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

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branches/development/src/nonbonded/Electrostatic.cpp (file contents), Revision 1616 by gezelter, Tue Aug 30 15:45:35 2011 UTC vs.
trunk/src/nonbonded/Electrostatic.cpp (file contents), Revision 1933 by gezelter, Fri Aug 23 15:59:23 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).
39	<	* [4]  Vardeman & Gezelter, in progress (2009).
38	>	* [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
39	>	* [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
40	>	* [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41		*/
42
43		#include <stdio.h>
44		#include <string.h>
45
46		#include <cmath>
47	+	#include <numeric>
48		#include "nonbonded/Electrostatic.hpp"
49		#include "utils/simError.h"
50		#include "types/NonBondedInteractionType.hpp"
51	<	#include "types/DirectionalAtomType.hpp"
51	>	#include "types/FixedChargeAdapter.hpp"
52	>	#include "types/FluctuatingChargeAdapter.hpp"
53	>	#include "types/MultipoleAdapter.hpp"
54		#include "io/Globals.hpp"
55	+	#include "nonbonded/SlaterIntegrals.hpp"
56	+	#include "utils/PhysicalConstants.hpp"
57	+	#include "math/erfc.hpp"
58	+	#include "math/SquareMatrix.hpp"
59	+	#include "primitives/Molecule.hpp"
60	+	#ifdef IS_MPI
61	+	#include <mpi.h>
62	+	#endif
63
64		namespace OpenMD {
65
#	Line 56 | Line 68 | namespace OpenMD {
68		haveCutoffRadius_(false),
69		haveDampingAlpha_(false),
70		haveDielectric_(false),
71	<	haveElectroSpline_(false)
71	>	haveElectroSplines_(false)
72		{}
73
74		void Electrostatic::initialize() {
#	Line 68 | Line 80 | namespace OpenMD {
80		summationMap_["SWITCHING_FUNCTION"] = esm_SWITCHING_FUNCTION;
81		summationMap_["SHIFTED_POTENTIAL"]  = esm_SHIFTED_POTENTIAL;
82		summationMap_["SHIFTED_FORCE"]      = esm_SHIFTED_FORCE;
83	+	summationMap_["TAYLOR_SHIFTED"]     = esm_TAYLOR_SHIFTED;
84		summationMap_["REACTION_FIELD"]     = esm_REACTION_FIELD;
85		summationMap_["EWALD_FULL"]         = esm_EWALD_FULL;
86		summationMap_["EWALD_PME"]          = esm_EWALD_PME;
#	Line 82 | Line 95 | namespace OpenMD {
95		// Charge-Dipole, assuming charges are measured in electrons, and
96		// dipoles are measured in debyes
97		pre12_ = 69.13373;
98	<	// Dipole-Dipole, assuming dipoles are measured in debyes
98	>	// Dipole-Dipole, assuming dipoles are measured in Debye
99		pre22_ = 14.39325;
100		// Charge-Quadrupole, assuming charges are measured in electrons, and
101		// quadrupoles are measured in 10^-26 esu cm^2
102	<	// This unit is also known affectionately as an esu centi-barn.
102	>	// This unit is also known affectionately as an esu centibarn.
103		pre14_ = 69.13373;
104	<
104	>	// Dipole-Quadrupole, assuming dipoles are measured in debyes and
105	>	// quadrupoles in esu centibarns:
106	>	pre24_ = 14.39325;
107	>	// Quadrupole-Quadrupole, assuming esu centibarns:
108	>	pre44_ = 14.39325;
109	>
110		// conversions for the simulation box dipole moment
111		chargeToC_ = 1.60217733e-19;
112		angstromToM_ = 1.0e-10;
113		debyeToCm_ = 3.33564095198e-30;
114
115	<	// number of points for electrostatic splines
115	>	// Default number of points for electrostatic splines
116		np_ = 100;
117
118		// variables to handle different summation methods for long-range
#	Line 102 | Line 120 | namespace OpenMD {
120		summationMethod_ = esm_HARD;
121		screeningMethod_ = UNDAMPED;
122		dielectric_ = 1.0;
105	–	one_third_ = 1.0 / 3.0;
123
124		// check the summation method:
125		if (simParams_->haveElectrostaticSummationMethod()) {
#	Line 118 | Line 135 | namespace OpenMD {
135		"Electrostatic::initialize: Unknown electrostaticSummationMethod.\n"
136		"\t(Input file specified %s .)\n"
137		"\telectrostaticSummationMethod must be one of: \"hard\",\n"
138	<	"\t\"shifted_potential\", \"shifted_force\", or \n"
139	<	"\t\"reaction_field\".\n", myMethod.c_str() );
138	>	"\t\"shifted_potential\", \"shifted_force\",\n"
139	>	"\t\"taylor_shifted\", or \"reaction_field\".\n",
140	>	myMethod.c_str() );
141		painCave.isFatal = 1;
142		simError();
143		}
#	Line 178 | Line 196 | namespace OpenMD {
196		simError();
197		}
198
199	<	if (screeningMethod_ == DAMPED) {
199	>	if (screeningMethod_ == DAMPED || summationMethod_ == esm_EWALD_FULL) {
200		if (!simParams_->haveDampingAlpha()) {
201		// first set a cutoff dependent alpha value
202		// we assume alpha depends linearly with rcut from 0 to 20.5 ang
203		dampingAlpha_ = 0.425 - cutoffRadius_* 0.02;
204	<	if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;
187	<
204	>	if (dampingAlpha_ < 0.0) dampingAlpha_ = 0.0;
205		// throw warning
206		sprintf( painCave.errMsg,
207	<	"Electrostatic::initialize: dampingAlpha was not specified in the input file.\n"
208	<	"\tA default value of %f (1/ang) will be used for the cutoff of\n\t%f (ang).\n",
207	>	"Electrostatic::initialize: dampingAlpha was not specified in the\n"
208	>	"\tinput file.  A default value of %f (1/ang) will be used for the\n"
209	>	"\tcutoff of %f (ang).\n",
210		dampingAlpha_, cutoffRadius_);
211		painCave.severity = OPENMD_INFO;
212		painCave.isFatal = 0;
#	Line 199 | Line 217 | namespace OpenMD {
217		haveDampingAlpha_ = true;
218		}
219
220	<	// find all of the Electrostatic atom Types:
221	<	ForceField::AtomTypeContainer* atomTypes = forceField_->getAtomTypes();
222	<	ForceField::AtomTypeContainer::MapTypeIterator i;
223	<	AtomType* at;
224	<
225	<	for (at = atomTypes->beginType(i); at != NULL;
226	<	at = atomTypes->nextType(i)) {
227	<
228	<	if (at->isElectrostatic())
229	<	addType(at);
220	>
221	>	Etypes.clear();
222	>	Etids.clear();
223	>	FQtypes.clear();
224	>	FQtids.clear();
225	>	ElectrostaticMap.clear();
226	>	Jij.clear();
227	>	nElectro_ = 0;
228	>	nFlucq_ = 0;
229	>
230	>	Etids.resize( forceField_->getNAtomType(), -1);
231	>	FQtids.resize( forceField_->getNAtomType(), -1);
232	>
233	>	set<AtomType*>::iterator at;
234	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
235	>	if ((*at)->isElectrostatic()) nElectro_++;
236	>	if ((*at)->isFluctuatingCharge()) nFlucq_++;
237		}
238
239	+	Jij.resize(nFlucq_);
240
241	<	cutoffRadius2_ = cutoffRadius_ * cutoffRadius_;
242	<	rcuti_ = 1.0 / cutoffRadius_;
243	<	rcuti2_ = rcuti_ * rcuti_;
244	<	rcuti3_ = rcuti2_ * rcuti_;
219	<	rcuti4_ = rcuti2_ * rcuti2_;
220	<
221	<	if (screeningMethod_ == DAMPED) {
222	<
223	<	alpha2_ = dampingAlpha_ * dampingAlpha_;
224	<	alpha4_ = alpha2_ * alpha2_;
225	<	alpha6_ = alpha4_ * alpha2_;
226	<	alpha8_ = alpha4_ * alpha4_;
227	<
228	<	constEXP_ = exp(-alpha2_ * cutoffRadius2_);
229	<	invRootPi_ = 0.56418958354775628695;
230	<	alphaPi_ = 2.0 * dampingAlpha_ * invRootPi_;
231	<
232	<	c1c_ = erfc(dampingAlpha_ * cutoffRadius_) * rcuti_;
233	<	c2c_ = alphaPi_ * constEXP_ * rcuti_ + c1c_ * rcuti_;
234	<	c3c_ = 2.0 * alphaPi_ * alpha2_ + 3.0 * c2c_ * rcuti_;
235	<	c4c_ = 4.0 * alphaPi_ * alpha4_ + 5.0 * c3c_ * rcuti2_;
236	<	c5c_ = 8.0 * alphaPi_ * alpha6_ + 7.0 * c4c_ * rcuti2_;
237	<	c6c_ = 16.0 * alphaPi_ * alpha8_ + 9.0 * c5c_ * rcuti2_;
238	<	} else {
239	<	c1c_ = rcuti_;
240	<	c2c_ = c1c_ * rcuti_;
241	<	c3c_ = 3.0 * c2c_ * rcuti_;
242	<	c4c_ = 5.0 * c3c_ * rcuti2_;
243	<	c5c_ = 7.0 * c4c_ * rcuti2_;
244	<	c6c_ = 9.0 * c5c_ * rcuti2_;
245	<	}
246	<
241	>	for (at = simTypes_.begin(); at != simTypes_.end(); ++at) {
242	>	if ((*at)->isElectrostatic()) addType(*at);
243	>	}
244	>
245		if (summationMethod_ == esm_REACTION_FIELD) {
246		preRF_ = (dielectric_ - 1.0) /
247	<	((2.0 * dielectric_ + 1.0) * cutoffRadius2_ * cutoffRadius_);
250	<	preRF2_ = 2.0 * preRF_;
247	>	((2.0 * dielectric_ + 1.0) * pow(cutoffRadius_,3) );
248		}
249
250	<	// Add a 2 angstrom safety window to deal with cutoffGroups that
251	<	// have charged atoms longer than the cutoffRadius away from each
252	<	// other.  Splining may not be the best choice here.  Direct calls
253	<	// to erfc might be preferrable.
