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xc_xpbe_hole_t_c_lr.F
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1!--------------------------------------------------------------------------------------------------!
2! CP2K: A general program to perform molecular dynamics simulations !
3! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
4! !
5! SPDX-License-Identifier: GPL-2.0-or-later !
6!--------------------------------------------------------------------------------------------------!
7
8! **************************************************************************************************
9!> \brief Calculates the exchange energy for the pbe hole model in a truncated
10!> coulomb potential, considering the long range part only. Can be used
11!> as longrange correction to a truncated Hartree Fock calculation
12!> \par History
13!> Manuel Guidon (01.2009) : initial version
14!> \author Manuel Guidon (01.2009)
15! **************************************************************************************************
16
17MODULE xc_xpbe_hole_t_c_lr
18 USE input_section_types, ONLY: section_vals_type,&
19 section_vals_val_get
20 USE kinds, ONLY: dp
21 USE mathconstants, ONLY: euler,&
22 pi,&
23 rootpi
24 USE xc_derivative_desc, ONLY: deriv_norm_drho,&
25 deriv_norm_drhoa,&
26 deriv_norm_drhob,&
27 deriv_rho,&
28 deriv_rhoa,&
29 deriv_rhob
30 USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
31 xc_dset_get_derivative
32 USE xc_derivative_types, ONLY: xc_derivative_get,&
33 xc_derivative_type
34 USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
35 USE xc_rho_set_types, ONLY: xc_rho_set_get,&
36 xc_rho_set_type
37#include "../base/base_uses.f90"
38
39 IMPLICIT NONE
40
41 PRIVATE
42
43! *** Global parameters ***
44
45 PUBLIC :: xpbe_hole_t_c_lr_lda_eval, xpbe_hole_t_c_lr_lda_info, &
46 xpbe_hole_t_c_lr_lda_calc_1, xpbe_hole_t_c_lr_lda_calc_2, &
47 xpbe_hole_t_c_lr_lsd_eval, xpbe_hole_t_c_lr_lsd_info
48
49 REAL(KIND=dp), PARAMETER :: a1 = 0.00979681_dp, &
50 a2 = 0.04108340_dp, &
51 a3 = 0.18744000_dp, &
52 a4 = 0.00120824_dp, &
53 a5 = 0.0347188_dp
54 REAL(KIND=dp), PARAMETER :: a = 1.0161144_dp, &
55 b = -0.37170836_dp, &
56 c = -0.077215461_dp, &
57 d = 0.57786348_dp, &
58 e = -0.051955731_dp, &
59 f2 = 0.47965830_dp, &
60 f1 = 6.4753871_dp, &
61 clda = -0.73855876638202240588423_dp
62 REAL(KIND=dp), PARAMETER :: expcutoff = 700.0_dp
63 REAL(KIND=dp), PARAMETER :: smax = 8.572844_dp, &
64 sconst = 18.79622316_dp, &
65 scutoff = 8.3_dp
66 REAL(KIND=dp), PARAMETER :: gcutoff = 0.08_dp, &
67 g1 = -0.02628417880_dp/e, &
68 g2 = -0.07117647788_dp/e, &
69 g3 = 0.08534541323_dp/e, &
70 g4 = 0.0_dp
71 REAL(KIND=dp), PARAMETER :: wcutoff = 14.0_dp
72
73 REAL(KIND=dp), PARAMETER :: eps_rho = 0.00000001_dp
74
75 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_xpbe_hole_t_c_lr'
76
77CONTAINS
78
79! **************************************************************************************************
80!> \brief returns various information on the functional
81!> \param reference string with the reference of the actual functional
82!> \param shortform string with the shortform of the functional name
83!> \param needs the components needed by this functional are set to
84!> true (does not set the unneeded components to false)
85!> \param max_deriv controls the number of derivatives
86!> \par History
87!> 01.2009 created [mguidon]
88!> \author mguidon
89! **************************************************************************************************
90 SUBROUTINE xpbe_hole_t_c_lr_lda_info(reference, shortform, needs, max_deriv)
91 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
92 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
93 INTEGER, INTENT(out), OPTIONAL :: max_deriv
94
95 IF (PRESENT(reference)) THEN
96 reference = "{LDA version}"
97 END IF
98 IF (PRESENT(shortform)) THEN
99 shortform = "{LDA}"
100 END IF
101 IF (PRESENT(needs)) THEN
102 needs%rho = .true.
103 needs%norm_drho = .true.
104 END IF
105 IF (PRESENT(max_deriv)) max_deriv = 1
106
107 END SUBROUTINE xpbe_hole_t_c_lr_lda_info
108
109! **************************************************************************************************
110!> \brief returns various information on the functional
111!> \param reference string with the reference of the actual functional
112!> \param shortform string with the shortform of the functional name
113!> \param needs the components needed by this functional are set to
114!> true (does not set the unneeded components to false)
115!> \param max_deriv controls the number of derivatives
116!> \par History
117!> 01.2009 created [mguidon]
118!> \author mguidon
119! **************************************************************************************************
120 SUBROUTINE xpbe_hole_t_c_lr_lsd_info(reference, shortform, needs, max_deriv)
121 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
122 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
123 INTEGER, INTENT(out), OPTIONAL :: max_deriv
124
125 IF (PRESENT(reference)) THEN
126 reference = "{LSD version}"
127 END IF
128 IF (PRESENT(shortform)) THEN
129 shortform = "{LSD}"
130 END IF
131 IF (PRESENT(needs)) THEN
132 needs%rho_spin = .true.
