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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 1907 by gezelter, Fri Jul 19 18:18:27 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 53 | Line 53
53		#include "io/Globals.hpp"
54		#include "nonbonded/SlaterIntegrals.hpp"
55		#include "utils/PhysicalConstants.hpp"
56	+	#include "math/erfc.hpp"
57	+	#include "math/SquareMatrix.hpp"
58
57	–
59		namespace OpenMD {
60
61		Electrostatic::Electrostatic(): name_("Electrostatic"), initialized_(false),
#	Line 62 | Line 63 | namespace OpenMD {
63		haveCutoffRadius_(false),
64		haveDampingAlpha_(false),
65		haveDielectric_(false),
66	<	haveElectroSpline_(false)
66	>	haveElectroSplines_(false)
67		{}
68
69		void Electrostatic::initialize() {
#	Line 74 | Line 75 | namespace OpenMD {
75		summationMap_["SWITCHING_FUNCTION"] = esm_SWITCHING_FUNCTION;
76		summationMap_["SHIFTED_POTENTIAL"]  = esm_SHIFTED_POTENTIAL;
77		summationMap_["SHIFTED_FORCE"]      = esm_SHIFTED_FORCE;
78	+	summationMap_["TAYLOR_SHIFTED"]     = esm_TAYLOR_SHIFTED;
79		summationMap_["REACTION_FIELD"]     = esm_REACTION_FIELD;
80		summationMap_["EWALD_FULL"]         = esm_EWALD_FULL;
81		summationMap_["EWALD_PME"]          = esm_EWALD_PME;
#	Line 88 | Line 90 | namespace OpenMD {
90		// Charge-Dipole, assuming charges are measured in electrons, and
91		// dipoles are measured in debyes
92		pre12_ = 69.13373;
93	<	// Dipole-Dipole, assuming dipoles are measured in debyes
93	>	// Dipole-Dipole, assuming dipoles are measured in Debye
94		pre22_ = 14.39325;
95		// Charge-Quadrupole, assuming charges are measured in electrons, and
96		// quadrupoles are measured in 10^-26 esu cm^2
97	<	// This unit is also known affectionately as an esu centi-barn.
97	>	// This unit is also known affectionately as an esu centibarn.
98		pre14_ = 69.13373;
99	<
99	>	// Dipole-Quadrupole, assuming dipoles are measured in debyes and
100	>	// quadrupoles in esu centibarns:
101	>	pre24_ = 14.39325;
102	>	// Quadrupole-Quadrupole, assuming esu centibarns:
103	>	pre44_ = 14.39325;
104	>
105		// conversions for the simulation box dipole moment
106		chargeToC_ = 1.60217733e-19;
107		angstromToM_ = 1.0e-10;
108		debyeToCm_ = 3.33564095198e-30;
109
110	<	// number of points for electrostatic splines
110	>	// Default number of points for electrostatic splines
111		np_ = 100;
112
113		// variables to handle different summation methods for long-range
#	Line 108 | Line 115 | namespace OpenMD {
115		summationMethod_ = esm_HARD;
116		screeningMethod_ = UNDAMPED;
117		dielectric_ = 1.0;
111	–	one_third_ = 1.0 / 3.0;
118
119		// check the summation method:
120		if (simParams_->haveElectrostaticSummationMethod()) {
#	Line 124 | Line 130 | namespace OpenMD {
130		"Electrostatic::initialize: Unknown electrostaticSummationMethod.\n"
131		"\t(Input file specified %s .)\n"
132		"\telectrostaticSummationMethod must be one of: \"hard\",\n"
133	<	"\t\"shifted_potential\", \"shifted_force\", or \n"
134	<	"\t\"reaction_field\".\n", myMethod.c_str() );
133	>	"\t\"shifted_potential\", \"shifted_force\",\n"
134	>	"\t\"taylor_shifted\", or \"reaction_field\".\n",
135	>	myMethod.c_str() );
136		painCave.isFatal = 1;
137		simError();
138		}
#	Line 206 | Line 213 | namespace OpenMD {
213		haveDampingAlpha_ = true;
214		}
215
216	<	// find all of the Electrostatic atom Types:
217	<	ForceField::AtomTypeContainer* atomTypes = forceField_->getAtomTypes();
218	<	ForceField::AtomTypeContainer::MapTypeIterator i;
219	<	AtomType* at;
216	>	Etypes.clear();
217	>	Etids.clear();
218	>	FQtypes.clear();
219	>	FQtids.clear();
220	>	ElectrostaticMap.clear();
221	>	Jij.clear();
222	>	nElectro_ = 0;
223	>	nFlucq_ = 0;
224	>
225	>	Etids.resize( forceField_->getNAtomType(), -1);
226	>	FQtids.resize( forceField_->getNAtomType(), -1);
227	>
228	>	set<AtomType*>::iterator at;
229	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
230	>	if ((*at)->isElectrostatic()) nElectro_++;
231	>	if ((*at)->isFluctuatingCharge()) nFlucq_++;
232	>	}
233
234	<	for (at = atomTypes->beginType(i); at != NULL;
235	<	at = atomTypes->nextType(i)) {
236	<
237	<	if (at->isElectrostatic())
238	<	addType(at);
219	<	}
234	>	Jij.resize(nFlucq_);
235	>
236	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
237	>	if ((*at)->isElectrostatic()) addType(*at);
238	>	}
239
221	–	cutoffRadius2_ = cutoffRadius_ * cutoffRadius_;
222	–	rcuti_ = 1.0 / cutoffRadius_;
223	–	rcuti2_ = rcuti_ * rcuti_;
224	–	rcuti3_ = rcuti2_ * rcuti_;
225	–	rcuti4_ = rcuti2_ * rcuti2_;
226	–
227	–	if (screeningMethod_ == DAMPED) {
228	–
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_;
237	–
238	–	c1c_ = erfc(dampingAlpha_ * cutoffRadius_) * rcuti_;
239	–	c2c_ = alphaPi_ * constEXP_ * rcuti_ + c1c_ * rcuti_;
240	–	c3c_ = 2.0 * alphaPi_ * alpha2_ + 3.0 * c2c_ * rcuti_;
241	–	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_;
251	–	}
252	–
240		if (summationMethod_ == esm_REACTION_FIELD) {
241		preRF_ = (dielectric_ - 1.0) /
242	<	((2.0 * dielectric_ + 1.0) * cutoffRadius2_ * cutoffRadius_);
243	<	preRF2_ = 2.0 * preRF_;
242	>	((2.0 * dielectric_ + 1.0) * pow(cutoffRadius_,3) );
243	>	}
244	>
245	>	RealType b0c, b1c, b2c, b3c, b4c, b5c;
246	>	RealType db0c_1, db0c_2, db0c_3, db0c_4, db0c_5;
247	>	RealType a2, expTerm, invArootPi;
248	>
249	>	RealType r = cutoffRadius_;
250	>	RealType r2 = r * r;
251	>	RealType ric = 1.0 / r;
252	>	RealType ric2 = ric * ric;
253	>
254	>	if (screeningMethod_ == DAMPED) {
255	>	a2 = dampingAlpha_ * dampingAlpha_;
256	>	invArootPi = 1.0 / (dampingAlpha_ * sqrt(M_PI));
257	>	expTerm = exp(-a2 * r2);
258	>	// values of Smith's B_l functions at the cutoff radius:
259	>	b0c = erfc(dampingAlpha_ * r) / r;
260	>	b1c = (      b0c     + 2.0*a2     * expTerm * invArootPi) / r2;
261	>	b2c = (3.0 * b1c + pow(2.0*a2, 2) * expTerm * invArootPi) / r2;
262	>	b3c = (5.0 * b2c + pow(2.0*a2, 3) * expTerm * invArootPi) / r2;
263	>	b4c = (7.0 * b3c + pow(2.0*a2, 4) * expTerm * invArootPi) / r2;
264	>	b5c = (9.0 * b4c + pow(2.0*a2, 5) * expTerm * invArootPi) / r2;
265	>	//selfMult1_ = - 2.0 * a2 * invArootPi;
266	>	//selfMult2_ = - 4.0 * a2 * a2 * invArootPi / 3.0;
267	>	//selfMult4_ = - 8.0 * a2 * a2 * a2 * invArootPi / 5.0;
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	+	selfMult1_ -= b0c;
293	+	selfMult2_ += (db0c_2 + 2.0*db0c_1*ric) /  3.0;
294	+	selfMult4_ -= (db0c_4 + 4.0*db0c_3*ric) / 15.0;
295	+
296	+	// working variables for the splines:
297	+	RealType ri, ri2;
298	+	RealType b0, b1, b2, b3, b4, b5;
299	+	RealType db0_1, db0_2, db0_3, db0_4, db0_5;
300	+	RealType f, fc, f0;
301	+	RealType g, gc, g0, g1, g2, g3, g4;
302	+	RealType h, hc, h1, h2, h3, h4;
303	+	RealType s, sc, s2, s3, s4;
304	+	RealType t, tc, t3, t4;
305	+	RealType u, uc, u4;
306	+
307	+	// working variables for Taylor expansion:
308	+	RealType rmRc, rmRc2, rmRc3, rmRc4;
309	+
310	+	// Approximate using splines using a maximum of 0.1 Angstroms
311	+	// between points.
