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

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branches/development/src/nonbonded/Electrostatic.cpp (file contents), Revision 1665 by gezelter, Tue Nov 22 20:38:56 2011 UTC vs.
trunk/src/nonbonded/Electrostatic.cpp (file contents), Revision 1894 by gezelter, Fri Jun 21 23:21:58 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 47 | Line 47
47		#include "nonbonded/Electrostatic.hpp"
48		#include "utils/simError.h"
49		#include "types/NonBondedInteractionType.hpp"
50	<	#include "types/DirectionalAtomType.hpp"
50	>	#include "types/FixedChargeAdapter.hpp"
51	>	#include "types/FluctuatingChargeAdapter.hpp"
52	>	#include "types/MultipoleAdapter.hpp"
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
59		namespace OpenMD {
60
#	Line 57 | 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 69 | 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 83 | 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 103 | Line 115 | namespace OpenMD {
115		summationMethod_ = esm_HARD;
116		screeningMethod_ = UNDAMPED;
117		dielectric_ = 1.0;
106	–	one_third_ = 1.0 / 3.0;
118
119		// check the summation method:
120		if (simParams_->haveElectrostaticSummationMethod()) {
#	Line 119 | 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 188 | Line 200 | namespace OpenMD {
200
201		// throw warning
202		sprintf( painCave.errMsg,
203	<	"Electrostatic::initialize: dampingAlpha was not specified in the input file.\n"
204	<	"\tA default value of %f (1/ang) will be used for the cutoff of\n\t%f (ang).\n",
203	>	"Electrostatic::initialize: dampingAlpha was not specified in the\n"
204	>	"\tinput file.  A default value of %f (1/ang) will be used for the\n"
205	>	"\tcutoff of %f (ang).\n",
206		dampingAlpha_, cutoffRadius_);
207		painCave.severity = OPENMD_INFO;
208		painCave.isFatal = 0;
#	Line 210 | Line 223 | namespace OpenMD {
223
224		if (at->isElectrostatic())
225		addType(at);
226	+	}
227	+
228	+	if (summationMethod_ == esm_REACTION_FIELD) {
229	+	preRF_ = (dielectric_ - 1.0) /
230	+	((2.0 * dielectric_ + 1.0) * pow(cutoffRadius_,3) );
231		}
232
233	+	RealType b0c, b1c, b2c, b3c, b4c, b5c;
234	+	RealType db0c_1, db0c_2, db0c_3, db0c_4, db0c_5;
235	+	RealType a2, expTerm, invArootPi;
236	+
237	+	RealType r = cutoffRadius_;
238	+	RealType r2 = r * r;
239	+	RealType ric = 1.0 / r;
240	+	RealType ric2 = ric * ric;
241
242	<	cutoffRadius2_ = cutoffRadius_ * cutoffRadius_;
243	<	rcuti_ = 1.0 / cutoffRadius_;
244	<	rcuti2_ = rcuti_ * rcuti_;
245	<	rcuti3_ = rcuti2_ * rcuti_;
246	<	rcuti4_ = rcuti2_ * rcuti2_;
247	<
248	<	if (screeningMethod_ == DAMPED) {
249	<
250	<	alpha2_ = dampingAlpha_ * dampingAlpha_;
251	<	alpha4_ = alpha2_ * alpha2_;
252	<	alpha6_ = alpha4_ * alpha2_;
253	<	alpha8_ = alpha4_ * alpha4_;
228	<
229	<	constEXP_ = exp(-alpha2_ * cutoffRadius2_);
230	<	invRootPi_ = 0.56418958354775628695;
231	<	alphaPi_ = 2.0 * dampingAlpha_ * invRootPi_;
232	<
233	<	c1c_ = erfc(dampingAlpha_ * cutoffRadius_) * rcuti_;
234	<	c2c_ = alphaPi_ * constEXP_ * rcuti_ + c1c_ * rcuti_;
235	<	c3c_ = 2.0 * alphaPi_ * alpha2_ + 3.0 * c2c_ * rcuti_;
236	<	c4c_ = 4.0 * alphaPi_ * alpha4_ + 5.0 * c3c_ * rcuti2_;
237	<	c5c_ = 8.0 * alphaPi_ * alpha6_ + 7.0 * c4c_ * rcuti2_;
238	<	c6c_ = 16.0 * alphaPi_ * alpha8_ + 9.0 * c5c_ * rcuti2_;
242	>	if (screeningMethod_ == DAMPED) {
243	>	a2 = dampingAlpha_ * dampingAlpha_;
244	>	invArootPi = 1.0 / (dampingAlpha_ * sqrt(M_PI));
245	>	expTerm = exp(-a2 * r2);
246	>	// values of Smith's B_l functions at the cutoff radius:
247	>	b0c = erfc(dampingAlpha_ * r) / r;
248	>	b1c = (      b0c     + 2.0*a2     * expTerm * invArootPi) / r2;
249	>	b2c = (3.0 * b1c + pow(2.0*a2, 2) * expTerm * invArootPi) / r2;
250	>	b3c = (5.0 * b2c + pow(2.0*a2, 3) * expTerm * invArootPi) / r2;
251	>	b4c = (7.0 * b3c + pow(2.0*a2, 4) * expTerm * invArootPi) / r2;
252	>	b5c = (9.0 * b4c + pow(2.0*a2, 5) * expTerm * invArootPi) / r2;
253	>	selfMult_ = b0c + a2 * invArootPi;
254		} else {
255	<	c1c_ = rcuti_;
256	<	c2c_ = c1c_ * rcuti_;
257	<	c3c_ = 3.0 * c2c_ * rcuti_;
258	<	c4c_ = 5.0 * c3c_ * rcuti2_;
259	<	c5c_ = 7.0 * c4c_ * rcuti2_;
260	<	c6c_ = 9.0 * c5c_ * rcuti2_;
255	>	a2 = 0.0;
256	>	b0c = 1.0 / r;
257	>	b1c = (      b0c) / r2;
258	>	b2c = (3.0 * b1c) / r2;
259	>	b3c = (5.0 * b2c) / r2;
260	>	b4c = (7.0 * b3c) / r2;
261	>	b5c = (9.0 * b4c) / r2;
262	>	selfMult_ = b0c;
263		}
264	<
265	<	if (summationMethod_ == esm_REACTION_FIELD) {
266	<	preRF_ = (dielectric_ - 1.0) /
267	<	((2.0 * dielectric_ + 1.0) * cutoffRadius2_ * cutoffRadius_);
268	<	preRF2_ = 2.0 * preRF_;
269	<	}
264	>
265	>	// higher derivatives of B_0 at the cutoff radius:
266	>	db0c_1 = -r * b1c;
267	>	db0c_2 =     -b1c + r2 * b2c;
268	>	db0c_3 =          3.0*r*b2c  - r2*r*b3c;
269	>	db0c_4 =          3.0*b2c  - 6.0*r2*b3c     + r2*r2*b4c;
270	>	db0c_5 =                    -15.0*r*b3c + 10.0*r2*r*b4c - r2*r2*r*b5c;
271
272	+
273	+	// working variables for the splines:
274	+	RealType ri, ri2;
275	+	RealType b0, b1, b2, b3, b4, b5;
276	+	RealType db0_1, db0_2, db0_3, db0_4, db0_5;
277	+	RealType f, fc, f0;
278	+	RealType g, gc, g0, g1, g2, g3, g4;
279	+	RealType h, hc, h1, h2, h3, h4;
280	+	RealType s, sc, s2, s3, s4;
281	+	RealType t, tc, t3, t4;
282	+	RealType u, uc, u4;
283	+
284	+	// working variables for Taylor expansion:
285	+	RealType rmRc, rmRc2, rmRc3, rmRc4;
286	+
287	+	// Approximate using splines using a maximum of 0.1 Angstroms
288	+	// between points.
289	+	int nptest = int((cutoffRadius_ + 2.0) / 0.1);
290	+	np_ = (np_ > nptest) ? np_ : nptest;
291	+
292		// Add a 2 angstrom safety window to deal with cutoffGroups that
293		// have charged atoms longer than the cutoffRadius away from each
294	<	// other.  Splining may not be the best choice here.  Direct calls
295	<	// to erfc might be preferrable.
294	>	// other.  Splining is almost certainly the best choice here.
295	>	// Direct calls to erfc would be preferrable if it is a very fast
296	>	// implementation.
