Newer
Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
#pragma once
/**
This header contains methods that pertain to polar contributions to SAFT models
Initially the contribution of Gross and Vrabec were implemented for PC-SAFT, but they can be used with other
non-polar base models as well, so this header collects all the things in one place
*/
#include "teqp/types.hpp"
#include "teqp/exceptions.hpp"
#include "correlation_integrals.hpp"
#include <Eigen/Dense>
namespace teqp{
namespace SAFTpolar{
/// Eq. 10 from Gross and Vrabec
template <typename Eta, typename MType, typename TType>
auto get_JDD_2ij(const Eta& eta, const MType& mij, const TType& Tstarij) {
static Eigen::ArrayXd a_0 = (Eigen::ArrayXd(5) << 0.3043504, -0.1358588, 1.4493329, 0.3556977, -2.0653308).finished();
static Eigen::ArrayXd a_1 = (Eigen::ArrayXd(5) << 0.9534641, -1.8396383, 2.0131180, -7.3724958, 8.2374135).finished();
static Eigen::ArrayXd a_2 = (Eigen::ArrayXd(5) << -1.1610080, 4.5258607, 0.9751222, -12.281038, 5.9397575).finished();
static Eigen::ArrayXd b_0 = (Eigen::ArrayXd(5) << 0.2187939, -1.1896431, 1.1626889, 0, 0).finished();
static Eigen::ArrayXd b_1 = (Eigen::ArrayXd(5) << -0.5873164, 1.2489132, -0.5085280, 0, 0).finished();
static Eigen::ArrayXd b_2 = (Eigen::ArrayXd(5) << 3.4869576, -14.915974, 15.372022, 0, 0).finished();
std::common_type_t<Eta, MType> summer = 0.0;
for (auto n = 0; n < 5; ++n){
auto anij = a_0[n] + (mij-1)/mij*a_1[n] + (mij-1)/mij*(mij-2)/mij*a_2[n]; // Eq. 12
auto bnij = b_0[n] + (mij-1)/mij*b_1[n] + (mij-1)/mij*(mij-2)/mij*b_2[n]; // Eq. 13
summer += (anij + bnij/Tstarij)*pow(eta, n);
}
return forceeval(summer);
}
/// Eq. 11 from Gross and Vrabec
template <typename Eta, typename MType>
auto get_JDD_3ijk(const Eta& eta, const MType& mijk) {
static Eigen::ArrayXd c_0 = (Eigen::ArrayXd(5) << -0.0646774, 0.1975882, -0.8087562, 0.6902849, 0.0).finished();
static Eigen::ArrayXd c_1 = (Eigen::ArrayXd(5) << -0.9520876, 2.9924258, -2.3802636, -0.2701261, 0.0).finished();
static Eigen::ArrayXd c_2 = (Eigen::ArrayXd(5) << -0.6260979, 1.2924686, 1.6542783, -3.4396744, 0.0).finished();
std::common_type_t<Eta, MType> summer = 0.0;
for (auto n = 0; n < 5; ++n){
auto cnijk = c_0[n] + (mijk-1)/mijk*c_1[n] + (mijk-1)/mijk*(mijk-2)/mijk*c_2[n]; // Eq. 14
summer += cnijk*pow(eta, n);
}
return forceeval(summer);
}
/// Eq. 12 from Gross and Vrabec, AICHEJ
template <typename Eta, typename MType, typename TType>
auto get_JQQ_2ij(const Eta& eta, const MType& mij, const TType& Tstarij) {
static Eigen::ArrayXd a_0 = (Eigen::ArrayXd(5) << 1.2378308, 2.4355031, 1.6330905, -1.6118152, 6.9771185).finished();
static Eigen::ArrayXd a_1 = (Eigen::ArrayXd(5) << 1.2854109, -11.465615, 22.086893, 7.4691383, -17.197772).finished();
static Eigen::ArrayXd a_2 = (Eigen::ArrayXd(5) << 1.7942954, 0.7695103, 7.2647923, 94.486699, -77.148458).finished();