250	>	RealType b0c, b1c, b2c, b3c, b4c, b5c;
251	>	RealType db0c_1, db0c_2, db0c_3, db0c_4, db0c_5;
252	>	RealType a2, expTerm, invArootPi;
253	>
254	>	RealType r = cutoffRadius_;
255	>	RealType r2 = r * r;
256	>	RealType ric = 1.0 / r;
257	>	RealType ric2 = ric * ric;
258
259	<	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));
259	>	if (screeningMethod_ == DAMPED) {
260	>	a2 = dampingAlpha_ * dampingAlpha_;
261	>	invArootPi = 1.0 / (dampingAlpha_ * sqrt(M_PI));
262	>	expTerm = exp(-a2 * r2);
263	>	// values of Smith's B_l functions at the cutoff radius:
264	>	b0c = erfc(dampingAlpha_ * r) / r;
265	>	b1c = (      b0c     + 2.0*a2     * expTerm * invArootPi) / r2;
266	>	b2c = (3.0 * b1c + pow(2.0*a2, 2) * expTerm * invArootPi) / r2;
267	>	b3c = (5.0 * b2c + pow(2.0*a2, 3) * expTerm * invArootPi) / r2;
268	>	b4c = (7.0 * b3c + pow(2.0*a2, 4) * expTerm * invArootPi) / r2;
269	>	b5c = (9.0 * b4c + pow(2.0*a2, 5) * expTerm * invArootPi) / r2;
270	>	// Half the Smith self piece:
271	>	selfMult1_ = - a2 * invArootPi;
272	>	selfMult2_ = - 2.0 * a2 * a2 * invArootPi / 3.0;
273	>	selfMult4_ = - 4.0 * a2 * a2 * a2 * invArootPi / 5.0;
274	>	} else {
275	>	a2 = 0.0;
276	>	b0c = 1.0 / r;
277	>	b1c = (      b0c) / r2;
278	>	b2c = (3.0 * b1c) / r2;
279	>	b3c = (5.0 * b2c) / r2;
280	>	b4c = (7.0 * b3c) / r2;
281	>	b5c = (9.0 * b4c) / r2;
282	>	selfMult1_ = 0.0;
283	>	selfMult2_ = 0.0;
284	>	selfMult4_ = 0.0;
285		}
267	–	erfcSpline_ = new CubicSpline();
268	–	erfcSpline_->addPoints(rvals, yvals);
269	–	haveElectroSpline_ = true;
286
287	<	initialized_ = true;
288	<	}
289	<
290	<	void Electrostatic::addType(AtomType* atomType){
287	>	// higher derivatives of B_0 at the cutoff radius:
288	>	db0c_1 = -r * b1c;
289	>	db0c_2 =     -b1c + r2 * b2c;
290	>	db0c_3 =          3.0*r*b2c  - r2*r*b3c;
291	>	db0c_4 =          3.0*b2c  - 6.0*r2*b3c     + r2*r2*b4c;
292	>	db0c_5 =                    -15.0*r*b3c + 10.0*r2*r*b4c - r2*r2*r*b5c;
293
294	<	ElectrostaticAtomData electrostaticAtomData;
295	<	electrostaticAtomData.is_Charge = false;
296	<	electrostaticAtomData.is_Dipole = false;
297	<	electrostaticAtomData.is_SplitDipole = false;
298	<	electrostaticAtomData.is_Quadrupole = false;
294	>	if (summationMethod_ != esm_EWALD_FULL) {
295	>	selfMult1_ -= b0c;
296	>	selfMult2_ += (db0c_2 + 2.0*db0c_1*ric) /  3.0;
297	>	selfMult4_ -= (db0c_4 + 4.0*db0c_3*ric) / 15.0;
298	>	}
299
300	<	if (atomType->isCharge()) {
301	<	GenericData* data = atomType->getPropertyByName("Charge");
300	>	// working variables for the splines:
301	>	RealType ri, ri2;
302	>	RealType b0, b1, b2, b3, b4, b5;
303	>	RealType db0_1, db0_2, db0_3, db0_4, db0_5;
304	>	RealType f, fc, f0;
305	>	RealType g, gc, g0, g1, g2, g3, g4;
306	>	RealType h, hc, h1, h2, h3, h4;
307	>	RealType s, sc, s2, s3, s4;
308	>	RealType t, tc, t3, t4;
309	>	RealType u, uc, u4;
310
311	<	if (data == NULL) {
312	<	sprintf( painCave.errMsg, "Electrostatic::addType could not find "
287	<	"Charge\n"
288	<	"\tparameters for atomType %s.\n",
289	<	atomType->getName().c_str());
290	<	painCave.severity = OPENMD_ERROR;
291	<	painCave.isFatal = 1;
292	<	simError();
293	<	}
294	<
295	<	DoubleGenericData* doubleData = dynamic_cast<DoubleGenericData*>(data);
296	<	if (doubleData == NULL) {
297	<	sprintf( painCave.errMsg,
298	<	"Electrostatic::addType could not convert GenericData to "
299	<	"Charge for\n"
300	<	"\tatom type %s\n", atomType->getName().c_str());
301	<	painCave.severity = OPENMD_ERROR;
302	<	painCave.isFatal = 1;
303	<	simError();
304	<	}
305	<	electrostaticAtomData.is_Charge = true;
306	<	electrostaticAtomData.charge = doubleData->getData();
307	<	}
311	>	// working variables for Taylor expansion:
312	>	RealType rmRc, rmRc2, rmRc3, rmRc4;
313
314	<	if (atomType->isDirectional()) {
315	<	DirectionalAtomType* daType = dynamic_cast<DirectionalAtomType*>(atomType);
316	<
317	<	if (daType->isDipole()) {
318	<	GenericData* data = daType->getPropertyByName("Dipole");
319	<
320	<	if (data == NULL) {
321	<	sprintf( painCave.errMsg,
322	<	"Electrostatic::addType could not find Dipole\n"
323	<	"\tparameters for atomType %s.\n",
324	<	daType->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	<	"Dipole Moment\n"
335	<	"\tfor atom type %s\n", daType->getName().c_str());
336	<	painCave.severity = OPENMD_ERROR;
337	<	painCave.isFatal = 1;
338	<	simError();
339	<	}
340	<	electrostaticAtomData.is_Dipole = true;
341	<	electrostaticAtomData.dipole_moment = doubleData->getData();
314	>	// Approximate using splines using a maximum of 0.1 Angstroms
315	>	// between points.
316	>	int nptest = int((cutoffRadius_ + 2.0) / 0.1);
317	>	np_ = (np_ > nptest) ? np_ : nptest;
318	>
319	>	// Add a 2 angstrom safety window to deal with cutoffGroups that
320	>	// have charged atoms longer than the cutoffRadius away from each
321	>	// other.  Splining is almost certainly the best choice here.
322	>	// Direct calls to erfc would be preferrable if it is a very fast
323	>	// implementation.
324	>
325	>	RealType dx = (cutoffRadius_ + 2.0) / RealType(np_);
326	>
327	>	// Storage vectors for the computed functions
328	>	vector<RealType> rv;
329	>	vector<RealType> v01v;
330	>	vector<RealType> v11v;
331	>	vector<RealType> v21v, v22v;
332	>	vector<RealType> v31v, v32v;
333	>	vector<RealType> v41v, v42v, v43v;
334	>
335	>	for (int i = 1; i < np_ + 1; i++) {
336	>	r = RealType(i) * dx;
337	>	rv.push_back(r);
338	>
339	>	ri = 1.0 / r;
340	>	ri2 = ri * ri;
341	>
342	>	r2 = r * r;
343	>	expTerm = exp(-a2 * r2);
344	>
345	>	// Taylor expansion factors (no need for factorials this way):
346	>	rmRc = r - cutoffRadius_;
347	>	rmRc2 = rmRc  * rmRc / 2.0;
348	>	rmRc3 = rmRc2 * rmRc / 3.0;
349	>	rmRc4 = rmRc3 * rmRc / 4.0;
350	>
351	>	// values of Smith's B_l functions at r:
352	>	if (screeningMethod_ == DAMPED) {
353	>	b0 = erfc(dampingAlpha_ * r) * ri;
354	>	b1 = (      b0 +     2.0*a2     * expTerm * invArootPi) * ri2;
355	>	b2 = (3.0 * b1 + pow(2.0*a2, 2) * expTerm * invArootPi) * ri2;
356	>	b3 = (5.0 * b2 + pow(2.0*a2, 3) * expTerm * invArootPi) * ri2;
357	>	b4 = (7.0 * b3 + pow(2.0*a2, 4) * expTerm * invArootPi) * ri2;
358	>	b5 = (9.0 * b4 + pow(2.0*a2, 5) * expTerm * invArootPi) * ri2;
359	>	} else {
360	>	b0 = ri;
361	>	b1 = (      b0) * ri2;
362	>	b2 = (3.0 * b1) * ri2;
363	>	b3 = (5.0 * b2) * ri2;
364	>	b4 = (7.0 * b3) * ri2;
365	>	b5 = (9.0 * b4) * ri2;
366		}
367	+
368	+	// higher derivatives of B_0 at r:
369	+	db0_1 = -r * b1;
370	+	db0_2 =     -b1 + r2 * b2;
371	+	db0_3 =          3.0*r*b2   - r2*r*b3;
372	+	db0_4 =          3.0*b2   - 6.0*r2*b3     + r2*r2*b4;
373	+	db0_5 =                    -15.0*r*b3 + 10.0*r2*r*b4 - r2*r2*r*b5;
374
375	<	if (daType->isSplitDipole()) {
376	<	GenericData* data = daType->getPropertyByName("SplitDipoleDistance");
377	<
378	<	if (data == NULL) {
379	<	sprintf(painCave.errMsg,
380	<	"Electrostatic::addType could not find SplitDipoleDistance\n"
381	<	"\tparameter for atomType %s.\n",
382	<	daType->getName().c_str());
383	<	painCave.severity = OPENMD_ERROR;
384	<	painCave.isFatal = 1;
385	<	simError();
386	<	}
375	>	f = b0;
376	>	fc = b0c;
377	>	f0 = f - fc - rmRc*db0c_1;
378	>
379	>	g = db0_1;
380	>	gc = db0c_1;
381	>	g0 = g - gc;
382	>	g1 = g0 - rmRc *db0c_2;
383	>	g2 = g1 - rmRc2*db0c_3;
384	>	g3 = g2 - rmRc3*db0c_4;
385	>	g4 = g3 - rmRc4*db0c_5;
386	>
387	>	h = db0_2;
388	>	hc = db0c_2;
389	>	h1 = h - hc;
390	>	h2 = h1 - rmRc *db0c_3;
391	>	h3 = h2 - rmRc2*db0c_4;
392	>	h4 = h3 - rmRc3*db0c_5;
393	>
394	>	s = db0_3;
395	>	sc = db0c_3;
396	>	s2 = s - sc;
397	>	s3 = s2 - rmRc *db0c_4;
398	>	s4 = s3 - rmRc2*db0c_5;
399	>
400	>	t = db0_4;
401	>	tc = db0c_4;
402	>	t3 = t - tc;
403	>	t4 = t3 - rmRc *db0c_5;
404
405	<	DoubleGenericData* doubleData = dynamic_cast<DoubleGenericData*>(data);
406	<	if (doubleData == NULL) {
407	<	sprintf( painCave.errMsg,
355	<	"Electrostatic::addType could not convert GenericData to "
356	<	"SplitDipoleDistance for\n"
357	<	"\tatom type %s\n", daType->getName().c_str());
358	<	painCave.severity = OPENMD_ERROR;
359	<	painCave.isFatal = 1;
360	<	simError();
361	<	}
362	<	electrostaticAtomData.is_SplitDipole = true;
363	<	electrostaticAtomData.split_dipole_distance = doubleData->getData();
364	<	}
405	>	u = db0_5;
406	>	uc = db0c_5;
407	>	u4 = u - uc;
408
409	<	if (daType->isQuadrupole()) {
410	<	GenericData* data = daType->getPropertyByName("QuadrupoleMoments");
409	>	// in what follows below, the various v functions are used for
410	>	// potentials and torques, while the w functions show up in the
411	>	// forces.
412	>
413	>	switch (summationMethod_) {
414	>	case esm_SHIFTED_FORCE:
415	>
416	>	v01 = f - fc - rmRc*gc;
417	>	v11 = g - gc - rmRc*hc;
418	>	v21 = g*ri - gc*ric - rmRc*(hc - gc*ric)*ric;
419	>	v22 = h - g*ri - (hc - gc*ric) - rmRc*(sc - (hc - gc*ric)*ric);
420	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric - rmRc*(sc-2.0*(hc-gc*ric)*ric)*ric;
421	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric)
422	>	- rmRc*(tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
423	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2
424	>	- rmRc*(sc - 3.0*(hc-gc*ric)*ric)*ric2;
425	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric
426	>	- rmRc*(tc - (4.0*sc - 9.0*(hc - gc*ric)*ric)*ric)*ric;
427
428	<	if (data == NULL) {
429	<	sprintf( painCave.errMsg,
430	<	"Electrostatic::addType could not find QuadrupoleMoments\n"
431	<	"\tparameter for atomType %s.\n",
432	<	daType->getName().c_str());
433	<	painCave.severity = OPENMD_ERROR;
434	<	painCave.isFatal = 1;
435	<	simError();
436	<	}
428	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
429	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric)
430	>	- rmRc*(uc-3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
431	>
432	>	dv01 = g - gc;
433	>	dv11 = h - hc;
434	>	dv21 = (h - g*ri)*ri - (hc - gc*ric)*ric;
435	>	dv22 = (s - (h - g*ri)*ri) - (sc - (hc - gc*ric)*ric);
436	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri - (sc - 2.0*(hc-gc*ric)*ric)*ric;
437	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri)
438	>	- (tc - 3.0*(sc-2.0*(hc-gc*ric)*ric)*ric);
439	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2 - (sc - 3.0*(hc - gc*ric)*ric)*ric2;
440	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri
441	>	- (tc - (4.0*sc - 9.0*(hc-gc*ric)*ric)*ric)*ric;
442	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri)
443	>	- (uc - 3.0*(2.0*tc - (7.0*sc - 15.0*(hc - gc*ric)*ric)*ric)*ric);
444
445	<	// Quadrupoles in OpenMD are set as the diagonal elements
380	<	// of the diagonalized traceless quadrupole moment tensor.
381	<	// The column vectors of the unitary matrix that diagonalizes
382	<	// the quadrupole moment tensor become the eFrame (or the
383	<	// electrostatic version of the body-fixed frame.