312	+	int nptest = int((cutoffRadius_ + 2.0) / 0.1);
313	+	np_ = (np_ > nptest) ? np_ : nptest;
314	+
315		// Add a 2 angstrom safety window to deal with cutoffGroups that
316		// have charged atoms longer than the cutoffRadius away from each
317	<	// other.  Splining may not be the best choice here.  Direct calls
318	<	// to erfc might be preferrable.
317	>	// other.  Splining is almost certainly the best choice here.
318	>	// Direct calls to erfc would be preferrable if it is a very fast
319	>	// implementation.
320
321	<	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
322	<	RealType rval;
323	<	vector<RealType> rvals;
324	<	vector<RealType> yvals;
325	<	for (int i = 0; i < np_; i++) {
326	<	rval = RealType(i) * dx;
327	<	rvals.push_back(rval);
328	<	yvals.push_back(erfc(dampingAlpha_ * rval));
321	>	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_);
322	>
323	>	// Storage vectors for the computed functions
324	>	vector<RealType> rv;
325	>	vector<RealType> v01v;
326	>	vector<RealType> v11v;
327	>	vector<RealType> v21v, v22v;
328	>	vector<RealType> v31v, v32v;
329	>	vector<RealType> v41v, v42v, v43v;
330	>
331	>	/*
332	>	vector<RealType> dv01v;
333	>	vector<RealType> dv11v;
334	>	vector<RealType> dv21v, dv22v;
335	>	vector<RealType> dv31v, dv32v;
336	>	vector<RealType> dv41v, dv42v, dv43v;
337	>	*/
338	>
339	>	for (int i = 1; i < np_ + 1; i++) {
340	>	r = RealType(i) * dx;
341	>	rv.push_back(r);
342	>
343	>	ri = 1.0 / r;
344	>	ri2 = ri * ri;
345	>
346	>	r2 = r * r;
347	>	expTerm = exp(-a2 * r2);
348	>
349	>	// Taylor expansion factors (no need for factorials this way):
350	>	rmRc = r - cutoffRadius_;
351	>	rmRc2 = rmRc  * rmRc / 2.0;
352	>	rmRc3 = rmRc2 * rmRc / 3.0;
353	>	rmRc4 = rmRc3 * rmRc / 4.0;
354	>
355	>	// values of Smith's B_l functions at r:
356	>	if (screeningMethod_ == DAMPED) {
357	>	b0 = erfc(dampingAlpha_ * r) * ri;
358	>	b1 = (      b0 +     2.0*a2     * expTerm * invArootPi) * ri2;
359	>	b2 = (3.0 * b1 + pow(2.0*a2, 2) * expTerm * invArootPi) * ri2;
360	>	b3 = (5.0 * b2 + pow(2.0*a2, 3) * expTerm * invArootPi) * ri2;
361	>	b4 = (7.0 * b3 + pow(2.0*a2, 4) * expTerm * invArootPi) * ri2;
362	>	b5 = (9.0 * b4 + pow(2.0*a2, 5) * expTerm * invArootPi) * ri2;
363	>	} else {
364	>	b0 = ri;
365	>	b1 = (      b0) * ri2;
366	>	b2 = (3.0 * b1) * ri2;
367	>	b3 = (5.0 * b2) * ri2;
368	>	b4 = (7.0 * b3) * ri2;
369	>	b5 = (9.0 * b4) * ri2;
370	>	}
371	>
372	>	// higher derivatives of B_0 at r:
373	>	db0_1 = -r * b1;
374	>	db0_2 =     -b1 + r2 * b2;
375	>	db0_3 =          3.0*r*b2   - r2*r*b3;
376	>	db0_4 =          3.0*b2   - 6.0*r2*b3     + r2*r2*b4;
377	>	db0_5 =                    -15.0*r*b3 + 10.0*r2*r*b4 - r2*r2*r*b5;
378	>
379	>	f = b0;
380	>	fc = b0c;
381	>	f0 = f - fc - rmRc*db0c_1;
382	>
383	>	g = db0_1;
384	>	gc = db0c_1;
385	>	g0 = g - gc;
386	>	g1 = g0 - rmRc *db0c_2;
387	>	g2 = g1 - rmRc2*db0c_3;
388	>	g3 = g2 - rmRc3*db0c_4;
389	>	g4 = g3 - rmRc4*db0c_5;
390	>
391	>	h = db0_2;
392	>	hc = db0c_2;
393	>	h1 = h - hc;
394	>	h2 = h1 - rmRc *db0c_3;
395	>	h3 = h2 - rmRc2*db0c_4;
396	>	h4 = h3 - rmRc3*db0c_5;
397	>
398	>	s = db0_3;
399	>	sc = db0c_3;
400	>	s2 = s - sc;
401	>	s3 = s2 - rmRc *db0c_4;
402	>	s4 = s3 - rmRc2*db0c_5;
403	>
404	>	t = db0_4;
405	>	tc = db0c_4;
406	>	t3 = t - tc;
407	>	t4 = t3 - rmRc *db0c_5;
408	>
409	>	u = db0_5;
410	>	uc = db0c_5;
411	>	u4 = u - uc;
412	>
413	>	// in what follows below, the various v functions are used for
414	>	// potentials and torques, while the w functions show up in the
415	>	// forces.