static Eigen::ArrayXd b_0 = (Eigen::ArrayXd(5) << 0.4542718, -4.5016264, 3.5858868, 0.0, 0.0).finished();
static Eigen::ArrayXd b_1 = (Eigen::ArrayXd(5) << -0.8137340, 10.064030, -10.876631, 0.0, 0.0).finished();
static Eigen::ArrayXd b_2 = (Eigen::ArrayXd(5) << 6.8682675, -5.1732238, -17.240207, 0.0, 0.0).finished();
std::common_type_t<Eta, MType> summer = 0.0;
for (auto n = 0; n < 5; ++n){
auto anij = a_0[n] + (mij-1)/mij*a_1[n] + (mij-1)/mij*(mij-2)/mij*a_2[n]; // Eq. 12
auto bnij = b_0[n] + (mij-1)/mij*b_1[n] + (mij-1)/mij*(mij-2)/mij*b_2[n]; // Eq. 13
summer += (anij + bnij/Tstarij)*pow(eta, n);
}
return forceeval(summer);
}
/// Eq. 13 from Gross and Vrabec, AICHEJ
template <typename Eta, typename MType>
auto get_JQQ_3ijk(const Eta& eta, const MType& mijk) {
static Eigen::ArrayXd c_0 = (Eigen::ArrayXd(5) << 0.5000437, 6.5318692, -16.014780, 14.425970, 0.0).finished();
static Eigen::ArrayXd c_1 = (Eigen::ArrayXd(5) << 2.0002094, -6.7838658, 20.383246, -10.895984, 0.0).finished();
static Eigen::ArrayXd c_2 = (Eigen::ArrayXd(5) << 3.1358271, 7.2475888, 3.0759478, 0.0, 0.0).finished();
std::common_type_t<Eta, MType> summer = 0.0;
for (auto n = 0; n < 5; ++n){
auto cnijk = c_0[n] + (mijk-1)/mijk*c_1[n] + (mijk-1)/mijk*(mijk-2)/mijk*c_2[n]; // Eq. 14
summer += cnijk*pow(eta, n);
}
return forceeval(summer);
}
/***
* \brief The dipolar contribution given in Gross and Vrabec
*/
class DipolarContributionGrossVrabec {
private:
const Eigen::ArrayXd m, sigma_Angstrom, epsilon_over_k, mustar2, nmu;
template<typename A> auto POW2(const A& x) const { return forceeval(x*x); }
template<typename A> auto POW3(const A& x) const { return forceeval(POW2(x)*x); }
public:
DipolarContributionGrossVrabec(const Eigen::ArrayX<double> &m, const Eigen::ArrayX<double> &sigma_Angstrom, const Eigen::ArrayX<double> &epsilon_over_k, const Eigen::ArrayX<double> &mustar2, const Eigen::ArrayX<double> &nmu) : m(m), sigma_Angstrom(sigma_Angstrom), epsilon_over_k(epsilon_over_k), mustar2(mustar2), nmu(nmu) {
// Check lengths match
if (m.size() != mustar2.size()){
throw teqp::InvalidArgument("bad size of mustar2");
}
if (m.size() != nmu.size()){
throw teqp::InvalidArgument("bad size of n");
}
}
/// Eq. 8 from Gross and Vrabec
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto get_alpha2DD(const TTYPE& T, const RhoType& rhoN_A3, const EtaType& eta, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_Angstrom; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summer = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
auto ninj = nmu[i]*nmu[j];
if (ninj > 0){
// Lorentz-Berthelot mixing rules
auto epskij = sqrt(epsilon_over_k[i]*epsilon_over_k[j]);
auto sigmaij = (sigma[i]+sigma[j])/2;
auto Tstarij = T/epskij;
auto mij = std::max(sqrt(m[i]*m[j]), 2.0);