297
298	<	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
260	<	RealType rval;
261	<	vector<RealType> rvals;
262	<	vector<RealType> yvals;
263	<	for (int i = 0; i < np_; i++) {
264	<	rval = RealType(i) * dx;
265	<	rvals.push_back(rval);
266	<	yvals.push_back(erfc(dampingAlpha_ * rval));
267	<	}
268	<	erfcSpline_ = new CubicSpline();
269	<	erfcSpline_->addPoints(rvals, yvals);
270	<	haveElectroSpline_ = true;
298	>	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_);
299
300	<	initialized_ = true;
301	<	}
302	<
303	<	void Electrostatic::addType(AtomType* atomType){
300	>	// Storage vectors for the computed functions
301	>	vector<RealType> rv;
302	>	vector<RealType> v01v;
303	>	vector<RealType> v11v;
304	>	vector<RealType> v21v, v22v;
305	>	vector<RealType> v31v, v32v;
306	>	vector<RealType> v41v, v42v, v43v;
307
308	<	ElectrostaticAtomData electrostaticAtomData;
309	<	electrostaticAtomData.is_Charge = false;
310	<	electrostaticAtomData.is_Dipole = false;
311	<	electrostaticAtomData.is_SplitDipole = false;
312	<	electrostaticAtomData.is_Quadrupole = false;
308	>	/*
309	>	vector<RealType> dv01v;
310	>	vector<RealType> dv11v;
311	>	vector<RealType> dv21v, dv22v;
312	>	vector<RealType> dv31v, dv32v;
313	>	vector<RealType> dv41v, dv42v, dv43v;
314	>	*/
315
316	<	if (atomType->isCharge()) {
317	<	GenericData* data = atomType->getPropertyByName("Charge");
316	>	for (int i = 1; i < np_ + 1; i++) {
317	>	r = RealType(i) * dx;
318	>	rv.push_back(r);
319
320	<	if (data == NULL) {
321	<	sprintf( painCave.errMsg, "Electrostatic::addType could not find "
322	<	"Charge\n"
323	<	"\tparameters for atomType %s.\n",
324	<	atomType->getName().c_str());
325	<	painCave.severity = OPENMD_ERROR;
326	<	painCave.isFatal = 1;
327	<	simError();
328	<	}
329	<
330	<	DoubleGenericData* doubleData = dynamic_cast<DoubleGenericData*>(data);
331	<	if (doubleData == NULL) {
332	<	sprintf( painCave.errMsg,
333	<	"Electrostatic::addType could not convert GenericData to "
334	<	"Charge for\n"
335	<	"\tatom type %s\n", atomType->getName().c_str());
336	<	painCave.severity = OPENMD_ERROR;
337	<	painCave.isFatal = 1;
338	<	simError();
339	<	}
340	<	electrostaticAtomData.is_Charge = true;
341	<	electrostaticAtomData.charge = doubleData->getData();
342	<	}
343	<
344	<	if (atomType->isDirectional()) {
345	<	DirectionalAtomType* daType = dynamic_cast<DirectionalAtomType*>(atomType);
346	<
313	<	if (daType->isDipole()) {
314	<	GenericData* data = daType->getPropertyByName("Dipole");
315	<
316	<	if (data == NULL) {
317	<	sprintf( painCave.errMsg,
318	<	"Electrostatic::addType could not find Dipole\n"
319	<	"\tparameters for atomType %s.\n",
320	<	daType->getName().c_str());
321	<	painCave.severity = OPENMD_ERROR;
322	<	painCave.isFatal = 1;
323	<	simError();
324	<	}
325	<
326	<	DoubleGenericData* doubleData = dynamic_cast<DoubleGenericData*>(data);
327	<	if (doubleData == NULL) {
328	<	sprintf( painCave.errMsg,
329	<	"Electrostatic::addType could not convert GenericData to "
330	<	"Dipole Moment\n"
331	<	"\tfor atom type %s\n", daType->getName().c_str());
332	<	painCave.severity = OPENMD_ERROR;
333	<	painCave.isFatal = 1;
334	<	simError();
335	<	}
336	<	electrostaticAtomData.is_Dipole = true;
337	<	electrostaticAtomData.dipole_moment = doubleData->getData();
320	>	ri = 1.0 / r;
321	>	ri2 = ri * ri;
322	>
323	>	r2 = r * r;
324	>	expTerm = exp(-a2 * r2);
325	>
326	>	// Taylor expansion factors (no need for factorials this way):
327	>	rmRc = r - cutoffRadius_;
328	>	rmRc2 = rmRc  * rmRc / 2.0;
329	>	rmRc3 = rmRc2 * rmRc / 3.0;
330	>	rmRc4 = rmRc3 * rmRc / 4.0;
331	>
332	>	// values of Smith's B_l functions at r:
333	>	if (screeningMethod_ == DAMPED) {
334	>	b0 = erfc(dampingAlpha_ * r) * ri;
335	>	b1 = (      b0 +     2.0*a2     * expTerm * invArootPi) * ri2;
336	>	b2 = (3.0 * b1 + pow(2.0*a2, 2) * expTerm * invArootPi) * ri2;
337	>	b3 = (5.0 * b2 + pow(2.0*a2, 3) * expTerm * invArootPi) * ri2;
338	>	b4 = (7.0 * b3 + pow(2.0*a2, 4) * expTerm * invArootPi) * ri2;
339	>	b5 = (9.0 * b4 + pow(2.0*a2, 5) * expTerm * invArootPi) * ri2;
340	>	} else {
341	>	b0 = ri;
342	>	b1 = (      b0) * ri2;
343	>	b2 = (3.0 * b1) * ri2;
344	>	b3 = (5.0 * b2) * ri2;
345	>	b4 = (7.0 * b3) * ri2;
346	>	b5 = (9.0 * b4) * ri2;
347		}
348	+
349	+	// higher derivatives of B_0 at r:
350	+	db0_1 = -r * b1;
351	+	db0_2 =     -b1 + r2 * b2;
352	+	db0_3 =          3.0*r*b2   - r2*r*b3;
353	+	db0_4 =          3.0*b2   - 6.0*r2*b3     + r2*r2*b4;
354	+	db0_5 =                    -15.0*r*b3 + 10.0*r2*r*b4 - r2*r2*r*b5;
355
356	<	if (daType->isSplitDipole()) {
357	<	GenericData* data = daType->getPropertyByName("SplitDipoleDistance");
358	<
359	<	if (data == NULL) {
360	<	sprintf(painCave.errMsg,
361	<	"Electrostatic::addType could not find SplitDipoleDistance\n"
362	<	"\tparameter for atomType %s.\n",
363	<	daType->getName().c_str());
364	<	painCave.severity = OPENMD_ERROR;
365	<	painCave.isFatal = 1;
366	<	simError();
367	<	}
356	>	f = b0;
357	>	fc = b0c;
358	>	f0 = f - fc - rmRc*db0c_1;
359	>
360	>	g = db0_1;
361	>	gc = db0c_1;
362	>	g0 = g - gc;
363	>	g1 = g0 - rmRc *db0c_2;
364	>	g2 = g1 - rmRc2*db0c_3;
365	>	g3 = g2 - rmRc3*db0c_4;
366	>	g4 = g3 - rmRc4*db0c_5;
367	>
368	>	h = db0_2;
369	>	hc = db0c_2;
370	>	h1 = h - hc;
371	>	h2 = h1 - rmRc *db0c_3;
372	>	h3 = h2 - rmRc2*db0c_4;
373	>	h4 = h3 - rmRc3*db0c_5;
374	>
375	>	s = db0_3;
376	>	sc = db0c_3;
377	>	s2 = s - sc;
378	>	s3 = s2 - rmRc *db0c_4;
379	>	s4 = s3 - rmRc2*db0c_5;
380	>
381	>	t = db0_4;
382	>	tc = db0c_4;
383	>	t3 = t - tc;
384	>	t4 = t3 - rmRc *db0c_5;
385
386	<	DoubleGenericData* doubleData = dynamic_cast<DoubleGenericData*>(data);
387	<	if (doubleData == NULL) {
388	<	sprintf( painCave.errMsg,
356	<	"Electrostatic::addType could not convert GenericData to "
357	<	"SplitDipoleDistance for\n"
358	<	"\tatom type %s\n", daType->getName().c_str());
359	<	painCave.severity = OPENMD_ERROR;
360	<	painCave.isFatal = 1;
361	<	simError();
362	<	}
363	<	electrostaticAtomData.is_SplitDipole = true;
364	<	electrostaticAtomData.split_dipole_distance = doubleData->getData();
365	<	}
386	>	u = db0_5;
387	>	uc = db0c_5;
388	>	u4 = u - uc;
389
390	<	if (daType->isQuadrupole()) {
391	<	GenericData* data = daType->getPropertyByName("QuadrupoleMoments");
390	>	// in what follows below, the various v functions are used for
391	>	// potentials and torques, while the w functions show up in the
392	>	// forces.
393	>
394	>	switch (summationMethod_) {
395	>	case esm_SHIFTED_FORCE:
396	>
397	>	v01 = f - fc - rmRc*gc;
398	>	v11 = g - gc - rmRc*hc;
399	>	v21 = g*ri - gc*ric - rmRc*(hc - gc*ric)*ric;
400	>	v22 = h - g*ri - (hc - gc*ric) - rmRc*(sc - (hc - gc*ric)*ric);
401	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric - rmRc*(sc-2.0*(hc-gc*ric)*ric)*ric;
402	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric)
403	>	- rmRc*(tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
404	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2
405	>	- rmRc*(sc - 3.0*(hc-gc*ric)*ric)*ric2;
406	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric
407	>	- rmRc*(tc - (4.0*sc - 9.0*(hc - gc*ric)*ric)*ric)*ric;
408
409	<	if (data == NULL) {
410	<	sprintf( painCave.errMsg,
411	<	"Electrostatic::addType could not find QuadrupoleMoments\n"
412	<	"\tparameter for atomType %s.\n",
413	<	daType->getName().c_str());
414	<	painCave.severity = OPENMD_ERROR;
415	<	painCave.isFatal = 1;
416	<	simError();
417	<	}
409	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
410	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric)
411	>	- rmRc*(uc-3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
412	>
413	>	dv01 = g - gc;
414	>	dv11 = h - hc;
415	>	dv21 = (h - g*ri)*ri - (hc - gc*ric)*ric;
416	>	dv22 = (s - (h - g*ri)*ri) - (sc - (hc - gc*ric)*ric);
417	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri - (sc - 2.0*(hc-gc*ric)*ric)*ric;
418	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri)
419	>	- (tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
420	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2 - (sc - 3.0*(hc - gc*ric)*ric)*ric2;
421	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri
422	>	- (tc - (4.0*sc - 9.0*(hc-gc*ric)*ric)*ric)*ric;
423	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri)
424	>	- (uc - 3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
425
426	<	// Quadrupoles in OpenMD are set as the diagonal elements
381	<	// of the diagonalized traceless quadrupole moment tensor.