416	>
417	>	switch (summationMethod_) {
418	>	case esm_SHIFTED_FORCE:
419	>
420	>	v01 = f - fc - rmRc*gc;
421	>	v11 = g - gc - rmRc*hc;
422	>	v21 = g*ri - gc*ric - rmRc*(hc - gc*ric)*ric;
423	>	v22 = h - g*ri - (hc - gc*ric) - rmRc*(sc - (hc - gc*ric)*ric);
424	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric - rmRc*(sc-2.0*(hc-gc*ric)*ric)*ric;
425	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric)
426	>	- rmRc*(tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
427	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2
428	>	- rmRc*(sc - 3.0*(hc-gc*ric)*ric)*ric2;
429	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric
430	>	- rmRc*(tc - (4.0*sc - 9.0*(hc - gc*ric)*ric)*ric)*ric;
431	>
432	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
433	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric)
434	>	- rmRc*(uc-3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
435	>
436	>	dv01 = g - gc;
437	>	dv11 = h - hc;
438	>	dv21 = (h - g*ri)*ri - (hc - gc*ric)*ric;
439	>	dv22 = (s - (h - g*ri)*ri) - (sc - (hc - gc*ric)*ric);
440	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri - (sc - 2.0*(hc-gc*ric)*ric)*ric;
441	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri)
442	>	- (tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
443	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2 - (sc - 3.0*(hc - gc*ric)*ric)*ric2;
444	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri
445	>	- (tc - (4.0*sc - 9.0*(hc-gc*ric)*ric)*ric)*ric;
446	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri)
447	>	- (uc - 3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
448	>
449	>	break;
450	>
451	>	case esm_TAYLOR_SHIFTED:
452	>
453	>	v01 = f0;
454	>	v11 = g1;
455	>	v21 = g2 * ri;
456	>	v22 = h2 - v21;
457	>	v31 = (h3 - g3 * ri) * ri;
458	>	v32 = s3 - 3.0*v31;
459	>	v41 = (h4 - g4 * ri) * ri2;
460	>	v42 = s4 * ri - 3.0*v41;
461	>	v43 = t4 - 6.0*v42 - 3.0*v41;
462	>
463	>	dv01 = g0;
464	>	dv11 = h1;
465	>	dv21 = (h2 - g2*ri)*ri;
466	>	dv22 = (s2 - (h2 - g2*ri)*ri);
467	>	dv31 = (s3 - 2.0*(h3-g3*ri)*ri)*ri;
468	>	dv32 = (t3 - 3.0*(s3-2.0*(h3-g3*ri)*ri)*ri);
469	>	dv41 = (s4 - 3.0*(h4 - g4*ri)*ri)*ri2;
470	>	dv42 = (t4 - (4.0*s4 - 9.0*(h4-g4*ri)*ri)*ri)*ri;
471	>	dv43 = (u4 - 3.0*(2.0*t4 - (7.0*s4 - 15.0*(h4 - g4*ri)*ri)*ri)*ri);
472	>
473	>	break;
474	>
475	>	case esm_SHIFTED_POTENTIAL:
476	>
477	>	v01 = f - fc;
478	>	v11 = g - gc;
479	>	v21 = g*ri - gc*ric;
480	>	v22 = h - g*ri - (hc - gc*ric);
481	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
482	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
483	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
484	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
485	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
486	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
487	>
488	>	dv01 = g;
489	>	dv11 = h;
490	>	dv21 = (h - g*ri)*ri;
491	>	dv22 = (s - (h - g*ri)*ri);
492	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
493	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
494	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
495	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
496	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
497	>
498	>	break;
499	>
500	>	case esm_SWITCHING_FUNCTION:
501	>	case esm_HARD:
502	>
503	>	v01 = f;
504	>	v11 = g;
505	>	v21 = g*ri;
506	>	v22 = h - g*ri;
507	>	v31 = (h-g*ri)*ri;
508	>	v32 = (s - 3.0*(h-g*ri)*ri);
509	>	v41 = (h - g*ri)*ri2;
510	>	v42 = (s-3.0*(h-g*ri)*ri)*ri;
511	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri);
512	>
513	>	dv01 = g;
514	>	dv11 = h;
515	>	dv21 = (h - g*ri)*ri;
516	>	dv22 = (s - (h - g*ri)*ri);
517	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
518	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
519	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
520	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
521	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
522	>
523	>	break;
524	>
525	>	case esm_REACTION_FIELD:
526	>
527	>	// following DL_POLY's lead for shifting the image charge potential:
528	>	f = b0 + preRF_ * r2;
529	>	fc = b0c + preRF_ * cutoffRadius_ * cutoffRadius_;
530	>
531	>	g = db0_1 + preRF_ * 2.0 * r;
532	>	gc = db0c_1 + preRF_ * 2.0 * cutoffRadius_;
533	>
534	>	h = db0_2 + preRF_ * 2.0;
535	>	hc = db0c_2 + preRF_ * 2.0;
536	>
537	>	v01 = f - fc;
538	>	v11 = g - gc;
539	>	v21 = g*ri - gc*ric;
540	>	v22 = h - g*ri - (hc - gc*ric);
541	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
542	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
543	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
544	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
545	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
546	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
547	>
548	>	dv01 = g;
549	>	dv11 = h;
550	>	dv21 = (h - g*ri)*ri;
551	>	dv22 = (s - (h - g*ri)*ri);
552	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
553	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
554	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
555	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
556	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
557	>
558	>	break;
559	>
560	>	case esm_EWALD_FULL:
561	>	case esm_EWALD_PME:
562	>	case esm_EWALD_SPME:
563	>	default :
564	>	map<string, ElectrostaticSummationMethod>::iterator i;
565	>	std::string meth;
566	>	for (i = summationMap_.begin(); i != summationMap_.end(); ++i) {
567	>	if ((*i).second == summationMethod_) meth = (*i).first;
568	>	}
569	>	sprintf( painCave.errMsg,
570	>	"Electrostatic::initialize: electrostaticSummationMethod %s \n"
571	>	"\thas not been implemented yet. Please select one of:\n"
572	>	"\t\"hard\", \"shifted_potential\", or \"shifted_force\"\n",
573	>	meth.c_str() );
574	>	painCave.isFatal = 1;
575	>	simError();
576	>	break;
577	>	}
578	>
579	>	// Add these computed values to the storage vectors for spline creation:
580	>	v01v.push_back(v01);
581	>	v11v.push_back(v11);
582	>	v21v.push_back(v21);
583	>	v22v.push_back(v22);
584	>	v31v.push_back(v31);
585	>	v32v.push_back(v32);
586	>	v41v.push_back(v41);
587	>	v42v.push_back(v42);
588	>	v43v.push_back(v43);
589	>	/*
590	>	dv01v.push_back(dv01);
591	>	dv11v.push_back(dv11);
592	>	dv21v.push_back(dv21);
593	>	dv22v.push_back(dv22);
594	>	dv31v.push_back(dv31);
595	>	dv32v.push_back(dv32);
596	>	dv41v.push_back(dv41);
597	>	dv42v.push_back(dv42);
598	>	dv43v.push_back(dv43);
599	>	*/
600		}
273	–	erfcSpline_ = new CubicSpline();
274	–	erfcSpline_->addPoints(rvals, yvals);
275	–	haveElectroSpline_ = true;
601
602	+	// construct the spline structures and fill them with the values we've
603	+	// computed:
604	+
605	+	v01s = new CubicSpline();
606	+	v01s->addPoints(rv, v01v);
607	+	v11s = new CubicSpline();
608	+	v11s->addPoints(rv, v11v);
609	+	v21s = new CubicSpline();
610	+	v21s->addPoints(rv, v21v);
611	+	v22s = new CubicSpline();
612	+	v22s->addPoints(rv, v22v);
613	+	v31s = new CubicSpline();
614	+	v31s->addPoints(rv, v31v);
615	+	v32s = new CubicSpline();
616	+	v32s->addPoints(rv, v32v);
617	+	v41s = new CubicSpline();
618	+	v41s->addPoints(rv, v41v);
619	+	v42s = new CubicSpline();
620	+	v42s->addPoints(rv, v42v);
621	+	v43s = new CubicSpline();
622	+	v43s->addPoints(rv, v43v);
623	+
624	+	/*
625	+	dv01s = new CubicSpline();
626	+	dv01s->addPoints(rv, dv01v);
627	+	dv11s = new CubicSpline();
628	+	dv11s->addPoints(rv, dv11v);
629	+	dv21s = new CubicSpline();
630	+	dv21s->addPoints(rv, dv21v);
631	+	dv22s = new CubicSpline();
632	+	dv22s->addPoints(rv, dv22v);
633	+	dv31s = new CubicSpline();
634	+	dv31s->addPoints(rv, dv31v);
635	+	dv32s = new CubicSpline();
636	+	dv32s->addPoints(rv, dv32v);
637	+	dv41s = new CubicSpline();
638	+	dv41s->addPoints(rv, dv41v);
639	+	dv42s = new CubicSpline();
640	+	dv42s->addPoints(rv, dv42v);
641	+	dv43s = new CubicSpline();
642	+	dv43s->addPoints(rv, dv43v);
643	+	*/
644	+
645	+	haveElectroSplines_ = true;
646	+
647		initialized_ = true;
648		}
649
650		void Electrostatic::addType(AtomType* atomType){
651	<
651	>
652		ElectrostaticAtomData electrostaticAtomData;
653		electrostaticAtomData.is_Charge = false;
654		electrostaticAtomData.is_Dipole = false;
285	–	electrostaticAtomData.is_SplitDipole = false;
655		electrostaticAtomData.is_Quadrupole = false;
656		electrostaticAtomData.is_Fluctuating = false;
657
#	Line 297 | Line 666 | namespace OpenMD {
666		if (ma.isMultipole()) {
667		if (ma.isDipole()) {
668		electrostaticAtomData.is_Dipole = true;
669	<	electrostaticAtomData.dipole_moment = ma.getDipoleMoment();
669	>	electrostaticAtomData.dipole = ma.getDipole();
670		}
302	–	if (ma.isSplitDipole()) {
303	–	electrostaticAtomData.is_SplitDipole = true;
304	–	electrostaticAtomData.split_dipole_distance = ma.getSplitDipoleDistance();
305	–	}
671		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.