summer += x[i]*x[j]*epsilon_over_k[i]/T*epsilon_over_k[j]/T*POW3(sigma[i]*sigma[j]/sigmaij)*ninj*mustar2[i]*mustar2[j]*get_JDD_2ij(eta, mij, Tstarij);
}
}
}
return forceeval(-static_cast<double>(EIGEN_PI)*rhoN_A3*summer);
}
/// Eq. 9 from Gross and Vrabec
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto get_alpha3DD(const TTYPE& T, const RhoType& rhoN_A3, const EtaType& eta, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_Angstrom; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summer = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
for (auto k = 0; k < N; ++k){
auto ninjnk = nmu[i]*nmu[j]*nmu[k];
if (ninjnk > 0){
// Lorentz-Berthelot mixing rules for sigma
auto sigmaij = (sigma[i]+sigma[j])/2;
auto sigmaik = (sigma[i]+sigma[k])/2;
auto sigmajk = (sigma[j]+sigma[k])/2;
auto mijk = std::max(pow(m[i]*m[j]*m[k], 1.0/3.0), 2.0);
summer += x[i]*x[j]*x[k]*epsilon_over_k[i]/T*epsilon_over_k[j]/T*epsilon_over_k[k]/T*POW3(sigma[i]*sigma[j]*sigma[k])/(sigmaij*sigmaik*sigmajk)*ninjnk*mustar2[i]*mustar2[j]*mustar2[k]*get_JDD_3ijk(eta, mijk);
}
}
}
}
return forceeval(-4.0*POW2(static_cast<double>(EIGEN_PI))/3.0*POW2(rhoN_A3)*summer);
}
/***
* \brief Get the dipolar contribution to \f$ \alpha = A/(NkT) \f$
*/
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto eval(const TTYPE& T, const RhoType& rho_A3, const EtaType& eta, const VecType& mole_fractions) const {
auto alpha2 = get_alpha2DD(T, rho_A3, eta, mole_fractions);
auto alpha3 = get_alpha3DD(T, rho_A3, eta, mole_fractions);
auto alpha = forceeval(alpha2/(1.0-alpha3/alpha2));
using alpha2_t = decltype(alpha2);
using alpha3_t = decltype(alpha3);
using alpha_t = decltype(alpha);
struct DipolarContributionTerms{
alpha2_t alpha2;
alpha3_t alpha3;
alpha_t alpha;
};
return DipolarContributionTerms{alpha2, alpha3, alpha};
}
};
/***
* \brief The quadrupolar contribution from Gross and Vrabec
*
*/
class QuadrupolarContributionGrossVrabec {
private:
const Eigen::ArrayXd m, sigma_Angstrom, epsilon_over_k, Qstar2, nQ;
template<typename A> auto POW2(const A& x) const { return forceeval(x*x); }
template<typename A> auto POW3(const A& x) const { return forceeval(POW2(x)*x); }
template<typename A> auto POW5(const A& x) const { return forceeval(POW2(x)*POW3(x)); }
template<typename A> auto POW7(const A& x) const { return forceeval(POW2(x)*POW5(x)); }
public:
QuadrupolarContributionGrossVrabec(const Eigen::ArrayX<double> &m, const Eigen::ArrayX<double> &sigma_Angstrom, const Eigen::ArrayX<double> &epsilon_over_k, const Eigen::ArrayX<double> &Qstar2, const Eigen::ArrayX<double> &nQ) : m(m), sigma_Angstrom(sigma_Angstrom), epsilon_over_k(epsilon_over_k), Qstar2(Qstar2), nQ(nQ) {
// Check lengths match
if (m.size() != Qstar2.size()){
throw teqp::InvalidArgument("bad size of mustar2");
}
if (m.size() != nQ.size()){
throw teqp::InvalidArgument("bad size of n");
}
}