382	<	// The column vectors of the unitary matrix that diagonalizes
383	<	// the quadrupole moment tensor become the eFrame (or the
384	<	// electrostatic version of the body-fixed frame.
426	>	break;
427
428	<	Vector3dGenericData* v3dData = dynamic_cast<Vector3dGenericData*>(data);
429	<	if (v3dData == NULL) {
430	<	sprintf( painCave.errMsg,
431	<	"Electrostatic::addType could not convert GenericData to "
432	<	"Quadrupole Moments for\n"
433	<	"\tatom type %s\n", daType->getName().c_str());
434	<	painCave.severity = OPENMD_ERROR;
435	<	painCave.isFatal = 1;
436	<	simError();
428	>	case esm_TAYLOR_SHIFTED:
429	>
430	>	v01 = f0;
431	>	v11 = g1;
432	>	v21 = g2 * ri;
433	>	v22 = h2 - v21;
434	>	v31 = (h3 - g3 * ri) * ri;
435	>	v32 = s3 - 3.0*v31;
436	>	v41 = (h4 - g4 * ri) * ri2;
437	>	v42 = s4 * ri - 3.0*v41;
438	>	v43 = t4 - 6.0*v42 - 3.0*v41;
439	>
440	>	dv01 = g0;
441	>	dv11 = h1;
442	>	dv21 = (h2 - g2*ri)*ri;
443	>	dv22 = (s2 - (h2 - g2*ri)*ri);
444	>	dv31 = (s3 - 2.0*(h3-g3*ri)*ri)*ri;
445	>	dv32 = (t3 - 3.0*(s3-2.0*(h3-g3*ri)*ri)*ri);
446	>	dv41 = (s4 - 3.0*(h4 - g4*ri)*ri)*ri2;
447	>	dv42 = (t4 - (4.0*s4 - 9.0*(h4-g4*ri)*ri)*ri)*ri;
448	>	dv43 = (u4 - 3.0*(2.0*t4 - (7.0*s4 - 15.0*(h4 - g4*ri)*ri)*ri)*ri);
449	>
450	>	break;
451	>
452	>	case esm_SHIFTED_POTENTIAL:
453	>
454	>	v01 = f - fc;
455	>	v11 = g - gc;
456	>	v21 = g*ri - gc*ric;
457	>	v22 = h - g*ri - (hc - gc*ric);
458	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
459	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
460	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
461	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
462	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
463	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
464	>
465	>	dv01 = g;
466	>	dv11 = h;
467	>	dv21 = (h - g*ri)*ri;
468	>	dv22 = (s - (h - g*ri)*ri);
469	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
470	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
471	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
472	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
473	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
474	>
475	>	break;
476	>
477	>	case esm_SWITCHING_FUNCTION:
478	>	case esm_HARD:
479	>
480	>	v01 = f;
481	>	v11 = g;
482	>	v21 = g*ri;
483	>	v22 = h - g*ri;
484	>	v31 = (h-g*ri)*ri;
485	>	v32 = (s - 3.0*(h-g*ri)*ri);
486	>	v41 = (h - g*ri)*ri2;
487	>	v42 = (s-3.0*(h-g*ri)*ri)*ri;
488	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri);
489	>
490	>	dv01 = g;
491	>	dv11 = h;
492	>	dv21 = (h - g*ri)*ri;
493	>	dv22 = (s - (h - g*ri)*ri);
494	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
495	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
496	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
497	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
498	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
499	>
500	>	break;
501	>
502	>	case esm_REACTION_FIELD:
503	>
504	>	// following DL_POLY's lead for shifting the image charge potential:
505	>	f = b0 + preRF_ * r2;
506	>	fc = b0c + preRF_ * cutoffRadius_ * cutoffRadius_;
507	>
508	>	g = db0_1 + preRF_ * 2.0 * r;
509	>	gc = db0c_1 + preRF_ * 2.0 * cutoffRadius_;
510	>
511	>	h = db0_2 + preRF_ * 2.0;
512	>	hc = db0c_2 + preRF_ * 2.0;
513	>
514	>	v01 = f - fc;
515	>	v11 = g - gc;
516	>	v21 = g*ri - gc*ric;
517	>	v22 = h - g*ri - (hc - gc*ric);
518	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
519	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
520	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
521	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
522	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
523	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
524	>
525	>	dv01 = g;
526	>	dv11 = h;
527	>	dv21 = (h - g*ri)*ri;
528	>	dv22 = (s - (h - g*ri)*ri);
529	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
530	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
531	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
532	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
533	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
534	>
535	>	break;
536	>
537	>	case esm_EWALD_FULL:
538	>	case esm_EWALD_PME:
539	>	case esm_EWALD_SPME:
540	>	default :
541	>	map<string, ElectrostaticSummationMethod>::iterator i;
542	>	std::string meth;
543	>	for (i = summationMap_.begin(); i != summationMap_.end(); ++i) {
544	>	if ((*i).second == summationMethod_) meth = (*i).first;
545		}
546	+	sprintf( painCave.errMsg,
547	+	"Electrostatic::initialize: electrostaticSummationMethod %s \n"
548	+	"\thas not been implemented yet. Please select one of:\n"
549	+	"\t\"hard\", \"shifted_potential\", or \"shifted_force\"\n",
550	+	meth.c_str() );
551	+	painCave.isFatal = 1;
552	+	simError();
553	+	break;
554	+	}
555	+
556	+	// Add these computed values to the storage vectors for spline creation:
557	+	v01v.push_back(v01);
558	+	v11v.push_back(v11);
559	+	v21v.push_back(v21);
560	+	v22v.push_back(v22);
561	+	v31v.push_back(v31);
562	+	v32v.push_back(v32);
563	+	v41v.push_back(v41);
564	+	v42v.push_back(v42);
565	+	v43v.push_back(v43);
566	+	/*
567	+	dv01v.push_back(dv01);
568	+	dv11v.push_back(dv11);
569	+	dv21v.push_back(dv21);
570	+	dv22v.push_back(dv22);
571	+	dv31v.push_back(dv31);
572	+	dv32v.push_back(dv32);
573	+	dv41v.push_back(dv41);
574	+	dv42v.push_back(dv42);
575	+	dv43v.push_back(dv43);
576	+	*/
577	+	}
578	+
579	+	// construct the spline structures and fill them with the values we've
580	+	// computed:
581	+
582	+	v01s = new CubicSpline();
583	+	v01s->addPoints(rv, v01v);
584	+	v11s = new CubicSpline();
585	+	v11s->addPoints(rv, v11v);
586	+	v21s = new CubicSpline();
587	+	v21s->addPoints(rv, v21v);
588	+	v22s = new CubicSpline();
589	+	v22s->addPoints(rv, v22v);
590	+	v31s = new CubicSpline();
591	+	v31s->addPoints(rv, v31v);
592	+	v32s = new CubicSpline();
593	+	v32s->addPoints(rv, v32v);
594	+	v41s = new CubicSpline();
595	+	v41s->addPoints(rv, v41v);
596	+	v42s = new CubicSpline();
597	+	v42s->addPoints(rv, v42v);
598	+	v43s = new CubicSpline();
599	+	v43s->addPoints(rv, v43v);
600	+
601	+	/*
602	+	dv01s = new CubicSpline();
603	+	dv01s->addPoints(rv, dv01v);
604	+	dv11s = new CubicSpline();
605	+	dv11s->addPoints(rv, dv11v);
606	+	dv21s = new CubicSpline();
607	+	dv21s->addPoints(rv, dv21v);
608	+	dv22s = new CubicSpline();
609	+	dv22s->addPoints(rv, dv22v);
610	+	dv31s = new CubicSpline();
611	+	dv31s->addPoints(rv, dv31v);
612	+	dv32s = new CubicSpline();
613	+	dv32s->addPoints(rv, dv32v);
614	+	dv41s = new CubicSpline();
615	+	dv41s->addPoints(rv, dv41v);
616	+	dv42s = new CubicSpline();
617	+	dv42s->addPoints(rv, dv42v);
618	+	dv43s = new CubicSpline();
619	+	dv43s->addPoints(rv, dv43v);
620	+	*/
621	+
622	+	haveElectroSplines_ = true;
623	+
624	+	initialized_ = true;
625	+	}
626	+
627	+	void Electrostatic::addType(AtomType* atomType){
628	+
629	+	ElectrostaticAtomData electrostaticAtomData;
630	+	electrostaticAtomData.is_Charge = false;
631	+	electrostaticAtomData.is_Dipole = false;
632	+	electrostaticAtomData.is_Quadrupole = false;
633	+	electrostaticAtomData.is_Fluctuating = false;
634	+
635	+	FixedChargeAdapter fca = FixedChargeAdapter(atomType);
636	+
637	+	if (fca.isFixedCharge()) {
638	+	electrostaticAtomData.is_Charge = true;
639	+	electrostaticAtomData.fixedCharge = fca.getCharge();
640	+	}
641	+
642	+	MultipoleAdapter ma = MultipoleAdapter(atomType);
643	+	if (ma.isMultipole()) {
644	+	if (ma.isDipole()) {
645	+	electrostaticAtomData.is_Dipole = true;
646	+	electrostaticAtomData.dipole = ma.getDipole();
647	+	}
648	+	if (ma.isQuadrupole()) {
649		electrostaticAtomData.is_Quadrupole = true;
650	<	electrostaticAtomData.quadrupole_moments = v3dData->getData();
650	>	electrostaticAtomData.quadrupole = ma.getQuadrupole();
651		}
652		}
653
654	<	AtomTypeProperties atp = atomType->getATP();
654	>	FluctuatingChargeAdapter fqa = FluctuatingChargeAdapter(atomType);
655
656	+	if (fqa.isFluctuatingCharge()) {
657	+	electrostaticAtomData.is_Fluctuating = true;
658	+	electrostaticAtomData.electronegativity = fqa.getElectronegativity();
659	+	electrostaticAtomData.hardness = fqa.getHardness();
660	+	electrostaticAtomData.slaterN = fqa.getSlaterN();
661	+	electrostaticAtomData.slaterZeta = fqa.getSlaterZeta();
662	+	}
663	+
664		pair<map<int,AtomType*>::iterator,bool> ret;
665	<	ret = ElectrostaticList.insert( pair<int,AtomType*>(atp.ident, atomType) );
665	>	ret = ElectrostaticList.insert( pair<int,AtomType*>(atomType->getIdent(),
666	>	atomType) );
667		if (ret.second == false) {
668		sprintf( painCave.errMsg,
669		"Electrostatic already had a previous entry with ident %d\n",
670	<	atp.ident);
670	>	atomType->getIdent() );
671		painCave.severity = OPENMD_INFO;
672		painCave.isFatal = 0;
673		simError();
674		}
675
676	<	ElectrostaticMap[atomType] = electrostaticAtomData;
676	>	ElectrostaticMap[atomType] = electrostaticAtomData;
677	>
678	>	// Now, iterate over all known types and add to the mixing map:
679	>
680	>	map<AtomType*, ElectrostaticAtomData>::iterator it;
681	>	for( it = ElectrostaticMap.begin(); it != ElectrostaticMap.end(); ++it) {
682	>	AtomType* atype2 = (*it).first;
683	>	ElectrostaticAtomData eaData2 = (*it).second;
684	>	if (eaData2.is_Fluctuating && electrostaticAtomData.is_Fluctuating) {
685	>
686	>	RealType a = electrostaticAtomData.slaterZeta;
687	>	RealType b = eaData2.slaterZeta;
688	>	int m = electrostaticAtomData.slaterN;
689	>	int n = eaData2.slaterN;
690	>
691	>	// Create the spline of the coulombic integral for s-type
692	>	// Slater orbitals.  Add a 2 angstrom safety window to deal
693	>	// with cutoffGroups that have charged atoms longer than the
694	>	// cutoffRadius away from each other.