672		electrostaticAtomData.is_Quadrupole = true;
673	<	electrostaticAtomData.quadrupole_moments = ma.getQuadrupoleMoments();
673	>	electrostaticAtomData.quadrupole = ma.getQuadrupole();
674		}
675		}
676
#	Line 324 | Line 684 | namespace OpenMD {
684		electrostaticAtomData.slaterZeta = fqa.getSlaterZeta();
685		}
686
687	<	pair<map<int,AtomType*>::iterator,bool> ret;
688	<	ret = ElectrostaticList.insert( pair<int,AtomType*>(atomType->getIdent(),
689	<	atomType) );
687	>	int atid = atomType->getIdent();
688	>	int etid = Etypes.size();
689	>	int fqtid = FQtypes.size();
690	>
691	>	pair<set<int>::iterator,bool> ret;
692	>	ret = Etypes.insert( atid );
693		if (ret.second == false) {
694		sprintf( painCave.errMsg,
695		"Electrostatic already had a previous entry with ident %d\n",
696	<	atomType->getIdent() );
696	>	atid);
697		painCave.severity = OPENMD_INFO;
698		painCave.isFatal = 0;
699		simError();
700		}
701
702	<	ElectrostaticMap[atomType] = electrostaticAtomData;
702	>	Etids[ atid ] = etid;
703	>	ElectrostaticMap.push_back(electrostaticAtomData);
704
705	<	// Now, iterate over all known types and add to the mixing map:
706	<
707	<	map<AtomType*, ElectrostaticAtomData>::iterator it;
708	<	for( it = ElectrostaticMap.begin(); it != ElectrostaticMap.end(); ++it) {
709	<	AtomType* atype2 = (*it).first;
710	<	ElectrostaticAtomData eaData2 = (*it).second;
711	<	if (eaData2.is_Fluctuating && electrostaticAtomData.is_Fluctuating) {
712	<
705	>	if (electrostaticAtomData.is_Fluctuating) {
706	>	ret = FQtypes.insert( atid );
707	>	if (ret.second == false) {
708	>	sprintf( painCave.errMsg,
709	>	"Electrostatic already had a previous fluctuating charge entry with ident %d\n",
710	>	atid );
711	>	painCave.severity = OPENMD_INFO;
712	>	painCave.isFatal = 0;
713	>	simError();
714	>	}
715	>	FQtids[atid] = fqtid;
716	>	Jij[fqtid].resize(nFlucq_);
717	>
718	>	// Now, iterate over all known fluctuating and add to the coulomb integral map:
719	>
720	>	std::set<int>::iterator it;
721	>	for( it = FQtypes.begin(); it != FQtypes.end(); ++it) {
722	>	int etid2 = Etids[ (*it) ];
723	>	int fqtid2 = FQtids[ (*it) ];
724	>	ElectrostaticAtomData eaData2 = ElectrostaticMap[ etid2 ];
725		RealType a = electrostaticAtomData.slaterZeta;
726		RealType b = eaData2.slaterZeta;
727		int m = electrostaticAtomData.slaterN;
728		int n = eaData2.slaterN;
729	<
729	>
730		// Create the spline of the coulombic integral for s-type
731		// Slater orbitals.  Add a 2 angstrom safety window to deal
732		// with cutoffGroups that have charged atoms longer than the
733		// cutoffRadius away from each other.
734	<
734	>
735		RealType rval;
736		RealType dr = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
737		vector<RealType> rvals;
738	<	vector<RealType> J1vals;
739	<	vector<RealType> J2vals;
740	<	for (int i = 0; i < np_; i++) {
738	>	vector<RealType> Jvals;
739	>	// don't start at i = 0, as rval = 0 is undefined for the
740	>	// slater overlap integrals.
741	>	for (int i = 1; i < np_+1; i++) {
742		rval = RealType(i) * dr;
743		rvals.push_back(rval);
744	<	J1vals.push_back(electrostaticAtomData.hardness * sSTOCoulInt( a, b, m, n, rval * PhysicalConstants::angstromsToBohr ) );
745	<	// may not be necessary if Slater coulomb integral is symmetric
746	<	J2vals.push_back(eaData2.hardness *  sSTOCoulInt( b, a, n, m, rval * PhysicalConstants::angstromsToBohr ) );
744	>	Jvals.push_back(sSTOCoulInt( a, b, m, n, rval *
745	>	PhysicalConstants::angstromToBohr ) *
746	>	PhysicalConstants::hartreeToKcal );
747		}
371	–
372	–	CubicSpline* J1 = new CubicSpline();
373	–	J1->addPoints(rvals, J1vals);
374	–	CubicSpline* J2 = new CubicSpline();
375	–	J2->addPoints(rvals, J2vals);
748
749	<	pair<AtomType*, AtomType*> key1, key2;
750	<	key1 = make_pair(atomType, atype2);
751	<	key2 = make_pair(atype2, atomType);
752	<
753	<	Jij[key1] = J1;
754	<	Jij[key2] = J2;
755	<	}
384	<	}
385	<
749	>	CubicSpline* J = new CubicSpline();
750	>	J->addPoints(rvals, Jvals);
751	>	Jij[fqtid][fqtid2] = J;
752	>	Jij[fqtid2].resize( nFlucq_ );
753	>	Jij[fqtid2][fqtid] = J;
754	>	}
755	>	}
756		return;
757		}
758
759		void Electrostatic::setCutoffRadius( RealType rCut ) {
760		cutoffRadius_ = rCut;
391	–	rrf_ = cutoffRadius_;
761		haveCutoffRadius_ = true;
762		}
763
395	–	void Electrostatic::setSwitchingRadius( RealType rSwitch ) {
396	–	rt_ = rSwitch;
397	–	}
764		void Electrostatic::setElectrostaticSummationMethod( ElectrostaticSummationMethod esm ) {
765		summationMethod_ = esm;
766		}
#	Line 412 | Line 778 | namespace OpenMD {
778
779		void Electrostatic::calcForce(InteractionData &idat) {
780
781	<	// utility variables.  Should clean these up and use the Vector3d and
782	<	// Mat3x3d to replace as many as we can in future versions:
783	<
784	<	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);
781	>	if (!initialized_) initialize();
782	>
783	>	data1 = ElectrostaticMap[Etids[idat.atid1]];
784	>	data2 = ElectrostaticMap[Etids[idat.atid2]];
785
786	<	Vector3d Q_i, Q_j;
787	<	Vector3d ux_i, uy_i, uz_i;
788	<	Vector3d ux_j, uy_j, uz_j;
789	<	Vector3d dudux_i, duduy_i, duduz_i;
790	<	Vector3d dudux_j, duduy_j, duduz_j;
791	<	Vector3d rhatdot2, rhatc4;
792	<	Vector3d dVdr;
786	>	U = 0.0;  // Potential
787	>	F.zero();  // Force
788	>	Ta.zero(); // Torque on site a
789	>	Tb.zero(); // Torque on site b
790	>	Ea.zero(); // Electric field at site a
791	>	Eb.zero(); // Electric field at site b
792	>	dUdCa = 0.0; // fluctuating charge force at site a
793	>	dUdCb = 0.0; // fluctuating charge force at site a
794	>
795	>	// Indirect interactions mediated by the reaction field.