QuadrupolarContributionGrossVrabec& operator=( const QuadrupolarContributionGrossVrabec& ) = delete; // non copyable
/// Eq. 9 from Gross and Vrabec
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto get_alpha2QQ(const TTYPE& T, const RhoType& rhoN_A3, const EtaType& eta, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_Angstrom; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summer = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
auto ninj = nQ[i]*nQ[j];
if (ninj > 0){
// Lorentz-Berthelot mixing rules
auto epskij = sqrt(epsilon_over_k[i]*epsilon_over_k[j]);
auto sigmaij = (sigma[i]+sigma[j])/2;
auto Tstarij = T/epskij;
auto mij = sqrt(m[i]*m[j]);
summer += x[i]*x[j]*epsilon_over_k[i]/T*epsilon_over_k[j]/T*POW5(sigma[i]*sigma[j])/POW7(sigmaij)*ninj*Qstar2[i]*Qstar2[j]*get_JQQ_2ij(eta, mij, Tstarij);
}
}
}
return forceeval(-static_cast<double>(EIGEN_PI)*POW2(3.0/4.0)*rhoN_A3*summer);
}
/// Eq. 1 from Gross and Vrabec
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto get_alpha3QQ(const TTYPE& T, const RhoType& rhoN_A3, const EtaType& eta, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_Angstrom; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summer = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
for (auto k = 0; k < N; ++k){
auto ninjnk = nQ[i]*nQ[j]*nQ[k];
if (ninjnk > 0){
// Lorentz-Berthelot mixing rules for sigma
auto sigmaij = (sigma[i]+sigma[j])/2;
auto sigmaik = (sigma[i]+sigma[k])/2;
auto sigmajk = (sigma[j]+sigma[k])/2;
auto mijk = pow(m[i]*m[j]*m[k], 1.0/3.0);
summer += x[i]*x[j]*x[k]*epsilon_over_k[i]/T*epsilon_over_k[j]/T*epsilon_over_k[k]/T*POW5(sigma[i]*sigma[j]*sigma[k])/POW3(sigmaij*sigmaik*sigmajk)*ninjnk*Qstar2[i]*Qstar2[j]*Qstar2[k]*get_JDD_3ijk(eta, mijk);
}
}
}
}
return forceeval(-4.0*POW2(static_cast<double>(EIGEN_PI))/3.0*POW3(3.0/4.0)*POW2(rhoN_A3)*summer);
}
/***
* \brief Get the quadrupolar contribution to \f$ \alpha = A/(NkT) \f$
*/
template<typename TTYPE, typename RhoType, typename EtaType, typename VecType>
auto eval(const TTYPE& T, const RhoType& rho_A3, const EtaType& eta, const VecType& mole_fractions) const {
auto alpha2 = get_alpha2QQ(T, rho_A3, eta, mole_fractions);
auto alpha3 = get_alpha3QQ(T, rho_A3, eta, mole_fractions);
auto alpha = forceeval(alpha2/(1.0-alpha3/alpha2));
using alpha2_t = decltype(alpha2);
using alpha3_t = decltype(alpha3);
using alpha_t = decltype(alpha);
struct QuadrupolarContributionTerms{
alpha2_t alpha2;
alpha3_t alpha3;
alpha_t alpha;
};
return QuadrupolarContributionTerms{alpha2, alpha3, alpha};
}
};
/**
\tparam JIntegral A type that can be indexed with a single integer n to give the J^{(n)} integral
\tparam KIntegral A type that can be indexed with a two integers a and b to give the K(a,b) integral
The flexibility was added to include J and K integrals from either Luckas et al. or Gubbins and Twu (or any others following the interface)