445	>	break;
446
447	<	Vector3dGenericData* v3dData = dynamic_cast<Vector3dGenericData*>(data);
448	<	if (v3dData == NULL) {
449	<	sprintf( painCave.errMsg,
450	<	"Electrostatic::addType could not convert GenericData to "
451	<	"Quadrupole Moments for\n"
452	<	"\tatom type %s\n", daType->getName().c_str());
453	<	painCave.severity = OPENMD_ERROR;
454	<	painCave.isFatal = 1;
455	<	simError();
447	>	case esm_TAYLOR_SHIFTED:
448	>
449	>	v01 = f0;
450	>	v11 = g1;
451	>	v21 = g2 * ri;
452	>	v22 = h2 - v21;
453	>	v31 = (h3 - g3 * ri) * ri;
454	>	v32 = s3 - 3.0*v31;
455	>	v41 = (h4 - g4 * ri) * ri2;
456	>	v42 = s4 * ri - 3.0*v41;
457	>	v43 = t4 - 6.0*v42 - 3.0*v41;
458	>
459	>	dv01 = g0;
460	>	dv11 = h1;
461	>	dv21 = (h2 - g2*ri)*ri;
462	>	dv22 = (s2 - (h2 - g2*ri)*ri);
463	>	dv31 = (s3 - 2.0*(h3-g3*ri)*ri)*ri;
464	>	dv32 = (t3 - 3.0*(s3-2.0*(h3-g3*ri)*ri)*ri);
465	>	dv41 = (s4 - 3.0*(h4 - g4*ri)*ri)*ri2;
466	>	dv42 = (t4 - (4.0*s4 - 9.0*(h4-g4*ri)*ri)*ri)*ri;
467	>	dv43 = (u4 - 3.0*(2.0*t4 - (7.0*s4 - 15.0*(h4 - g4*ri)*ri)*ri)*ri);
468	>
469	>	break;
470	>
471	>	case esm_SHIFTED_POTENTIAL:
472	>
473	>	v01 = f - fc;
474	>	v11 = g - gc;
475	>	v21 = g*ri - gc*ric;
476	>	v22 = h - g*ri - (hc - gc*ric);
477	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
478	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
479	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
480	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
481	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
482	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
483	>
484	>	dv01 = g;
485	>	dv11 = h;
486	>	dv21 = (h - g*ri)*ri;
487	>	dv22 = (s - (h - g*ri)*ri);
488	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
489	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
490	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
491	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
492	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
493	>
494	>	break;
495	>
496	>	case esm_SWITCHING_FUNCTION:
497	>	case esm_HARD:
498	>	case esm_EWALD_FULL:
499	>
500	>	v01 = f;
501	>	v11 = g;
502	>	v21 = g*ri;
503	>	v22 = h - g*ri;
504	>	v31 = (h-g*ri)*ri;
505	>	v32 = (s - 3.0*(h-g*ri)*ri);
506	>	v41 = (h - g*ri)*ri2;
507	>	v42 = (s-3.0*(h-g*ri)*ri)*ri;
508	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri);
509	>
510	>	dv01 = g;
511	>	dv11 = h;
512	>	dv21 = (h - g*ri)*ri;
513	>	dv22 = (s - (h - g*ri)*ri);
514	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
515	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
516	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
517	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
518	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
519	>
520	>	break;
521	>
522	>	case esm_REACTION_FIELD:
523	>
524	>	// following DL_POLY's lead for shifting the image charge potential:
525	>	f = b0 + preRF_ * r2;
526	>	fc = b0c + preRF_ * cutoffRadius_ * cutoffRadius_;
527	>
528	>	g = db0_1 + preRF_ * 2.0 * r;
529	>	gc = db0c_1 + preRF_ * 2.0 * cutoffRadius_;
530	>
531	>	h = db0_2 + preRF_ * 2.0;
532	>	hc = db0c_2 + preRF_ * 2.0;
533	>
534	>	v01 = f - fc;
535	>	v11 = g - gc;
536	>	v21 = g*ri - gc*ric;
537	>	v22 = h - g*ri - (hc - gc*ric);
538	>	v31 = (h-g*ri)*ri - (hc-gc*ric)*ric;
539	>	v32 = (s - 3.0*(h-g*ri)*ri) - (sc - 3.0*(hc-gc*ric)*ric);
540	>	v41 = (h - g*ri)*ri2 - (hc - gc*ric)*ric2;
541	>	v42 = (s-3.0*(h-g*ri)*ri)*ri - (sc-3.0*(hc-gc*ric)*ric)*ric;
542	>	v43 = (t - 3.0*(2.0*s - 5.0*(h - g*ri)*ri)*ri)
543	>	- (tc - 3.0*(2.0*sc - 5.0*(hc - gc*ric)*ric)*ric);
544	>
545	>	dv01 = g;
546	>	dv11 = h;
547	>	dv21 = (h - g*ri)*ri;
548	>	dv22 = (s - (h - g*ri)*ri);
549	>	dv31 = (s - 2.0*(h-g*ri)*ri)*ri;
550	>	dv32 = (t - 3.0*(s-2.0*(h-g*ri)*ri)*ri);
551	>	dv41 = (s - 3.0*(h - g*ri)*ri)*ri2;
552	>	dv42 = (t - (4.0*s - 9.0*(h-g*ri)*ri)*ri)*ri;
553	>	dv43 = (u - 3.0*(2.0*t - (7.0*s - 15.0*(h - g*ri)*ri)*ri)*ri);
554	>
555	>	break;
556	>
557	>	case esm_EWALD_PME:
558	>	case esm_EWALD_SPME:
559	>	default :
560	>	map<string, ElectrostaticSummationMethod>::iterator i;
561	>	std::string meth;
562	>	for (i = summationMap_.begin(); i != summationMap_.end(); ++i) {
563	>	if ((*i).second == summationMethod_) meth = (*i).first;
564		}
565	+	sprintf( painCave.errMsg,
566	+	"Electrostatic::initialize: electrostaticSummationMethod %s \n"
567	+	"\thas not been implemented yet. Please select one of:\n"
568	+	"\t\"hard\", \"shifted_potential\", or \"shifted_force\"\n",
569	+	meth.c_str() );
570	+	painCave.isFatal = 1;
571	+	simError();
572	+	break;
573	+	}
574	+
575	+	// Add these computed values to the storage vectors for spline creation:
576	+	v01v.push_back(v01);
577	+	v11v.push_back(v11);
578	+	v21v.push_back(v21);
579	+	v22v.push_back(v22);
580	+	v31v.push_back(v31);
581	+	v32v.push_back(v32);
582	+	v41v.push_back(v41);
583	+	v42v.push_back(v42);
584	+	v43v.push_back(v43);
585	+	}
586	+
587	+	// construct the spline structures and fill them with the values we've
588	+	// computed:
589	+
590	+	v01s = new CubicSpline();
591	+	v01s->addPoints(rv, v01v);
592	+	v11s = new CubicSpline();
593	+	v11s->addPoints(rv, v11v);
594	+	v21s = new CubicSpline();
595	+	v21s->addPoints(rv, v21v);
596	+	v22s = new CubicSpline();
597	+	v22s->addPoints(rv, v22v);
598	+	v31s = new CubicSpline();
599	+	v31s->addPoints(rv, v31v);
600	+	v32s = new CubicSpline();
601	+	v32s->addPoints(rv, v32v);
602	+	v41s = new CubicSpline();
603	+	v41s->addPoints(rv, v41v);
604	+	v42s = new CubicSpline();
605	+	v42s->addPoints(rv, v42v);
606	+	v43s = new CubicSpline();
607	+	v43s->addPoints(rv, v43v);
608	+
609	+	haveElectroSplines_ = true;
610	+
611	+	initialized_ = true;
612	+	}
613	+
614	+	void Electrostatic::addType(AtomType* atomType){
615	+
616	+	ElectrostaticAtomData electrostaticAtomData;
617	+	electrostaticAtomData.is_Charge = false;
618	+	electrostaticAtomData.is_Dipole = false;
619	+	electrostaticAtomData.is_Quadrupole = false;
620	+	electrostaticAtomData.is_Fluctuating = false;
621	+
622	+	FixedChargeAdapter fca = FixedChargeAdapter(atomType);
623	+
624	+	if (fca.isFixedCharge()) {
625	+	electrostaticAtomData.is_Charge = true;
626	+	electrostaticAtomData.fixedCharge = fca.getCharge();
627	+	}
628	+
629	+	MultipoleAdapter ma = MultipoleAdapter(atomType);
630	+	if (ma.isMultipole()) {
631	+	if (ma.isDipole()) {
632	+	electrostaticAtomData.is_Dipole = true;
633	+	electrostaticAtomData.dipole = ma.getDipole();
634	+	}
635	+	if (ma.isQuadrupole()) {
636		electrostaticAtomData.is_Quadrupole = true;
637	<	electrostaticAtomData.quadrupole_moments = v3dData->getData();
637	>	electrostaticAtomData.quadrupole = ma.getQuadrupole();
638		}
639		}
640
641	<	AtomTypeProperties atp = atomType->getATP();
641	>	FluctuatingChargeAdapter fqa = FluctuatingChargeAdapter(atomType);
642
643	<	pair<map<int,AtomType*>::iterator,bool> ret;
644	<	ret = ElectrostaticList.insert( pair<int,AtomType*>(atp.ident, atomType) );
643	>	if (fqa.isFluctuatingCharge()) {
644	>	electrostaticAtomData.is_Fluctuating = true;
645	>	electrostaticAtomData.electronegativity = fqa.getElectronegativity();
646	>	electrostaticAtomData.hardness = fqa.getHardness();
647	>	electrostaticAtomData.slaterN = fqa.getSlaterN();
648	>	electrostaticAtomData.slaterZeta = fqa.getSlaterZeta();
649	>	}
650	>
651	>	int atid = atomType->getIdent();
652	>	int etid = Etypes.size();
653	>	int fqtid = FQtypes.size();
654	>
655	>	pair<set<int>::iterator,bool> ret;
656	>	ret = Etypes.insert( atid );
657		if (ret.second == false) {
658		sprintf( painCave.errMsg,
659		"Electrostatic already had a previous entry with ident %d\n",
660	<	atp.ident);
660	>	atid);
661		painCave.severity = OPENMD_INFO;
662		painCave.isFatal = 0;
663		simError();
664		}
665
666	<	ElectrostaticMap[atomType] = electrostaticAtomData;
666	>	Etids[ atid ] = etid;
667	>	ElectrostaticMap.push_back(electrostaticAtomData);
668	>
669	>	if (electrostaticAtomData.is_Fluctuating) {
670	>	ret = FQtypes.insert( atid );
671	>	if (ret.second == false) {
672	>	sprintf( painCave.errMsg,
673	>	"Electrostatic already had a previous fluctuating charge entry with ident %d\n",
674	>	atid );
675	>	painCave.severity = OPENMD_INFO;
676	>	painCave.isFatal = 0;
677	>	simError();
678	>	}
679	>	FQtids[atid] = fqtid;
680	>	Jij[fqtid].resize(nFlucq_);
681	>
682	>	// Now, iterate over all known fluctuating and add to the
683	>	// coulomb integral map:
684	>
685	>	std::set<int>::iterator it;
686	>	for( it = FQtypes.begin(); it != FQtypes.end(); ++it) {
687	>	int etid2 = Etids[ (*it) ];
688	>	int fqtid2 = FQtids[ (*it) ];
689	>	ElectrostaticAtomData eaData2 = ElectrostaticMap[ etid2 ];
690	>	RealType a = electrostaticAtomData.slaterZeta;
691	>	RealType b = eaData2.slaterZeta;
692	>	int m = electrostaticAtomData.slaterN;
693	>	int n = eaData2.slaterN;
694	>
695	>	// Create the spline of the coulombic integral for s-type
696	>	// Slater orbitals.  Add a 2 angstrom safety window to deal
697	>	// with cutoffGroups that have charged atoms longer than the
698	>	// cutoffRadius away from each other.
699	>
700	>	RealType rval;
701	>	RealType dr = (cutoffRadius_ + 2.0) / RealType(np_ - 1);
702	>	vector<RealType> rvals;
703	>	vector<RealType> Jvals;
704	>	// don't start at i = 0, as rval = 0 is undefined for the
705	>	// slater overlap integrals.