695	>
696	>	RealType rval;
697	>	RealType dr = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
698	>	vector<RealType> rvals;
699	>	vector<RealType> Jvals;
700	>	// don't start at i = 0, as rval = 0 is undefined for the
701	>	// slater overlap integrals.
702	>	for (int i = 1; i < np_+1; i++) {
703	>	rval = RealType(i) * dr;
704	>	rvals.push_back(rval);
705	>	Jvals.push_back(sSTOCoulInt( a, b, m, n, rval *
706	>	PhysicalConstants::angstromToBohr ) *
707	>	PhysicalConstants::hartreeToKcal );
708	>	}
709	>
710	>	CubicSpline* J = new CubicSpline();
711	>	J->addPoints(rvals, Jvals);
712	>
713	>	pair<AtomType*, AtomType*> key1, key2;
714	>	key1 = make_pair(atomType, atype2);
715	>	key2 = make_pair(atype2, atomType);
716	>
717	>	Jij[key1] = J;
718	>	Jij[key2] = J;
719	>	}
720	>	}
721	>
722		return;
723		}
724
725		void Electrostatic::setCutoffRadius( RealType rCut ) {
726		cutoffRadius_ = rCut;
420	–	rrf_ = cutoffRadius_;
727		haveCutoffRadius_ = true;
728		}
729
424	–	void Electrostatic::setSwitchingRadius( RealType rSwitch ) {
425	–	rt_ = rSwitch;
426	–	}
730		void Electrostatic::setElectrostaticSummationMethod( ElectrostaticSummationMethod esm ) {
731		summationMethod_ = esm;
732		}
#	Line 441 | Line 744 | namespace OpenMD {
744
745		void Electrostatic::calcForce(InteractionData &idat) {
746
747	<	// utility variables.  Should clean these up and use the Vector3d and
748	<	// Mat3x3d to replace as many as we can in future versions:
747	>	if (!initialized_) initialize();
748	>
749	>	data1 = ElectrostaticMap[idat.atypes.first];
750	>	data2 = ElectrostaticMap[idat.atypes.second];
751
752	<	RealType q_i, q_j, mu_i, mu_j, d_i, d_j;
753	<	RealType qxx_i, qyy_i, qzz_i;
754	<	RealType qxx_j, qyy_j, qzz_j;
755	<	RealType cx_i, cy_i, cz_i;
756	<	RealType cx_j, cy_j, cz_j;
757	<	RealType cx2, cy2, cz2;
758	<	RealType ct_i, ct_j, ct_ij, a1;
759	<	RealType riji, ri, ri2, ri3, ri4;
760	<	RealType pref, vterm, epot, dudr;
761	<	RealType vpair(0.0);
762	<	RealType scale, sc2;
763	<	RealType pot_term, preVal, rfVal;
764	<	RealType c2ri, c3ri, c4rij, cti3, ctj3, ctidotj;
765	<	RealType preSw, preSwSc;
461	<	RealType c1, c2, c3, c4;
462	<	RealType erfcVal(1.0), derfcVal(0.0);
463	<	RealType BigR;
752	>	U = 0.0;  // Potential
753	>	F.zero();  // Force
754	>	Ta.zero(); // Torque on site a
755	>	Tb.zero(); // Torque on site b
756	>	Ea.zero(); // Electric field at site a
757	>	Eb.zero(); // Electric field at site b
758	>	dUdCa = 0.0; // fluctuating charge force at site a
759	>	dUdCb = 0.0; // fluctuating charge force at site a
760	>
761	>	// Indirect interactions mediated by the reaction field.
762	>	indirect_Pot = 0.0;   // Potential
763	>	indirect_F.zero();    // Force
764	>	indirect_Ta.zero();   // Torque on site a
765	>	indirect_Tb.zero();   // Torque on site b
766
767	<	Vector3d Q_i, Q_j;
768	<	Vector3d ux_i, uy_i, uz_i;
467	<	Vector3d ux_j, uy_j, uz_j;
468	<	Vector3d dudux_i, duduy_i, duduz_i;
469	<	Vector3d dudux_j, duduy_j, duduz_j;
470	<	Vector3d rhatdot2, rhatc4;
471	<	Vector3d dVdr;
767	>	// Excluded potential that is still computed for fluctuating charges
768	>	excluded_Pot= 0.0;
769
473	–	// variables for indirect (reaction field) interactions for excluded pairs:
474	–	RealType indirect_Pot(0.0);
475	–	RealType indirect_vpair(0.0);
476	–	Vector3d indirect_dVdr(V3Zero);
477	–	Vector3d indirect_duduz_i(V3Zero), indirect_duduz_j(V3Zero);
770
479	–	pair<RealType, RealType> res;
480	–
481	–	if (!initialized_) initialize();
482	–
483	–	ElectrostaticAtomData data1 = ElectrostaticMap[idat.atypes.first];
484	–	ElectrostaticAtomData data2 = ElectrostaticMap[idat.atypes.second];
485	–
771		// some variables we'll need independent of electrostatic type:
772
773	<	riji = 1.0 /  *(idat.rij) ;
774	<	Vector3d rhat =  *(idat.d)   * riji;
775	<
773	>	ri = 1.0 /  *(idat.rij);
774	>	rhat =  *(idat.d)  * ri;
775	>
776		// logicals
777
778	<	bool i_is_Charge = data1.is_Charge;
779	<	bool i_is_Dipole = data1.is_Dipole;
780	<	bool i_is_SplitDipole = data1.is_SplitDipole;
781	<	bool i_is_Quadrupole = data1.is_Quadrupole;
778	>	a_is_Charge = data1.is_Charge;
779	>	a_is_Dipole = data1.is_Dipole;
780	>	a_is_Quadrupole = data1.is_Quadrupole;
781	>	a_is_Fluctuating = data1.is_Fluctuating;
782
783	<	bool j_is_Charge = data2.is_Charge;
784	<	bool j_is_Dipole = data2.is_Dipole;
785	<	bool j_is_SplitDipole = data2.is_SplitDipole;
786	<	bool j_is_Quadrupole = data2.is_Quadrupole;
783	>	b_is_Charge = data2.is_Charge;
784	>	b_is_Dipole = data2.is_Dipole;
785	>	b_is_Quadrupole = data2.is_Quadrupole;
786	>	b_is_Fluctuating = data2.is_Fluctuating;
787	>
788	>	// Obtain all of the required radial function values from the
789	>	// spline structures:
790
791	<	if (i_is_Charge) {
792	<	q_i = data1.charge;
793	<	if (idat.excluded) {
506	<	*(idat.skippedCharge2) += q_i;
507	<	}
791	>	// needed for fields (and forces):
792	>	if (a_is_Charge || b_is_Charge) {
793	>	v01s->getValueAndDerivativeAt( *(idat.rij), v01, dv01);
794		}
795	+	if (a_is_Dipole || b_is_Dipole) {
796	+	v11s->getValueAndDerivativeAt( *(idat.rij), v11, dv11);
797	+	v11or = ri * v11;
798	+	}
799	+	if (a_is_Quadrupole || b_is_Quadrupole ||  (a_is_Dipole && b_is_Dipole)) {
800	+	v21s->getValueAndDerivativeAt( *(idat.rij), v21, dv21);
801	+	v22s->getValueAndDerivativeAt( *(idat.rij), v22, dv22);
802	+	v22or = ri * v22;
803	+	}
804
805	<	if (i_is_Dipole) {
806	<	mu_i = data1.dipole_moment;
807	<	uz_i = idat.eFrame1->getColumn(2);
808	<
809	<	ct_i = dot(uz_i, rhat);
810	<
811	<	if (i_is_SplitDipole)
517	<	d_i = data1.split_dipole_distance;
518	<
519	<	duduz_i = V3Zero;
805	>	// needed for potentials (and forces and torques):
806	>	if ((a_is_Dipole && b_is_Quadrupole) ||
807	>	(b_is_Dipole && a_is_Quadrupole)) {
808	>	v31s->getValueAndDerivativeAt( *(idat.rij), v31, dv31);
809	>	v32s->getValueAndDerivativeAt( *(idat.rij), v32, dv32);
810	>	v31or = v31 * ri;
811	>	v32or = v32 * ri;
812		}
813	+	if (a_is_Quadrupole && b_is_Quadrupole) {
814	+	v41s->getValueAndDerivativeAt( *(idat.rij), v41, dv41);
815	+	v42s->getValueAndDerivativeAt( *(idat.rij), v42, dv42);
816	+	v43s->getValueAndDerivativeAt( *(idat.rij), v43, dv43);
817	+	v42or = v42 * ri;
818	+	v43or = v43 * ri;
819	+	}
820	+
821	+	// calculate the single-site contributions (fields, etc).