133 needs%norm_drho_spin = .true.
134 END IF
135 IF (PRESENT(max_deriv)) max_deriv = 1
136
137 END SUBROUTINE xpbe_hole_t_c_lr_lsd_info
138
139! **************************************************************************************************
140!> \brief evaluates the pbe-hole exchange in a truncated coulomb potential
141!> \param rho_set the density where you want to evaluate the functional
142!> \param deriv_set place where to store the functional derivatives (they are
143!> added to the derivatives)
144!> \param order degree of the derivative that should be evaluated,
145!> if positive all the derivatives up to the given degree are evaluated,
146!> if negative only the given degree is calculated
147!> \param params input parameters (scaling,cutoff)
148!> \par History
149!> 01.2009 created [Manuel Guidon]
150!> \author Manuel Guidon
151!> \note
152! **************************************************************************************************
153 SUBROUTINE xpbe_hole_t_c_lr_lda_eval(rho_set, deriv_set, order, params)
154
155 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
156 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
157 INTEGER, INTENT(IN) :: order
158 TYPE(section_vals_type), POINTER :: params
159
160 CHARACTER(len=*), PARAMETER :: routinen = 'xpbe_hole_t_c_lr_lda_eval'
161
162 INTEGER :: handle, npoints
163 INTEGER, DIMENSION(2, 3) :: bo
164 REAL(kind=dp) :: epsilon_rho, r, sx
165 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
166 POINTER :: dummy, e_0, e_ndrho, e_rho, norm_drho, &
167 rho
168 TYPE(xc_derivative_type), POINTER :: deriv
169
170 CALL timeset(routinen, handle)
171
172 CALL section_vals_val_get(params, "SCALE_X", r_val=sx)
173 CALL section_vals_val_get(params, "CUTOFF_RADIUS", r_val=r)
174
175 CALL xc_rho_set_get(rho_set, rho=rho, &
176 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho)
177 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
178
179 dummy => rho
180
181 e_0 => dummy
182 e_rho => dummy
183 e_ndrho => dummy
184
185 IF (order >= 0) THEN
186 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
187 allocate_deriv=.true.)
188 CALL xc_derivative_get(deriv, deriv_data=e_0)
189 END IF
190 IF (order >= 1 .OR. order == -1) THEN
191 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
192 allocate_deriv=.true.)
193 CALL xc_derivative_get(deriv, deriv_data=e_rho)
194 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
195 allocate_deriv=.true.)
196 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
197 END IF
198 IF (order > 1 .OR. order < -1) THEN
199 cpabort("derivatives bigger than 1 not implemented")
200 END IF
201
202 IF (r == 0.0_dp) THEN
203 cpabort("Cutoff_Radius 0.0 not implemented")
204 END IF
205
206!$OMP PARALLEL DEFAULT(NONE) &
207!$OMP SHARED(npoints, order, rho, norm_drho, e_0, e_rho) &
208!$OMP SHARED(e_ndrho, epsilon_rho) &
209!$OMP SHARED(sx, r)
210
211 CALL xpbe_hole_t_c_lr_lda_calc(npoints, order, rho=rho, norm_drho=norm_drho, &
212 e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, &
213 epsilon_rho=epsilon_rho, &
214 sx=sx, r=r)
215
216!$OMP END PARALLEL
217
218 CALL timestop(handle)
219
220 END SUBROUTINE xpbe_hole_t_c_lr_lda_eval
221
222! **************************************************************************************************
223!> \brief intermediate level routine in order to decide which branch has to be
224!> taken
225!> \param npoints number of points on the grid
226!> \param order order of the derivatives
227!> \param rho value of density on the grid
228!> \param norm_drho value of gradient on the grid
229!> \param e_0 derivatives of the energy on the grid
230!> \param e_rho derivatives of the energy on the grid
231!> \param e_ndrho derivatives of the energy on the grid
232!> \param epsilon_rho cutoffs
233!> \param sx functional parameters
234!> \param R functional parameters
235!> \par History
236!> 01.2009 created [Manuel Guidon]
237!> \author Manuel Guidon
238!> \note For numerical reasons there are two different branches
239!>
240! **************************************************************************************************