706	>	for (int i = 1; i < np_+1; i++) {
707	>	rval = RealType(i) * dr;
708	>	rvals.push_back(rval);
709	>	Jvals.push_back(sSTOCoulInt( a, b, m, n, rval *
710	>	PhysicalConstants::angstromToBohr ) *
711	>	PhysicalConstants::hartreeToKcal );
712	>	}
713	>
714	>	CubicSpline* J = new CubicSpline();
715	>	J->addPoints(rvals, Jvals);
716	>	Jij[fqtid][fqtid2] = J;
717	>	Jij[fqtid2].resize( nFlucq_ );
718	>	Jij[fqtid2][fqtid] = J;
719	>	}
720	>	}
721		return;
722		}
723
724		void Electrostatic::setCutoffRadius( RealType rCut ) {
725		cutoffRadius_ = rCut;
419	–	rrf_ = cutoffRadius_;
726		haveCutoffRadius_ = true;
727		}
728
423	–	void Electrostatic::setSwitchingRadius( RealType rSwitch ) {
424	–	rt_ = rSwitch;
425	–	}
729		void Electrostatic::setElectrostaticSummationMethod( ElectrostaticSummationMethod esm ) {
730		summationMethod_ = esm;
731		}
#	Line 440 | Line 743 | namespace OpenMD {
743
744		void Electrostatic::calcForce(InteractionData &idat) {
745
443	–	// utility variables.  Should clean these up and use the Vector3d and
444	–	// Mat3x3d to replace as many as we can in future versions:
445	–
446	–	RealType q_i, q_j, mu_i, mu_j, d_i, d_j;
447	–	RealType qxx_i, qyy_i, qzz_i;
448	–	RealType qxx_j, qyy_j, qzz_j;
449	–	RealType cx_i, cy_i, cz_i;
450	–	RealType cx_j, cy_j, cz_j;
451	–	RealType cx2, cy2, cz2;
452	–	RealType ct_i, ct_j, ct_ij, a1;
453	–	RealType riji, ri, ri2, ri3, ri4;
454	–	RealType pref, vterm, epot, dudr;
455	–	RealType vpair(0.0);
456	–	RealType scale, sc2;
457	–	RealType pot_term, preVal, rfVal;
458	–	RealType c2ri, c3ri, c4rij, cti3, ctj3, ctidotj;
459	–	RealType preSw, preSwSc;
460	–	RealType c1, c2, c3, c4;
461	–	RealType erfcVal(1.0), derfcVal(0.0);
462	–	RealType BigR;
463	–
464	–	Vector3d Q_i, Q_j;
465	–	Vector3d ux_i, uy_i, uz_i;
466	–	Vector3d ux_j, uy_j, uz_j;
467	–	Vector3d dudux_i, duduy_i, duduz_i;
468	–	Vector3d dudux_j, duduy_j, duduz_j;
469	–	Vector3d rhatdot2, rhatc4;
470	–	Vector3d dVdr;
471	–
472	–	// variables for indirect (reaction field) interactions for excluded pairs:
473	–	RealType indirect_Pot(0.0);
474	–	RealType indirect_vpair(0.0);
475	–	Vector3d indirect_dVdr(V3Zero);
476	–	Vector3d indirect_duduz_i(V3Zero), indirect_duduz_j(V3Zero);
477	–
478	–	pair<RealType, RealType> res;
479	–
746		if (!initialized_) initialize();
747
748	<	ElectrostaticAtomData data1 = ElectrostaticMap[idat.atypes.first];
749	<	ElectrostaticAtomData data2 = ElectrostaticMap[idat.atypes.second];
748	>	data1 = ElectrostaticMap[Etids[idat.atid1]];
749	>	data2 = ElectrostaticMap[Etids[idat.atid2]];
750	>
751	>	U = 0.0;  // Potential
752	>	F.zero();  // Force
753	>	Ta.zero(); // Torque on site a
754	>	Tb.zero(); // Torque on site b
755	>	Ea.zero(); // Electric field at site a
756	>	Eb.zero(); // Electric field at site b
757	>	dUdCa = 0.0; // fluctuating charge force at site a
758	>	dUdCb = 0.0; // fluctuating charge force at site a
759
760	<	// some variables we'll need independent of electrostatic type:
760	>	// Indirect interactions mediated by the reaction field.
761	>	indirect_Pot = 0.0;   // Potential
762	>	indirect_F.zero();    // Force
763	>	indirect_Ta.zero();   // Torque on site a
764	>	indirect_Tb.zero();   // Torque on site b
765
766	<	riji = 1.0 /  *(idat.rij) ;
767	<	Vector3d rhat =  *(idat.d)   * riji;
766	>	// Excluded potential that is still computed for fluctuating charges
767	>	excluded_Pot= 0.0;
768
769	+	// some variables we'll need independent of electrostatic type:
770	+
771	+	ri = 1.0 /  *(idat.rij);
772	+	rhat =  *(idat.d)  * ri;
773	+
774		// logicals
775
776	<	bool i_is_Charge = data1.is_Charge;
777	<	bool i_is_Dipole = data1.is_Dipole;
778	<	bool i_is_SplitDipole = data1.is_SplitDipole;
779	<	bool i_is_Quadrupole = data1.is_Quadrupole;
496	<
497	<	bool j_is_Charge = data2.is_Charge;
498	<	bool j_is_Dipole = data2.is_Dipole;
499	<	bool j_is_SplitDipole = data2.is_SplitDipole;
500	<	bool j_is_Quadrupole = data2.is_Quadrupole;
501	<
502	<	if (i_is_Charge) {
503	<	q_i = data1.charge;
504	<	if (idat.excluded) {
505	<	*(idat.skippedCharge2) += q_i;
506	<	}
507	<	}
776	>	a_is_Charge = data1.is_Charge;
777	>	a_is_Dipole = data1.is_Dipole;
778	>	a_is_Quadrupole = data1.is_Quadrupole;
779	>	a_is_Fluctuating = data1.is_Fluctuating;
780
781	<	if (i_is_Dipole) {
782	<	mu_i = data1.dipole_moment;
783	<	uz_i = idat.eFrame1->getColumn(2);
784	<
513	<	ct_i = dot(uz_i, rhat);
781	>	b_is_Charge = data2.is_Charge;
782	>	b_is_Dipole = data2.is_Dipole;
783	>	b_is_Quadrupole = data2.is_Quadrupole;
784	>	b_is_Fluctuating = data2.is_Fluctuating;
785
786	<	if (i_is_SplitDipole)
787	<	d_i = data1.split_dipole_distance;
517	<
518	<	duduz_i = V3Zero;
519	<	}
786	>	// Obtain all of the required radial function values from the
787	>	// spline structures:
788
789	<	if (i_is_Quadrupole) {
790	<	Q_i = data1.quadrupole_moments;
791	<	qxx_i = Q_i.x();
792	<	qyy_i = Q_i.y();
793	<	qzz_i = Q_i.z();
794	<
795	<	ux_i = idat.eFrame1->getColumn(0);
796	<	uy_i = idat.eFrame1->getColumn(1);
797	<	uz_i = idat.eFrame1->getColumn(2);
789	>	// needed for fields (and forces):
790	>	if (a_is_Charge || b_is_Charge) {
791	>	v01s->getValueAndDerivativeAt( *(idat.rij), v01, dv01);
792	>	}
793	>	if (a_is_Dipole || b_is_Dipole) {
794	>	v11s->getValueAndDerivativeAt( *(idat.rij), v11, dv11);
795	>	v11or = ri * v11;
796	>	}
797	>	if (a_is_Quadrupole || b_is_Quadrupole ||  (a_is_Dipole && b_is_Dipole)) {
798	>	v21s->getValueAndDerivativeAt( *(idat.rij), v21, dv21);
799	>	v22s->getValueAndDerivativeAt( *(idat.rij), v22, dv22);
800	>	v22or = ri * v22;
801	>	}
802
803	<	cx_i = dot(ux_i, rhat);
804	<	cy_i = dot(uy_i, rhat);
805	<	cz_i = dot(uz_i, rhat);
806	<
807	<	dudux_i = V3Zero;
808	<	duduy_i = V3Zero;
809	<	duduz_i = V3Zero;
803	>	// needed for potentials (and forces and torques):
804	>	if ((a_is_Dipole && b_is_Quadrupole) ||
805	>	(b_is_Dipole && a_is_Quadrupole)) {
806	>	v31s->getValueAndDerivativeAt( *(idat.rij), v31, dv31);
807	>	v32s->getValueAndDerivativeAt( *(idat.rij), v32, dv32);
808	>	v31or = v31 * ri;
809	>	v32or = v32 * ri;
810		}
811	+	if (a_is_Quadrupole && b_is_Quadrupole) {
812	+	v41s->getValueAndDerivativeAt( *(idat.rij), v41, dv41);
813	+	v42s->getValueAndDerivativeAt( *(idat.rij), v42, dv42);
814	+	v43s->getValueAndDerivativeAt( *(idat.rij), v43, dv43);
815	+	v42or = v42 * ri;
816	+	v43or = v43 * ri;
817	+	}
818
819	<	if (j_is_Charge) {
820	<	q_j = data2.charge;
819	>	// calculate the single-site contributions (fields, etc).
820	>
821	>	if (a_is_Charge) {
822	>	C_a = data1.fixedCharge;
823	>
824	>	if (a_is_Fluctuating) {
825	>	C_a += *(idat.flucQ1);
826	>	}
827	>
828		if (idat.excluded) {
829	<	*(idat.skippedCharge1) += q_j;
829	>	*(idat.skippedCharge2) += C_a;
830	>	} else {
831	>	// only do the field if we're not excluded:
832	>	Eb -= C_a *  pre11_ * dv01 * rhat;
833		}
834		}
835	<
836	<
837	<	if (j_is_Dipole) {
838	<	mu_j = data2.dipole_moment;
839	<	uz_j = idat.eFrame2->getColumn(2);
835	>
836	>	if (a_is_Dipole) {
837	>	D_a = *(idat.dipole1);
838	>	rdDa = dot(rhat, D_a);
839	>	rxDa = cross(rhat, D_a);
840	>	if (!idat.excluded)
841	>	Eb -=  pre12_ * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
842	>	}
843	>
844	>	if (a_is_Quadrupole) {
845	>	Q_a = *(idat.quadrupole1);
846	>	trQa =  Q_a.trace();
847	>	Qar =   Q_a * rhat;
848	>	rQa = rhat * Q_a;
849	>	rdQar = dot(rhat, Qar);
850	>	rxQar = cross(rhat, Qar);
851	>	if (!idat.excluded)
852	>	Eb -= pre14_ * (trQa * rhat * dv21 + 2.0 * Qar * v22or
853	>	+ rdQar * rhat * (dv22 - 2.0*v22or));
854	>	}
855	>
856	>	if (b_is_Charge) {
857	>	C_b = data2.fixedCharge;
858
859	<	ct_j = dot(uz_j, rhat);
860	<
554	<	if (j_is_SplitDipole)
555	<	d_j = data2.split_dipole_distance;
859	>	if (b_is_Fluctuating)
860	>	C_b += *(idat.flucQ2);
861
862	<	duduz_j = V3Zero;
862	>	if (idat.excluded) {
863	>	*(idat.skippedCharge1) += C_b;
864	>	} else {
865	>	// only do the field if we're not excluded:
866	>	Ea += C_b *  pre11_ * dv01 * rhat;
867	>	}
868		}
869
870	<	if (j_is_Quadrupole) {
871	<	Q_j = data2.quadrupole_moments;
872	<	qxx_j = Q_j.x();
873	<	qyy_j = Q_j.y();
874	<	qzz_j = Q_j.z();
875	<
566	<	ux_j = idat.eFrame2->getColumn(0);
567	<	uy_j = idat.eFrame2->getColumn(1);
568	<	uz_j = idat.eFrame2->getColumn(2);
569	<
570	<	cx_j = dot(ux_j, rhat);
571	<	cy_j = dot(uy_j, rhat);
572	<	cz_j = dot(uz_j, rhat);
573	<
574	<	dudux_j = V3Zero;
575	<	duduy_j = V3Zero;
576	<	duduz_j = V3Zero;
870	>	if (b_is_Dipole) {
871	>	D_b = *(idat.dipole2);
872	>	rdDb = dot(rhat, D_b);
873	>	rxDb = cross(rhat, D_b);
874	>	if (!idat.excluded)
875	>	Ea += pre12_ * ((dv11-v11or) * rdDb * rhat + v11or * D_b);
876		}
877
878	<	epot = 0.0;
879	<	dVdr = V3Zero;
880	<
881	<	if (i_is_Charge) {
878	>	if (b_is_Quadrupole) {
879	>	Q_b = *(idat.quadrupole2);
880	>	trQb =  Q_b.trace();
881	>	Qbr =   Q_b * rhat;
882	>	rQb = rhat * Q_b;
883	>	rdQbr = dot(rhat, Qbr);
884	>	rxQbr = cross(rhat, Qbr);
885	>	if (!idat.excluded)
886	>	Ea += pre14_ * (trQb * rhat * dv21 + 2.0 * Qbr * v22or
887	>	+ rdQbr * rhat * (dv22 - 2.0*v22or));
888	>	}
889	>
890	>
891	>	if ((a_is_Fluctuating || b_is_Fluctuating) && idat.excluded) {
892	>	J = Jij[FQtids[idat.atid1]][FQtids[idat.atid2]];
893	>	}
894	>
895	>	if (a_is_Charge) {
896
897	<	if (j_is_Charge) {
898	<	if (screeningMethod_ == DAMPED) {
899	<	// assemble the damping variables
900	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
588	<	//erfcVal = res.first;
589	<	//derfcVal = res.second;
897	>	if (b_is_Charge) {
898	>	pref =  pre11_ * *(idat.electroMult);
899	>	U  += C_a * C_b * pref * v01;
900	>	F  += C_a * C_b * pref * dv01 * rhat;
901
902	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
903	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
902	>	// If this is an excluded pair, there are still indirect
903	>	// interactions via the reaction field we must worry about:
904
905	<	c1 = erfcVal * riji;
906	<	c2 = (-derfcVal + c1) * riji;
907	<	} else {
908	<	c1 = riji;
598	<	c2 = c1 * riji;
905	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
906	>	rfContrib = preRF_ * pref * C_a * C_b * *(idat.r2);
907	>	indirect_Pot += rfContrib;
908	>	indirect_F   += rfContrib * 2.0 * ri * rhat;
909		}
910
911	<	preVal =  *(idat.electroMult) * pre11_ * q_i * q_j;
912	<
913	<	if (summationMethod_ == esm_SHIFTED_POTENTIAL) {
604	<	vterm = preVal * (c1 - c1c_);
605	<	dudr  = - *(idat.sw)  * preVal * c2;
911	>	// Fluctuating charge forces are handled via Coulomb integrals
912	>	// for excluded pairs (i.e. those connected via bonds) and
913	>	// with the standard charge-charge interaction otherwise.
