 + pow(2.0*a2, 3) * expTerm * invArootPi) * ri2;
355	>	b4 = (7.0 * b3 + pow(2.0*a2, 4) * expTerm * invArootPi) * ri2;
356	>	b5 = (9.0 * b4 + pow(2.0*a2, 5) * expTerm * invArootPi) * ri2;
357	>	} else {
358	>	b0 = ri;
359	>	b1 = (      b0) * ri2;
360	>	b2 = (3.0 * b1) * ri2;
361	>	b3 = (5.0 * b2) * ri2;
362	>	b4 = (7.0 * b3) * ri2;
363	>	b5 = (9.0 * b4) * ri2;
364	>	}
365	>
366	>	// higher derivatives of B_0 at r:
367	>	db0_1 = -r * b1;
368	>	db0_2 =     -b1 + r2 * b2;
369	>	db0_3 =          3.0*r*b2   - r2*r*b3;
370	>	db0_4 =          3.0*b2   - 6.0*r2*b3     + r2*r2*b4;
371	>	db0_5 =                    -15.0*r*b3 + 10.0*r2*r*b4 - r2*r2*r*b5;
372	>
373	>	f = b0;
374	>	fc = b0c;
375	>	f0 = f - fc - rmRc*db0c_1;
376	>
377	>	g = db0_1;
378	>	gc = db0c_1;
379	>	g0 = g - gc;
380	>	g1 = g0 - rmRc *db0c_2;
381	>	g2 = g1 - rmRc2*db0c_3;
382	>	g3 = g2 - rmRc3*db0c_4;
383	>	g4 = g3 - rmRc4*db0c_5;
384	>
385	>	h = db0_2;
386	>	hc = db0c_2;
387	>	h1 = h - hc;
388	>	h2 = h1 - rmRc *db0c_3;
389	>	h3 = h2 - rmRc2*db0c_4;
390	>	h4 = h3 - rmRc3*db0c_5;
391	>
392	>	s = db0_3;
393	>	sc = db0c_3;
394	>	s2 = s - sc;
395	>	s3 = s2 - rmRc *db0c_4;
396	>	s4 = s3 - rmRc2*db0c_5;
397	>
398	>	t = db0_4;
399	>	tc = db0c_4;
400	>	t3 = t - tc;
401	>	t4 = t3 - rmRc *db0c_5;
402	>
403	>	u = db0_5;
404	>	uc = db0c_5;
405	>	u4 = u - uc;
406	>
407	>	// in what follows below, the various v functions are used for
408	>	// potentials and torques, while the w functions show up in the
409	>	// forces.
410	>
411	>	switch (summationMethod_) {
412	>	case esm_SHIFTED_FORCE:
413	>
414	>	v01 = f - fc - rmRc*gc;
415	>	v11 = g - gc - rmRc*hc;
416	>	v21 = g*ri - gc*ric - rmRc*(hc - gc*ric)*ric;
417	>	v22 = h - g*ri - (hc - gc*ric) - rmRc*(sc - (hc - gc*ric)*ric);
418	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric - rmRc*(sc-2.0*(hc-gc*ric)*ric)*ric;
419	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric)
420	>	- rmRc*(tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
421	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2
422	>	- rmRc*(sc - 3.0*(hc-gc*ric)*ric)*ric2;
423	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric
424	>	- rmRc*(tc - (4.0*sc - 9.0*(hc - gc*ric)*ric)*ric)*ric;
425	>
426	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
427	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric)
428	>	- rmRc*(uc-3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
429	>
430	>	dv01 = g - gc;
431	>	dv11 = h - hc;
432	>	dv21 = (h - g*ri)*ri - (hc - gc*ric)*ric;
433	>	dv22 = (s - (h - g*ri)*ri) - (sc - (hc - gc*ric)*ric);
434	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri - (sc - 2.0*(hc-gc*ric)*ric)*ric;
435	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri)
436	>	- (tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
437	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2 - (sc - 3.0*(hc - gc*ric)*ric)*ric2;
438	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri
439	>	- (tc - (4.0*sc - 9.0*(hc-gc*ric)*ric)*ric)*ric;
440	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri)
441	>	- (uc - 3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
442	>
443	>	break;
444	>
445	>	case esm_TAYLOR_SHIFTED:
446	>
447	>	v01 = f0;
448	>	v11 = g1;
449	>	v21 = g2 * ri;
450	>	v22 = h2 - v21;
451	>	v31 = (h3 - g3 * ri) * ri;
452	>	v32 = s3 - 3.0*v31;
453	>	v41 = (h4 - g4 * ri) * ri2;
454	>	v42 = s4 * ri - 3.0*v41;
455	>	v43 = t4 - 6.0*v42 - 3.0*v41;
456	>
457	>	dv01 = g0;
458	>	dv11 = h1;
459	>	dv21 = (h2 - g2*ri)*ri;
460	>	dv22 = (s2 - (h2 - g2*ri)*ri);
461	>	dv31 = (s3 - 2.0*(h3-g3*ri)*ri)*ri;
462	>	dv32 = (t3 - 3.0*(s3-2.0*(h3-g3*ri)*ri)*ri);
463	>	dv41 = (s4 - 3.0*(h4 - g4*ri)*ri)*ri2;
464	>	dv42 = (t4 - (4.0*s4 - 9.0*(h4-g4*ri)*ri)*ri)*ri;
465	>	dv43 = (u4 - 3.0*(2.0*t4 - (7.0*s4 - 15.0*(h4 - g4*ri)*ri)*ri)*ri);
466	>
467	>	break;
468	>
469	>	case esm_SHIFTED_POTENTIAL:
470	>
471	>	v01 = f - fc;
472	>	v11 = g - gc;
473	>	v21 = g*ri - gc*ric;
474	>	v22 = h - g*ri - (hc - gc*ric);
475	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
476	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
477	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
478	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
479	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
480	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
481	>
482	>	dv01 = g;
483	>	dv11 = h;
484	>	dv21 = (h - g*ri)*ri;
485	>	dv22 = (s - (h - g*ri)*ri);
486	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
487	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
488	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
489	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
490	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
491	>
492	>	break;
493	>
494	>	case esm_SWITCHING_FUNCTION:
495	>	case esm_HARD:
496	>	case esm_EWALD_FULL:
497	>
498	>	v01 = f;
499	>	v11 = g;
500	>	v21 = g*ri;
501	>	v22 = h - g*ri;
502	>	v31 = (h-g*ri)*ri;
503	>	v32 = (s - 3.0*(h-g*ri)*ri);
504	>	v41 = (h - g*ri)*ri2;
505	>	v42 = (s-3.0*(h-g*ri)*ri)*ri;
506	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri);
507	>
508	>	dv01 = g;
509	>	dv11 = h;
510	>	dv21 = (h - g*ri)*ri;
511	>	dv22 = (s - (h - g*ri)*ri);
512	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
513	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
514	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
515	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
516	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
517	>
518	>	break;
519	>
520	>	case esm_REACTION_FIELD:
521	>
522	>	// following DL_POLY's lead for shifting the image charge potential:
523	>	f = b0 + preRF_ * r2;
524	>	fc = b0c + preRF_ * cutoffRadius_ * cutoffRadius_;
525	>
526	>	g = db0_1 + preRF_ * 2.0 * r;
527	>	gc = db0c_1 + preRF_ * 2.0 * cutoffRadius_;
528	>
529	>	h = db0_2 + preRF_ * 2.0;
530	>	hc = db0c_2 + preRF_ * 2.0;
531	>
532	>	v01 = f - fc;
533	>	v11 = g - gc;
534	>	v21 = g*ri - gc*ric;
535	>	v22 = h - g*ri - (hc - gc*ric);
536	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
537	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
538	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
539	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