241 SUBROUTINE xpbe_hole_t_c_lr_lda_calc(npoints, order, rho, norm_drho, e_0, e_rho, e_ndrho, &
242 epsilon_rho, sx, R)
243
244 INTEGER, INTENT(in) :: npoints, order
245 REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: rho, norm_drho, e_0, e_rho, e_ndrho
246 REAL(kind=dp), INTENT(in) :: epsilon_rho, sx, r
247
248 INTEGER :: ip
249 REAL(dp) :: my_ndrho, my_rho
250 REAL(kind=dp) :: ss, ss2, sscale, t1, t2, t3, t4, t6, t7, &
251 t8
252
253!$OMP DO
254
255 DO ip = 1, npoints
256 my_rho = max(rho(ip), 0.0_dp)
257 IF (my_rho > epsilon_rho) THEN
258 my_ndrho = max(norm_drho(ip), epsilon(0.0_dp)*1.e4_dp)
259 ! *** Do some precalculation in order to catch the correct branch afterwards
260 sscale = 1.0_dp
261 t1 = pi**2
262 t2 = t1*my_rho
263 t3 = t2**(0.1e1_dp/0.3e1_dp)
264 t4 = 0.1e1_dp/t3
265 t6 = my_ndrho*t4
266 t7 = 0.1e1_dp/my_rho
267 t8 = t7*sscale
268 ss = 0.3466806371753173524216762e0_dp*t6*t8
269 IF (ss > scutoff) THEN
270 ss2 = ss*ss
271 sscale = (smax*ss2 - sconst)/(ss2*ss)
272 END IF
273 IF (ss*sscale > gcutoff) THEN
274 CALL xpbe_hole_t_c_lr_lda_calc_1(e_0(ip), e_rho(ip), e_ndrho(ip), &
275 my_rho, &
276 my_ndrho, sscale, sx, r, order)
277 ELSE
278 CALL xpbe_hole_t_c_lr_lda_calc_2(e_0(ip), e_rho(ip), e_ndrho(ip), &
279 my_rho, &
280 my_ndrho, sscale, sx, r, order)
281 END IF
282 END IF
283 END DO
284
285!$OMP END DO
286
287 END SUBROUTINE xpbe_hole_t_c_lr_lda_calc
288
289! **************************************************************************************************
290!> \brief evaluates the pbe-hole exchange in a truncated coulomb potential
291!> \param rho_set the density where you want to evaluate the functional
292!> \param deriv_set place where to store the functional derivatives (they are
293!> added to the derivatives)
294!> \param order degree of the derivative that should be evaluated,
295!> if positive all the derivatives up to the given degree are evaluated,
296!> if negative only the given degree is calculated
297!> \param params input parameters (scaling,cutoff)
298!> \par History
299!> 01.2009 created [Manuel Guidon]
300!> \author Manuel Guidon
301!> \note
302! **************************************************************************************************
303 SUBROUTINE xpbe_hole_t_c_lr_lsd_eval(rho_set, deriv_set, order, params)
304
305 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
306 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
307 INTEGER, INTENT(IN) :: order
308 TYPE(section_vals_type), POINTER :: params
309
310 CHARACTER(len=*), PARAMETER :: routinen = 'xpbe_hole_t_c_lr_lsd_eval'
311
312 INTEGER :: handle, npoints
313 INTEGER, DIMENSION(2, 3) :: bo
314 REAL(kind=dp) :: epsilon_rho, r, sx
315 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
316 POINTER :: dummy, e_0, e_ndrhoa, e_ndrhob, e_rhoa, &
317 e_rhob, norm_drhoa, norm_drhob, rhoa, &
318 rhob
319 TYPE(xc_derivative_type), POINTER :: deriv
320
321 CALL timeset(routinen, handle)
322
323 CALL section_vals_val_get(params, "SCALE_X", r_val=sx)
324 CALL section_vals_val_get(params, "CUTOFF_RADIUS", r_val=r)
325
326 CALL xc_rho_set_get(rho_set, rhoa=rhoa, rhob=rhob, &
327 norm_drhoa=norm_drhoa, norm_drhob=norm_drhob, local_bounds=bo, rho_cutoff=epsilon_rho)
328 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
329
330 dummy => rhoa
331
332 e_0 => dummy
333 e_rhoa => dummy
334 e_rhob => dummy
335 e_ndrhoa => dummy
336 e_ndrhob => dummy
337
338 IF (order >= 0) THEN
339 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
340 allocate_deriv=.true.)
341 CALL xc_derivative_get(deriv, deriv_data=e_0)
342 END IF
343 IF (order >= 1 .OR. order == -1) THEN
344 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
345 allocate_deriv=.true.)
346 CALL xc_derivative_get(deriv, deriv_data=e_rhoa)
347 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
348 allocate_deriv=.true.)
349 CALL xc_derivative_get(deriv, deriv_data=e_rhob)
350 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
351 allocate_deriv=.true.)
352 CALL xc_derivative_get(deriv, deriv_data=e_ndrhoa)
353 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
354 allocate_deriv=.true.)