*/
template<class JIntegral, class KIntegral>
class MultipolarContributionGubbinsTwu {
private:
const Eigen::ArrayXd sigma_m, epsilon_over_k, mubar2, Qbar2;
template<typename A> auto POW2(const A& x) const { return forceeval(x*x); }
template<typename A> auto POW3(const A& x) const { return forceeval(POW2(x)*x); }
template<typename A> auto POW4(const A& x) const { return forceeval(POW2(x)*POW2(x)); }
template<typename A> auto POW5(const A& x) const { return forceeval(POW2(x)*POW3(x)); }
template<typename A> auto POW7(const A& x) const { return forceeval(POW2(x)*POW5(x)); }
template<typename A> auto POW8(const A& x) const { return forceeval(POW4(x)*POW4(x)); }
template<typename A> auto POW10(const A& x) const { return forceeval(POW2(x)*POW8(x)); }
template<typename A> auto POW12(const A& x) const { return forceeval(POW4(x)*POW8(x)); }
const JIntegral J6{6};
const JIntegral J8{8};
const JIntegral J10{10};
const JIntegral J11{11};
const JIntegral J13{13};
const JIntegral J15{15};
const KIntegral K222_333{222, 333};
const KIntegral K233_344{233, 344};
const KIntegral K334_445{334, 445};
const KIntegral K444_555{444, 555};
const double epsilon_0 = 8.8541878128e-12; // https://en.wikipedia.org/wiki/Vacuum_permittivity, in F/m, or C^2⋅N^−1⋅m^−2
const double PI_ = static_cast<double>(EIGEN_PI);
public:
MultipolarContributionGubbinsTwu(const Eigen::ArrayX<double> &sigma_m, const Eigen::ArrayX<double> &epsilon_over_k, const Eigen::ArrayX<double> &mubar2, const Eigen::ArrayX<double> &Qbar2) : sigma_m(sigma_m), epsilon_over_k(epsilon_over_k), mubar2(mubar2), Qbar2(Qbar2) {
// Check lengths match
if (sigma_m.size() != mubar2.size()){
throw teqp::InvalidArgument("bad size of mubar2");
}
if (sigma_m.size() != Qbar2.size()){
throw teqp::InvalidArgument("bad size of Qbar2");
}
}
MultipolarContributionGubbinsTwu& operator=( const MultipolarContributionGubbinsTwu& ) = delete; // non copyable
template<typename TTYPE, typename RhoType, typename VecType>
auto get_alpha2(const TTYPE& T, const RhoType& rhoN, const RhoType& rhostar, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_m; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summer112 = 0.0, summer123 = 0.0, summer224 = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
// Lorentz-Berthelot mixing rules
auto epskij = sqrt(epsilon_over_k[i]*epsilon_over_k[j]);
auto sigmaij = (sigma[i]+sigma[j])/2;
auto Tstari = T/epsilon_over_k[i], Tstarj = T/epsilon_over_k[j];
auto leading = x[i]*x[j]/(Tstari*Tstarj); // common for all alpha_2 terms
auto Tstarij = forceeval(T/epskij);
summer112 += leading*POW3(sigma[i]*sigma[j])/POW3(sigmaij)*mubar2[i]*mubar2[j]*J6.get_J(Tstarij, rhostar);
summer123 += leading*POW3(sigma[i])*POW5(sigma[j])/POW5(sigmaij)*mubar2[i]*Qbar2[j]*J8.get_J(Tstarij, rhostar);