796	>	indirect_Pot = 0.0;   // Potential
797	>	indirect_F.zero();    // Force
798	>	indirect_Ta.zero();   // Torque on site a
799	>	indirect_Tb.zero();   // Torque on site b
800
801	<	// variables for indirect (reaction field) interactions for excluded pairs:
802	<	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);
801	>	// Excluded potential that is still computed for fluctuating charges
802	>	excluded_Pot= 0.0;
803
804	<	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	<
804	>
805		// some variables we'll need independent of electrostatic type:
806
807	<	riji = 1.0 /  *(idat.rij) ;
808	<	Vector3d rhat =  *(idat.d)   * riji;
809	<
807	>	ri = 1.0 /  *(idat.rij);
808	>	rhat =  *(idat.d)  * ri;
809	>
810		// logicals
811
812	<	bool i_is_Charge = data1.is_Charge;
813	<	bool i_is_Dipole = data1.is_Dipole;
814	<	bool i_is_SplitDipole = data1.is_SplitDipole;
815	<	bool i_is_Quadrupole = data1.is_Quadrupole;
474	<	bool i_is_Fluctuating = data1.is_Fluctuating;
812	>	a_is_Charge = data1.is_Charge;
813	>	a_is_Dipole = data1.is_Dipole;
814	>	a_is_Quadrupole = data1.is_Quadrupole;
815	>	a_is_Fluctuating = data1.is_Fluctuating;
816
817	<	bool j_is_Charge = data2.is_Charge;
818	<	bool j_is_Dipole = data2.is_Dipole;
819	<	bool j_is_SplitDipole = data2.is_SplitDipole;
820	<	bool j_is_Quadrupole = data2.is_Quadrupole;
821	<	bool j_is_Fluctuating = data2.is_Fluctuating;
817	>	b_is_Charge = data2.is_Charge;
818	>	b_is_Dipole = data2.is_Dipole;
819	>	b_is_Quadrupole = data2.is_Quadrupole;
820	>	b_is_Fluctuating = data2.is_Fluctuating;
821	>
822	>	// Obtain all of the required radial function values from the
823	>	// spline structures:
824
825	<	if (i_is_Charge) {
826	<	q_i = data1.fixedCharge;
825	>	// needed for fields (and forces):
826	>	if (a_is_Charge || b_is_Charge) {
827	>	v01s->getValueAndDerivativeAt( *(idat.rij), v01, dv01);
828	>	}
829	>	if (a_is_Dipole || b_is_Dipole) {
830	>	v11s->getValueAndDerivativeAt( *(idat.rij), v11, dv11);
831	>	v11or = ri * v11;
832	>	}
833	>	if (a_is_Quadrupole || b_is_Quadrupole ||  (a_is_Dipole && b_is_Dipole)) {
834	>	v21s->getValueAndDerivativeAt( *(idat.rij), v21, dv21);
835	>	v22s->getValueAndDerivativeAt( *(idat.rij), v22, dv22);
836	>	v22or = ri * v22;
837	>	}
838
839	<	if (i_is_Fluctuating) {
840	<	q_i += *(idat.flucQ1);
839	>	// needed for potentials (and forces and torques):
840	>	if ((a_is_Dipole && b_is_Quadrupole) ||
841	>	(b_is_Dipole && a_is_Quadrupole)) {
842	>	v31s->getValueAndDerivativeAt( *(idat.rij), v31, dv31);
843	>	v32s->getValueAndDerivativeAt( *(idat.rij), v32, dv32);
844	>	v31or = v31 * ri;
845	>	v32or = v32 * ri;
846	>	}
847	>	if (a_is_Quadrupole && b_is_Quadrupole) {
848	>	v41s->getValueAndDerivativeAt( *(idat.rij), v41, dv41);
849	>	v42s->getValueAndDerivativeAt( *(idat.rij), v42, dv42);
850	>	v43s->getValueAndDerivativeAt( *(idat.rij), v43, dv43);
851	>	v42or = v42 * ri;
852	>	v43or = v43 * ri;
853	>	}
854	>
855	>	// calculate the single-site contributions (fields, etc).
856	>
857	>	if (a_is_Charge) {
858	>	C_a = data1.fixedCharge;
859	>
860	>	if (a_is_Fluctuating) {
861	>	C_a += *(idat.flucQ1);
862		}
863
864		if (idat.excluded) {
865	<	*(idat.skippedCharge2) += q_i;
865	>	*(idat.skippedCharge2) += C_a;
866	>	} else {
867	>	// only do the field if we're not excluded:
868	>	Eb -= C_a *  pre11_ * dv01 * rhat;
869		}
870		}
871	<
872	<	if (i_is_Dipole) {
873	<	mu_i = data1.dipole_moment;
874	<	uz_i = idat.eFrame1->getColumn(2);
875	<
876	<	ct_i = dot(uz_i, rhat);
877	<
500	<	if (i_is_SplitDipole)
501	<	d_i = data1.split_dipole_distance;
502	<
503	<	duduz_i = V3Zero;
871	>
872	>	if (a_is_Dipole) {
873	>	D_a = *(idat.dipole1);
874	>	rdDa = dot(rhat, D_a);
875	>	rxDa = cross(rhat, D_a);
876	>	if (!idat.excluded)
877	>	Eb -=  pre12_ * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
878		}
879
880	<	if (i_is_Quadrupole) {
881	<	Q_i = data1.quadrupole_moments;
882	<	qxx_i = Q_i.x();
883	<	qyy_i = Q_i.y();
884	<	qzz_i = Q_i.z();
885	<
886	<	ux_i = idat.eFrame1->getColumn(0);
887	<	uy_i = idat.eFrame1->getColumn(1);
888	<	uz_i = idat.eFrame1->getColumn(2);
889	<
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;
880	>	if (a_is_Quadrupole) {
881	>	Q_a = *(idat.quadrupole1);
882	>	trQa =  Q_a.trace();
883	>	Qar =   Q_a * rhat;
884	>	rQa = rhat * Q_a;
885	>	rdQar = dot(rhat, Qar);
886	>	rxQar = cross(rhat, Qar);
887	>	if (!idat.excluded)
888	>	Eb -= pre14_ * (trQa * rhat * dv21 + 2.0 * Qar * v22or
889	>	+ rdQar * rhat * (dv22 - 2.0*v22or));
890		}
891	<
892	<	if (j_is_Charge) {
893	<	q_j = data2.fixedCharge;
894	<
895	<	if (j_is_Fluctuating)
896	<	q_j += *(idat.flucQ2);
897	<
891	>
892	>	if (b_is_Charge) {
893	>	C_b = data2.fixedCharge;
894	>
895	>	if (b_is_Fluctuating)
896	>	C_b += *(idat.flucQ2);
897	>
898		if (idat.excluded) {
899	<	*(idat.skippedCharge1) += q_j;
899	>	*(idat.skippedCharge1) += C_b;
900	>	} else {
901	>	// only do the field if we're not excluded:
902	>	Ea += C_b *  pre11_ * dv01 * rhat;
903		}
904		}
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	–	}
905
906	<	if (j_is_Quadrupole) {
907	<	Q_j = data2.quadrupole_moments;
908	<	qxx_j = Q_j.x();
909	<	qyy_j = Q_j.y();
910	<	qzz_j = Q_j.z();
911	<
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;
906	>	if (b_is_Dipole) {
907	>	D_b = *(idat.dipole2);
908	>	rdDb = dot(rhat, D_b);
909	>	rxDb = cross(rhat, D_b);
910	>	if (!idat.excluded)
911	>	Ea += pre12_ * ((dv11-v11or) * rdDb * rhat + v11or * D_b);
912		}
913
914	<	if (i_is_Fluctuating && j_is_Fluctuating) {
915	<	J1 = Jij[idat.atypes];
916	<	J2 = Jij[make_pair(idat.atypes.second, idat.atypes.first)];
914	>	if (b_is_Quadrupole) {
915	>	Q_b = *(idat.quadrupole2);
916	>	trQb =  Q_b.trace();
917	>	Qbr =   Q_b * rhat;
918	>	rQb = rhat * Q_b;
919	>	rdQbr = dot(rhat, Qbr);
920	>	rxQbr = cross(rhat, Qbr);
921	>	if (!idat.excluded)
922	>	Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
923	>	+ rdQbr * rhat * (dv22 - 2.0*v22or));
924		}
572	–
573	–	epot = 0.0;
574	–	dVdr = V3Zero;
925
926	<	if (i_is_Charge) {
926	>	if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
927	>	J = Jij[FQtids[idat.atid1]][FQtids[idat.atid2]];
928	>	}
929	>
930	>	if (a_is_Charge) {
931
932	<	if (j_is_Charge) {
933	<	if (screeningMethod_ == DAMPED) {
934	<	// assemble the damping variables
935	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
936	<	//erfcVal = res.first;
937	<	//derfcVal = res.second;
932	>	if (b_is_Charge) {
933	>	pref =  pre11_ * *(idat.electroMult);
934	>	U  += C_a * C_b * pref * v01;
935	>	F  += C_a * C_b * pref * dv01 * rhat;
936	>
937	>	// If this is an excluded pair, there are still indirect
938	>	// interactions via the reaction field we must worry about:
939
940	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
941	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
940	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
941	>	rfContrib = preRF_ * pref * C_a * C_b * *(idat.r2);
942	>	indirect_Pot += rfContrib;
943	>	indirect_F   += rfContrib * 2.0 * ri * rhat;
944	>	}
945	>
946	>	// Fluctuating charge forces are handled via Coulomb integrals
947	>	// for excluded pairs (i.e. those connected via bonds) and
948	>	// with the standard charge-charge interaction otherwise.