355 CALL xc_derivative_get(deriv, deriv_data=e_ndrhob)
356 END IF
357 IF (order > 1 .OR. order < -1) THEN
358 cpabort("derivatives bigger than 1 not implemented")
359 END IF
360
361 IF (r == 0.0_dp) THEN
362 cpabort("Cutoff_Radius 0.0 not implemented")
363 END IF
364
365!$OMP PARALLEL DEFAULT(NONE) &
366!$OMP SHARED(npoints, order, rhoa, norm_drhoa, e_0, e_rhoa) &
367!$OMP SHARED(epsilon_rho, sx, r) &
368!$OMP SHARED(rhob, norm_drhob, e_rhob, e_ndrhoa, e_ndrhob)
369
370 CALL xpbe_hole_t_c_lr_lsd_calc(npoints, order, rho=rhoa, norm_drho=norm_drhoa, &
371 e_0=e_0, e_rho=e_rhoa, e_ndrho=e_ndrhoa, &
372 epsilon_rho=epsilon_rho, sx=sx, r=r)
373 CALL xpbe_hole_t_c_lr_lsd_calc(npoints, order, rho=rhob, norm_drho=norm_drhob, &
374 e_0=e_0, e_rho=e_rhob, e_ndrho=e_ndrhob, &
375 epsilon_rho=epsilon_rho, sx=sx, r=r)
376
377!$OMP END PARALLEL
378
379 CALL timestop(handle)
380
381 END SUBROUTINE xpbe_hole_t_c_lr_lsd_eval
382
383! **************************************************************************************************
384!> \brief intermediate level routine in order to decide which branch has to be
385!> taken
386!> \param npoints number of points on the grid
387!> \param order order of the derivatives
388!> \param rho density on the grid
389!> \param norm_drho gradient on the grid
390!> \param e_0 derivatives of the energy on the grid
391!> \param e_rho derivatives of the energy on the grid
392!> \param e_ndrho derivatives of the energy on the grid
393!> \param epsilon_rho cutoffs
394!> \param sx functional parameters
395!> \param R functional parameters
396!> \par History
397!> 01.2009 created [Manuel Guidon]
398!> \author Manuel Guidon
399!> \note For numerical reasons there are two different branches. This code calls
400!> the lda version applying spin scaling relations
401! **************************************************************************************************
402 SUBROUTINE xpbe_hole_t_c_lr_lsd_calc(npoints, order, rho, norm_drho, e_0, e_rho, e_ndrho, &
403 epsilon_rho, sx, R)
404
405 INTEGER, INTENT(in) :: npoints, order
406 REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: rho, norm_drho, e_0, e_rho, e_ndrho
407 REAL(kind=dp), INTENT(in) :: epsilon_rho, sx, r
408
409 INTEGER :: ip
410 REAL(dp) :: my_ndrho, my_rho
411 REAL(kind=dp) :: e_tmp, ss, ss2, sscale, t1, t2, t3, t4, &
412 t6, t7, t8
413
414!$OMP DO
415
416 DO ip = 1, npoints
417 my_rho = max(2.0_dp*rho(ip), 0.0_dp)
418 IF (my_rho > epsilon_rho) THEN
419 my_ndrho = max(2.0_dp*norm_drho(ip), 0.0_dp)
420
421 ! *** Do some precalculation in order to catch the correct branch afterwards
422 sscale = 1.0_dp
423 t1 = pi**2
424 t2 = t1*my_rho
425 t3 = t2**(0.1e1_dp/0.3e1_dp)
426 t4 = 0.1e1_dp/t3
427 t6 = my_ndrho*t4
428 t7 = 0.1e1_dp/my_rho
429 t8 = t7*sscale
430 ss = 0.3466806371753173524216762e0_dp*t6*t8
431 IF (ss > scutoff) THEN
432 ss2 = ss*ss
433 sscale = (smax*ss2 - sconst)/(ss2*ss)
434 END IF
435 e_tmp = 0.0_dp
436 IF (ss*sscale > gcutoff) THEN
437 CALL xpbe_hole_t_c_lr_lda_calc_1(e_tmp, e_rho(ip), e_ndrho(ip), &
438 my_rho, &
439 my_ndrho, sscale, sx, r, order)
440 ELSE
441 CALL xpbe_hole_t_c_lr_lda_calc_2(e_tmp, e_rho(ip), e_ndrho(ip), &
442 my_rho, &
443 my_ndrho, sscale, sx, r, order)
444 END IF
445 e_0(ip) = e_0(ip) + 0.5_dp*e_tmp
446
447 END IF
448 END DO
449