summer224 += leading*POW5(sigma[i]*sigma[j])/POW7(sigmaij)*Qbar2[i]*Qbar2[j]*J10.get_J(Tstarij, rhostar);
}
}
auto alpha2_112 = -2.0*PI_*rhoN*POW2(4*PI_*epsilon_0)/3.0*summer112;
auto alpha2_123 = -PI_*rhoN*POW2(4*PI_*epsilon_0)/3.0*summer123;
auto alpha2_224 = -14.0*PI_*rhoN*POW2(4*PI_*epsilon_0)/5.0*summer224;
return forceeval(alpha2_112 + 2.0*alpha2_123 + alpha2_224);
}
template<typename TTYPE, typename RhoType, typename VecType>
auto get_alpha3(const TTYPE& T, const RhoType& rhoN, const RhoType& rhostar, const VecType& mole_fractions) const{
const auto& x = mole_fractions; // concision
const auto& sigma = sigma_m; // concision
const auto N = mole_fractions.size();
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summerA_112_112_224 = 0.0, summerA_112_123_213 = 0.0, summerA_123_123_224 = 0.0, summerA_224_224_224 = 0.0;
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> summerB_112_112_112 = 0.0, summerB_112_123_123 = 0.0, summerB_123_123_224 = 0.0, summerB_224_224_224 = 0.0;
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
// Lorentz-Berthelot mixing rules
auto epskij = sqrt(epsilon_over_k[i]*epsilon_over_k[j]);
auto sigmaij = (sigma[i]+sigma[j])/2;
auto Tstari = T/epsilon_over_k[i], Tstarj = T/epsilon_over_k[j];
auto Tstarij = forceeval(T/epskij);
auto leading = x[i]*x[j]/pow(Tstari*Tstarj, 3.0/2.0); // common for all alpha_3A terms
summerA_112_112_224 += leading*pow(sigma[i]*sigma[j], 11.0/2.0)/POW8(sigmaij)*mubar2[i]*mubar2[j]*sqrt(Qbar2[i]*Qbar2[j])*J11.get_J(Tstarij, rhostar);
summerA_112_123_213 += leading*pow(sigma[i]*sigma[j], 11.0/2.0)/POW8(sigmaij)*mubar2[i]*mubar2[j]*sqrt(Qbar2[i]*Qbar2[j])*J11.get_J(Tstarij, rhostar);
summerA_123_123_224 += leading*pow(sigma[i], 11.0/2.0)*pow(sigma[j], 15.0/2.0)/POW10(sigmaij)*mubar2[i]*sqrt(Qbar2[i])*pow(Qbar2[j], 3.0/2.0)*J13.get_J(Tstarij, rhostar);
summerA_224_224_224 += leading*pow(sigma[i]*sigma[j], 15.0/2.0)/POW12(sigmaij)*Qbar2[i]*Qbar2[j]*J15.get_J(Tstarij, rhostar);
for (auto k = 0; k < N; ++k){
auto Tstark = T/epsilon_over_k[k];
auto epskik = sqrt(epsilon_over_k[i]*epsilon_over_k[k]);
auto epskjk = sqrt(epsilon_over_k[j]*epsilon_over_k[k]);
auto Tstarik = T/epskik;
auto Tstarjk = T/epskjk;
// Lorentz-Berthelot mixing rules for sigma
auto sigmaij = (sigma[i]+sigma[j])/2;
auto sigmaik = (sigma[i]+sigma[k])/2;
auto sigmajk = (sigma[j]+sigma[k])/2;
auto leadingijk = x[i]*x[j]*x[k]/(Tstari*Tstarj*Tstark);
auto K222333 = pow(K222_333.get_K(Tstarij, rhostar)*K222_333.get_K(Tstarik, rhostar)*K222_333.get_K(Tstarjk, rhostar), 1.0/3.0);
summerB_112_112_112 += leadingijk*POW3(sigma[i]*sigma[j]*sigma[k])/(sigmaij*sigmaik*sigmajk)*mubar2[i]*mubar2[j]*mubar2[k]*K222333;
auto K233344 = pow(K233_344.get_K(Tstarij, rhostar)*K233_344.get_K(Tstarik, rhostar)*K233_344.get_K(Tstarjk, rhostar), 1.0/3.0);