540	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
541	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
542	>
543	>	dv01 = g;
544	>	dv11 = h;
545	>	dv21 = (h - g*ri)*ri;
546	>	dv22 = (s - (h - g*ri)*ri);
547	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
548	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
549	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
550	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
551	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
552	>
553	>	break;
554	>
555	>	case esm_EWALD_PME:
556	>	case esm_EWALD_SPME:
557	>	default :
558	>	map<string, ElectrostaticSummationMethod>::iterator i;
559	>	std::string meth;
560	>	for (i = summationMap_.begin(); i != summationMap_.end(); ++i) {
561	>	if ((*i).second == summationMethod_) meth = (*i).first;
562	>	}
563	>	sprintf( painCave.errMsg,
564	>	"Electrostatic::initialize: electrostaticSummationMethod %s \n"
565	>	"\thas not been implemented yet. Please select one of:\n"
566	>	"\t\"hard\", \"shifted_potential\", or \"shifted_force\"\n",
567	>	meth.c_str() );
568	>	painCave.isFatal = 1;
569	>	simError();
570	>	break;
571	>	}
572	>
573	>	// Add these computed values to the storage vectors for spline creation:
574	>	v01v.push_back(v01);
575	>	v11v.push_back(v11);
576	>	v21v.push_back(v21);
577	>	v22v.push_back(v22);
578	>	v31v.push_back(v31);
579	>	v32v.push_back(v32);
580	>	v41v.push_back(v41);
581	>	v42v.push_back(v42);
582	>	v43v.push_back(v43);
583		}
273	–	erfcSpline_ = new CubicSpline();
274	–	erfcSpline_->addPoints(rvals, yvals);
275	–	haveElectroSpline_ = true;
584
585	+	// construct the spline structures and fill them with the values we've
586	+	// computed:
587	+
588	+	v01s = new CubicSpline();
589	+	v01s->addPoints(rv, v01v);
590	+	v11s = new CubicSpline();
591	+	v11s->addPoints(rv, v11v);
592	+	v21s = new CubicSpline();
593	+	v21s->addPoints(rv, v21v);
594	+	v22s = new CubicSpline();
595	+	v22s->addPoints(rv, v22v);
596	+	v31s = new CubicSpline();
597	+	v31s->addPoints(rv, v31v);
598	+	v32s = new CubicSpline();
599	+	v32s->addPoints(rv, v32v);
600	+	v41s = new CubicSpline();
601	+	v41s->addPoints(rv, v41v);
602	+	v42s = new CubicSpline();
603	+	v42s->addPoints(rv, v42v);
604	+	v43s = new CubicSpline();
605	+	v43s->addPoints(rv, v43v);
606	+
607	+	haveElectroSplines_ = true;
608	+
609		initialized_ = true;
610		}
611
612		void Electrostatic::addType(AtomType* atomType){
613	<
613	>
614		ElectrostaticAtomData electrostaticAtomData;
615		electrostaticAtomData.is_Charge = false;
616		electrostaticAtomData.is_Dipole = false;
285	–	electrostaticAtomData.is_SplitDipole = false;
617		electrostaticAtomData.is_Quadrupole = false;
618		electrostaticAtomData.is_Fluctuating = false;
619
#	Line 297 | Line 628 | namespace OpenMD {
628		if (ma.isMultipole()) {
629		if (ma.isDipole()) {
630		electrostaticAtomData.is_Dipole = true;
631	<	electrostaticAtomData.dipole_moment = ma.getDipoleMoment();
631	>	electrostaticAtomData.dipole = ma.getDipole();
632		}
302	–	if (ma.isSplitDipole()) {
303	–	electrostaticAtomData.is_SplitDipole = true;
304	–	electrostaticAtomData.split_dipole_distance = ma.getSplitDipoleDistance();
305	–	}
633		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.
634		electrostaticAtomData.is_Quadrupole = true;
635	<	electrostaticAtomData.quadrupole_moments = ma.getQuadrupoleMoments();
635	>	electrostaticAtomData.quadrupole = ma.getQuadrupole();
636		}
637		}
638
#	Line 324 | Line 646 | namespace OpenMD {
646		electrostaticAtomData.slaterZeta = fqa.getSlaterZeta();
647		}
648
649	<	pair<map<int,AtomType*>::iterator,bool> ret;
650	<	ret = ElectrostaticList.insert( pair<int,AtomType*>(atomType->getIdent(),
651	<	atomType) );
649	>	int atid = atomType->getIdent();
650	>	int etid = Etypes.size();
651	>	int fqtid = FQtypes.size();
652	>
653	>	pair<set<int>::iterator,bool> ret;
654	>	ret = Etypes.insert( atid );
655		if (ret.second == false) {
656		sprintf( painCave.errMsg,
657		"Electrostatic already had a previous entry with ident %d\n",
658	<	atomType->getIdent() );
658	>	atid);
659		painCave.severity = OPENMD_INFO;
660		painCave.isFatal = 0;
661		simError();
662		}
663
664	<	ElectrostaticMap[atomType] = electrostaticAtomData;
664	>	Etids[ atid ] = etid;
665	>	ElectrostaticMap.push_back(electrostaticAtomData);
666
667	<	// Now, iterate over all known types and add to the mixing map:
668	<
669	<	map<AtomType*, ElectrostaticAtomData>::iterator it;
670	<	for( it = ElectrostaticMap.begin(); it != ElectrostaticMap.end(); ++it) {
671	<	AtomType* atype2 = (*it).first;
672	<	ElectrostaticAtomData eaData2 = (*it).second;
673	<	if (eaData2.is_Fluctuating && electrostaticAtomData.is_Fluctuating) {
674	<
667	>	if (electrostaticAtomData.is_Fluctuating) {
668	>	ret = FQtypes.insert( atid );
669	>	if (ret.second == false) {
670	>	sprintf( painCave.errMsg,
671	>	"Electrostatic already had a previous fluctuating charge entry with ident %d\n",
672	>	atid );
673	>	painCave.severity = OPENMD_INFO;
674	>	painCave.isFatal = 0;
675	>	simError();
676	>	}
677	>	FQtids[atid] = fqtid;
678	>	Jij[fqtid].resize(nFlucq_);
679	>
680	>	// Now, iterate over all known fluctuating and add to the
681	>	// coulomb integral map:
682	>
683	>	std::set<int>::iterator it;
684	>	for( it = FQtypes.begin(); it != FQtypes.end(); ++it) {
685	>	int etid2 = Etids[ (*it) ];
686	>	int fqtid2 = FQtids[ (*it) ];
687	>	ElectrostaticAtomData eaData2 = ElectrostaticMap[ etid2 ];
688		RealType a = electrostaticAtomData.slaterZeta;
689		RealType b = eaData2.slaterZeta;
690		int m = electrostaticAtomData.slaterN;
691		int n = eaData2.slaterN;
692	<
692	>
693		// Create the spline of the coulombic integral for s-type
694		// Slater orbitals.  Add a 2 angstrom safety window to deal
695		// with cutoffGroups that have charged atoms longer than the
696		// cutoffRadius away from each other.
697	<
697	>
698		RealType rval;
699		RealType dr = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
700		vector<RealType> rvals;
701	<	vector<RealType> J1vals;
702	<	vector<RealType> J2vals;
703	<	for (int i = 0; i < np_; i++) {
701	>	vector<RealType> Jvals;
702	>	// don't start at i = 0, as rval = 0 is undefined for the
703	>	// slater overlap integrals.