450!$OMP END DO
451
452 END SUBROUTINE xpbe_hole_t_c_lr_lsd_calc
453
454! **************************************************************************************************
455!> \brief low level routine that calculates the energy derivatives in one point
456!> \param e_0 derivatives of the energy on the grid
457!> \param e_rho derivatives of the energy on the grid
458!> \param e_ndrho derivatives of the energy on the grid
459!> \param rho value of density on the grid
460!> \param ndrho value of gradient on the grid
461!> \param sscale functional parameters
462!> \param sx functional parameters
463!> \param R functional parameters
464!> \param order order of the derivatives
465!> \par History
466!> 01.2009 created [Manuel Guidon]
467!> \author Manuel Guidon
468! **************************************************************************************************
469 ELEMENTAL SUBROUTINE xpbe_hole_t_c_lr_lda_calc_1(e_0, e_rho, e_ndrho, &
470 rho, ndrho, sscale, sx, R, order)
471 REAL(kind=dp), INTENT(INOUT) :: e_0, e_rho, e_ndrho
472 REAL(kind=dp), INTENT(IN) :: rho, ndrho, sscale, sx, r
473 INTEGER, INTENT(IN) :: order
474
475 REAL(kind=dp) :: p, pndrho, prho, q, qndrho, qrho, sndrho, srho, ssval, t1, t103, t104, &
476 t105, t106, t107, t108, t109, t11, t113, t115, t116, t117, t118, t119, t12, t121, t123, &
477 t125, t126, t129, t13, t133, t136, t14, t140, t142, t143, t144, t147, t150, t152, t155, &
478 t156, t159, t162, t163, t164, t167, t17, t170, t173, t175, t176, t177, t178, t181, t183, &
479 t187, t19, t190, t194, t195, t196, t199, t2, t202, t209, t21, t214, t216, t217, t218, &
480 t22, t222, t223, t224, t227, t228, t229, t232, t234, t235, t236, t237, t240, t244, t248, &
481 t25, t251, t255, t256, t257, t261, t262, t265, t269, t27, t273, t276
482 REAL(kind=dp) :: t279, t280, t281, t29, t292, t3, t308, t31, t312, t314, t318, t320, t322, &
483 t33, t331, t334, t339, t34, t341, t347, t349, t35, t359, t362, t368, t37, t370, t373, &
484 t38, t382, t385, t39, t393, t4, t40, t401, t402, t404, t405, t409, t41, t42, t420, t421, &
485 t424, t425, t426, t429, t430, t431, t437, t44, t445, t446, t45, t451, t46, t473, t475, &
486 t479, t48, t484, t497, t498, t5, t50, t503, t504, t51, t517, t52, t523, t524, t527, t53, &
487 t533, t534, t54, t541, t56, t568, t57, t58, t581, t590, t6, t60, t603, t604, t61, t611, &
488 t612, t64, t640, t65, t653, t667, t675, t677, t69, t7, t71, t716
489 REAL(kind=dp) :: t717, t720, t723, t73, t739, t758, t762, t77, t8, t800, t803, t808, t85, &
490 t86, t87, t88, t91, t92, t93, t94, t95, t98, t99
491
492 IF (order >= 0) THEN
493 t1 = 3**(0.1e1_dp/0.3e1_dp)
494 t2 = t1**2
495 t3 = ndrho*t2
496 t4 = pi**2
497 t5 = t4*rho
498 t6 = t5**(0.1e1_dp/0.3e1_dp)
499 t7 = 0.1e1_dp/t6
500 t8 = 0.1e1_dp/rho
501 ssval = t3*t7*t8/0.6e1_dp
502 t11 = red(rho, ndrho)
503 t12 = t11**2
504 t13 = sscale**2
505 t14 = t12*t13
506 t17 = t12**2
507 t19 = t13**2
508 t21 = a1*t12*t13 + a2*t17*t19
509 t22 = t14*t21
510 t25 = t17*t11
511 t27 = t19*sscale
512 t29 = t17*t12
513 t31 = t19*t13
514 t33 = 1 + a3*t17*t19 + a4*t25*t27 + a5*t29*t31
515 t34 = 0.1e1_dp/t33
516 t35 = r**2
517 t37 = t6**2
518 t38 = t2*t37
519 t39 = t34*t35*t38
520 q = t22*t39
521 t40 = t21*t34
522 t41 = 0.1e1_dp/a
523 t42 = t40*t41
524 p = 0.9e1_dp/0.4e1_dp*t14*t42
525 t44 = rho**(0.1e1_dp/0.3e1_dp)