summerB_112_123_123 += leadingijk*POW3(sigma[i]*sigma[j])*POW5(sigma[k])/(sigmaij*POW2(sigmaik*sigmajk))*mubar2[i]*mubar2[j]*Qbar2[k]*K233344;
auto K334445 = pow(K334_445.get_K(Tstarij, rhostar)*K334_445.get_K(Tstarik, rhostar)*K334_445.get_K(Tstarjk, rhostar), 1.0/3.0);
summerB_123_123_224 += leadingijk*POW3(sigma[i])*POW5(sigma[j]*sigma[k])/(POW2(sigmaij*sigmaik)*POW3(sigmajk))*mubar2[i]*Qbar2[j]*Qbar2[k]*K334445;
auto K444555 = pow(K444_555.get_K(Tstarij, rhostar)*K444_555.get_K(Tstarik, rhostar)*K444_555.get_K(Tstarjk, rhostar), 1.0/3.0);
summerB_224_224_224 += leadingijk*POW5(sigma[i]*sigma[j]*sigma[k])/(POW3(sigmaij*sigmaik*sigmajk))*Qbar2[i]*Qbar2[j]*Qbar2[k]*K444555;
}
}
}
auto alpha3A_112_112_224 = 8.0*PI_*rhoN*POW3(4*PI_*epsilon_0)/25.0*summerA_112_112_224;
auto alpha3A_112_123_213 = 8.0*PI_*rhoN*POW3(4*PI_*epsilon_0)/75.0*summerA_112_123_213;
auto alpha3A_123_123_224 = 8.0*PI_*rhoN*POW3(4*PI_*epsilon_0)/35.0*summerA_123_123_224;
auto alpha3A_224_224_224 = 144.0*PI_*rhoN*POW3(4*PI_*epsilon_0)/245.0*summerA_224_224_224;
auto alpha3A = 3.0*alpha3A_112_112_224 + 6.0*alpha3A_112_123_213 + 6.0*alpha3A_123_123_224 + alpha3A_224_224_224;
auto alpha3B_112_112_112 = 32.0*POW3(PI_)*POW2(rhoN)*POW3(4*PI_*epsilon_0)/135.0*sqrt(14*PI_/5.0)*summerB_112_112_112;
auto alpha3B_112_123_123 = 64.0*POW3(PI_)*POW2(rhoN)*POW3(4*PI_*epsilon_0)/315.0*sqrt(3.0*PI_)*summerB_112_123_123;
auto alpha3B_123_123_224 = -32.0*POW3(PI_)*POW2(rhoN)*POW3(4*PI_*epsilon_0)/45.0*sqrt(22.0*PI_/63.0)*summerB_123_123_224;
auto alpha3B_224_224_224 = 32.0*POW3(PI_)*POW2(rhoN)*POW3(4*PI_*epsilon_0)/2025.0*sqrt(2002.0*PI_)*summerB_224_224_224;
auto alpha3B = alpha3B_112_112_112 + 3.0*alpha3B_112_123_123 + 3.0*alpha3B_123_123_224 + alpha3B_224_224_224;
return forceeval(alpha3A + alpha3B);
}
/***
* \brief Get the contribution to \f$ \alpha = A/(NkT) \f$
*/
template<typename TTYPE, typename RhoType, typename VecType>
auto eval(const TTYPE& T, const RhoType& rhoN, const VecType& mole_fractions) const {
// Calculate the effective reduced diameter (cubed) to be used for evaluation
// Eq. 24 from Gubbins
std::common_type_t<TTYPE, RhoType, decltype(mole_fractions[0])> sigma_x3 = 0.0;
auto N = mole_fractions.size();
for (auto i = 0; i < N; ++i){
for (auto j = 0; j < N; ++j){
auto sigmaij = (sigma_m[i] + sigma_m[j])/2;
sigma_x3 += mole_fractions[i]*mole_fractions[j]*POW3(sigmaij);
}
}
auto rhostar = rhoN*sigma_x3;
auto alpha2 = get_alpha2(T, rhoN, rhostar, mole_fractions);
auto alpha3 = get_alpha3(T, rhoN, rhostar, mole_fractions);
auto alpha = forceeval(alpha2/(1.0-alpha3/alpha2));
using alpha2_t = decltype(alpha2);
using alpha3_t = decltype(alpha3);
using alpha_t = decltype(alpha);
struct Terms{
alpha2_t alpha2;
alpha3_t alpha3;
alpha_t alpha;
};
return Terms{alpha2, alpha3, alpha};
}
};
using MCGTL = MultipolarContributionGubbinsTwu<LuckasJIntegral, LuckasKIntegral>;
}
}