704	>	for (int i = 1; i < np_+1; i++) {
705		rval = RealType(i) * dr;
706		rvals.push_back(rval);
707	<	J1vals.push_back(electrostaticAtomData.hardness * sSTOCoulInt( a, b, m, n, rval * PhysicalConstants::angstromsToBohr ) );
708	<	// may not be necessary if Slater coulomb integral is symmetric
709	<	J2vals.push_back(eaData2.hardness *  sSTOCoulInt( b, a, n, m, rval * PhysicalConstants::angstromsToBohr ) );
707	>	Jvals.push_back(sSTOCoulInt( a, b, m, n, rval *
708	>	PhysicalConstants::angstromToBohr ) *
709	>	PhysicalConstants::hartreeToKcal );
710		}
371	–
372	–	CubicSpline* J1 = new CubicSpline();
373	–	J1->addPoints(rvals, J1vals);
374	–	CubicSpline* J2 = new CubicSpline();
375	–	J2->addPoints(rvals, J2vals);
711
712	<	pair<AtomType*, AtomType*> key1, key2;
713	<	key1 = make_pair(atomType, atype2);
714	<	key2 = make_pair(atype2, atomType);
715	<
716	<	Jij[key1] = J1;
717	<	Jij[key2] = J2;
718	<	}
384	<	}
385	<
712	>	CubicSpline* J = new CubicSpline();
713	>	J->addPoints(rvals, Jvals);
714	>	Jij[fqtid][fqtid2] = J;
715	>	Jij[fqtid2].resize( nFlucq_ );
716	>	Jij[fqtid2][fqtid] = J;
717	>	}
718	>	}
719		return;
720		}
721
722		void Electrostatic::setCutoffRadius( RealType rCut ) {
723		cutoffRadius_ = rCut;
391	–	rrf_ = cutoffRadius_;
724		haveCutoffRadius_ = true;
725		}
726
395	–	void Electrostatic::setSwitchingRadius( RealType rSwitch ) {
396	–	rt_ = rSwitch;
397	–	}
727		void Electrostatic::setElectrostaticSummationMethod( ElectrostaticSummationMethod esm ) {
728		summationMethod_ = esm;
729		}
#	Line 412 | Line 741 | namespace OpenMD {
741
742		void Electrostatic::calcForce(InteractionData &idat) {
743
744	<	// utility variables.  Should clean these up and use the Vector3d and
745	<	// Mat3x3d to replace as many as we can in future versions:
744	>	if (!initialized_) initialize();
745	>
746	>	data1 = ElectrostaticMap[Etids[idat.atid1]];
747	>	data2 = ElectrostaticMap[Etids[idat.atid2]];
748
749	<	RealType q_i, q_j, mu_i, mu_j, d_i, d_j;
750	<	RealType qxx_i, qyy_i, qzz_i;
751	<	RealType qxx_j, qyy_j, qzz_j;
752	<	RealType cx_i, cy_i, cz_i;
753	<	RealType cx_j, cy_j, cz_j;
754	<	RealType cx2, cy2, cz2;
755	<	RealType ct_i, ct_j, ct_ij, a1;
756	<	RealType riji, ri, ri2, ri3, ri4;
757	<	RealType pref, vterm, epot, dudr;
758	<	RealType vpair(0.0);
759	<	RealType scale, sc2;
760	<	RealType pot_term, preVal, rfVal;
761	<	RealType c2ri, c3ri, c4rij, cti3, ctj3, ctidotj;
762	<	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);
749	>	U = 0.0;  // Potential
750	>	F.zero();  // Force
751	>	Ta.zero(); // Torque on site a
752	>	Tb.zero(); // Torque on site b
753	>	Ea.zero(); // Electric field at site a
754	>	Eb.zero(); // Electric field at site b
755	>	dUdCa = 0.0; // fluctuating charge force at site a
756	>	dUdCb = 0.0; // fluctuating charge force at site a
757	>
758	>	// Indirect interactions mediated by the reaction field.
759	>	indirect_Pot = 0.0;   // Potential
760	>	indirect_F.zero();    // Force
761	>	indirect_Ta.zero();   // Torque on site a
762	>	indirect_Tb.zero();   // Torque on site b
763
764	<	Vector3d Q_i, Q_j;
765	<	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;
764	>	// Excluded potential that is still computed for fluctuating charges
765	>	excluded_Pot= 0.0;
766
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);
767
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	–
458	–	if (!initialized_) initialize();
459	–
460	–	ElectrostaticAtomData data1 = ElectrostaticMap[idat.atypes.first];
461	–	ElectrostaticAtomData data2 = ElectrostaticMap[idat.atypes.second];
462	–
768		// some variables we'll need independent of electrostatic type:
769
770	<	riji = 1.0 /  *(idat.rij) ;
771	<	Vector3d rhat =  *(idat.d)   * riji;
772	<
770	>	ri = 1.0 /  *(idat.rij);
771	>	rhat =  *(idat.d)  * ri;
772	>
773		// logicals
774
775	<	bool i_is_Charge = data1.is_Charge;
776	<	bool i_is_Dipole = data1.is_Dipole;
777	<	bool i_is_SplitDipole = data1.is_SplitDipole;
778	<	bool i_is_Quadrupole = data1.is_Quadrupole;
474	<	bool i_is_Fluctuating = data1.is_Fluctuating;
775	>	a_is_Charge = data1.is_Charge;
776	>	a_is_Dipole = data1.is_Dipole;
777	>	a_is_Quadrupole = data1.is_Quadrupole;
778	>	a_is_Fluctuating = data1.is_Fluctuating;
779
780	<	bool j_is_Charge = data2.is_Charge;
781	<	bool j_is_Dipole = data2.is_Dipole;
782	<	bool j_is_SplitDipole = data2.is_SplitDipole;
783	<	bool j_is_Quadrupole = data2.is_Quadrupole;
784	<	bool j_is_Fluctuating = data2.is_Fluctuating;
780	>	b_is_Charge = data2.is_Charge;
781	>	b_is_Dipole = data2.is_Dipole;
782	>	b_is_Quadrupole = data2.is_Quadrupole;
783	>	b_is_Fluctuating = data2.is_Fluctuating;
784	>
785	>	// Obtain all of the required radial function values from the
786	>	// spline structures:
787
788	<	if (i_is_Charge) {
789	<	q_i = data1.fixedCharge;
788	>	// needed for fields (and forces):
789	>	if (a_is_Charge || b_is_Charge) {
790	>	v01s->getValueAndDerivativeAt( *(idat.rij), v01, dv01);
791	>	}
792	>	if (a_is_Dipole || b_is_Dipole) {
793	>	v11s->getValueAndDerivativeAt( *(idat.rij), v11, dv11);
794	>	v11or = ri * v11;
795	>	}
796	>	if (a_is_Quadrupole || b_is_Quadrupole ||  (a_is_Dipole && b_is_Dipole)) {
797	>	v21s->getValueAndDerivativeAt( *(idat.rij), v21, dv21);
798	>	v22s->getValueAndDerivativeAt( *(idat.rij), v22, dv22);
799	>	v22or = ri * v22;
800	>	}
801
802	<	if (i_is_Fluctuating) {
803	<	q_i += *(idat.flucQ1);
802	>	// needed for potentials (and forces and torques):
803	>	if ((a_is_Dipole && b_is_Quadrupole) ||
804	>	(b_is_Dipole && a_is_Quadrupole)) {
805	>	v31s->getValueAndDerivativeAt( *(idat.rij), v31, dv31);
806	>	v32s->getValueAndDerivativeAt( *(idat.rij), v32, dv32);
807	>	v31or = v31 * ri;
808	>	v32or = v32 * ri;
809	>	}
810	>	if (a_is_Quadrupole && b_is_Quadrupole) {
811	>	v41s->getValueAndDerivativeAt( *(idat.rij), v41, dv41);
812	>	v42s->getValueAndDerivativeAt( *(idat.rij), v42, dv42);
813	>	v43s->getValueAndDerivativeAt( *(idat.rij), v43, dv43);
814	>	v42or = v42 * ri;
815	>	v43or = v43 * ri;
816	>	}
817	>
818	>	// calculate the single-site contributions (fields, etc).