949
950	<	c1 = erfcVal * riji;
951	<	c2 = (-derfcVal + c1) * riji;
950	>	if (idat.excluded) {
951	>	if (a_is_Fluctuating || b_is_Fluctuating) {
952	>	coulInt = J->getValueAt( *(idat.rij) );
953	>	if (a_is_Fluctuating)  dUdCa += coulInt * C_b;
954	>	if (b_is_Fluctuating)  dUdCb += coulInt * C_a;
955	>	excluded_Pot += C_a * C_b * coulInt;
956	>	}
957		} else {
958	<	c1 = riji;
959	<	c2 = c1 * riji;
958	>	if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
959	>	if (a_is_Fluctuating) dUdCb += C_a * pref * v01;
960		}
961	+	}
962
963	<	preVal =  *(idat.electroMult) * pre11_;
964	<
965	<	if (summationMethod_ == esm_SHIFTED_POTENTIAL) {
966	<	vterm = preVal * (c1 - c1c_);
967	<	dudr  = - *(idat.sw)  * preVal * c2;
963	>	if (b_is_Dipole) {
964	>	pref =  pre12_ * *(idat.electroMult);
965	>	U  += C_a * pref * v11 * rdDb;
966	>	F  += C_a * pref * ((dv11 - v11or) * rdDb * rhat + v11or * D_b);
967	>	Tb += C_a * pref * v11 * rxDb;
968
969	<	} else if (summationMethod_ == esm_SHIFTED_FORCE)  {
602	<	vterm = preVal * ( c1 - c1c_ + c2c_*( *(idat.rij)  - cutoffRadius_) );
603	<	dudr  =  *(idat.sw)  * preVal * (c2c_ - c2);
969	>	if (a_is_Fluctuating) dUdCa += pref * v11 * rdDb;
970
971	<	} else if (summationMethod_ == esm_REACTION_FIELD) {
972	<	rfVal = preRF_ *  *(idat.rij)  *  *(idat.rij);
971	>	// Even if we excluded this pair from direct interactions, we
972	>	// still have the reaction-field-mediated charge-dipole
973	>	// interaction:
974
975	<	vterm = preVal * ( riji + rfVal );
976	<	dudr  =  *(idat.sw)  * preVal * ( 2.0 * rfVal - riji ) * riji;
977	<
978	<	// if this is an excluded pair, there are still indirect
979	<	// 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	<
975	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
976	>	rfContrib = C_a * pref * preRF_ * 2.0 * *(idat.rij);
977	>	indirect_Pot += rfContrib * rdDb;
978	>	indirect_F   += rfContrib * D_b / (*idat.rij);
979	>	indirect_Tb  += C_a * pref * preRF_ * rxDb;
980		}
981	<
627	<	vpair += vterm * q_i * q_j;
628	<	epot +=  *(idat.sw)  * vterm * q_i * q_j;
629	<	dVdr += dudr * rhat * q_i * q_j;
981	>	}
982
983	<	if (i_is_Fluctuating) {
984	<	if (idat.excluded) {
985	<	// vFluc1 is the difference between the direct coulomb integral
986	<	// and the normal 1/r-like  interaction between point charges.
987	<	coulInt = J1->getValueAt( *(idat.rij) );
988	<	vFluc1 = coulInt - (*(idat.sw) * vterm);
637	<	} else {
638	<	vFluc1 = 0.0;
639	<	}
640	<	*(idat.dVdFQ1) += ( *(idat.sw) * vterm + vFluc1 ) * q_j;
641	<	}
983	>	if (b_is_Quadrupole) {
984	>	pref = pre14_ * *(idat.electroMult);
985	>	U  +=  C_a * pref * (v21 * trQb + v22 * rdQbr);
986	>	F  +=  C_a * pref * (trQb * dv21 * rhat + 2.0 * Qbr * v22or);
987	>	F  +=  C_a * pref * rdQbr * rhat * (dv22 - 2.0*v22or);
988	>	Tb +=  C_a * pref * 2.0 * rxQbr * v22;
989
990	<	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	<
990	>	if (a_is_Fluctuating) dUdCa += pref * (v21 * trQb + v22 * rdQbr);
991		}
992	+	}
993
994	<	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;
994	>	if (a_is_Dipole) {
995
996	<	if (summationMethod_ == esm_REACTION_FIELD) {
997	<	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;
996	>	if (b_is_Charge) {
997	>	pref = pre12_ * *(idat.electroMult);
998
999	<	dVdr +=  -preSw * (ri3 * (uz_j - three * ct_j * rhat) - preRF2_*uz_j);
1000	<	duduz_j += -preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
999	>	U  -= C_b * pref * v11 * rdDa;
1000	>	F  -= C_b * pref * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
1001	>	Ta -= C_b * pref * v11 * rxDa;
1002
1003	<	// Even if we excluded this pair from direct interactions,
675	<	// we still have the reaction-field-mediated charge-dipole
676	<	// interaction:
1003	>	if (b_is_Fluctuating) dUdCb -= pref * v11 * rdDa;
1004
1005	<	if (idat.excluded) {
1006	<	indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij);
1007	<	indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij);
1008	<	indirect_dVdr += preSw * preRF2_ * uz_j;
1009	<	indirect_duduz_j += preSw * rhat * preRF2_ *  *(idat.rij);
1010	<	}
1011	<
1012	<	} 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	<
1005	>	// Even if we excluded this pair from direct interactions,
1006	>	// we still have the reaction-field-mediated charge-dipole
1007	>	// interaction:
1008	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
1009	>	rfContrib = C_b * pref * preRF_ * 2.0 * *(idat.rij);
1010	>	indirect_Pot -= rfContrib * rdDa;
1011	>	indirect_F   -= rfContrib * D_a / (*idat.rij);
1012	>	indirect_Ta  -= C_b * pref * preRF_ * rxDa;
1013		}
728	–	if (i_is_Fluctuating) {
729	–	*(idat.dVdFQ1) += ( *(idat.sw) * vterm ) / q_i;
730	–	}
1014		}
1015
1016	<	if (j_is_Quadrupole) {
1017	<	// first precalculate some necessary variables
1018	<	cx2 = cx_j * cx_j;
1019	<	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	<	}
1016	>	if (b_is_Dipole) {
1017	>	pref = pre22_ * *(idat.electroMult);
1018	>	DadDb = dot(D_a, D_b);
1019	>	DaxDb = cross(D_a, D_b);
1020
1021	<	// precompute variables for convenience
1022	<	preSw =  *(idat.sw)  * pref;
1023	<	c2ri = c2 * riji;
1024	<	c3ri = c3 * riji;
1025	<	c4rij = c4 *  *(idat.rij) ;
763	<	rhatdot2 = two * rhat * c3;
764	<	rhatc4 = rhat * c4rij;
1021	>	U  -= pref * (DadDb * v21 + rdDa * rdDb * v22);
1022	>	F  -= pref * (dv21 * DadDb * rhat + v22or * (rdDb * D_a + rdDa * D_b));
1023	>	F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
1024	>	Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
1025	>	Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