822
823	<	if (i_is_Quadrupole) {
824	<	Q_i = data1.quadrupole_moments;
524	<	qxx_i = Q_i.x();
525	<	qyy_i = Q_i.y();
526	<	qzz_i = Q_i.z();
823	>	if (a_is_Charge) {
824	>	C_a = data1.fixedCharge;
825
826	<	ux_i = idat.eFrame1->getColumn(0);
827	<	uy_i = idat.eFrame1->getColumn(1);
828	<	uz_i = idat.eFrame1->getColumn(2);
829	<
532	<	cx_i = dot(ux_i, rhat);
533	<	cy_i = dot(uy_i, rhat);
534	<	cz_i = dot(uz_i, rhat);
535	<
536	<	dudux_i = V3Zero;
537	<	duduy_i = V3Zero;
538	<	duduz_i = V3Zero;
539	<	}
540	<
541	<	if (j_is_Charge) {
542	<	q_j = data2.charge;
826	>	if (a_is_Fluctuating) {
827	>	C_a += *(idat.flucQ1);
828	>	}
829	>
830		if (idat.excluded) {
831	<	*(idat.skippedCharge1) += q_j;
831	>	*(idat.skippedCharge2) += C_a;
832	>	} else {
833	>	// only do the field if we're not excluded:
834	>	Eb -= C_a *  pre11_ * dv01 * rhat;
835		}
836		}
837	<
838	<
839	<	if (j_is_Dipole) {
840	<	mu_j = data2.dipole_moment;
841	<	uz_j = idat.eFrame2->getColumn(2);
837	>
838	>	if (a_is_Dipole) {
839	>	D_a = *(idat.dipole1);
840	>	rdDa = dot(rhat, D_a);
841	>	rxDa = cross(rhat, D_a);
842	>	if (!idat.excluded)
843	>	Eb -=  pre12_ * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
844	>	}
845	>
846	>	if (a_is_Quadrupole) {
847	>	Q_a = *(idat.quadrupole1);
848	>	trQa =  Q_a.trace();
849	>	Qar =   Q_a * rhat;
850	>	rQa = rhat * Q_a;
851	>	rdQar = dot(rhat, Qar);
852	>	rxQar = cross(rhat, Qar);
853	>	if (!idat.excluded)
854	>	Eb -= pre14_ * (trQa * rhat * dv21 + 2.0 * Qar * v22or
855	>	+ rdQar * rhat * (dv22 - 2.0*v22or));
856	>	}
857	>
858	>	if (b_is_Charge) {
859	>	C_b = data2.fixedCharge;
860
861	<	ct_j = dot(uz_j, rhat);
862	<
555	<	if (j_is_SplitDipole)
556	<	d_j = data2.split_dipole_distance;
861	>	if (b_is_Fluctuating)
862	>	C_b += *(idat.flucQ2);
863
864	<	duduz_j = V3Zero;
864	>	if (idat.excluded) {
865	>	*(idat.skippedCharge1) += C_b;
866	>	} else {
867	>	// only do the field if we're not excluded:
868	>	Ea += C_b *  pre11_ * dv01 * rhat;
869	>	}
870		}
871
872	<	if (j_is_Quadrupole) {
873	<	Q_j = data2.quadrupole_moments;
874	<	qxx_j = Q_j.x();
875	<	qyy_j = Q_j.y();
876	<	qzz_j = Q_j.z();
877	<
567	<	ux_j = idat.eFrame2->getColumn(0);
568	<	uy_j = idat.eFrame2->getColumn(1);
569	<	uz_j = idat.eFrame2->getColumn(2);
570	<
571	<	cx_j = dot(ux_j, rhat);
572	<	cy_j = dot(uy_j, rhat);
573	<	cz_j = dot(uz_j, rhat);
574	<
575	<	dudux_j = V3Zero;
576	<	duduy_j = V3Zero;
577	<	duduz_j = V3Zero;
872	>	if (b_is_Dipole) {
873	>	D_b = *(idat.dipole2);
874	>	rdDb = dot(rhat, D_b);
875	>	rxDb = cross(rhat, D_b);
876	>	if (!idat.excluded)
877	>	Ea += pre12_ * ((dv11-v11or) * rdDb * rhat + v11or * D_b);
878		}
879
880	<	epot = 0.0;
881	<	dVdr = V3Zero;
880	>	if (b_is_Quadrupole) {
881	>	Q_b = *(idat.quadrupole2);
882	>	trQb =  Q_b.trace();
883	>	Qbr =   Q_b * rhat;
884	>	rQb = rhat * Q_b;
885	>	rdQbr = dot(rhat, Qbr);
886	>	rxQbr = cross(rhat, Qbr);
887	>	if (!idat.excluded)
888	>	Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
889	>	+ rdQbr * rhat * (dv22 - 2.0*v22or));
890	>	}
891
892	<	if (i_is_Charge) {
892	>	if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
893	>	J = Jij[idat.atypes];
894	>	}
895	>
896	>	if (a_is_Charge) {
897
898	<	if (j_is_Charge) {
899	<	if (screeningMethod_ == DAMPED) {
900	<	// assemble the damping variables
901	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
902	<	//erfcVal = res.first;
903	<	//derfcVal = res.second;
898	>	if (b_is_Charge) {
899	>	pref =  pre11_ * *(idat.electroMult);
900	>	U  += C_a * C_b * pref * v01;
901	>	F  += C_a * C_b * pref * dv01 * rhat;
902	>
903	>	// If this is an excluded pair, there are still indirect
904	>	// interactions via the reaction field we must worry about:
905
906	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
907	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
906	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
907	>	rfContrib = preRF_ * pref * C_a * C_b * *(idat.r2);
908	>	indirect_Pot += rfContrib;
909	>	indirect_F   += rfContrib * 2.0 * ri * rhat;
910	>	}
911	>
912	>	// Fluctuating charge forces are handled via Coulomb integrals
913	>	// for excluded pairs (i.e. those connected via bonds) and
914	>	// with the standard charge-charge interaction otherwise.