819	>
820	>	if (a_is_Charge) {
821	>	C_a = data1.fixedCharge;
822	>
823	>	if (a_is_Fluctuating) {
824	>	C_a += *(idat.flucQ1);
825		}
826
827		if (idat.excluded) {
828	<	*(idat.skippedCharge2) += q_i;
828	>	*(idat.skippedCharge2) += C_a;
829	>	} else {
830	>	// only do the field if we're not excluded:
831	>	Eb -= C_a *  pre11_ * dv01 * rhat;
832		}
833		}
834	<
835	<	if (i_is_Dipole) {
836	<	mu_i = data1.dipole_moment;
837	<	uz_i = idat.eFrame1->getColumn(2);
838	<
839	<	ct_i = dot(uz_i, rhat);
840	<
500	<	if (i_is_SplitDipole)
501	<	d_i = data1.split_dipole_distance;
502	<
503	<	duduz_i = V3Zero;
834	>
835	>	if (a_is_Dipole) {
836	>	D_a = *(idat.dipole1);
837	>	rdDa = dot(rhat, D_a);
838	>	rxDa = cross(rhat, D_a);
839	>	if (!idat.excluded)
840	>	Eb -=  pre12_ * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
841		}
842
843	<	if (i_is_Quadrupole) {
844	<	Q_i = data1.quadrupole_moments;
845	<	qxx_i = Q_i.x();
846	<	qyy_i = Q_i.y();
847	<	qzz_i = Q_i.z();
848	<
849	<	ux_i = idat.eFrame1->getColumn(0);
850	<	uy_i = idat.eFrame1->getColumn(1);
851	<	uz_i = idat.eFrame1->getColumn(2);
852	<
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;
843	>	if (a_is_Quadrupole) {
844	>	Q_a = *(idat.quadrupole1);
845	>	trQa =  Q_a.trace();
846	>	Qar =   Q_a * rhat;
847	>	rQa = rhat * Q_a;
848	>	rdQar = dot(rhat, Qar);
849	>	rxQar = cross(rhat, Qar);
850	>	if (!idat.excluded)
851	>	Eb -= pre14_ * (trQa * rhat * dv21 + 2.0 * Qar * v22or
852	>	+ rdQar * rhat * (dv22 - 2.0*v22or));
853		}
854	<
855	<	if (j_is_Charge) {
856	<	q_j = data2.fixedCharge;
857	<
858	<	if (j_is_Fluctuating)
859	<	q_j += *(idat.flucQ2);
860	<
854	>
855	>	if (b_is_Charge) {
856	>	C_b = data2.fixedCharge;
857	>
858	>	if (b_is_Fluctuating)
859	>	C_b += *(idat.flucQ2);
860	>
861		if (idat.excluded) {
862	<	*(idat.skippedCharge1) += q_j;
862	>	*(idat.skippedCharge1) += C_b;
863	>	} else {
864	>	// only do the field if we're not excluded:
865	>	Ea += C_b *  pre11_ * dv01 * rhat;
866		}
867		}
535	–
536	–
537	–	if (j_is_Dipole) {
538	–	mu_j = data2.dipole_moment;
539	–	uz_j = idat.eFrame2->getColumn(2);
540	–
541	–	ct_j = dot(uz_j, rhat);
542	–
543	–	if (j_is_SplitDipole)
544	–	d_j = data2.split_dipole_distance;
545	–
546	–	duduz_j = V3Zero;
547	–	}
868
869	<	if (j_is_Quadrupole) {
870	<	Q_j = data2.quadrupole_moments;
871	<	qxx_j = Q_j.x();
872	<	qyy_j = Q_j.y();
873	<	qzz_j = Q_j.z();
874	<
555	<	ux_j = idat.eFrame2->getColumn(0);
556	<	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;
869	>	if (b_is_Dipole) {
870	>	D_b = *(idat.dipole2);
871	>	rdDb = dot(rhat, D_b);
872	>	rxDb = cross(rhat, D_b);
873	>	if (!idat.excluded)
874	>	Ea += pre12_ * ((dv11-v11or) * rdDb * rhat + v11or * D_b);
875		}
876
877	<	if (i_is_Fluctuating && j_is_Fluctuating) {
878	<	J1 = Jij[idat.atypes];
879	<	J2 = Jij[make_pair(idat.atypes.second, idat.atypes.first)];
877	>	if (b_is_Quadrupole) {
878	>	Q_b = *(idat.quadrupole2);
879	>	trQb =  Q_b.trace();
880	>	Qbr =   Q_b * rhat;
881	>	rQb = rhat * Q_b;
882	>	rdQbr = dot(rhat, Qbr);
883	>	rxQbr = cross(rhat, Qbr);
884	>	if (!idat.excluded)
885	>	Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
886	>	+ rdQbr * rhat * (dv22 - 2.0*v22or));
887		}
572	–
573	–	epot = 0.0;
574	–	dVdr = V3Zero;
888
889	<	if (i_is_Charge) {
889	>	if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
890	>	J = Jij[FQtids[idat.atid1]][FQtids[idat.atid2]];
891	>	}
892	>
893	>	if (a_is_Charge) {
894
895	<	if (j_is_Charge) {
896	<	if (screeningMethod_ == DAMPED) {
897	<	// assemble the damping variables
898	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
899	<	//erfcVal = res.first;
900	<	//derfcVal = res.second;
895	>	if (b_is_Charge) {
896	>	pref =  pre11_ * *(idat.electroMult);
897	>	U  += C_a * C_b * pref * v01;
898	>	F  += C_a * C_b * pref * dv01 * rhat;
899	>
900	>	// If this is an excluded pair, there are still indirect
901	>	// interactions via the reaction field we must worry about:
902
903	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
904	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
903	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
904	>	rfContrib = preRF_ * pref * C_a * C_b * *(idat.r2);
905	>	indirect_Pot += rfContrib;
906	>	indirect_F   += rfContrib * 2.0 * ri * rhat;
907	>	}
908	>
909	>	// Fluctuating charge forces are handled via Coulomb integrals
910	>	// for excluded pairs (i.e. those connected via bonds) and
911	>	// with the standard charge-charge interaction otherwise.
912
913	<	c1 = erfcVal * riji;
914	<	c2 = (-derfcVal + c1) * riji;
913	>	if (idat.excluded) {
914	>	if (a_is_Fluctuating || b_is_Fluctuating) {
915	>	coulInt = J->getValueAt( *(idat.rij) );
916	>	if (a_is_Fluctuating)  dUdCa += coulInt * C_b;
917	>	if (b_is_Fluctuating)  dUdCb += coulInt * C_a;
918	>	excluded_Pot += C_a * C_b * coulInt;
919	>	}
920		} else {
921	<	c1 = riji;
922	<	c2 = c1 * riji;
921	>	if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
922	>	if (a_is_Fluctuating) dUdCb += C_a * pref * v01;
923		}
924	+	}
925
926	<	preVal =  *(idat.electroMult) * pre11_;
927	<
928	<	if (summationMethod_ == esm_SHIFTED_POTENTIAL) {
929	<	vterm = preVal * (c1 - c1c_);
930	<	dudr  = - *(idat.sw)  * preVal * c2;
926	>	if (b_is_Dipole) {
927	>	pref =  pre12_ * *(idat.electroMult);
928	>	U  += C_a * pref * v11 * rdDb;
929	>	F  += C_a * pref * ((dv11 - v11or) * rdDb * rhat + v11or * D_b);
930	>	Tb += C_a * pref * v11 * rxDb;
931
932	<	} else if (summationMethod_ == esm_SHIFTED_FORCE)  {
602	<	vterm = preVal * ( c1 - c1c_ + c2c_*( *(idat.rij)  - cutoffRadius_) );
603	<	dudr  =  *(idat.sw)  * preVal * (c2c_ - c2);
932	>	if (a_is_Fluctuating) dUdCa += pref * v11 * rdDb;
933
934	<	} else if (summationMethod_ == esm_REACTION_FIELD) {
935	<	rfVal = preRF_ *  *(idat.rij)  *  *(idat.rij);
934	>	// Even if we excluded this pair from direct interactions, we
935	>	// still have the reaction-field-mediated charge-dipole
936	>	// interaction:
937
938	<	vterm = preVal * ( riji + rfVal );
939	<	dudr  =  *(idat.sw)  * preVal * ( 2.0 * rfVal - riji ) * riji;
940	<
941	<	// if this is an excluded pair, there are still indirect
942	<	// interactions via the reaction field we must worry about:
613	<
614	<	if (idat.excluded) {
615	<	indirect_vpair += preVal * rfVal;
616	<	indirect_Pot += *(idat.sw) * preVal * rfVal;
617	<	indirect_dVdr += *(idat.sw)  * preVal * two * rfVal  * riji * rhat;
618	<	}
619	<
620	<	} else {
621	<
622	<	vterm = preVal * riji * erfcVal;
623	<	dudr  = -  *(idat.sw)  * preVal * c2;
624	<
938	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
939	>	rfContrib = C_a * pref * preRF_ * 2.0 * *(idat.rij);
940	>	indirect_Pot += rfContrib * rdDb;
941	>	indirect_F   += rfContrib * D_b / (*idat.rij);
942	>	indirect_Tb  += C_a * pref * preRF_ * rxDb;
943		}
944	<
627	<	vpair += vterm * q_i * q_j;
628	<	epot +=  *(idat.sw)  * vterm * q_i * q_j;
629	<	dVdr += dudr * rhat * q_i * q_j;
944	>	}
945
946	<	if (i_is_Fluctuating) {
947	<	if (idat.excluded) {
948	<	// vFluc1 is the difference between the direct coulomb integral
949	<	// and the normal 1/r-like  interaction between point charges.