914
915	<	} else if (summationMethod_ == esm_SHIFTED_FORCE)  {
916	<	vterm = preVal * ( c1 - c1c_ + c2c_*( *(idat.rij)  - cutoffRadius_) );
917	<	dudr  =  *(idat.sw)  * preVal * (c2c_ - c2);
918	<
919	<	} else if (summationMethod_ == esm_REACTION_FIELD) {
612	<	rfVal = preRF_ *  *(idat.rij)  *  *(idat.rij);
613	<
614	<	vterm = preVal * ( riji + rfVal );
615	<	dudr  =  *(idat.sw)  * preVal * ( 2.0 * rfVal - riji ) * riji;
616	<
617	<	// if this is an excluded pair, there are still indirect
618	<	// interactions via the reaction field we must worry about:
619	<
620	<	if (idat.excluded) {
621	<	indirect_vpair += preVal * rfVal;
622	<	indirect_Pot += *(idat.sw) * preVal * rfVal;
623	<	indirect_dVdr += *(idat.sw)  * preVal * 2.0 * rfVal  * riji * rhat;
915	>	if (idat.excluded) {
916	>	if (a_is_Fluctuating || b_is_Fluctuating) {
917	>	coulInt = J->getValueAt( *(idat.rij) );
918	>	if (a_is_Fluctuating) dUdCa += C_b * coulInt;
919	>	if (b_is_Fluctuating) dUdCb += C_a * coulInt;
920		}
625	–
921		} else {
922	+	if (a_is_Fluctuating) dUdCa += C_b * pref * v01;
923	+	if (b_is_Fluctuating) dUdCb += C_a * pref * v01;
924	+	}
925	+	}
926
927	<	vterm = preVal * riji * erfcVal;
928	<	dudr  = -  *(idat.sw)  * preVal * c2;
927	>	if (b_is_Dipole) {
928	>	pref =  pre12_ * *(idat.electroMult);
929	>	U  += C_a * pref * v11 * rdDb;
930	>	F  += C_a * pref * ((dv11 - v11or) * rdDb * rhat + v11or * D_b);
931	>	Tb += C_a * pref * v11 * rxDb;
932
933	<	}
933	>	if (a_is_Fluctuating) dUdCa += pref * v11 * rdDb;
934
935	<	vpair += vterm;
936	<	epot +=  *(idat.sw)  * vterm;
937	<	dVdr += dudr * rhat;
935	>	// Even if we excluded this pair from direct interactions, we
936	>	// still have the reaction-field-mediated charge-dipole
937	>	// interaction:
938	>
939	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
940	>	rfContrib = C_a * pref * preRF_ * 2.0 * *(idat.rij);
941	>	indirect_Pot += rfContrib * rdDb;
942	>	indirect_F   += rfContrib * D_b / (*idat.rij);
943	>	indirect_Tb  += C_a * pref * preRF_ * rxDb;
944	>	}
945		}
946
947	<	if (j_is_Dipole) {
948	<	// pref is used by all the possible methods
949	<	pref =  *(idat.electroMult) * pre12_ * q_i * mu_j;
950	<	preSw =  *(idat.sw)  * pref;
947	>	if (b_is_Quadrupole) {
948	>	pref = pre14_ * *(idat.electroMult);
949	>	U  +=  C_a * pref * (v21 * trQb + v22 * rdQbr);
950	>	F  +=  C_a * pref * (trQb * dv21 * rhat + 2.0 * Qbr * v22or);
951	>	F  +=  C_a * pref * rdQbr * rhat * (dv22 - 2.0*v22or);
952	>	Tb +=  C_a * pref * 2.0 * rxQbr * v22;
953
954	<	if (summationMethod_ == esm_REACTION_FIELD) {
955	<	ri2 = riji * riji;
956	<	ri3 = ri2 * riji;
646	<
647	<	vterm = - pref * ct_j * ( ri2 - preRF2_ *  *(idat.rij)  );
648	<	vpair += vterm;
649	<	epot +=  *(idat.sw)  * vterm;
954	>	if (a_is_Fluctuating) dUdCa += pref * (v21 * trQb + v22 * rdQbr);
955	>	}
956	>	}
957
958	<	dVdr +=  -preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j);
652	<	duduz_j += -preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
958	>	if (a_is_Dipole) {
959
960	<	// Even if we excluded this pair from direct interactions,
961	<	// we still have the reaction-field-mediated charge-dipole
656	<	// interaction:
960	>	if (b_is_Charge) {
961	>	pref = pre12_ * *(idat.electroMult);
962
963	<	if (idat.excluded) {
964	<	indirect_vpair += pref * ct_j * preRF2_ * *(idat.rij);
965	<	indirect_Pot += preSw * ct_j * preRF2_ * *(idat.rij);
661	<	indirect_dVdr += preSw * preRF2_ * uz_j;
662	<	indirect_duduz_j += preSw * rhat * preRF2_ *  *(idat.rij);
663	<	}
664	<
665	<	} else {
666	<	// determine the inverse r used if we have split dipoles
667	<	if (j_is_SplitDipole) {
668	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
669	<	ri = 1.0 / BigR;
670	<	scale =  *(idat.rij)  * ri;
671	<	} else {
672	<	ri = riji;
673	<	scale = 1.0;
674	<	}
675	<
676	<	sc2 = scale * scale;
963	>	U  -= C_b * pref * v11 * rdDa;
964	>	F  -= C_b * pref * ((dv11-v11or) * rdDa * rhat + v11or * D_a);
965	>	Ta -= C_b * pref * v11 * rxDa;
966
967	<	if (screeningMethod_ == DAMPED) {
679	<	// assemble the damping variables
680	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
681	<	//erfcVal = res.first;
682	<	//derfcVal = res.second;
683	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
684	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
685	<	c1 = erfcVal * ri;
686	<	c2 = (-derfcVal + c1) * ri;
687	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
688	<	} else {
689	<	c1 = ri;
690	<	c2 = c1 * ri;
691	<	c3 = 3.0 * c2 * ri;
692	<	}
693	<
694	<	c2ri = c2 * ri;
967	>	if (b_is_Fluctuating) dUdCb -= pref * v11 * rdDa;
968
969	<	// calculate the potential
970	<	pot_term =  scale * c2;
971	<	vterm = -pref * ct_j * pot_term;
972	<	vpair += vterm;
973	<	epot +=  *(idat.sw)  * vterm;
974	<
975	<	// calculate derivatives for forces and torques
969	>	// Even if we excluded this pair from direct interactions,
970	>	// we still have the reaction-field-mediated charge-dipole
971	>	// interaction:
972	>	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
973	>	rfContrib = C_b * pref * preRF_ * 2.0 * *(idat.rij);
974	>	indirect_Pot -= rfContrib * rdDa;
975	>	indirect_F   -= rfContrib * D_a / (*idat.rij);
976	>	indirect_Ta  -= C_b * pref * preRF_ * rxDa;
977	>	}
978	>	}
979
980	<	dVdr += -preSw * (uz_j * c2ri - ct_j * rhat * sc2 * c3);
981	<	duduz_j += -preSw * pot_term * rhat;
980	>	if (b_is_Dipole) {
981	>	pref = pre22_ * *(idat.electroMult);
982	>	DadDb = dot(D_a, D_b);
983	>	DaxDb = cross(D_a, D_b);
984
985	+	U  -= pref * (DadDb * v21 + rdDa * rdDb * v22);
986	+	F  -= pref * (dv21 * DadDb * rhat + v22or * (rdDb * D_a + rdDa * D_b));
987	+	F  -= pref * (rdDa * rdDb) * (dv22 - 2.0*v22or) * rhat;
988	+	Ta += pref * ( v21 * DaxDb - v22 * rdDb * rxDa);
989	+	Tb += pref * (-v21 * DaxDb - v22 * rdDa * rxDb);
990	+	// Even if we excluded this pair from direct interactions, we
991	+	// still have the reaction-field-mediated dipole-dipole
992	+	// interaction:
993	+	if (summationMethod_ == esm_REACTION_FIELD && idat.excluded) {
994	+	rfContrib = -pref * preRF_ * 2.0;
995	+	indirect_Pot += rfContrib * DadDb;
996	+	indirect_Ta  += rfContrib * DaxDb;
997	+	indirect_Tb  -= rfContrib * DaxDb;
998		}
999		}
1000
1001	<	if (j_is_Quadrupole) {
1002	<	// first precalculate some necessary variables
1003	<	cx2 = cx_j * cx_j;
1004	<	cy2 = cy_j * cy_j;
1005	<	cz2 = cz_j * cz_j;
715	<	pref =   *(idat.electroMult) * pre14_ * q_i * one_third_;
716	<
717	<	if (screeningMethod_ == DAMPED) {
718	<	// assemble the damping variables
719	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
720	<	//erfcVal = res.first;
721	<	//derfcVal = res.second;
722	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
723	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
724	<	c1 = erfcVal * riji;
725	<	c2 = (-derfcVal + c1) * riji;
726	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
727	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
728	<	} else {
729	<	c1 = riji;
730	<	c2 = c1 * riji;
731	<	c3 = 3.0 * c2 * riji;
732	<	c4 = 5.0 * c3 * riji * riji;
733	<	}
1001	>	if (b_is_Quadrupole) {
1002	>	pref = pre24_ * *(idat.electroMult);
1003	>	DadQb = D_a * Q_b;
1004	>	DadQbr = dot(D_a, Qbr);
1005	>	DaxQbr = cross(D_a, Qbr);
1006
1007	<	// precompute variables for convenience
1008	<	preSw =  *(idat.sw)  * pref;
1009	<	c2ri = c2 * riji;
1010	<	c3ri = c3 * riji;
1011	<	c4rij = c4 *  *(idat.rij) ;
1012	<	rhatdot2 = 2.0 * rhat * c3;
1013	<	rhatc4 = rhat * c4rij;
1014	<
743	<	// calculate the potential
744	<	pot_term = ( qxx_j * (cx2*c3 - c2ri) +
745	<	qyy_j * (cy2*c3 - c2ri) +
746	<	qzz_j * (cz2*c3 - c2ri) );
747	<	vterm = pref * pot_term;
748	<	vpair += vterm;
749	<	epot +=  *(idat.sw)  * vterm;
750	<
751	<	// calculate derivatives for the forces and torques
752	<
753	<	dVdr += -preSw * ( qxx_j* (cx2*rhatc4 - (2.0*cx_j*ux_j + rhat)*c3ri) +
754	<	qyy_j* (cy2*rhatc4 - (2.0*cy_j*uy_j + rhat)*c3ri) +
755	<	qzz_j* (cz2*rhatc4 - (2.0*cz_j*uz_j + rhat)*c3ri));
756	<
757	<	dudux_j += preSw * qxx_j * cx_j * rhatdot2;
758	<	duduy_j += preSw * qyy_j * cy_j * rhatdot2;
759	<	duduz_j += preSw * qzz_j * cz_j * rhatdot2;
1007	>	U  -= pref * ((trQb*rdDa + 2.0*DadQbr)*v31 + rdDa*rdQbr*v32);
1008	>	F  -= pref * (trQb*D_a + 2.0*DadQb) * v31or;
1009	>	F  -= pref * (trQb*rdDa + 2.0*DadQbr) * (dv31-v31or) * rhat;
1010	>	F  -= pref * (D_a*rdQbr + 2.0*rdDa*rQb) * v32or;
1011	>	F  -= pref * (rdDa * rdQbr * rhat * (dv32-3.0*v32or));
1012	>	Ta += pref * ((-trQb*rxDa + 2.0 * DaxQbr)*v31 - rxDa*rdQbr*v32);
1013	>	Tb += pref * ((2.0*cross(DadQb, rhat) - 2.0*DaxQbr)*v31
1014	>	- 2.0*rdDa*rxQbr*v32);
1015		}
1016		}
762	–
763	–	if (i_is_Dipole) {
1017
1018	<	if (j_is_Charge) {
1019	<	// variables used by all the methods
1020	<	pref =  *(idat.electroMult) * pre12_ * q_j * mu_i;
1021	<	preSw =  *(idat.sw)  * pref;
1018	>	if (a_is_Quadrupole) {
1019	>	if (b_is_Charge) {
1020	>	pref = pre14_ * *(idat.electroMult);
1021	>	U  += C_b * pref * (v21 * trQa + v22 * rdQar);
1022	>	F  += C_b * pref * (trQa * rhat * dv21 + 2.0 * Qar * v22or);
1023	>	F  += C_b * pref * rdQar * rhat * (dv22 - 2.0*v22or);
1024	>	Ta += C_b * pref * 2.0 * rxQar * v22;
1025
1026	<	if (summationMethod_ == esm_REACTION_FIELD) {
1026	>	if (b_is_Fluctuating) dUdCb += pref * (v21 * trQa + v22 * rdQar);
1027	>	}
1028	>	if (b_is_Dipole) {
1029	>	pref = pre24_ * *(idat.electroMult);
1030	>	DbdQa = D_b * Q_a;
1031	>	DbdQar = dot(D_b, Qar);
1032	>	DbxQar = cross(D_b, Qar);
1033
1034	<	ri2 = riji * riji;
1035	<	ri3 = ri2 * riji;
1036	<
1037	<	vterm = pref * ct_i * ( ri2 - preRF2_ *  *(idat.rij)  );
1038	<	vpair += vterm;
1039	<	epot +=  *(idat.sw)  * vterm;
1040	<
1041	<	dVdr += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_ * uz_i);