915
916	<	c1 = erfcVal * riji;
917	<	c2 = (-derfcVal + c1) * riji;
916	>	if (idat.excluded) {
917	>	if (a_is_Fluctuating || b_is_Fluctuating) {
918	>	coulInt = J->getValueAt( *(idat.rij) );
919	>	if (a_is_Fluctuating)  dUdCa += coulInt * C_b;
920	>	if (b_is_Fluctuating)  dUdCb += coulInt * C_a;
921	>	excluded_Pot += C_a * C_b * coulInt;
922	>	}
923		} else {
924	<	c1 = riji;
925	<	c2 = c1 * riji;
924	>	if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
925	>	if (a_is_Fluctuating) dUdCb += C_a * pref * v01;
926		}
927	+	}
928
929	<	preVal =  *(idat.electroMult) * pre11_ * q_i * q_j;
930	<
931	<	if (summationMethod_ == esm_SHIFTED_POTENTIAL) {
932	<	vterm = preVal * (c1 - c1c_);
933	<	dudr  = - *(idat.sw)  * preVal * c2;
929	>	if (b_is_Dipole) {
930	>	pref =  pre12_ * *(idat.electroMult);
931	>	U  += C_a * pref * v11 * rdDb;
932	>	F  += C_a * pref * ((dv11 - v11or) * rdDb * rhat + v11or * D_b);
933	>	Tb += C_a * pref * v11 * rxDb;
934
935	<	} else if (summationMethod_ == esm_SHIFTED_FORCE)  {
609	<	vterm = preVal * ( c1 - c1c_ + c2c_*( *(idat.rij)  - cutoffRadius_) );
610	<	dudr  =  *(idat.sw)  * preVal * (c2c_ - c2);
935	>	if (a_is_Fluctuating) dUdCa += pref * v11 * rdDb;
936
937	<	} else if (summationMethod_ == esm_REACTION_FIELD) {
938	<	rfVal = preRF_ *  *(idat.rij)  *  *(idat.rij);
937	>	// Even if we excluded this pair from direct interactions, we
938	>	// still have the reaction-field-mediated charge-dipole
939	>	// interaction:
940
941	<	vterm = preVal * ( riji + rfVal );
942	<	dudr  =  *(idat.sw)  * preVal * ( 2.0 * rfVal - riji ) * riji;
943	<
944	<	// if this is an excluded pair, there are still indirect
945	<	// interactions via the reaction field we must worry about:
620	<
621	<	if (idat.excluded) {
622	<	indirect_vpair += preVal * rfVal;
623	<	indirect_Pot += *(idat.sw) * preVal * rfVal;
624	<	indirect_dVdr += *(idat.sw)  * preVal * 2.0 * rfVal  * riji * rhat;
625	<	}
626	<
627	<	} else {
628	<
629	<	vterm = preVal * riji * erfcVal;
630	<	dudr  = -  *(idat.sw)  * preVal * c2;
631	<
941	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
942	>	rfContrib = C_a * pref * preRF_ * 2.0 * *(idat.rij);
943	>	indirect_Pot += rfContrib * rdDb;
944	>	indirect_F   += rfContrib * D_b / (*idat.rij);
945	>	indirect_Tb  += C_a * pref * preRF_ * rxDb;
946		}
633	–
634	–	vpair += vterm;
635	–	epot +=  *(idat.sw)  * vterm;
636	–	dVdr += dudr * rhat;
947		}
948
949	<	if (j_is_Dipole) {
950	<	// pref is used by all the possible methods
951	<	pref =  *(idat.electroMult) * pre12_ * q_i * mu_j;
952	<	preSw =  *(idat.sw)  * pref;
949	>	if (b_is_Quadrupole) {
950	>	pref = pre14_ * *(idat.electroMult);
951	>	U  +=  C_a * pref * (v21 * trQb + v22 * rdQbr);
952	>	F  +=  C_a * pref * (trQb * dv21 * rhat + 2.0 * Qbr * v22or);
953	>	F  +=  C_a * pref * rdQbr * rhat * (dv22 - 2.0*v22or);
954	>	Tb +=  C_a * pref * 2.0 * rxQbr * v22;
955
956	<	if (summationMethod_ == esm_REACTION_FIELD) {
957	<	ri2 = riji * riji;
958	<	ri3 = ri2 * riji;
647	<
648	<	vterm = - pref * ct_j * ( ri2 - preRF2_ *  *(idat.rij)  );
649	<	vpair += vterm;
650	<	epot +=  *(idat.sw)  * vterm;
956	>	if (a_is_Fluctuating) dUdCa += pref * (v21 * trQb + v22 * rdQbr);
957	>	}
958	>	}
959
960	<	dVdr +=  -preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j);
653	<	duduz_j += -preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
960	>	if (a_is_Dipole) {
961
962	<	// Even if we excluded this pair from direct interactions,
963	<	// we still have the reaction-field-mediated charge-dipole
657	<	// interaction:
962	>	if (b_is_Charge) {
963	>	pref = pre12_ * *(idat.electroMult);
964
965	<	if (idat.excluded) {
966	<	indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij);
967	<	indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij);
662	<	indirect_dVdr += preSw * preRF2_ * uz_j;
663	<	indirect_duduz_j += preSw * rhat * preRF2_ *  *(idat.rij);
664	<	}
665	<
666	<	} else {
667	<	// determine the inverse r used if we have split dipoles
668	<	if (j_is_SplitDipole) {
669	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
670	<	ri = 1.0 / BigR;
671	<	scale =  *(idat.rij)  * ri;
672	<	} else {
673	<	ri = riji;
674	<	scale = 1.0;
675	<	}
676	<
677	<	sc2 = scale * scale;
965	>	U  -= C_b * pref * v11 * rdDa;
966	>	F  -= C_b * pref * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
967	>	Ta -= C_b * pref * v11 * rxDa;
968
969	<	if (screeningMethod_ == DAMPED) {
680	<	// assemble the damping variables
681	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
682	<	//erfcVal = res.first;
683	<	//derfcVal = res.second;
684	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
685	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
686	<	c1 = erfcVal * ri;
687	<	c2 = (-derfcVal + c1) * ri;
688	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
689	<	} else {
690	<	c1 = ri;
691	<	c2 = c1 * ri;
692	<	c3 = 3.0 * c2 * ri;
693	<	}
694	<
695	<	c2ri = c2 * ri;
969	>	if (b_is_Fluctuating) dUdCb -= pref * v11 * rdDa;
970
971	<	// calculate the potential
972	<	pot_term =  scale * c2;
973	<	vterm = -pref * ct_j * pot_term;
974	<	vpair += vterm;
975	<	epot +=  *(idat.sw)  * vterm;
976	<
977	<	// calculate derivatives for forces and torques
978	<
705	<	dVdr += -preSw * (uz_j * c2ri - ct_j * rhat * sc2 * c3);
706	<	duduz_j += -preSw * pot_term * rhat;
707	<
971	>	// Even if we excluded this pair from direct interactions,
972	>	// we still have the reaction-field-mediated charge-dipole
973	>	// interaction:
974	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
975	>	rfContrib = C_b * pref * preRF_ * 2.0 * *(idat.rij);
976	>	indirect_Pot -= rfContrib * rdDa;
977	>	indirect_F   -= rfContrib * D_a / (*idat.rij);
978	>	indirect_Ta  -= C_b * pref * preRF_ * rxDa;
979		}
980		}
981
982	<	if (j_is_Quadrupole) {
983	<	// first precalculate some necessary variables
984	<	cx2 = cx_j * cx_j;
985	<	cy2 = cy_j * cy_j;
715	<	cz2 = cz_j * cz_j;
716	<	pref =   *(idat.electroMult) * pre14_ * q_i * one_third_;
717	<
718	<	if (screeningMethod_ == DAMPED) {
719	<	// assemble the damping variables
720	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
721	<	//erfcVal = res.first;
722	<	//derfcVal = res.second;
723	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
724	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
725	<	c1 = erfcVal * riji;
726	<	c2 = (-derfcVal + c1) * riji;
727	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
728	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
729	<	} else {
730	<	c1 = riji;
731	<	c2 = c1 * riji;
732	<	c3 = 3.0 * c2 * riji;
733	<	c4 = 5.0 * c3 * riji * riji;
734	<	}
982	>	if (b_is_Dipole) {
983	>	pref = pre22_ * *(idat.electroMult);
984	>	DadDb = dot(D_a, D_b);
985	>	DaxDb = cross(D_a, D_b);
986
987	<	// precompute variables for convenience
988	<	preSw =  *(idat.sw)  * pref;
989	<	c2ri = c2 * riji;
990	<	c3ri = c3 * riji;
991	<	c4rij = c4 *  *(idat.rij) ;
741	<	rhatdot2 = 2.0 * rhat * c3;
742	<	rhatc4 = rhat * c4rij;
987	>	U  -= pref * (DadDb * v21 + rdDa * rdDb * v22);
988	>	F  -= pref * (dv21 * DadDb * rhat + v22or * (rdDb * D_a + rdDa * D_b));
989	>	F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
990	>	Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
991	>	Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
992
993	<	// calculate the potential
994	<	pot_term = ( qxx_j * (cx2*c3 - c2ri) +
995	<	qyy_j * (cy2*c3 - c2ri) +
996	<	qzz_j * (cz2*c3 - c2ri) );
997	<	vterm = pref * pot_term;
998	<	vpair += vterm;
999	<	epot +=  *(idat.sw)  * vterm;
1000	<
1001	<	// calculate derivatives for the forces and torques
993	>	// Even if we excluded this pair from direct interactions, we
994	>	// still have the reaction-field-mediated dipole-dipole
995	>	// interaction:
996	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
997	>	rfContrib = -pref * preRF_ * 2.0;
998	>	indirect_Pot += rfContrib * DadDb;