950	<	coulInt = J1->getValueAt( *(idat.rij) );
951	<	vFluc1 = coulInt - (*(idat.sw) * vterm);
637	<	} else {
638	<	vFluc1 = 0.0;
639	<	}
640	<	*(idat.dVdFQ1) += ( *(idat.sw) * vterm + vFluc1 ) * q_j;
641	<	}
946	>	if (b_is_Quadrupole) {
947	>	pref = pre14_ * *(idat.electroMult);
948	>	U  +=  C_a * pref * (v21 * trQb + v22 * rdQbr);
949	>	F  +=  C_a * pref * (trQb * dv21 * rhat + 2.0 * Qbr * v22or);
950	>	F  +=  C_a * pref * rdQbr * rhat * (dv22 - 2.0*v22or);
951	>	Tb +=  C_a * pref * 2.0 * rxQbr * v22;
952
953	<	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	<
953	>	if (a_is_Fluctuating) dUdCa += pref * (v21 * trQb + v22 * rdQbr);
954		}
955	+	}
956
957	<	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;
957	>	if (a_is_Dipole) {
958
959	<	if (summationMethod_ == esm_REACTION_FIELD) {
960	<	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;
959	>	if (b_is_Charge) {
960	>	pref = pre12_ * *(idat.electroMult);
961
962	<	dVdr +=  -preSw * (ri3 * (uz_j - three * ct_j * rhat) - preRF2_*uz_j);
963	<	duduz_j += -preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
962	>	U  -= C_b * pref * v11 * rdDa;
963	>	F  -= C_b * pref * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
964	>	Ta -= C_b * pref * v11 * rxDa;
965
966	<	// Even if we excluded this pair from direct interactions,
675	<	// we still have the reaction-field-mediated charge-dipole
676	<	// interaction:
966	>	if (b_is_Fluctuating) dUdCb -= pref * v11 * rdDa;
967
968	<	if (idat.excluded) {
969	<	indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij);
970	<	indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij);
971	<	indirect_dVdr += preSw * preRF2_ * uz_j;
972	<	indirect_duduz_j += preSw * rhat * preRF2_ *  *(idat.rij);
973	<	}
974	<
975	<	} 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	<
968	>	// Even if we excluded this pair from direct interactions,
969	>	// we still have the reaction-field-mediated charge-dipole
970	>	// interaction:
971	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
972	>	rfContrib = C_b * pref * preRF_ * 2.0 * *(idat.rij);
973	>	indirect_Pot -= rfContrib * rdDa;
974	>	indirect_F   -= rfContrib * D_a / (*idat.rij);
975	>	indirect_Ta  -= C_b * pref * preRF_ * rxDa;
976		}
728	–	if (i_is_Fluctuating) {
729	–	*(idat.dVdFQ1) += ( *(idat.sw) * vterm ) / q_i;
730	–	}
977		}
978
979	<	if (j_is_Quadrupole) {
980	<	// first precalculate some necessary variables
981	<	cx2 = cx_j * cx_j;
982	<	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	<	}
979	>	if (b_is_Dipole) {
980	>	pref = pre22_ * *(idat.electroMult);
981	>	DadDb = dot(D_a, D_b);
982	>	DaxDb = cross(D_a, D_b);
983
984	<	// precompute variables for convenience
985	<	preSw =  *(idat.sw)  * pref;
986	<	c2ri = c2 * riji;
987	<	c3ri = c3 * riji;
988	<	c4rij = c4 *  *(idat.rij) ;
763	<	rhatdot2 = two * rhat * c3;
764	<	rhatc4 = rhat * c4rij;
984	>	U  -= pref * (DadDb * v21 + rdDa * rdDb * v22);
985	>	F  -= pref * (dv21 * DadDb * rhat + v22or * (rdDb * D_a + rdDa * D_b));
986	>	F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
987	>	Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
988	>	Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
989
990	<	// calculate the potential
991	<	pot_term = ( qxx_j * (cx2*c3 - c2ri) +
992	<	qyy_j * (cy2*c3 - c2ri) +
993	<	qzz_j * (cz2*c3 - c2ri) );
994	<	vterm = pref * pot_term;
995	<	vpair += vterm;
996	<	epot +=  *(idat.sw)  * vterm;
997	<
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;
990	>	// Even if we excluded this pair from direct interactions, we
991	>	// still have the reaction-field-mediated dipole-dipole
992	>	// interaction:
993	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
994	>	rfContrib = -pref * preRF_ * 2.0;
995	>	indirect_Pot += rfContrib * DadDb;
996	>	indirect_Ta  += rfContrib * DaxDb;
997	>	indirect_Tb  -= rfContrib * DaxDb;
998		}
999	+	}
1000
1001	+	if (b_is_Quadrupole) {
1002	+	pref = pre24_ * *(idat.electroMult);
1003	+	DadQb = D_a * Q_b;
1004	+	DadQbr = dot(D_a, Qbr);
1005	+	DaxQbr = cross(D_a, Qbr);
1006	+
1007	+	U  -= pref * ((trQb*rdDa + 2.0*DadQbr)*v31 + rdDa*rdQbr*v32);
1008	+	F  -= pref * (trQb*D_a + 2.0*DadQb) * v31or;
1009	+	F  -= pref * (trQb*rdDa + 2.0*DadQbr) * (dv31-v31or) * rhat;
1010	+	F  -= pref * (D_a*rdQbr + 2.0*rdDa*rQb) * v32or;
1011	+	F  -= pref * (rdDa * rdQbr * rhat * (dv32-3.0*v32or));
1012	+	Ta += pref * ((-trQb*rxDa + 2.0 * DaxQbr)*v31 - rxDa*rdQbr*v32);
1013	+	Tb += pref * ((2.0*cross(DadQb, rhat) - 2.0*DaxQbr)*v31
1014	+	- 2.0*rdDa*rxQbr*v32);
1015		}
1016		}
789	–
790	–	if (i_is_Dipole) {
1017
1018	<	if (j_is_Charge) {
1019	<	// variables used by all the methods
1020	<	pref =  *(idat.electroMult) * pre12_ * q_j * mu_i;
1021	<	preSw =  *(idat.sw)  * pref;
1018	>	if (a_is_Quadrupole) {
1019	>	if (b_is_Charge) {
1020	>	pref = pre14_ * *(idat.electroMult);
1021	>	U  += C_b * pref * (v21 * trQa + v22 * rdQar);
1022	>	F  += C_b * pref * (trQa * rhat * dv21 + 2.0 * Qar * v22or);
1023	>	F  += C_b * pref * rdQar * rhat * (dv22 - 2.0*v22or);
1024	>	Ta += C_b * pref * 2.0 * rxQar * v22;
1025
1026	<	if (summationMethod_ == esm_REACTION_FIELD) {
1026	>	if (b_is_Fluctuating) dUdCb += pref * (v21 * trQa + v22 * rdQar);
1027	>	}
1028	>	if (b_is_Dipole) {
1029	>	pref = pre24_ * *(idat.electroMult);
1030	>	DbdQa = D_b * Q_a;
1031	>	DbdQar = dot(D_b, Qar);
1032	>	DbxQar = cross(D_b, Qar);
1033
1034	<	ri2 = riji * riji;
1035	<	ri3 = ri2 * riji;
1034	>	U  += pref * ((trQa*rdDb + 2.0*DbdQar)*v31 + rdDb*rdQar*v32);
1035	>	F  += pref * (trQa*D_b + 2.0*DbdQa) * v31or;
1036	>	F  += pref * (trQa*rdDb + 2.0*DbdQar) * (dv31-v31or) * rhat;
1037	>	F  += pref * (D_b*rdQar + 2.0*rdDb*rQa) * v32or;
1038	>	F  += pref * (rdDb * rdQar * rhat * (dv32-3.0*v32or));
1039	>	Ta += pref * ((-2.0*cross(DbdQa, rhat) + 2.0*DbxQar)*v31
1040	>	+ 2.0*rdDb*rxQar*v32);
1041	>	Tb += pref * ((trQa*rxDb - 2.0 * DbxQar)*v31 + rxDb*rdQar*v32);
1042	>	}
1043	>	if (b_is_Quadrupole) {
1044	>	pref = pre44_ * *(idat.electroMult);  // yes
1045	>	QaQb = Q_a * Q_b;
1046	>	trQaQb = QaQb.trace();
1047	>	rQaQb = rhat * QaQb;
1048	>	QaQbr = QaQb * rhat;
1049	>	QaxQb = cross(Q_a, Q_b);
1050	>	rQaQbr = dot(rQa, Qbr);
1051	>	rQaxQbr = cross(rQa, Qbr);
1052	>
1053	>	U  += pref * (trQa * trQb + 2.0 * trQaQb) * v41;