1026
1027	<	// calculate the potential
1028	<	pot_term = ( qxx_j * (cx2*c3 - c2ri) +
1029	<	qyy_j * (cy2*c3 - c2ri) +
1030	<	qzz_j * (cz2*c3 - c2ri) );
1031	<	vterm = pref * pot_term;
1032	<	vpair += vterm;
1033	<	epot +=  *(idat.sw)  * vterm;
1034	<
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;
1027	>	// Even if we excluded this pair from direct interactions, we
1028	>	// still have the reaction-field-mediated dipole-dipole
1029	>	// interaction:
1030	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
1031	>	rfContrib = -pref * preRF_ * 2.0;
1032	>	indirect_Pot += rfContrib * DadDb;
1033	>	indirect_Ta  += rfContrib * DaxDb;
1034	>	indirect_Tb  -= rfContrib * DaxDb;
1035		}
1036	+	}
1037
1038	+	if (b_is_Quadrupole) {
1039	+	pref = pre24_ * *(idat.electroMult);
1040	+	DadQb = D_a * Q_b;
1041	+	DadQbr = dot(D_a, Qbr);
1042	+	DaxQbr = cross(D_a, Qbr);
1043	+
1044	+	U  -= pref * ((trQb*rdDa + 2.0*DadQbr)*v31 + rdDa*rdQbr*v32);
1045	+	F  -= pref * (trQb*D_a + 2.0*DadQb) * v31or;
1046	+	F  -= pref * (trQb*rdDa + 2.0*DadQbr) * (dv31-v31or) * rhat;
1047	+	F  -= pref * (D_a*rdQbr + 2.0*rdDa*rQb) * v32or;
1048	+	F  -= pref * (rdDa * rdQbr * rhat * (dv32-3.0*v32or));
1049	+	Ta += pref * ((-trQb*rxDa + 2.0 * DaxQbr)*v31 - rxDa*rdQbr*v32);
1050	+	Tb += pref * ((2.0*cross(DadQb, rhat) - 2.0*DaxQbr)*v31
1051	+	- 2.0*rdDa*rxQbr*v32);
1052		}
1053		}
789	–
790	–	if (i_is_Dipole) {
1054
1055	<	if (j_is_Charge) {
1056	<	// variables used by all the methods
1057	<	pref =  *(idat.electroMult) * pre12_ * q_j * mu_i;
1058	<	preSw =  *(idat.sw)  * pref;
1055	>	if (a_is_Quadrupole) {
1056	>	if (b_is_Charge) {
1057	>	pref = pre14_ * *(idat.electroMult);
1058	>	U  += C_b * pref * (v21 * trQa + v22 * rdQar);
1059	>	F  += C_b * pref * (trQa * rhat * dv21 + 2.0 * Qar * v22or);
1060	>	F  += C_b * pref * rdQar * rhat * (dv22 - 2.0*v22or);
1061	>	Ta += C_b * pref * 2.0 * rxQar * v22;
1062
1063	<	if (summationMethod_ == esm_REACTION_FIELD) {
1063	>	if (b_is_Fluctuating) dUdCb += pref * (v21 * trQa + v22 * rdQar);
1064	>	}
1065	>	if (b_is_Dipole) {
1066	>	pref = pre24_ * *(idat.electroMult);
1067	>	DbdQa = D_b * Q_a;
1068	>	DbdQar = dot(D_b, Qar);
1069	>	DbxQar = cross(D_b, Qar);
1070
1071	<	ri2 = riji * riji;
1072	<	ri3 = ri2 * riji;
1073	<
1074	<	vterm = pref * ct_i * ( ri2 - preRF2_ *  *(idat.rij)  );
1075	<	vpair += vterm;
1076	<	epot +=  *(idat.sw)  * vterm;
1077	<
1078	<	dVdr += preSw * (ri3 * (uz_i - three * ct_i * rhat) - preRF2_ * uz_i);
1079	<
1080	<	duduz_i += preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
1081	<
1082	<	// Even if we excluded this pair from direct interactions,
1083	<	// we still have the reaction-field-mediated charge-dipole
1084	<	// interaction:
1071	>	U  += pref * ((trQa*rdDb + 2.0*DbdQar)*v31 + rdDb*rdQar*v32);
1072	>	F  += pref * (trQa*D_b + 2.0*DbdQa) * v31or;
1073	>	F  += pref * (trQa*rdDb + 2.0*DbdQar) * (dv31-v31or) * rhat;
1074	>	F  += pref * (D_b*rdQar + 2.0*rdDb*rQa) * v32or;
1075	>	F  += pref * (rdDb * rdQar * rhat * (dv32-3.0*v32or));
1076	>	Ta += pref * ((-2.0*cross(DbdQa, rhat) + 2.0*DbxQar)*v31
1077	>	+ 2.0*rdDb*rxQar*v32);
1078	>	Tb += pref * ((trQa*rxDb - 2.0 * DbxQar)*v31 + rxDb*rdQar*v32);
1079	>	}
1080	>	if (b_is_Quadrupole) {
1081	>	pref = pre44_ * *(idat.electroMult);  // yes
1082	>	QaQb = Q_a * Q_b;
1083	>	trQaQb = QaQb.trace();
1084	>	rQaQb = rhat * QaQb;
1085	>	QaQbr = QaQb * rhat;
1086	>	QaxQb = cross(Q_a, Q_b);
1087	>	rQaQbr = dot(rQa, Qbr);
1088	>	rQaxQbr = cross(rQa, Qbr);
1089	>
1090	>	U  += pref * (trQa * trQb + 2.0 * trQaQb) * v41;
1091	>	U  += pref * (trQa * rdQbr + trQb * rdQar  + 4.0 * rQaQbr) * v42;
1092	>	U  += pref * (rdQar * rdQbr) * v43;
1093
1094	<	if (idat.excluded) {
1095	<	indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij);
1096	<	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;
1094	>	F  += pref * rhat * (trQa * trQb + 2.0 * trQaQb)*dv41;
1095	>	F  += pref*rhat*(trQa*rdQbr + trQb*rdQar + 4.0*rQaQbr)*(dv42-2.0*v42or);
1096	>	F  += pref * rhat * (rdQar * rdQbr)*(dv43 - 4.0*v43or);
1097
1098	<	// calculate derivatives for the forces and torques
1099	<	dVdr += preSw * (uz_i * c2ri - ct_i * rhat * sc2 * c3);
1100	<	duduz_i += preSw * pot_term * rhat;
862	<	}
1098	>	F  += pref * 2.0 * (trQb*rQa + trQa*rQb) * v42or;
1099	>	F  += pref * 4.0 * (rQaQb + QaQbr) * v42or;
1100	>	F  += pref * 2.0 * (rQa*rdQbr + rdQar*rQb) * v43or;
1101
1102	<	if (j_is_Fluctuating) {
1103	<	*(idat.dVdFQ2) += ( *(idat.sw) * vterm ) / q_j;
1104	<	}
1102	>	Ta += pref * (- 4.0 * QaxQb * v41);
1103	>	Ta += pref * (- 2.0 * trQb * cross(rQa, rhat)
1104	>	+ 4.0 * cross(rhat, QaQbr)
1105	>	- 4.0 * rQaxQbr) * v42;
1106	>	Ta += pref * 2.0 * cross(rhat,Qar) * rdQbr * v43;
1107
868	–	}
1108
1109	<	if (j_is_Dipole) {
1110	<	// variables used by all methods
1111	<	ct_ij = dot(uz_i, uz_j);
1109	>	Tb += pref * (+ 4.0 * QaxQb * v41);
1110	>	Tb += pref * (- 2.0 * trQa * cross(rQb, rhat)
1111	>	- 4.0 * cross(rQaQb, rhat)
1112	>	+ 4.0 * rQaxQbr) * v42;
1113	>	// Possible replacement for line 2 above:
1114	>	//             + 4.0 * cross(rhat, QbQar)
1115
1116	<	pref =  *(idat.electroMult) * pre22_ * mu_i * mu_j;
875	<	preSw =  *(idat.sw)  * pref;
1116	>	Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1117
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	–	}
1118		}
1119		}
1120
1121	<	if (i_is_Quadrupole) {
1122	<	if (j_is_Charge) {
1123	<	// 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	<	}
1121	>	if (idat.doElectricField) {