999	>	indirect_Ta  += rfContrib * DaxDb;
1000	>	indirect_Tb  -= rfContrib * DaxDb;
1001	>	}
1002	>	}
1003
1004	<	dVdr += -preSw * ( qxx_j* (cx2*rhatc4 - (2.0*cx_j*ux_j + rhat)*c3ri) +
1005	<	qyy_j* (cy2*rhatc4 - (2.0*cy_j*uy_j + rhat)*c3ri) +
1006	<	qzz_j* (cz2*rhatc4 - (2.0*cz_j*uz_j + rhat)*c3ri));
1007	<
1008	<	dudux_j += preSw * qxx_j * cx_j * rhatdot2;
1009	<	duduy_j += preSw * qyy_j * cy_j * rhatdot2;
1010	<	duduz_j += preSw * qzz_j * cz_j * rhatdot2;
1004	>	if (b_is_Quadrupole) {
1005	>	pref = pre24_ * *(idat.electroMult);
1006	>	DadQb = D_a * Q_b;
1007	>	DadQbr = dot(D_a, Qbr);
1008	>	DaxQbr = cross(D_a, Qbr);
1009	>
1010	>	U  -= pref * ((trQb*rdDa + 2.0*DadQbr)*v31 + rdDa*rdQbr*v32);
1011	>	F  -= pref * (trQb*D_a + 2.0*DadQb) * v31or;
1012	>	F  -= pref * (trQb*rdDa + 2.0*DadQbr) * (dv31-v31or) * rhat;
1013	>	F  -= pref * (D_a*rdQbr + 2.0*rdDa*rQb) * v32or;
1014	>	F  -= pref * (rdDa * rdQbr * rhat * (dv32-3.0*v32or));
1015	>	Ta += pref * ((-trQb*rxDa + 2.0 * DaxQbr)*v31 - rxDa*rdQbr*v32);
1016	>	Tb += pref * ((2.0*cross(DadQb, rhat) - 2.0*DaxQbr)*v31
1017	>	- 2.0*rdDa*rxQbr*v32);
1018		}
1019		}
763	–
764	–	if (i_is_Dipole) {
1020
1021	<	if (j_is_Charge) {
1022	<	// variables used by all the methods
1023	<	pref =  *(idat.electroMult) * pre12_ * q_j * mu_i;
1024	<	preSw =  *(idat.sw)  * pref;
1021	>	if (a_is_Quadrupole) {
1022	>	if (b_is_Charge) {
1023	>	pref = pre14_ * *(idat.electroMult);
1024	>	U  += C_b * pref * (v21 * trQa + v22 * rdQar);
1025	>	F  += C_b * pref * (trQa * rhat * dv21 + 2.0 * Qar * v22or);
1026	>	F  += C_b * pref * rdQar * rhat * (dv22 - 2.0*v22or);
1027	>	Ta += C_b * pref * 2.0 * rxQar * v22;
1028
1029	<	if (summationMethod_ == esm_REACTION_FIELD) {
1029	>	if (b_is_Fluctuating) dUdCb += pref * (v21 * trQa + v22 * rdQar);
1030	>	}
1031	>	if (b_is_Dipole) {
1032	>	pref = pre24_ * *(idat.electroMult);
1033	>	DbdQa = D_b * Q_a;
1034	>	DbdQar = dot(D_b, Qar);
1035	>	DbxQar = cross(D_b, Qar);
1036
1037	<	ri2 = riji * riji;
1038	<	ri3 = ri2 * riji;
1039	<
1040	<	vterm = pref * ct_i * ( ri2 - preRF2_ *  *(idat.rij)  );
1041	<	vpair += vterm;
1042	<	epot +=  *(idat.sw)  * vterm;
1043	<
1044	<	dVdr += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_ * uz_i);
781	<
782	<	duduz_i += preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
783	<
784	<	// Even if we excluded this pair from direct interactions,
785	<	// we still have the reaction-field-mediated charge-dipole
786	<	// interaction:
787	<
788	<	if (idat.excluded) {
789	<	indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij);
790	<	indirect_Pot += -preSw * ct_i * preRF2_ * *(idat.rij);
791	<	indirect_dVdr += -preSw * preRF2_ * uz_i;
792	<	indirect_duduz_i += -preSw * rhat * preRF2_ *  *(idat.rij);
793	<	}
794	<
795	<	} else {
796	<
797	<	// determine inverse r if we are using split dipoles
798	<	if (i_is_SplitDipole) {
799	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
800	<	ri = 1.0 / BigR;
801	<	scale =  *(idat.rij)  * ri;
802	<	} else {
803	<	ri = riji;
804	<	scale = 1.0;
805	<	}
806	<
807	<	sc2 = scale * scale;
808	<
809	<	if (screeningMethod_ == DAMPED) {
810	<	// assemble the damping variables
811	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
812	<	//erfcVal = res.first;
813	<	//derfcVal = res.second;
814	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
815	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
816	<	c1 = erfcVal * ri;
817	<	c2 = (-derfcVal + c1) * ri;
818	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
819	<	} else {
820	<	c1 = ri;
821	<	c2 = c1 * ri;
822	<	c3 = 3.0 * c2 * ri;
823	<	}
824	<
825	<	c2ri = c2 * ri;
826	<
827	<	// calculate the potential
828	<	pot_term = c2 * scale;
829	<	vterm = pref * ct_i * pot_term;
830	<	vpair += vterm;
831	<	epot +=  *(idat.sw)  * vterm;
832	<
833	<	// calculate derivatives for the forces and torques
834	<	dVdr += preSw * (uz_i * c2ri - ct_i * rhat * sc2 * c3);
835	<	duduz_i += preSw * pot_term * rhat;
836	<	}
1037	>	U  += pref * ((trQa*rdDb + 2.0*DbdQar)*v31 + rdDb*rdQar*v32);
1038	>	F  += pref * (trQa*D_b + 2.0*DbdQa) * v31or;
1039	>	F  += pref * (trQa*rdDb + 2.0*DbdQar) * (dv31-v31or) * rhat;
1040	>	F  += pref * (D_b*rdQar + 2.0*rdDb*rQa) * v32or;
1041	>	F  += pref * (rdDb * rdQar * rhat * (dv32-3.0*v32or));
1042	>	Ta += pref * ((-2.0*cross(DbdQa, rhat) + 2.0*DbxQar)*v31
1043	>	+ 2.0*rdDb*rxQar*v32);
1044	>	Tb += pref * ((trQa*rxDb - 2.0 * DbxQar)*v31 + rxDb*rdQar*v32);
1045		}
1046	+	if (b_is_Quadrupole) {
1047	+	pref = pre44_ * *(idat.electroMult);  // yes
1048	+	QaQb = Q_a * Q_b;
1049	+	trQaQb = QaQb.trace();
1050	+	rQaQb = rhat * QaQb;
1051	+	QaQbr = QaQb * rhat;
1052	+	QaxQb = cross(Q_a, Q_b);
1053	+	rQaQbr = dot(rQa, Qbr);
1054	+	rQaxQbr = cross(rQa, Qbr);
1055	+
1056	+	U  += pref * (trQa * trQb + 2.0 * trQaQb) * v41;
1057	+	U  += pref * (trQa * rdQbr + trQb * rdQar  + 4.0 * rQaQbr) * v42;
1058	+	U  += pref * (rdQar * rdQbr) * v43;
1059
1060	<	if (j_is_Dipole) {
1061	<	// variables used by all methods
1062	<	ct_ij = dot(uz_i, uz_j);
1060	>	F  += pref * rhat * (trQa * trQb + 2.0 * trQaQb)*dv41;
1061	>	F  += pref*rhat*(trQa*rdQbr + trQb*rdQar + 4.0*rQaQbr)*(dv42-2.0*v42or);
1062	>	F  += pref * rhat * (rdQar * rdQbr)*(dv43 - 4.0*v43or);
1063
1064	<	pref =  *(idat.electroMult) * pre22_ * mu_i * mu_j;
1065	<	preSw =  *(idat.sw)  * pref;
1064	>	F  += pref * 2.0 * (trQb*rQa + trQa*rQb) * v42or;
1065	>	F  += pref * 4.0 * (rQaQb + QaQbr) * v42or;
1066	>	F  += pref * 2.0 * (rQa*rdQbr + rdQar*rQb) * v43or;
1067
1068	<	if (summationMethod_ == esm_REACTION_FIELD) {
1069	<	ri2 = riji * riji;
1070	<	ri3 = ri2 * riji;
1071	<	ri4 = ri2 * ri2;
1068	>	Ta += pref * (- 4.0 * QaxQb * v41);
1069	>	Ta += pref * (- 2.0 * trQb * cross(rQa, rhat)
1070	>	+ 4.0 * cross(rhat, QaQbr)
1071	>	- 4.0 * rQaxQbr) * v42;
1072	>	Ta += pref * 2.0 * cross(rhat,Qar) * rdQbr * v43;
1073
851	–	vterm = pref * ( ri3 * (ct_ij - 3.0 * ct_i * ct_j) -
852	–	preRF2_ * ct_ij );
853	–	vpair += vterm;
854	–	epot +=  *(idat.sw)  * vterm;
855	–
856	–	a1 = 5.0 * ct_i * ct_j - ct_ij;
857	–
858	–	dVdr += preSw * 3.0 * ri4 * (a1 * rhat - ct_i * uz_j - ct_j * uz_i);
1074
1075	<	duduz_i += preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j);
1076	<	duduz_j += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_*uz_i);
1075	>	Tb += pref * (+ 4.0 * QaxQb * v41);
1076	>	Tb += pref * (- 2.0 * trQa * cross(rQb, rhat)
1077	>	- 4.0 * cross(rQaQb, rhat)
1078	>	+ 4.0 * rQaxQbr) * v42;
1079	>	// Possible replacement for line 2 above:
1080	>	//             + 4.0 * cross(rhat, QbQar)
1081
1082	<	if (idat.excluded) {
864	<	indirect_vpair +=  - pref * preRF2_ * ct_ij;
865	<	indirect_Pot +=    - preSw * preRF2_ * ct_ij;
866	<	indirect_duduz_i += -preSw * preRF2_ * uz_j;
867	<	indirect_duduz_j += -preSw * preRF2_ * uz_i;
868	<	}
1082	>	Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1083
1084	<	} else {
871	<
872	<	if (i_is_SplitDipole) {
873	<	if (j_is_SplitDipole) {
874	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i + 0.25 * d_j * d_j);
875	<	} else {
876	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
877	<	}
878	<	ri = 1.0 / BigR;
879	<	scale =  *(idat.rij)  * ri;
880	<	} else {
881	<	if (j_is_SplitDipole) {
882	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
883	<	ri = 1.0 / BigR;
884	<	scale =  *(idat.rij)  * ri;
885	<	} else {
886	<	ri = riji;
887	<	scale = 1.0;
888	<	}
889	<	}
890	<	if (screeningMethod_ == DAMPED) {
891	<	// assemble damping variables
892	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
893	<	//erfcVal = res.first;
894	<	//derfcVal = res.second;
895	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
896	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
897	<	c1 = erfcVal * ri;
898	<	c2 = (-derfcVal + c1) * ri;
899	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