526 t45 = t44*rho
527 t46 = exei(p, q)
528 t48 = expint(1, q)
529 t50 = t14*t40
530 t51 = d + t50
531 t52 = t51*t35
532 t53 = t52*t38
533 t54 = expint(1, t53)
534 t56 = t51**2
535 t57 = t56*t51
536 t58 = 0.1e1_dp/t57
537 t60 = d*c
538 t61 = d**2
539 t64 = d*t21
540 t65 = t34*b
541 t69 = rootpi
542 t71 = f1*t21
543 t73 = t71*t34 + f2
544 t77 = c*(1 + t73*t12*t13)
545 t85 = t69*(15*e + 6*t77*t51 + 4*b*t56 + 8*a*t57)
546 t86 = sqrt(t51)
547 t87 = t86*t57
548 t88 = 0.1e1_dp/t87
549 t91 = sqrt(a)
550 t92 = pi*t91
551 t93 = exp(p)
552 t94 = t11*sscale
553 t95 = sqrt(t42)
554 t98 = erf(0.3e1_dp/0.2e1_dp*t94*t95)
555 t99 = 1 - t98
556 t103 = 0.3e1_dp/0.4e1_dp*pi + t85*t88/0.16e2_dp - 0.3e1_dp/0.4e1_dp*t92 &
557 *t93*t99
558 t104 = 0.1e1_dp/t69
559 t105 = t103*t104
560 t106 = 0.1e1_dp/t12
561 t107 = 0.1e1_dp/t13
562 t108 = t106*t107
563 t109 = t108*t87
564 t113 = t40*c + real(2*t64*t65, kind=dp) - 0.32e2_dp/0.15e2_dp*t105*t109 &
565 + t60*t73
566 t115 = t17*t19
567 t116 = t21**2
568 t117 = t33**2
569 t118 = 0.1e1_dp/t117
570 t119 = t116*t118
571 t121 = c*t73
572 t123 = t119*b + t40*t121
573 t125 = t35*t2
574 t126 = t61*c
575 t129 = e*t21
576 t133 = d*t103*t104
577 t136 = t34*c
578 t140 = real(2*t129*t34, kind=dp) - 0.32e2_dp/0.15e2_dp*t133*t109 + real(2 &
579 *t64*t136, kind=dp) + t126*t73
580 t142 = t105*t106
581 t143 = t107*t87
582 t144 = t143*t40
583 t147 = t136*t73
584 t150 = c*t116
585 t152 = -0.32e2_dp/0.15e2_dp*t142*t144 + real(2*t64*t147, kind=dp) + t150 &
586 *t118
587 t155 = t29*t31*c
588 t156 = t73*t116
589 t159 = t126 + 2*d*e + t14*t140 + t115*t152 + t155*t156* &
590 t118
591 t162 = t35**2
592 t163 = t162*t1
593 t164 = t6*t5
594 t167 = t61*t103*t104
595 t170 = t34*e
596 t173 = -0.16e2_dp/0.15e2_dp*t167*t109 + real(2*t64*t170, kind=dp)
597 t175 = t34*t103
598 t176 = t64*t175
599 t177 = t104*t106
600 t178 = t177*t143
601 t181 = e*t116
602 t183 = -0.32e2_dp/0.15e2_dp*t176*t178 + t181*t118
603 t187 = t104*t87*t119
604 t190 = t61*e + t14*t173 + t115*t183 - 0.16e2_dp/0.15e2_dp*t115 &
605 *t103*t187
606 t194 = 2*e + t60 + t61*b + t14*t113 + t115*t123 + t125*t37 &
607 *t159 + 3*t163*t164*t190
608 t195 = t58*t194
609 t196 = d*t35
610 t199 = exp(-t196*t38 - q)
611 t202 = -0.4e1_dp/0.9e1_dp*a*t46 + 0.4e1_dp/0.9e1_dp*a*t48 - 0.4e1_dp/ &
612 0.9e1_dp*a*t54 - 0.4e1_dp/0.9e1_dp*t195*t199
613 e_0 = e_0 + (t45*t202*clda)*sx
614 END IF
615 IF (order >= 1 .OR. order >= -1) THEN
616 t209 = rho**2
617 srho = -t3/t164*t8*t4/0.18e2_dp - t3*t7/t209/0.6e1_dp
618
619 t214 = t2*t7
620 sndrho = t214*t8/0.6e1_dp
621 t216 = t11*t13
622 t217 = t216*t40
623 t218 = dsdrho(rho, ndrho)
624 t222 = 2*t217*t125*t37*t218
625 t223 = a1*t11
626 t224 = t13*t218
627 t227 = t12*t11
628 t228 = a2*t227
629 t229 = t19*t218
630 t232 = 2*t223*t224 + 4*t228*t229
631 t234 = t14*t232*t39
632 t235 = t21*t118
633 t236 = t14*t235
634 t237 = a3*t227
635 t240 = a4*t17
636 t244 = a5*t25
637 t248 = 4*t237*t229 + 5*t240*t27*t218 + 6*t244*t31*t218
638 t251 = t236*t125*t37*t248
639 t255 = 0.2e1_dp/0.3e1_dp*t50*t125*t7*t4
640 qrho = t222 + t234 - t251 + t255
641 t256 = t216*t21
642 t257 = t34*t41
643 t261 = t232*t34
644 t262 = t261*t41
645 t265 = t118*t41
646 prho = 0.9e1_dp/0.2e1_dp*t256*t257*t218 + 0.9e1_dp/0.4e1_dp*t14*t262 &
647 - 0.9e1_dp/0.4e1_dp*t22*t265*t248
648 t269 = dsdndrho(rho)