1042	<
1043	<	duduz_i += preSw * rhat * (ri2 - preRF2_ *  *(idat.rij) );
1034	>	U  += pref * ((trQa*rdDb + 2.0*DbdQar)*v31 + rdDb*rdQar*v32);
1035	>	F  += pref * (trQa*D_b + 2.0*DbdQa) * v31or;
1036	>	F  += pref * (trQa*rdDb + 2.0*DbdQar) * (dv31-v31or) * rhat;
1037	>	F  += pref * (D_b*rdQar + 2.0*rdDb*rQa) * v32or;
1038	>	F  += pref * (rdDb * rdQar * rhat * (dv32-3.0*v32or));
1039	>	Ta += pref * ((-2.0*cross(DbdQa, rhat) + 2.0*DbxQar)*v31
1040	>	+ 2.0*rdDb*rxQar*v32);
1041	>	Tb += pref * ((trQa*rxDb - 2.0 * DbxQar)*v31 + rxDb*rdQar*v32);
1042	>	}
1043	>	if (b_is_Quadrupole) {
1044	>	pref = pre44_ * *(idat.electroMult);  // yes
1045	>	QaQb = Q_a * Q_b;
1046	>	trQaQb = QaQb.trace();
1047	>	rQaQb = rhat * QaQb;
1048	>	QaQbr = QaQb * rhat;
1049	>	QaxQb = mCross(Q_a, Q_b);
1050	>	rQaQbr = dot(rQa, Qbr);
1051	>	rQaxQbr = cross(rQa, Qbr);
1052	>
1053	>	U  += pref * (trQa * trQb + 2.0 * trQaQb) * v41;
1054	>	U  += pref * (trQa * rdQbr + trQb * rdQar  + 4.0 * rQaQbr) * v42;
1055	>	U  += pref * (rdQar * rdQbr) * v43;
1056
1057	<	// Even if we excluded this pair from direct interactions,
1058	<	// we still have the reaction-field-mediated charge-dipole
1059	<	// interaction:
1057	>	F  += pref * rhat * (trQa * trQb + 2.0 * trQaQb)*dv41;
1058	>	F  += pref*rhat*(trQa*rdQbr + trQb*rdQar + 4.0*rQaQbr)*(dv42-2.0*v42or);
1059	>	F  += pref * rhat * (rdQar * rdQbr)*(dv43 - 4.0*v43or);
1060
1061	<	if (idat.excluded) {
1062	<	indirect_vpair += -pref * ct_i * preRF2_ * *(idat.rij);
1063	<	indirect_Pot += -preSw * ct_i * preRF2_ * *(idat.rij);
790	<	indirect_dVdr += -preSw * preRF2_ * uz_i;
791	<	indirect_duduz_i += -preSw * rhat * preRF2_ *  *(idat.rij);
792	<	}
793	<
794	<	} else {
795	<
796	<	// determine inverse r if we are using split dipoles
797	<	if (i_is_SplitDipole) {
798	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
799	<	ri = 1.0 / BigR;
800	<	scale =  *(idat.rij)  * ri;
801	<	} else {
802	<	ri = riji;
803	<	scale = 1.0;
804	<	}
805	<
806	<	sc2 = scale * scale;
807	<
808	<	if (screeningMethod_ == DAMPED) {
809	<	// assemble the damping variables
810	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
811	<	//erfcVal = res.first;
812	<	//derfcVal = res.second;
813	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
814	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
815	<	c1 = erfcVal * ri;
816	<	c2 = (-derfcVal + c1) * ri;
817	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
818	<	} else {
819	<	c1 = ri;
820	<	c2 = c1 * ri;
821	<	c3 = 3.0 * c2 * ri;
822	<	}
823	<
824	<	c2ri = c2 * ri;
825	<
826	<	// calculate the potential
827	<	pot_term = c2 * scale;
828	<	vterm = pref * ct_i * pot_term;
829	<	vpair += vterm;
830	<	epot +=  *(idat.sw)  * vterm;
1061	>	F  += pref * 2.0 * (trQb*rQa + trQa*rQb) * v42or;
1062	>	F  += pref * 4.0 * (rQaQb + QaQbr) * v42or;
1063	>	F  += pref * 2.0 * (rQa*rdQbr + rdQar*rQb) * v43or;
1064
1065	<	// calculate derivatives for the forces and torques
1066	<	dVdr += preSw * (uz_i * c2ri - ct_i * rhat * sc2 * c3);
1067	<	duduz_i += preSw * pot_term * rhat;
1068	<	}
1069	<	}
1065	>	Ta += pref * (- 4.0 * QaxQb * v41);
1066	>	Ta += pref * (- 2.0 * trQb * cross(rQa, rhat)
1067	>	+ 4.0 * cross(rhat, QaQbr)
1068	>	- 4.0 * rQaxQbr) * v42;
1069	>	Ta += pref * 2.0 * cross(rhat,Qar) * rdQbr * v43;
1070
838	–	if (j_is_Dipole) {
839	–	// variables used by all methods
840	–	ct_ij = dot(uz_i, uz_j);
1071
1072	<	pref =  *(idat.electroMult) * pre22_ * mu_i * mu_j;
1073	<	preSw =  *(idat.sw)  * pref;
1072	>	Tb += pref * (+ 4.0 * QaxQb * v41);
1073	>	Tb += pref * (- 2.0 * trQa * cross(rQb, rhat)
1074	>	- 4.0 * cross(rQaQb, rhat)
1075	>	+ 4.0 * rQaxQbr) * v42;
1076	>	// Possible replacement for line 2 above:
1077	>	//             + 4.0 * cross(rhat, QbQar)
1078
1079	<	if (summationMethod_ == esm_REACTION_FIELD) {
846	<	ri2 = riji * riji;
847	<	ri3 = ri2 * riji;
848	<	ri4 = ri2 * ri2;
849	<
850	<	vterm = pref * ( ri3 * (ct_ij - 3.0 * ct_i * ct_j) -
851	<	preRF2_ * ct_ij );
852	<	vpair += vterm;
853	<	epot +=  *(idat.sw)  * vterm;
854	<
855	<	a1 = 5.0 * ct_i * ct_j - ct_ij;
856	<
857	<	dVdr += preSw * 3.0 * ri4 * (a1 * rhat - ct_i * uz_j - ct_j * uz_i);
858	<
859	<	duduz_i += preSw * (ri3 * (uz_j - 3.0 * ct_j * rhat) - preRF2_*uz_j);
860	<	duduz_j += preSw * (ri3 * (uz_i - 3.0 * ct_i * rhat) - preRF2_*uz_i);
861	<
862	<	if (idat.excluded) {
863	<	indirect_vpair +=  - pref * preRF2_ * ct_ij;
864	<	indirect_Pot +=    - preSw * preRF2_ * ct_ij;
865	<	indirect_duduz_i += -preSw * preRF2_ * uz_j;
866	<	indirect_duduz_j += -preSw * preRF2_ * uz_i;
867	<	}
868	<
869	<	} else {
870	<
871	<	if (i_is_SplitDipole) {
872	<	if (j_is_SplitDipole) {
873	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i + 0.25 * d_j * d_j);
874	<	} else {
875	<	BigR = sqrt( *(idat.r2) + 0.25 * d_i * d_i);
876	<	}
877	<	ri = 1.0 / BigR;
878	<	scale =  *(idat.rij)  * ri;
879	<	} else {
880	<	if (j_is_SplitDipole) {
881	<	BigR = sqrt( *(idat.r2) + 0.25 * d_j * d_j);
882	<	ri = 1.0 / BigR;
883	<	scale =  *(idat.rij)  * ri;
884	<	} else {
885	<	ri = riji;
886	<	scale = 1.0;
887	<	}
888	<	}
889	<	if (screeningMethod_ == DAMPED) {
890	<	// assemble damping variables
891	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
892	<	//erfcVal = res.first;
893	<	//derfcVal = res.second;
894	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
895	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
896	<	c1 = erfcVal * ri;
897	<	c2 = (-derfcVal + c1) * ri;
898	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * ri;
899	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * ri * ri;
900	<	} else {
901	<	c1 = ri;
902	<	c2 = c1 * ri;
903	<	c3 = 3.0 * c2 * ri;
904	<	c4 = 5.0 * c3 * ri * ri;
905	<	}
906	<
907	<	// precompute variables for convenience
908	<	sc2 = scale * scale;
909	<	cti3 = ct_i * sc2 * c3;
910	<	ctj3 = ct_j * sc2 * c3;
911	<	ctidotj = ct_i * ct_j * sc2;
912	<	preSwSc = preSw * scale;
913	<	c2ri = c2 * ri;
914	<	c3ri = c3 * ri;
915	<	c4rij = c4 *  *(idat.rij) ;
916	<
917	<	// calculate the potential
918	<	pot_term = (ct_ij * c2ri - ctidotj * c3);
919	<	vterm = pref * pot_term;
920	<	vpair += vterm;
921	<	epot +=  *(idat.sw)  * vterm;
922	<
923	<	// calculate derivatives for the forces and torques
924	<	dVdr += preSwSc * ( ctidotj * rhat * c4rij  -
925	<	(ct_i*uz_j + ct_j*uz_i + ct_ij*rhat) * c3ri);
926	<
927	<	duduz_i += preSw * (uz_j * c2ri - ctj3 * rhat);
928	<	duduz_j += preSw * (uz_i * c2ri - cti3 * rhat);
929	<	}
1079	>	Tb += pref * 2.0 * cross(rhat,Qbr) * rdQar * v43;
1080		}
1081		}
1082
1083	<	if (i_is_Quadrupole) {
1084	<	if (j_is_Charge) {
1085	<	// precompute some necessary variables
936	<	cx2 = cx_i * cx_i;
937	<	cy2 = cy_i * cy_i;
938	<	cz2 = cz_i * cz_i;
939	<
940	<	pref =  *(idat.electroMult) * pre14_ * q_j * one_third_;
941	<
942	<	if (screeningMethod_ == DAMPED) {
943	<	// assemble the damping variables
944	<	//res = erfcSpline_->getValueAndDerivativeAt( *(idat.rij) );
945	<	//erfcVal = res.first;
946	<	//derfcVal = res.second;
947	<	erfcVal = erfc(dampingAlpha_ * *(idat.rij));
948	<	derfcVal = - alphaPi_ * exp(-alpha2_ * *(idat.r2));
949	<	c1 = erfcVal * riji;
950	<	c2 = (-derfcVal + c1) * riji;
951	<	c3 = -2.0 * derfcVal * alpha2_ + 3.0 * c2 * riji;
952	<	c4 = -4.0 * derfcVal * alpha4_ + 5.0 * c3 * riji * riji;
953	<	} else {
954	<	c1 = riji;
955	<	c2 = c1 * riji;
956	<	c3 = 3.0 * c2 * riji;
957	<	c4 = 5.0 * c3 * riji * riji;
958	<	}
959	<
960	<	// precompute some variables for convenience
961	<	preSw =  *(idat.sw)  * pref;
962	<	c2ri = c2 * riji;
963	<	c3ri = c3 * riji;
964	<	c4rij = c4 *  *(idat.rij) ;
965	<	rhatdot2 = 2.0 * rhat * c3;
966	<	rhatc4 = rhat * c4rij;
967	<
968	<	// calculate the potential
969	<	pot_term = ( qxx_i * (cx2 * c3 - c2ri) +
970	<	qyy_i * (cy2 * c3 - c2ri) +
971	<	qzz_i * (cz2 * c3 - c2ri) );
972	<
973	<	vterm = pref * pot_term;
974	<	vpair += vterm;
975	<	epot +=  *(idat.sw)  * vterm;
976	<
977	<	// calculate the derivatives for the forces and torques
978	<
979	<	dVdr += -preSw * (qxx_i* (cx2*rhatc4 - (2.0*cx_i*ux_i + rhat)*c3ri) +
980	<	qyy_i* (cy2*rhatc4 - (2.0*cy_i*uy_i + rhat)*c3ri) +
981	<	qzz_i* (cz2*rhatc4 - (2.0*cz_i*uz_i + rhat)*c3ri));
982	<
983	<	dudux_i += preSw * qxx_i * cx_i *  rhatdot2;
984	<	duduy_i += preSw * qyy_i * cy_i *  rhatdot2;
985	<	duduz_i += preSw * qzz_i * cz_i *  rhatdot2;
986	<	}
1083	>	if (idat.doElectricField) {
1084	>	*(idat.eField1) += Ea * *(idat.electroMult);
1085	>	*(idat.eField2) += Eb * *(idat.electroMult);
1086		}
1087
1088	<
1089	<	if (!idat.excluded) {
1090	<	*(idat.vpair) += vpair;
1091	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += epot;
993	<	*(idat.f1) += dVdr;
1088	>	if (a_is_Fluctuating) *(idat.dVdFQ1) += dUdCa * *(idat.sw);
1089	>	if (b_is_Fluctuating) *(idat.dVdFQ2) += dUdCb * *(idat.sw);
1090	>
1091	>	if (!idat.excluded) {
1092
1093	<	if (i_is_Dipole || i_is_Quadrupole)
1094	<	*(idat.t1) -= cross(uz_i, duduz_i);
1095	<	if (i_is_Quadrupole) {
998	<	*(idat.t1) -= cross(ux_i, dudux_i);
999	<	*(idat.t1) -= cross(uy_i, duduy_i);
1000	<	}
1093	>	*(idat.vpair) += U;
1094	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += U * *(idat.sw);
1095	>	*(idat.f1) += F * *(idat.sw);
1096
1097	<	if (j_is_Dipole || j_is_Quadrupole)
1098	<	*(idat.t2) -= cross(uz_j, duduz_j);
1004	<	if (j_is_Quadrupole) {
1005	<	*(idat.t2) -= cross(uz_j, dudux_j);
1006	<	*(idat.t2) -= cross(uz_j, duduy_j);
1007	<	}
1097	>	if (a_is_Dipole || a_is_Quadrupole)
1098	>	*(idat.t1) += Ta * *(idat.sw);
1099
1100	+	if (b_is_Dipole || b_is_Quadrupole)
1101	+	*(idat.t2) += Tb * *(idat.sw);
1102	+
1103		} else {
1104
1105		// only accumulate the forces and torques resulting from the
1106		// indirect reaction field terms.