900	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * ri * ri;
901	<	} else {
902	<	c1 = ri;
903	<	c2 = c1 * ri;
904	<	c3 = 3.0 * c2 * ri;
905	<	c4 = 5.0 * c3 * ri * ri;
906	<	}
907	<
908	<	// precompute variables for convenience
909	<	sc2 = scale * scale;
910	<	cti3 = ct_i * sc2 * c3;
911	<	ctj3 = ct_j * sc2 * c3;
912	<	ctidotj = ct_i * ct_j * sc2;
913	<	preSwSc = preSw * scale;
914	<	c2ri = c2 * ri;
915	<	c3ri = c3 * ri;
916	<	c4rij = c4 *  *(idat.rij) ;
917	<
918	<	// calculate the potential
919	<	pot_term = (ct_ij * c2ri - ctidotj * c3);
920	<	vterm = pref * pot_term;
921	<	vpair += vterm;
922	<	epot +=  *(idat.sw)  * vterm;
923	<
924	<	// calculate derivatives for the forces and torques
925	<	dVdr += preSwSc * ( ctidotj * rhat * c4rij  -
926	<	(ct_i*uz_j + ct_j*uz_i + ct_ij*rhat) * c3ri);
927	<
928	<	duduz_i += preSw * (uz_j * c2ri - ctj3 * rhat);
929	<	duduz_j += preSw * (uz_i * c2ri - cti3 * rhat);
930	<	}
1084	>	//  cerr << " tsum = " << Ta + Tb - cross(  *(idat.d) , F ) << "\n";
1085		}
1086		}
1087
1088	<	if (i_is_Quadrupole) {
1089	<	if (j_is_Charge) {
1090	<	// precompute some necessary variables
937	<	cx2 = cx_i * cx_i;
938	<	cy2 = cy_i * cy_i;
939	<	cz2 = cz_i * cz_i;
940	<
941	<	pref =  *(idat.electroMult) * pre14_ * q_j * one_third_;
942	<
943	<	if (screeningMethod_ == DAMPED) {
944	<	// assemble the damping variables
945	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
946	<	//erfcVal = res.first;
947	<	//derfcVal = res.second;
948	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
949	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
950	<	c1 = erfcVal * riji;
951	<	c2 = (-derfcVal + c1) * riji;
952	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
953	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
954	<	} else {
955	<	c1 = riji;
956	<	c2 = c1 * riji;
957	<	c3 = 3.0 * c2 * riji;
958	<	c4 = 5.0 * c3 * riji * riji;
959	<	}
960	<
961	<	// precompute some variables for convenience
962	<	preSw =  *(idat.sw)  * pref;
963	<	c2ri = c2 * riji;
964	<	c3ri = c3 * riji;
965	<	c4rij = c4 *  *(idat.rij) ;
966	<	rhatdot2 = 2.0 * rhat * c3;
967	<	rhatc4 = rhat * c4rij;
968	<
969	<	// calculate the potential
970	<	pot_term = ( qxx_i * (cx2 * c3 - c2ri) +
971	<	qyy_i * (cy2 * c3 - c2ri) +
972	<	qzz_i * (cz2 * c3 - c2ri) );
973	<
974	<	vterm = pref * pot_term;
975	<	vpair += vterm;
976	<	epot +=  *(idat.sw)  * vterm;
977	<
978	<	// calculate the derivatives for the forces and torques
979	<
980	<	dVdr += -preSw * (qxx_i* (cx2*rhatc4 - (2.0*cx_i*ux_i + rhat)*c3ri) +
981	<	qyy_i* (cy2*rhatc4 - (2.0*cy_i*uy_i + rhat)*c3ri) +
982	<	qzz_i* (cz2*rhatc4 - (2.0*cz_i*uz_i + rhat)*c3ri));
983	<
984	<	dudux_i += preSw * qxx_i * cx_i *  rhatdot2;
985	<	duduy_i += preSw * qyy_i * cy_i *  rhatdot2;
986	<	duduz_i += preSw * qzz_i * cz_i *  rhatdot2;
987	<	}
1088	>	if (idat.doElectricField) {
1089	>	*(idat.eField1) += Ea * *(idat.electroMult);
1090	>	*(idat.eField2) += Eb * *(idat.electroMult);
1091		}
1092
1093	+	if (a_is_Fluctuating) *(idat.dVdFQ1) += dUdCa * *(idat.sw);
1094	+	if (b_is_Fluctuating) *(idat.dVdFQ2) += dUdCb * *(idat.sw);
1095
1096		if (!idat.excluded) {
992	–	*(idat.vpair) += vpair;
993	–	(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot;
994	–	*(idat.f1) += dVdr;
1097
1098	<	if (i_is_Dipole || i_is_Quadrupole)
1099	<	*(idat.t1) -= cross(uz_i, duduz_i);
1100	<	if (i_is_Quadrupole) {
999	<	*(idat.t1) -= cross(ux_i, dudux_i);
1000	<	*(idat.t1) -= cross(uy_i, duduy_i);
1001	<	}
1098	>	*(idat.vpair) += U;
1099	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += U * *(idat.sw);
1100	>	*(idat.f1) += F * *(idat.sw);
1101
1102	<	if (j_is_Dipole || j_is_Quadrupole)
1103	<	*(idat.t2) -= cross(uz_j, duduz_j);
1005	<	if (j_is_Quadrupole) {
1006	<	*(idat.t2) -= cross(uz_j, dudux_j);
1007	<	*(idat.t2) -= cross(uz_j, duduy_j);
1008	<	}
1102	>	if (a_is_Dipole || a_is_Quadrupole)
1103	>	*(idat.t1) += Ta * *(idat.sw);
1104
1105	+	if (b_is_Dipole || b_is_Quadrupole)
1106	+	*(idat.t2) += Tb * *(idat.sw);
1107	+
1108		} else {
1109
1110		// only accumulate the forces and torques resulting from the
1111		// indirect reaction field terms.
1112
1113	<	*(idat.vpair) += indirect_vpair;
1114	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot;
1115	<	*(idat.f1) += indirect_dVdr;
1113	>	*(idat.vpair) += indirect_Pot;
1114	>	(*(idat.excludedPot))[ELECTROSTATIC_FAMILY] +=  excluded_Pot;
1115	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += *(idat.sw) * indirect_Pot;
1116	>	*(idat.f1) += *(idat.sw) * indirect_F;
1117
1118	<	if (i_is_Dipole)
1119	<	*(idat.t1) -= cross(uz_i, indirect_duduz_i);
1120	<	if (j_is_Dipole)
1121	<	*(idat.t2) -= cross(uz_j, indirect_duduz_j);
1118	>	if (a_is_Dipole || a_is_Quadrupole)
1119	>	*(idat.t1) += *(idat.sw) * indirect_Ta;
1120	>
1121	>	if (b_is_Dipole || b_is_Quadrupole)
1122	>	*(idat.t2) += *(idat.sw) * indirect_Tb;
1123		}
1024	–
1025	–
1124		return;
1125	<	}
1125	>	}
1126
1127		void Electrostatic::calcSelfCorrection(SelfData &sdat) {
1128	<	RealType mu1, preVal, chg1, self;
1031	<
1128	>
1129		if (!initialized_) initialize();
1130
1131		ElectrostaticAtomData data = ElectrostaticMap[sdat.atype];
1132	<
1132	>
1133		// logicals
1134		bool i_is_Charge = data.is_Charge;
1135		bool i_is_Dipole = data.is_Dipole;
1136	+	bool i_is_Fluctuating = data.is_Fluctuating;
1137	+	RealType C_a = data.fixedCharge;
1138	+	RealType self, preVal, DadDa;
1139	+
1140	+	if (i_is_Fluctuating) {
1141	+	C_a += *(sdat.flucQ);
1142	+	// dVdFQ is really a force, so this is negative the derivative
1143	+	*(sdat.dVdFQ) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1144	+	(*(sdat.excludedPot))[ELECTROSTATIC_FAMILY] += (*sdat.flucQ) *
1145	+	(*(sdat.flucQ) * data.hardness * 0.5 + data.electronegativity);
1146	+	}
1147
1148	<	if (summationMethod_ == esm_REACTION_FIELD) {
1149	<	if (i_is_Dipole) {
1150	<	mu1 = data.dipole_moment;
1151	<	preVal = pre22_ * preRF2_ * mu1 * mu1;
1152	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal;
1153	<
1154	<	// The self-correction term adds into the reaction field vector
1155	<	Vector3d uz_i = sdat.eFrame->getColumn(2);
1156	<	Vector3d ei = preVal * uz_i;
1148	>	switch (summationMethod_) {
1149	>	case esm_REACTION_FIELD:
1150	>
1151	>	if (i_is_Charge) {
1152	>	// Self potential [see Wang and Hermans, "Reaction Field
1153	>	// Molecular Dynamics Simulation with Friedman’s Image Charge
1154	>	// Method," J. Phys. Chem. 99, 12001-12007 (1995).]
1155	>	preVal = pre11_ * preRF_ * C_a * C_a;
1156	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal / cutoffRadius_;
1157	>	}
1158
1159	<	// This looks very wrong.  A vector crossed with itself is zero.
1160	<	*(sdat.t) -= cross(uz_i, ei);
1159	>	if (i_is_Dipole) {
1160	>	DadDa = data.dipole.lengthSquare();
1161	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DadDa;
1162		}
1163	<	} else if (summationMethod_ == esm_SHIFTED_FORCE || summationMethod_ == esm_SHIFTED_POTENTIAL) {
1164	<	if (i_is_Charge) {
1165	<	chg1 = data.charge;
1166	<	if (screeningMethod_ == DAMPED) {
1167	<	self = - 0.5 * (c1c_ + alphaPi_) * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_;
1168	<	} else {
1169	<	self = - 0.5 * rcuti_ * chg1 * (chg1 +  *(sdat.skippedCharge)) * pre11_;
1060	<	}
1163	>
1164	>	break;
1165	>
1166	>	case esm_SHIFTED_FORCE:
1167	>	case esm_SHIFTED_POTENTIAL:
1168	>	if (i_is_Charge) {
1169	>	self = - selfMult_ * C_a * (C_a + *(sdat.skippedCharge)) * pre11_;
1170		(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1171		}
1172	+	break;
1173	+	default:
1174	+	break;
1175		}
1176		}
1177	<
1177	>
1178		RealType Electrostatic::getSuggestedCutoffRadius(pair<AtomType*, AtomType*> atypes) {
1179		// This seems to work moderately well as a default.  There's no
1180		// inherent scale for 1/r interactions that we can standardize.

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