649 t273 = t13*t269
650 t276 = t19*t269
651 t279 = 2*t223*t273 + 4*t228*t276
652 t280 = t279*t34
653 t281 = t280*t41
654 t292 = 4*t237*t276 + 5*t240*t27*t269 + 6*t244*t31*t269
655 pndrho = 0.9e1_dp/0.2e1_dp*t256*t257*t269 + 0.9e1_dp/0.4e1_dp*t14* &
656 t281 - 0.9e1_dp/0.4e1_dp*t22*t265*t292
657 qndrho = 2*t217*t125*t37*t269 + t14*t279*t39 - t236*t125 &
658 *t37*t292
659 t308 = dexeirho(p, q, prho, qrho)
660 t312 = exp(-q)
661 t314 = t312*t106*t107
662 t318 = 0.1e1_dp/t35
663 t320 = 0.1e1_dp/t37
664 t322 = 0.1e1_dp/t21*t33*t318*t1*t320
665 t331 = 2*t216*t40*t218 + t14*t261 - t14*t235*t248
666 t334 = t214*t4
667 t339 = exp(-t53)
668 t341 = 0.1e1_dp/t51
669 t347 = t56**2
670 t349 = 0.1e1_dp/t347*t194
671 t359 = d*t232
672 t362 = t118*b
673 t368 = t118*t248
674 t370 = f1*t232*t34 - t71*t368
675 t373 = t73*t11
676 t382 = b*t51
677 t385 = a*t56
678 t393 = 0.1e1_dp/t86/t347
679 t401 = t92*t93
680 t402 = sqrt(0.31415926535897932385e1_dp)
681 t404 = exp(-p)
682 t405 = 0.1e1_dp/t402*t404
683 t409 = 0.1e1_dp/t95
684 t420 = real(t69*(6*c*(t370*t12*t13 + 2*t373*t224)*t51 &
685 + 6*t77*t331 + 8*t382*t331 + 24*t385*t331)*t88, kind=dp)/ &
686 0.16e2_dp - 0.7e1_dp/0.32e2_dp*real(t85, kind=dp)*real(t393, kind=dp)* &
687 REAL(t331, kind=dp) - 0.3e1_dp &
688 /0.4e1_dp*t92*prho*t93*t99 + 0.3e1_dp/0.2e1_dp*t401*t405 &
689 *(0.3e1_dp/0.2e1_dp*t218*sscale*t95 + 0.3e1_dp/0.4e1_dp*t94*t409 &
690 *(t262 - t235*t41*t248))
691 t421 = t420*t104
692 t424 = 0.1e1_dp/t227
693 t425 = t105*t424
694 t426 = t143*t218
695 t429 = t86*t56
696 t430 = t107*t429
697 t431 = t430*t331
698 t437 = t227*t19
699 t445 = 0.1e1_dp/t117/t33
700 t446 = t116*t445
701 t451 = t121*t248
702 t473 = t424*t107
703 t475 = t473*t87*t218
704 t479 = t108*t429*t331
705 t484 = t118*c
706 t497 = t105*t473
707 t498 = t87*t21
708 t503 = t105*t108
709 t504 = t429*t21
710 t517 = t64*t118
711 t523 = c*t21
712 t524 = t118*t232
713 t527 = t445*t248
714 t533 = t25*t31*c
715 t534 = t118*t218
716 t541 = t73*t21
717 t568 = t118*e
718 t581 = t64*t118*t103
719 t590 = t104*t424
720 t603 = t437*t105
721 t604 = t87*t116
722 t611 = t115*t105
723 t612 = t429*t116
724 e_rho = e_rho + (0.4e1_dp/0.3e1_dp*t44*t202*clda + t45*(-0.4e1_dp/0.9e1_dp* &
725 a*t308 - 0.4e1_dp/0.27e2_dp*a*qrho*t314*t322 + 0.4e1_dp/0.27e2_dp &
726 *a*(t331*t35*t38 + 0.2e1_dp/0.3e1_dp*t52*t334)*t339*t341 &
727 *t318*t1*t320 + 0.4e1_dp/0.3e1_dp*t349*t199*t331 - 0.4e1_dp &
728 /0.9e1_dp*t58*(real(2*t216*t113*t218, kind=dp) + t14*(t261*c &
729 - t235*c*real(t248, kind=dp) + real(2*t359*t65, kind=dp) - real(2*t64*t362 &
730 *t248, kind=dp) - 0.32e2_dp/0.15e2_dp*t421*t109 + 0.64e2_dp/0.15e2_dp*t425 &
731 *t426 - 0.112e3_dp/0.15e2_dp*t142*t431 + t60*t370) + real(4* &
732 t437*t123*t218, kind=dp) + t115*(0.2e1_dp*t235*b*t232 - 0.2e1_dp*t446 &
733 *b*real(t248, kind=dp) + t261*t121 - t235*t451 + t40*c*t370) &
734 + 0.2e1_dp/0.3e1_dp*t125*t7*t159*t4 + t125*t37*(real(2* &
735 t216*t140*t218, kind=dp) + t14*(0.2e1_dp*e*t232*t34 - real(2*t129 &
736 *t368, kind=dp) - 0.32e2_dp/0.15e2_dp*d*t420*t104*t109 + 0.64e2_dp/0.15e2_dp &
737 *t133*t475 - 0.112e3_dp/0.15e2_dp*t133*t479 + real(2*t359 &
738 *t136, kind=dp) - real(2*t64*t484*t248, kind=dp) + t126*t370) + real(4* &
739 t437*t152*t218, kind=dp) + t115*(-0.32e2_dp/0.15e2_dp*t421*t106*t144 &