1122	>	*(idat.eField1) += Ea * *(idat.electroMult);
1123	>	*(idat.eField2) += Eb * *(idat.electroMult);
1124		}
1125
1126	+	if (a_is_Fluctuating) *(idat.dVdFQ1) += dUdCa * *(idat.sw);
1127	+	if (b_is_Fluctuating) *(idat.dVdFQ2) += dUdCb * *(idat.sw);
1128
1129		if (!idat.excluded) {
1028	–	*(idat.vpair) += vpair;
1029	–	(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot;
1030	–	*(idat.f1) += dVdr;
1130
1131	<	if (i_is_Dipole || i_is_Quadrupole)
1132	<	*(idat.t1) -= cross(uz_i, duduz_i);
1133	<	if (i_is_Quadrupole) {
1035	<	*(idat.t1) -= cross(ux_i, dudux_i);
1036	<	*(idat.t1) -= cross(uy_i, duduy_i);
1037	<	}
1131	>	*(idat.vpair) += U;
1132	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += U * *(idat.sw);
1133	>	*(idat.f1) += F * *(idat.sw);
1134
1135	<	if (j_is_Dipole || j_is_Quadrupole)
1136	<	*(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	<	}
1135	>	if (a_is_Dipole || a_is_Quadrupole)
1136	>	*(idat.t1) += Ta * *(idat.sw);
1137
1138	+	if (b_is_Dipole || b_is_Quadrupole)
1139	+	*(idat.t2) += Tb * *(idat.sw);
1140	+
1141		} else {
1142
1143		// only accumulate the forces and torques resulting from the
1144		// indirect reaction field terms.
1145
1146	<	*(idat.vpair) += indirect_vpair;
1147	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot;
1148	<	*(idat.f1) += indirect_dVdr;
1146	>	*(idat.vpair) += indirect_Pot;
1147	>	(*(idat.excludedPot))[ELECTROSTATIC_FAMILY] +=  excluded_Pot;
1148	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += *(idat.sw) * indirect_Pot;
1149	>	*(idat.f1) += *(idat.sw) * indirect_F;
1150
1151	<	if (i_is_Dipole)
1152	<	*(idat.t1) -= cross(uz_i, indirect_duduz_i);
1153	<	if (j_is_Dipole)
1154	<	*(idat.t2) -= cross(uz_j, indirect_duduz_j);
1151	>	if (a_is_Dipole || a_is_Quadrupole)
1152	>	*(idat.t1) += *(idat.sw) * indirect_Ta;
1153	>
1154	>	if (b_is_Dipole || b_is_Quadrupole)
1155	>	*(idat.t2) += *(idat.sw) * indirect_Tb;
1156		}
1060	–
1157		return;
1158	<	}
1158	>	}
1159
1160		void Electrostatic::calcSelfCorrection(SelfData &sdat) {
1161	<	RealType mu1, preVal, self;
1161	>
1162		if (!initialized_) initialize();
1163
1164	<	ElectrostaticAtomData data = ElectrostaticMap[sdat.atype];
1165	<
1164	>	ElectrostaticAtomData data = ElectrostaticMap[Etids[sdat.atid]];
1165	>
1166		// logicals
1167		bool i_is_Charge = data.is_Charge;
1168		bool i_is_Dipole = data.is_Dipole;
1169	+	bool i_is_Quadrupole = data.is_Quadrupole;
1170		bool i_is_Fluctuating = data.is_Fluctuating;
1171	<	RealType chg1 = data.fixedCharge;
1172	<
1171	>	RealType C_a = data.fixedCharge;
1172	>	RealType self(0.0), preVal, DdD, trQ, trQQ;
1173	>
1174	>	if (i_is_Dipole) {
1175	>	DdD = data.dipole.lengthSquare();
1176	>	}
1177	>
1178		if (i_is_Fluctuating) {
1179	<	chg1 += *(sdat.flucQ);
1179	>	C_a += *(sdat.flucQ);
1180		// dVdFQ is really a force, so this is negative the derivative
1181		*(sdat.dVdFQ) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1182	+	(*(sdat.excludedPot))[ELECTROSTATIC_FAMILY] += (*sdat.flucQ) *
1183	+	(*(sdat.flucQ) * data.hardness * 0.5 + data.electronegativity);
1184		}
1185
1186	<	if (summationMethod_ == esm_REACTION_FIELD) {
1187	<	if (i_is_Dipole) {
1188	<	mu1 = data.dipole_moment;
1189	<	preVal = pre22_ * preRF2_ * mu1 * mu1;
1190	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal;
1191	<
1192	<	// The self-correction term adds into the reaction field vector
1193	<	Vector3d uz_i = sdat.eFrame->getColumn(2);
1194	<	Vector3d ei = preVal * uz_i;
1186	>	switch (summationMethod_) {
1187	>	case esm_REACTION_FIELD:
1188	>
1189	>	if (i_is_Charge) {
1190	>	// Self potential [see Wang and Hermans, "Reaction Field
1191	>	// Molecular Dynamics Simulation with Friedman’s Image Charge
1192	>	// Method," J. Phys. Chem. 99, 12001-12007 (1995).]
1193	>	preVal = pre11_ * preRF_ * C_a * C_a;
1194	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal / cutoffRadius_;
1195	>	}
1196
1197	<	// This looks very wrong.  A vector crossed with itself is zero.
1198	<	*(sdat.t) -= cross(uz_i, ei);
1197	>	if (i_is_Dipole) {
1198	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DdD;
1199		}
1200	<	} else if (summationMethod_ == esm_SHIFTED_FORCE || summationMethod_ == esm_SHIFTED_POTENTIAL) {
1201	<	if (i_is_Charge) {
1202	<	if (screeningMethod_ == DAMPED) {
1203	<	self = - 0.5 * (c1c_ + alphaPi_) * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_;
1204	<	} else {
1205	<	self = - 0.5 * rcuti_ * chg1 * (chg1 +  *(sdat.skippedCharge)) * pre11_;
1206	<	}
1207	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1200	>
1201	>	break;
1202	>
1203	>	case esm_SHIFTED_FORCE:
1204	>	case esm_SHIFTED_POTENTIAL:
1205	>	case esm_TAYLOR_SHIFTED:
1206	>	if (i_is_Charge)
1207	>	self += selfMult1_ * pre11_ * C_a * (C_a + *(sdat.skippedCharge));
1208	>	if (i_is_Dipole)
1209	>	self += selfMult2_ * pre22_ * DdD;
1210	>	if (i_is_Quadrupole) {
1211	>	trQ = data.quadrupole.trace();
1212	>	trQQ = (data.quadrupole * data.quadrupole).trace();
1213	>	self += selfMult4_ * pre44_ * (2.0*trQQ + trQ*trQ);
1214	>	if (i_is_Charge)
1215	>	self -= selfMult2_ * pre14_ * 2.0 * C_a * trQ;
1216		}
1217	+	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1218	+	break;
1219	+	default:
1220	+	break;
1221		}
1222		}
1223	<
1223	>
1224		RealType Electrostatic::getSuggestedCutoffRadius(pair<AtomType*, AtomType*> atypes) {
1225		// This seems to work moderately well as a default.  There's no
1226		// inherent scale for 1/r interactions that we can standardize.

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