1054	>	U  += pref * (trQa * rdQbr + trQb * rdQar  + 4.0 * rQaQbr) * v42;
1055	>	U  += pref * (rdQar * rdQbr) * v43;
1056
1057	<	vterm = pref * ct_i * ( ri2 - preRF2_ *  *(idat.rij)  );
1058	<	vpair += vterm;
1059	<	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) );
809	<
810	<	// Even if we excluded this pair from direct interactions,
811	<	// we still have the reaction-field-mediated charge-dipole
812	<	// interaction:
813	<
814	<	if (idat.excluded) {
815	<	indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij);
816	<	indirect_Pot += -preSw * ct_i * preRF2_ * *(idat.rij);
817	<	indirect_dVdr += -preSw * preRF2_ * uz_i;
818	<	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;
1057	>	F  += pref * rhat * (trQa * trQb + 2.0 * trQaQb)*dv41;
1058	>	F  += pref*rhat*(trQa*rdQbr + trQb*rdQar + 4.0*rQaQbr)*(dv42-2.0*v42or);
1059	>	F  += pref * rhat * (rdQar * rdQbr)*(dv43 - 4.0*v43or);
1060
1061	<	// calculate derivatives for the forces and torques
1062	<	dVdr += preSw * (uz_i * c2ri - ct_i * rhat * sc2 * c3);
1063	<	duduz_i += preSw * pot_term * rhat;
862	<	}
1061	>	F  += pref * 2.0 * (trQb*rQa + trQa*rQb) * v42or;
1062	>	F  += pref * 4.0 * (rQaQb + QaQbr) * v42or;
1063	>	F  += pref * 2.0 * (rQa*rdQbr + rdQar*rQb) * v43or;
1064
1065	<	if (j_is_Fluctuating) {
1066	<	*(idat.dVdFQ2) += ( *(idat.sw) * vterm ) / q_j;
1067	<	}
1065	>	Ta += pref * (- 4.0 * QaxQb * v41);
1066	>	Ta += pref * (- 2.0 * trQb * cross(rQa, rhat)
1067	>	+ 4.0 * cross(rhat, QaQbr)
1068	>	- 4.0 * rQaxQbr) * v42;
1069	>	Ta += pref * 2.0 * cross(rhat,Qar) * rdQbr * v43;
1070
868	–	}
1071
1072	<	if (j_is_Dipole) {
1073	<	// variables used by all methods
1074	<	ct_ij = dot(uz_i, uz_j);
1072	>	Tb += pref * (+ 4.0 * QaxQb * v41);
1073	>	Tb += pref * (- 2.0 * trQa * cross(rQb, rhat)
1074	>	- 4.0 * cross(rQaQb, rhat)
1075	>	+ 4.0 * rQaxQbr) * v42;
1076	>	// Possible replacement for line 2 above:
1077	>	//             + 4.0 * cross(rhat, QbQar)
1078
1079	<	pref =  *(idat.electroMult) * pre22_ * mu_i * mu_j;
875	<	preSw =  *(idat.sw)  * pref;
1079	>	Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1080
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	–	}
1081		}
1082		}
1083
1084	<	if (i_is_Quadrupole) {
1085	<	if (j_is_Charge) {
1086	<	// 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	<	}
1084	>	if (idat.doElectricField) {
1085	>	*(idat.eField1) += Ea * *(idat.electroMult);
1086	>	*(idat.eField2) += Eb * *(idat.electroMult);
1087		}
1088
1089	+	if (a_is_Fluctuating) *(idat.dVdFQ1) += dUdCa * *(idat.sw);
1090	+	if (b_is_Fluctuating) *(idat.dVdFQ2) += dUdCb * *(idat.sw);
1091
1092		if (!idat.excluded) {
1028	–	*(idat.vpair) += vpair;
1029	–	(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot;
1030	–	*(idat.f1) += dVdr;
1093
1094	<	if (i_is_Dipole || i_is_Quadrupole)
1095	<	*(idat.t1) -= cross(uz_i, duduz_i);
1096	<	if (i_is_Quadrupole) {
1035	<	*(idat.t1) -= cross(ux_i, dudux_i);
1036	<	*(idat.t1) -= cross(uy_i, duduy_i);
1037	<	}
1094	>	*(idat.vpair) += U;
1095	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += U * *(idat.sw);
1096	>	*(idat.f1) += F * *(idat.sw);
1097
1098	<	if (j_is_Dipole || j_is_Quadrupole)
1099	<	*(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	<	}
1098	>	if (a_is_Dipole || a_is_Quadrupole)
1099	>	*(idat.t1) += Ta * *(idat.sw);
1100
1101	+	if (b_is_Dipole || b_is_Quadrupole)
1102	+	*(idat.t2) += Tb * *(idat.sw);
1103	+
1104		} else {
1105
1106		// only accumulate the forces and torques resulting from the
1107		// indirect reaction field terms.
1108
1109	<	*(idat.vpair) += indirect_vpair;
1110	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot;
1111	<	*(idat.f1) += indirect_dVdr;
1109	>	*(idat.vpair) += indirect_Pot;
1110	>	(*(idat.excludedPot))[ELECTROSTATIC_FAMILY] +=  excluded_Pot;
1111	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += *(idat.sw) * indirect_Pot;
1112	>	*(idat.f1) += *(idat.sw) * indirect_F;
1113
1114	<	if (i_is_Dipole)
1115	<	*(idat.t1) -= cross(uz_i, indirect_duduz_i);
1116	<	if (j_is_Dipole)
1117	<	*(idat.t2) -= cross(uz_j, indirect_duduz_j);
1114	>	if (a_is_Dipole || a_is_Quadrupole)
1115	>	*(idat.t1) += *(idat.sw) * indirect_Ta;
1116	>
1117	>	if (b_is_Dipole || b_is_Quadrupole)
1118	>	*(idat.t2) += *(idat.sw) * indirect_Tb;
1119		}
1060	–
1120		return;
1121	<	}
1121	>	}
1122
1123		void Electrostatic::calcSelfCorrection(SelfData &sdat) {
1124	<	RealType mu1, preVal, self;
1124	>
1125		if (!initialized_) initialize();
1126
1127	<	ElectrostaticAtomData data = ElectrostaticMap[sdat.atype];
1128	<
1127	>	ElectrostaticAtomData data = ElectrostaticMap[Etids[sdat.atid]];
1128	>
1129		// logicals
1130		bool i_is_Charge = data.is_Charge;
1131		bool i_is_Dipole = data.is_Dipole;
1132	+	bool i_is_Quadrupole = data.is_Quadrupole;
1133		bool i_is_Fluctuating = data.is_Fluctuating;
1134	<	RealType chg1 = data.fixedCharge;
1135	<
1134	>	RealType C_a = data.fixedCharge;
1135	>	RealType self(0.0), preVal, DdD, trQ, trQQ;
1136	>
1137	>	if (i_is_Dipole) {
1138	>	DdD = data.dipole.lengthSquare();
1139	>	}
1140	>
1141		if (i_is_Fluctuating) {
1142	<	chg1 += *(sdat.flucQ);
1142	>	C_a += *(sdat.flucQ);
1143		// dVdFQ is really a force, so this is negative the derivative
1144		*(sdat.dVdFQ) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1145	+	(*(sdat.excludedPot))[ELECTROSTATIC_FAMILY] += (*sdat.flucQ) *
1146	+	(*(sdat.flucQ) * data.hardness * 0.5 + data.electronegativity);
1147		}
1148
1149	<	if (summationMethod_ == esm_REACTION_FIELD) {
1150	<	if (i_is_Dipole) {
1151	<	mu1 = data.dipole_moment;
1152	<	preVal = pre22_ * preRF2_ * mu1 * mu1;
1153	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal;
1154	<
1155	<	// The self-correction term adds into the reaction field vector
1156	<	Vector3d uz_i = sdat.eFrame->getColumn(2);
1157	<	Vector3d ei = preVal * uz_i;
1149	>	switch (summationMethod_) {
1150	>	case esm_REACTION_FIELD:
1151	>
1152	>	if (i_is_Charge) {
1153	>	// Self potential [see Wang and Hermans, "Reaction Field
1154	>	// Molecular Dynamics Simulation with Friedman’s Image Charge
1155	>	// Method," J. Phys. Chem. 99, 12001-12007 (1995).]
1156	>	preVal = pre11_ * preRF_ * C_a * C_a;
1157	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal / cutoffRadius_;
1158	>	}
1159
1160	<	// This looks very wrong.  A vector crossed with itself is zero.