1107
1108	<	*(idat.vpair) += indirect_vpair;
1109	<	(*(idat.pot))[ELECTROSTATIC_FAMILY] += indirect_Pot;
1110	<	*(idat.f1) += indirect_dVdr;
1108	>	*(idat.vpair) += indirect_Pot;
1109	>	(*(idat.excludedPot))[ELECTROSTATIC_FAMILY] +=  excluded_Pot;
1110	>	(*(idat.pot))[ELECTROSTATIC_FAMILY] += *(idat.sw) * indirect_Pot;
1111	>	*(idat.f1) += *(idat.sw) * indirect_F;
1112
1113	<	if (i_is_Dipole)
1114	<	*(idat.t1) -= cross(uz_i, indirect_duduz_i);
1115	<	if (j_is_Dipole)
1116	<	*(idat.t2) -= cross(uz_j, indirect_duduz_j);
1113	>	if (a_is_Dipole || a_is_Quadrupole)
1114	>	*(idat.t1) += *(idat.sw) * indirect_Ta;
1115	>
1116	>	if (b_is_Dipole || b_is_Quadrupole)
1117	>	*(idat.t2) += *(idat.sw) * indirect_Tb;
1118		}
1023	–
1024	–
1119		return;
1120	<	}
1120	>	}
1121
1122		void Electrostatic::calcSelfCorrection(SelfData &sdat) {
1123	<	RealType mu1, preVal, chg1, self;
1030	<
1123	>
1124		if (!initialized_) initialize();
1125
1126	<	ElectrostaticAtomData data = ElectrostaticMap[sdat.atype];
1127	<
1126	>	ElectrostaticAtomData data = ElectrostaticMap[Etids[sdat.atid]];
1127	>
1128		// logicals
1129		bool i_is_Charge = data.is_Charge;
1130		bool i_is_Dipole = data.is_Dipole;
1131	+	bool i_is_Quadrupole = data.is_Quadrupole;
1132	+	bool i_is_Fluctuating = data.is_Fluctuating;
1133	+	RealType C_a = data.fixedCharge;
1134	+	RealType self(0.0), preVal, DdD, trQ, trQQ;
1135
1136	<	if (summationMethod_ == esm_REACTION_FIELD) {
1137	<	if (i_is_Dipole) {
1138	<	mu1 = data.dipole_moment;
1042	<	preVal = pre22_ * preRF2_ * mu1 * mu1;
1043	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal;
1136	>	if (i_is_Dipole) {
1137	>	DdD = data.dipole.lengthSquare();
1138	>	}
1139
1140	<	// The self-correction term adds into the reaction field vector
1141	<	Vector3d uz_i = sdat.eFrame->getColumn(2);
1142	<	Vector3d ei = preVal * uz_i;
1140	>	if (i_is_Fluctuating) {
1141	>	C_a += *(sdat.flucQ);
1142	>	*(sdat.flucQfrc) -=  *(sdat.flucQ) * data.hardness + data.electronegativity;
1143	>	(*(sdat.excludedPot))[ELECTROSTATIC_FAMILY] += (*sdat.flucQ) *
1144	>	(*(sdat.flucQ) * data.hardness * 0.5 + data.electronegativity);
1145	>	}
1146
1147	<	// This looks very wrong.  A vector crossed with itself is zero.
1148	<	*(sdat.t) -= cross(uz_i, ei);
1147	>	switch (summationMethod_) {
1148	>	case esm_REACTION_FIELD:
1149	>
1150	>	if (i_is_Charge) {
1151	>	// Self potential [see Wang and Hermans, "Reaction Field
1152	>	// Molecular Dynamics Simulation with Friedman’s Image Charge
1153	>	// Method," J. Phys. Chem. 99, 12001-12007 (1995).]
1154	>	preVal = pre11_ * preRF_ * C_a * C_a;
1155	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= 0.5 * preVal / cutoffRadius_;
1156		}
1157	<	} else if (summationMethod_ == esm_SHIFTED_FORCE || summationMethod_ == esm_SHIFTED_POTENTIAL) {
1158	<	if (i_is_Charge) {
1159	<	chg1 = data.charge;
1055	<	if (screeningMethod_ == DAMPED) {
1056	<	self = - 0.5 * (c1c_ + alphaPi_) * chg1 * (chg1 + *(sdat.skippedCharge)) * pre11_;
1057	<	} else {
1058	<	self = - 0.5 * rcuti_ * chg1 * (chg1 +  *(sdat.skippedCharge)) * pre11_;
1059	<	}
1060	<	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1157	>
1158	>	if (i_is_Dipole) {
1159	>	(*(sdat.pot))[ELECTROSTATIC_FAMILY] -= pre22_ * preRF_ * DdD;
1160		}
1161	+
1162	+	break;
1163	+
1164	+	case esm_SHIFTED_FORCE:
1165	+	case esm_SHIFTED_POTENTIAL:
1166	+	case esm_TAYLOR_SHIFTED:
1167	+	case esm_EWALD_FULL:
1168	+	if (i_is_Charge)
1169	+	self += selfMult1_ * pre11_ * C_a * (C_a + *(sdat.skippedCharge));
1170	+	if (i_is_Dipole)
1171	+	self += selfMult2_ * pre22_ * DdD;
1172	+	if (i_is_Quadrupole) {
1173	+	trQ = data.quadrupole.trace();
1174	+	trQQ = (data.quadrupole * data.quadrupole).trace();
1175	+	self += selfMult4_ * pre44_ * (2.0*trQQ + trQ*trQ);
1176	+	if (i_is_Charge)
1177	+	self -= selfMult2_ * pre14_ * 2.0 * C_a * trQ;
1178	+	}
1179	+	(*(sdat.pot))[ELECTROSTATIC_FAMILY] += self;
1180	+	break;
1181	+	default:
1182	+	break;
1183		}
1184		}
1185	<
1185	>
1186		RealType Electrostatic::getSuggestedCutoffRadius(pair<AtomType*, AtomType*> atypes) {
1187		// This seems to work moderately well as a default.  There's no
1188		// inherent scale for 1/r interactions that we can standardize.
#	Line 1069 | Line 1190 | namespace OpenMD {
1190		// cases.
1191		return 12.0;
1192		}
1193	+
1194	+
1195	+	void Electrostatic::ReciprocalSpaceSum(RealType& pot) {
1196	+
1197	+	RealType kPot = 0.0;
1198	+	RealType kVir = 0.0;
1199	+
1200	+	const RealType mPoleConverter = 0.20819434; // converts from the
1201	+	// internal units of
1202	+	// Debye (for dipoles)
1203	+	// or Debye-angstroms
1204	+	// (for quadrupoles) to
1205	+	// electron angstroms or
1206	+	// electron-angstroms^2
1207	+
1208	+	const RealType eConverter = 332.0637778; // convert the
1209	+	// Charge-Charge
1210	+	// electrostatic
1211	+	// interactions into kcal /
1212	+	// mol assuming distances
1213	+	// are measured in
1214	+	// angstroms.
1215	+
1216	+	Mat3x3d hmat = info_->getSnapshotManager()->getCurrentSnapshot()->getHmat();
1217	+	Vector3d box = hmat.diagonals();
1218	+	RealType boxMax = box.max();
1219	+
1220	+	//int kMax = int(2.0 * M_PI / (pow(dampingAlpha_,2)*cutoffRadius_ * boxMax) );
1221	+	int kMax = 7;
1222	+	int kSqMax = kMax*kMax + 2;
1223	+
1224	+	int kLimit = kMax+1;
1225	+	int kLim2 = 2*kMax+1;
1226	+	int kSqLim = kSqMax;
1227	+
1228	+	vector<RealType> AK(kSqLim+1, 0.0);
1229	+	RealType xcl = 2.0 * M_PI / box.x();
1230	+	RealType ycl = 2.0 * M_PI / box.y();
1231	+	RealType zcl = 2.0 * M_PI / box.z();
1232	+	RealType rcl = 2.0 * M_PI / boxMax;
1233	+	RealType rvol = 2.0 * M_PI /(box.x() * box.y() * box.z());
1234	+
1235	+	if(dampingAlpha_ < 1.0e-12) return;
1236	+
1237	+	RealType ralph = -0.25/pow(dampingAlpha_,2);
1238	+
1239	+	// Calculate and store exponential factors
1240	+
1241	+	vector<vector<RealType> > elc;
1242	+	vector<vector<RealType> > emc;
1243	+	vector<vector<RealType> > enc;
1244	+	vector<vector<RealType> > els;
1245	+	vector<vector<RealType> > ems;
1246	+	vector<vector<RealType> > ens;
1247	+
1248	+
1249	+	int nMax = info_->getNAtoms();
1250	+
1251	+	elc.resize(kLimit+1);
1252	+	emc.resize(kLimit+1);
1253	+	enc.resize(kLimit+1);
1254	+	els.resize(kLimit+1);
1255	+	ems.resize(kLimit+1);
1256	+	ens.resize(kLimit+1);
1257	+
1258	+	for (int j = 0; j < kLimit+1; j++) {
1259	+	elc[j].resize(nMax);
1260	+	emc[j].resize(nMax);
1261	+	enc[j].resize(nMax);
1262	+	els[j].resize(nMax);
1263	+	ems[j].resize(nMax);
1264	+	ens[j].resize(nMax);
1265	+	}
1266	+
1267	+	Vector3d t( 2.0 * M_PI );
1268	+	t.Vdiv(t, box);
1269	+
1270	+
1271	+	SimInfo::MoleculeIterator mi;
1272	+	Molecule::AtomIterator ai;
1273	+	int i;
1274	+	Vector3d r;
1275	+	Vector3d tt;
1276	+
1277	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1278	+	mol = info_->nextMolecule(mi)) {
1279	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1280	+	atom = mol->nextAtom(ai)) {
1281	+
1282	+	i = atom->getLocalIndex();
1283	+	r = atom->getPos();
1284	+	info_->getSnapshotManager()->getCurrentSnapshot()->wrapVector(r);
1285	+
1286	+	tt.Vmul(t, r);
1287	+
1288	+	elc[1][i] = 1.0;
1289	+	emc[1][i] = 1.0;
1290	+	enc[1][i] = 1.0;
1291	+	els[1][i] = 0.0;
1292	+	ems[1][i] = 0.0;
1293	+	ens[1][i] = 0.0;
1294	+
1295	+	elc[2][i] = cos(tt.x());
1296	+	emc[2][i] = cos(tt.y());
1297	+	enc[2][i] = cos(tt.z());
1298	+	els[2][i] = sin(tt.x());
1299	+	ems[2][i] = sin(tt.y());
1300	+	ens[2][i] = sin(tt.z());
1301	+
1302	+	for(int l = 3; l <= kLimit; l++) {
1303	+	elc[l][i]=elc[l-1][i]*elc[2][i]-els[l-1][i]*els[2][i];
1304	+	emc[l][i]=emc[l-1][i]*emc[2][i]-ems[l-1][i]*ems[2][i];
1305	+	enc[l][i]=enc[l-1][i]*enc[2][i]-ens[l-1][i]*ens[2][i];
1306	+	els[l][i]=els[l-1][i]*elc[2][i]+elc[l-1][i]*els[2][i];
1307	+	ems[l][i]=ems[l-1][i]*emc[2][i]+emc[l-1][i]*ems[2][i];
1308	+	ens[l][i]=ens[l-1][i]*enc[2][i]+enc[l-1][i]*ens[2][i];
1309	+	}
1310	+	}
1311	+	}
1312	+
1313	+	// Calculate and store AK coefficients:
1314	+
1315	+	RealType eksq = 1.0;
1316	+	RealType expf = 0.0;
1317	+	if (ralph < 0.0) expf = exp(ralph*rcl*rcl);
1318	+	for (i = 1; i <= kSqLim; i++) {
1319	+	RealType rksq = float(i)*rcl*rcl;
1320	+	eksq = expf*eksq;
1321	+	AK[i] = eConverter * eksq/rksq;
1322	+	}
1323	+
1324	+	/*
1325	+	* Loop over all k vectors k = 2 pi (ll/Lx, mm/Ly, nn/Lz)
1326	+	* the values of ll, mm and nn are selected so that the symmetry of
1327	+	* reciprocal lattice is taken into account i.e. the following
1328	+	* rules apply.
1329	+	*
1330	+	* ll ranges over the values 0 to kMax only.
1331	+	*
1332	+	* mm ranges over 0 to kMax when ll=0 and over
1333	+	*            -kMax to kMax otherwise.
1334	+	* nn ranges over 1 to kMax when ll=mm=0 and over
1335	+	*            -kMax to kMax otherwise.
1336	+	*
1337	+	* Hence the result of the summation must be doubled at the end.
1338	+	*/
1339	+
1340	+	std::vector<RealType> clm(nMax, 0.0);
1341	+	std::vector<RealType> slm(nMax, 0.0);
1342	+	std::vector<RealType> ckr(nMax, 0.0);
1343	+	std::vector<RealType> skr(nMax, 0.0);
1344	+	std::vector<RealType> ckc(nMax, 0.0);
1345	+	std::vector<RealType> cks(nMax, 0.0);
1346	+	std::vector<RealType> dkc(nMax, 0.0);
1347	+	std::vector<RealType> dks(nMax, 0.0);
1348	+	std::vector<RealType> qkc(nMax, 0.0);
1349	+	std::vector<RealType> qks(nMax, 0.0);
1350	+	std::vector<Vector3d> dxk(nMax, V3Zero);
1351	+	std::vector<Vector3d> qxk(nMax, V3Zero);
1352	+	RealType rl, rm, rn;
1353	+	Vector3d kVec;
1354	+	Vector3d Qk;
1355	+	Mat3x3d k2;
1356	+	RealType ckcs, ckss, dkcs, dkss, qkcs, qkss;
1357	+	int atid;
1358	+	ElectrostaticAtomData data;
1359	+	RealType C, dk, qk;
1360	+	Vector3d D;
1361	+	Mat3x3d  Q;
1362	+
1363	+	int mMin = kLimit;
1364	+	int nMin = kLimit + 1;
1365	+	for (int l = 1; l <= kLimit; l++) {
1366	+	int ll = l - 1;
1367	+	rl = xcl * float(ll);
1368	+	for (int mmm = mMin; mmm <= kLim2; mmm++) {
1369	+	int mm = mmm - kLimit;
1370	+	int m = abs(mm) + 1;
1371	+	rm = ycl * float(mm);
1372	+	// Set temporary products of exponential terms
1373	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1374	+	mol = info_->nextMolecule(mi)) {
1375	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1376	+	atom = mol->nextAtom(ai)) {
1377	+
1378	+	i = atom->getLocalIndex();
1379	+	if(mm < 0) {
1380	+	clm[i]=elc[l][i]*emc[m][i]+els[l][i]*ems[m][i];
1381	+	slm[i]=els[l][i]*emc[m][i]-ems[m][i]*elc[l][i];
1382	+	} else {
1383	+	clm[i]=elc[l][i]*emc[m][i]-els[l][i]*ems[m][i];
1384	+	slm[i]=els[l][i]*emc[m][i]+ems[m][i]*elc[l][i];
1385	+	}
1386	+	}
1387	+	}
1388	+	for (int nnn = nMin; nnn <= kLim2; nnn++) {
1389	+	int nn = nnn - kLimit;
1390	+	int n = abs(nn) + 1;
1391	+	rn = zcl * float(nn);
1392	+	// Test on magnitude of k vector:
1393	+	int kk=ll*ll + mm*mm + nn*nn;
1394	+	if(kk <= kSqLim) {
1395	+	kVec = Vector3d(rl, rm, rn);
1396	+	k2 = outProduct(kVec, kVec);
1397	+	// Calculate exp(ikr) terms
1398	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1399	+	mol = info_->nextMolecule(mi)) {
1400	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1401	+	atom = mol->nextAtom(ai)) {
1402	+	i = atom->getLocalIndex();
1403	+
1404	+	if (nn < 0) {
1405	+	ckr[i]=clm[i]*enc[n][i]+slm[i]*ens[n][i];
1406	+	skr[i]=slm[i]*enc[n][i]-clm[i]*ens[n][i];
1407	+
1408	+	} else {
1409	+	ckr[i]=clm[i]*enc[n][i]-slm[i]*ens[n][i];
1410	+	skr[i]=slm[i]*enc[n][i]+clm[i]*ens[n][i];
1411	+	}
1412	+	}
1413	+	}
1414	+
1415	+	// Calculate scalar and vector products for each site:
1416	+
1417	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1418	+	mol = info_->nextMolecule(mi)) {
1419	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1420	+	atom = mol->nextAtom(ai)) {
1421	+	i = atom->getLocalIndex();
1422	+	int atid = atom->getAtomType()->getIdent();
1423	+	data = ElectrostaticMap[Etids[atid]];
1424	+
1425	+	if (data.is_Charge) {
1426	+	C = data.fixedCharge;
1427	+	if (atom->isFluctuatingCharge()) C += atom->getFlucQPos();
1428	+	ckc[i] = C * ckr[i];
1429	+	cks[i] = C * skr[i];
1430	+	}
1431	+
1432	+	if (data.is_Dipole) {
1433	+	D = atom->getDipole() * mPoleConverter;
1434	+	dk = dot(D, kVec);
1435	+	dxk[i] = cross(D, kVec);
1436	+	dkc[i] = dk * ckr[i];
1437	+	dks[i] = dk * skr[i];
1438	+	}
1439	+	if (data.is_Quadrupole) {
1440	+	Q = atom->getQuadrupole() * mPoleConverter;
1441	+	Qk = Q * kVec;
1442	+	qk = dot(kVec, Qk);
1443	+	qxk[i] = cross(kVec, Qk);
1444	+	qkc[i] = qk * ckr[i];
1445	+	qks[i] = qk * skr[i];
1446	+	}
1447	+	}
1448	+	}
1449	+
1450	+	// calculate vector sums
1451	+
1452	+	ckcs = std::accumulate(ckc.begin(),ckc.end(),0.0);
1453	+	ckss = std::accumulate(cks.begin(),cks.end(),0.0);
1454	+	dkcs = std::accumulate(dkc.begin(),dkc.end(),0.0);
1455	+	dkss = std::accumulate(dks.begin(),dks.end(),0.0);
1456	+	qkcs = std::accumulate(qkc.begin(),qkc.end(),0.0);
1457	+	qkss = std::accumulate(qks.begin(),qks.end(),0.0);
1458	+
1459	+	#ifdef IS_MPI
1460	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &ckcs, 1, MPI::REALTYPE,
1461	+	MPI::SUM);
1462	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &ckss, 1, MPI::REALTYPE,
1463	+	MPI::SUM);
1464	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &dkcs, 1, MPI::REALTYPE,
1465	+	MPI::SUM);
1466	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &dkss, 1, MPI::REALTYPE,
1467	+	MPI::SUM);
1468	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &qkcs, 1, MPI::REALTYPE,
1469	+	MPI::SUM);
1470	+	MPI::COMM_WORLD.Allreduce(MPI::IN_PLACE, &qkss, 1, MPI::REALTYPE,
1471	+	MPI::SUM);
1472	+	#endif
1473	+
1474	+	// Accumulate potential energy and virial contribution:
1475	+
1476	+	kPot += 2.0 * rvol * AK[kk]*((ckss+dkcs-qkss)*(ckss+dkcs-qkss)
1477	+	+ (ckcs-dkss-qkcs)*(ckcs-dkss-qkcs));
1478	+
1479	+	kVir += 2.0 * rvol  * AK[kk]*(ckcs*ckcs+ckss*ckss
1480	+	+4.0*(ckss*dkcs-ckcs*dkss)
1481	+	+3.0*(dkcs*dkcs+dkss*dkss)
1482	+	-6.0*(ckss*qkss+ckcs*qkcs)
1483	+	+8.0*(dkss*qkcs-dkcs*qkss)
1484	+	+5.0*(qkss*qkss+qkcs*qkcs));
1485	+
1486	+	// Calculate force and torque for each site:
1487	+
1488	+	for (Molecule* mol = info_->beginMolecule(mi); mol != NULL;
1489	+	mol = info_->nextMolecule(mi)) {
1490	+	for(Atom* atom = mol->beginAtom(ai); atom != NULL;
1491	+	atom = mol->nextAtom(ai)) {
1492	+
1493	+	i = atom->getLocalIndex();
1494	+	atid = atom->getAtomType()->getIdent();
1495	+	data = ElectrostaticMap[Etids[atid]];
1496	+
1497	+	RealType qfrc = AK[kk]*((cks[i]+dkc[i]-qks[i])*(ckcs-dkss-qkcs)
1498	+	- (ckc[i]-dks[i]-qkc[i])*(ckss+dkcs-qkss));
1499	+	RealType qtrq1 = AK[kk]*(skr[i]*(ckcs-dkss-qkcs)
1500	+	-ckr[i]*(ckss+dkcs-qkss));
1501	+	RealType qtrq2 = 2.0*AK[kk]*(ckr[i]*(ckcs-dkss-qkcs)
1502	+	+skr[i]*(ckss+dkcs-qkss));
1503	+
1504	+	atom->addFrc( 4.0 * rvol * qfrc * kVec );
1505	+
1506	+	if (data.is_Dipole) {
1507	+	atom->addTrq( 4.0 * rvol * qtrq1 * dxk[i] );
1508	+	}
1509	+	if (data.is_Quadrupole) {
1510	+	atom->addTrq( 4.0 * rvol * qtrq2 * qxk[i] );
1511	+	}
1512	+	}
1513	+	}
1514	+	}
1515	+	}
1516	+	nMin = 1;
1517	+	}
1518	+	mMin = 1;
1519	+	}
1520	+	pot += kPot;
1521	+	}
1522		}

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