1161	<	*(sdat.t) -= cross(uz_i, ei);
1160	>	if (i_is_Dipole) {
1161	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DdD;
1162		}
1163	<	} else if (summationMethod_ == esm_SHIFTED_FORCE || summationMethod_ == esm_SHIFTED_POTENTIAL) {
1164	<	if (i_is_Charge) {
1165	<	if (screeningMethod_ == DAMPED) {
1166	<	self = - 0.5 * (c1c_ + alphaPi_) * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_;
1167	<	} else {
1168	<	self = - 0.5 * rcuti_ * chg1 * (chg1 +  *(sdat.skippedCharge)) * pre11_;
1169	<	}
1170	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1163	>
1164	>	break;
1165	>
1166	>	case esm_SHIFTED_FORCE:
1167	>	case esm_SHIFTED_POTENTIAL:
1168	>	case esm_TAYLOR_SHIFTED:
1169	>	case esm_EWALD_FULL:
1170	>	if (i_is_Charge)
1171	>	self += selfMult1_ * pre11_ * C_a * (C_a + *(sdat.skippedCharge));
1172	>	if (i_is_Dipole)
1173	>	self += selfMult2_ * pre22_ * DdD;
1174	>	if (i_is_Quadrupole) {
1175	>	trQ = data.quadrupole.trace();
1176	>	trQQ = (data.quadrupole * data.quadrupole).trace();
1177	>	self += selfMult4_ * pre44_ * (2.0*trQQ + trQ*trQ);
1178	>	if (i_is_Charge)
1179	>	self -= selfMult2_ * pre14_ * 2.0 * C_a * trQ;
1180		}
1181	+	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1182	+	break;
1183	+	default:
1184	+	break;
1185		}
1186		}
1187	<
1187	>
1188		RealType Electrostatic::getSuggestedCutoffRadius(pair<AtomType*, AtomType*> atypes) {
1189		// This seems to work moderately well as a default.  There's no
1190		// inherent scale for 1/r interactions that we can standardize.
#	Line 1111 | Line 1192 | namespace OpenMD {
1192		// cases.
1193		return 12.0;
1194		}
1195	+
1196	+
1197	+	void Electrostatic::ReciprocalSpaceSum(potVec& pot) {
1198	+
1199	+	RealType kPot = 0.0;
1200	+	RealType kVir = 0.0;
1201	+
1202	+	const RealType mPoleConverter = 0.20819434; // converts from the
1203	+	// internal units of
1204	+	// Debye (for dipoles)
1205	+	// or Debye-angstroms
1206	+	// (for quadrupoles) to
1207	+	// electron angstroms or
1208	+	// electron-angstroms^2
1209	+
1210	+	const RealType eConverter = 332.0637778; // convert the
1211	+	// Charge-Charge
1212	+	// electrostatic
1213	+	// interactions into kcal /
1214	+	// mol assuming distances
1215	+	// are measured in
1216	+	// angstroms.
1217	+
1218	+	Mat3x3d hmat = info_->getSnapshotManager()->getCurrentSnapshot()->getHmat();
1219	+	Vector3d box = hmat.diagonals();
1220	+	RealType boxMax = box.max();
1221	+
1222	+	//int kMax = int(2.0 * M_PI / (pow(dampingAlpha_,2)*cutoffRadius_ * boxMax) );
1223	+	int kMax = 7;
1224	+	int kSqMax = kMax*kMax + 2;
1225	+
1226	+	int kLimit = kMax+1;
1227	+	int kLim2 = 2*kMax+1;
1228	+	int kSqLim = kSqMax;
1229	+
1230	+	vector<RealType> AK(kSqLim+1, 0.0);
1231	+	RealType xcl = 2.0 * M_PI / box.x();
1232	+	RealType ycl = 2.0 * M_PI / box.y();
1233	+	RealType zcl = 2.0 * M_PI / box.z();
1234	+	RealType rcl = 2.0 * M_PI / boxMax;
1235	+	RealType rvol = 2.0 * M_PI /(box.x() * box.y() * box.z());
1236	+
1237	+	if(dampingAlpha_ < 1.0e-12) return;
1238	+
1239	+	RealType ralph = -0.25/pow(dampingAlpha_,2);
1240	+
1241	+	// Calculate and store exponential factors
1242	+
1243	+	vector<vector<Vector3d> > eCos;
1244	+	vector<vector<Vector3d> > eSin;
1245	+
1246	+	int nMax = info_->getNAtoms();
1247	+
1248	+	eCos.resize(kLimit+1);
1249	+	eSin.resize(kLimit+1);
1250	+	for (int j = 0; j < kLimit+1; j++) {
1251	+	eCos[j].resize(nMax);
1252	+	eSin[j].resize(nMax);
1253	+	}
1254	+
1255	+	Vector3d t( 2.0 * M_PI );
1256	+	t.Vdiv(t, box);
1257	+
1258	+
1259	+	SimInfo::MoleculeIterator mi;
1260	+	Molecule::AtomIterator ai;
1261	+	int i;
1262	+	Vector3d r;
1263	+	Vector3d tt;
1264	+	Vector3d w;
1265	+	Vector3d u;
1266	+	Vector3d a;
1267	+	Vector3d b;
1268	+
1269	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1270	+	mol = info_->nextMolecule(mi)) {
1271	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1272	+	atom = mol->nextAtom(ai)) {
1273	+
1274	+	i = atom->getLocalIndex();
1275	+	r = atom->getPos();
1276	+	info_->getSnapshotManager()->getCurrentSnapshot()->wrapVector(r);
1277	+
1278	+	tt.Vmul(t, r);
1279	+
1280	+
1281	+	eCos[1][i] = Vector3d(1.0, 1.0, 1.0);
1282	+	eSin[1][i] = Vector3d(0.0, 0.0, 0.0);
1283	+	eCos[2][i] = Vector3d(cos(tt.x()), cos(tt.y()), cos(tt.z()));
1284	+	eSin[2][i] = Vector3d(sin(tt.x()), sin(tt.y()), sin(tt.z()));
1285	+
1286	+	u = eCos[2][i];
1287	+	w = eSin[2][i];
1288	+
1289	+	for(int l = 3; l <= kLimit; l++) {
1290	+	eCos[l][i].x() = eCos[l-1][i].x()*eCos[2][i].x() - eSin[l-1][i].x()*eSin[2][i].x();
1291	+	eCos[l][i].y() = eCos[l-1][i].y()*eCos[2][i].y() - eSin[l-1][i].y()*eSin[2][i].y();
1292	+	eCos[l][i].z() = eCos[l-1][i].z()*eCos[2][i].z() - eSin[l-1][i].z()*eSin[2][i].z();
1293	+
1294	+	eSin[l][i].x() = eSin[l-1][i].x()*eCos[2][i].x() + eCos[l-1][i].x()*eSin[2][i].x();
1295	+	eSin[l][i].y() = eSin[l-1][i].y()*eCos[2][i].y() + eCos[l-1][i].y()*eSin[2][i].z();
1296	+	eSin[l][i].z() = eSin[l-1][i].z()*eCos[2][i].z() + eCos[l-1][i].z()*eSin[2][i].y();
1297	+
1298	+
1299	+	// a.Vmul(eCos[l-1][i], u);
1300	+	// b.Vmul(eSin[l-1][i], w);
1301	+	// eCos[l][i] = a - b;
1302	+	// a.Vmul(eSin[l-1][i], u);
1303	+	// b.Vmul(eCos[l-1][i], w);
1304	+	// eSin[l][i] = a + b;
1305	+
1306	+	}
1307	+	}
1308	+	}
1309	+
1310	+	// Calculate and store AK coefficients:
1311	+
1312	+	RealType eksq = 1.0;
1313	+	RealType expf = 0.0;
1314	+	if (ralph < 0.0) expf = exp(ralph*rcl*rcl);
1315	+	for (i = 1; i <= kSqLim; i++) {
1316	+	RealType rksq = float(i)*rcl*rcl;
1317	+	eksq = expf*eksq;
1318	+	AK[i] = eConverter * eksq/rksq;
1319	+	}
1320	+
1321	+	/*
1322	+	* Loop over all k vectors k = 2 pi (ll/Lx, mm/Ly, nn/Lz)
1323	+	* the values of ll, mm and nn are selected so that the symmetry of
1324	+	* reciprocal lattice is taken into account i.e. the following
1325	+	* rules apply.
1326	+	*
1327	+	* ll ranges over the values 0 to kMax only.
1328	+	*
1329	+	* mm ranges over 0 to kMax when ll=0 and over
1330	+	*            -kMax to kMax otherwise.
1331	+	* nn ranges over 1 to kMax when ll=mm=0 and over
1332	+	*            -kMax to kMax otherwise.
1333	+	*
1334	+	* Hence the result of the summation must be doubled at the end.
1335	+	*/
1336	+
1337	+	std::vector<RealType> clm(nMax, 0.0);
1338	+	std::vector<RealType> slm(nMax, 0.0);
1339	+	std::vector<RealType> ckr(nMax, 0.0);
1340	+	std::vector<RealType> skr(nMax, 0.0);
1341	+	std::vector<RealType> ckc(nMax, 0.0);
1342	+	std::vector<RealType> cks(nMax, 0.0);
1343	+	std::vector<RealType> dkc(nMax, 0.0);
1344	+	std::vector<RealType> dks(nMax, 0.0);
1345	+	std::vector<RealType> qkc(nMax, 0.0);
1346	+	std::vector<RealType> qks(nMax, 0.0);
1347	+	std::vector<Vector3d> dxk(nMax, V3Zero);
1348	+	std::vector<Vector3d> qxk(nMax, V3Zero);
1349	+
1350	+	int mMin = kLimit;
1351	+	int nMin = kLimit + 1;
1352	+	for (int l = 1; l <= kLimit; l++) {
1353	+	int ll = l - 1;
1354	+	RealType rl = xcl * float(ll);
1355	+	for (int mmm = mMin; mmm <= kLim2; mmm++) {
1356	+	int mm = mmm - kLimit;
1357	+	int m = abs(mm) + 1;
1358	+	RealType rm = ycl * float(mm);
1359	+	// Set temporary products of exponential terms
1360	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1361	+	mol = info_->nextMolecule(mi)) {
1362	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1363	+	atom = mol->nextAtom(ai)) {
1364	+
1365	+	i = atom->getLocalIndex();
1366	+	if(mm < 0) {
1367	+	clm[i] = eCos[l][i].x()*eCos[m][i].y()
1368	+	+ eSin[l][i].x()*eSin[m][i].y();
1369	+	slm[i] = eSin[l][i].x()*eCos[m][i].y()
1370	+	- eSin[m][i].y()*eCos[l][i].x();
1371	+	} else {
1372	+	clm[i] = eCos[l][i].x()*eCos[m][i].y()
1373	+	- eSin[l][i].x()*eSin[m][i].y();
1374	+	slm[i] = eSin[l][i].x()*eCos[m][i].y()
1375	+	+ eSin[m][i].y()*eCos[l][i].x();
1376	+	}
1377	+	}
1378	+	}
1379	+	for (int nnn = nMin; nnn <= kLim2; nnn++) {
1380	+	int nn = nnn - kLimit;
1381	+	int n = abs(nn) + 1;
1382	+	RealType rn = zcl * float(nn);
1383	+	// Test on magnitude of k vector:
1384	+	int kk=ll*ll + mm*mm + nn*nn;
1385	+	if(kk <= kSqLim) {
1386	+	Vector3d kVec = Vector3d(rl, rm, rn);
1387	+	Mat3x3d  k2 = outProduct(kVec, kVec);
1388	+	// Calculate exp(ikr) terms
1389	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1390	+	mol = info_->nextMolecule(mi)) {
1391	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1392	+	atom = mol->nextAtom(ai)) {
1393	+	i = atom->getLocalIndex();
1394	+
1395	+	if (nn < 0) {
1396	+	ckr[i]=clm[i]*eCos[n][i].z()+slm[i]*eSin[n][i].z();
1397	+	skr[i]=slm[i]*eCos[n][i].z()-clm[i]*eSin[n][i].z();
1398	+	} else {
1399	+	ckr[i]=clm[i]*eCos[n][i].z()-slm[i]*eSin[n][i].z();
1400	+	skr[i]=slm[i]*eCos[n][i].z()+clm[i]*eSin[n][i].z();
1401	+	}
1402	+	}
1403	+	}
1404	+
1405	+	// Calculate scalar and vector products for each site:
1406	+
1407	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1408	+	mol = info_->nextMolecule(mi)) {
1409	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1410	+	atom = mol->nextAtom(ai)) {
1411	+	i = atom->getLocalIndex();
1412	+	int atid = atom->getAtomType()->getIdent();
1413	+	ElectrostaticAtomData data = ElectrostaticMap[Etids[atid]];
1414	+
1415	+	if (data.is_Charge) {
1416	+	RealType C = data.fixedCharge;
1417	+	if (atom->isFluctuatingCharge()) C += atom->getFlucQPos();
1418	+	ckc[i] = C * ckr[i];
1419	+	cks[i] = C * skr[i];
1420	+	}
1421	+
1422	+	if (data.is_Dipole) {
1423	+	Vector3d D = atom->getDipole() * mPoleConverter;
1424	+	RealType dk = dot(kVec, D);
1425	+	dxk[i] = cross(kVec, D);
1426	+	dkc[i] = dk * ckr[i];
1427	+	dks[i] = dk * skr[i];
1428	+	}
1429	+	if (data.is_Quadrupole) {
1430	+	Mat3x3d Q = atom->getQuadrupole();
1431	+	Q *= mPoleConverter;
1432	+	RealType qk = -( Q * k2 ).trace();
1433	+	qxk[i] = -2.0 * cross(k2, Q);
1434	+	qkc[i] = qk * ckr[i];
1435	+	qks[i] = qk * skr[i];
1436	+	}
1437	+	}
1438	+	}
1439	+
1440	+	// calculate vector sums
1441	+
1442	+	RealType ckcs = std::accumulate(ckc.begin(),ckc.end(),0.0);
1443	+	RealType ckss = std::accumulate(cks.begin(),cks.end(),0.0);
1444	+	RealType dkcs = std::accumulate(dkc.begin(),dkc.end(),0.0);
1445	+	RealType dkss = std::accumulate(dks.begin(),dks.end(),0.0);
1446	+	RealType qkcs = std::accumulate(qkc.begin(),qkc.end(),0.0);
1447	+	RealType qkss = std::accumulate(qks.begin(),qks.end(),0.0);
1448	+
1449	+
1450	+	#ifdef IS_MPI
1451	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &ckcs, 1, MPI::REALTYPE,
1452	+	MPI::SUM);
1453	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &ckss, 1, MPI::REALTYPE,
1454	+	MPI::SUM);
1455	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &dkcs, 1, MPI::REALTYPE,
1456	+	MPI::SUM);
1457	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &dkss, 1, MPI::REALTYPE,
1458	+	MPI::SUM);
1459	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &qkcs, 1, MPI::REALTYPE,
1460	+	MPI::SUM);
1461	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &qkss, 1, MPI::REALTYPE,
1462	+	MPI::SUM);
1463	+	#endif
1464	+
1465	+	// Accumulate potential energy and virial contribution:
1466	+
1467	+	kPot += 2.0 * rvol * AK[kk]*((ckss+dkcs-qkss)*(ckss+dkcs-qkss)
1468	+	+ (ckcs-dkss-qkcs)*(ckcs-dkss-qkss));
1469	+
1470	+	kVir -= 2.0 * rvol * AK[kk]*(ckcs*ckcs+ckss*ckss
1471	+	+4.0*(ckss*dkcs-ckcs*dkss)
1472	+	+3.0*(dkcs*dkcs+dkss*dkss)
1473	+	-6.0*(ckss*qkss+ckcs*qkcs)
1474	+	+8.0*(dkss*qkcs-dkcs*qkss)
1475	+	+5.0*(qkss*qkss+qkcs*qkcs));
1476	+
1477	+	// Calculate force and torque for each site:
1478	+
1479	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1480	+	mol = info_->nextMolecule(mi)) {
1481	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1482	+	atom = mol->nextAtom(ai)) {
1483	+
1484	+	i = atom->getLocalIndex();
1485	+	int atid = atom->getAtomType()->getIdent();
1486	+	ElectrostaticAtomData data = ElectrostaticMap[Etids[atid]];
1487	+
1488	+	RealType qfrc = AK[kk]*((cks[i]+dkc[i]-qks[i])*(ckcs-dkss-qkcs)
1489	+	- (ckc[i]-dks[i]-qkc[i])*(ckss+dkcs-qkss));
1490	+	RealType qtrq1 = AK[kk]*(skr[i]*(ckcs-dkss-qkcs)
1491	+	-ckr[i]*(ckss+dkcs-qkss));
1492	+	RealType qtrq2 = 2.0*AK[kk]*(ckr[i]*(ckcs-dkss-qkcs)+
1493	+	skr[i]*(ckss+dkcs-qkss));
1494	+
1495	+	atom->addFrc( 4.0 * rvol * qfrc * kVec );
1496	+
1497	+	if (data.is_Dipole) {
1498	+	atom->addTrq( 4.0 * rvol * qtrq1 * dxk[i] );
1499	+	}
1500	+	if (data.is_Quadrupole) {
1501	+	atom->addTrq( 4.0 * rvol * qtrq2 * qxk[i] );
1502	+	}
1503	+	}
1504	+	}
1505	+	}
1506	+	}
1507	+	nMin = 1;
1508	+	}
1509	+	mMin = 1;
1510	+	}
1511	+	cerr << "kPot = " << kPot << "\n";
1512	+	pot[ELECTROSTATIC_FAMILY] += kPot;
1513	+	}
1514		}

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