740 + 0.64e2_dp/0.15e2_dp*t497*t498*t34*real(t218, kind=dp) - 0.112e3_dp/0.15e2_dp &
741 *t503*t504*t34*t331 - 0.32e2_dp/0.15e2_dp*t142*t143* &
742 t261 + 0.32e2_dp/0.15e2_dp*t503*t498*real(t368, kind=dp) + real(2*t359 &
743 *t147, kind=dp) - 0.2e1_dp*t517*t451 + 0.2e1_dp*real(t64, kind=dp)*real(t136, kind=dp)* &
744 t370 + real(2*t523*t524, kind=dp) - real(2*t150*t527, kind=dp)) + real(6*t533 &
745 *t156*t534, kind=dp) + t155*t370*t116*t118 + 0.2e1_dp*t155*t541 &
746 *real(t524, kind=dp) - 0.2e1_dp*t155*real(t156, kind=dp)*real(t527, kind=dp)) + 0.4e1_dp &
747 *t163*t6*t190*t4 + 0.3e1_dp*t163*t164*(real(2*t216*t173 &
748 *t218, kind=dp) + t14*(-0.16e2_dp/0.15e2_dp*t61*t420*t104*t109 + &
749 0.32e2_dp/0.15e2_dp*t167*t475 - 0.56e2_dp/0.15e2_dp*t167*t479 + real(2 &
750 *t359*t170, kind=dp) - real(2*t64*t568*t248, kind=dp)) + real(4*t437 &
751 *t183*t218, kind=dp) + t115*(-0.32e2_dp/0.15e2_dp*real(t359, kind=dp)*real(t175, kind=dp) &
752 *real(t178, kind=dp) + 0.32e2_dp/0.15e2_dp*t581*t177*t143*real(t248, kind=dp) &
753 - 0.32e2_dp/0.15e2_dp*real(t64, kind=dp)*t34*t420*real(t178, kind=dp) + 0.64e2_dp &
754 /0.15e2_dp*t176*t590*t426 - 0.112e3_dp/0.15e2_dp*t176*t177* &
755 t431 + real(2*t129*t524, kind=dp) - real(2*t181*t527, kind=dp)) - 0.64e2_dp/ &
756 0.15e2_dp*real(t603, kind=dp)*real(t604, kind=dp)*real(t534, kind=dp) - 0.16e2_dp/0.15e2_dp* &
757 t115*t420*t187 - 0.56e2_dp/0.15e2_dp*t611*t612*t118*t331 - &
758 0.32e2_dp/0.15e2_dp*t611*t498*real(t524, kind=dp) + 0.32e2_dp/0.15e2_dp*t611 &
759 *real(t604, kind=dp)*real(t527, kind=dp)))*t199 - 0.4e1_dp/0.9e1_dp*t195*(-0.2e1_dp &
760 /0.3e1_dp*t196*t334 - t222 - t234 + t251 - t255)*t199)* &
761 clda)*sx
762 t640 = dexeindrho(p, q, pndrho, qndrho)
763 t653 = 2*t216*t40*t269 + t14*t280 - t14*t235*t292
764 t667 = d*t279
765 t675 = t118*t292
766 t677 = f1*t279*t34 - t71*t675
767 t716 = real(t69*(6*c*(t677*t12*t13 + 2*t373*t273)*t51 &
768 + 6*t77*t653 + 8*t382*t653 + 24*t385*t653)*t88, kind=dp)/ &
769 0.16e2_dp - 0.7e1_dp/0.32e2_dp*real(t85, kind=dp)*real(t393, kind=dp)* &
770 REAL(t653, kind=dp) - 0.3e1_dp &
771 /0.4e1_dp*t92*pndrho*t93*t99 + 0.3e1_dp/0.2e1_dp*t401*t405 &
772 *(0.3e1_dp/0.2e1_dp*t269*sscale*t95 + 0.3e1_dp/0.4e1_dp*t94* &
773 t409*(t281 - t235*t41*t292))
774 t717 = t716*t104
775 t720 = t143*t269
776 t723 = t430*t653
777 t739 = t121*t292
778 t758 = t473*t87*t269
779 t762 = t108*t429*t653
780 t800 = t118*t279
781 t803 = t445*t292
782 t808 = t118*t269
783 e_ndrho = e_ndrho + (t45*(-0.4e1_dp/0.9e1_dp*a*t640 - 0.4e1_dp/0.27e2_dp*a*qndrho &
784 *t314*t322 + 0.4e1_dp/0.9e1_dp*a*t653*t339*t341 + 0.4e1_dp &
785 /0.3e1_dp*t349*t199*t653 - 0.4e1_dp/0.9e1_dp*t58*(real(2*t216 &
786 *t113*t269, kind=dp) + t14*(t280*c - t235*c*real(t292, kind=dp) + real(2 &
787 *t667*t65, kind=dp) - real(2*t64*t362*t292, kind=dp) - 0.32e2_dp/0.15e2_dp &
788 *t717*t109 + 0.64e2_dp/0.15e2_dp*t425*t720 - 0.112e3_dp/0.15e2_dp* &
789 t142*t723 + t60*t677) + real(4*t437*t123*t269, kind=dp) + t115* &
790 (0.2e1_dp*t235*b*t279 - 0.2e1_dp*t446*b*real(t292, kind=dp) + t280* &
791 t121 - t235*t739 + t40*c*t677) + t125*t37*(real(2*t216 &
792 *t140*t269, kind=dp) + t14*(0.2e1_dp*e*t279*t34 - real(2*t129* &
793 t675, kind=dp) - 0.32e2_dp/0.15e2_dp*d*t716*t104*t109 + 0.64e2_dp/0.15e2_dp &
794 *t133*t758 - 0.112e3_dp/0.15e2_dp*t133*t762 + real(2*t667* &
795 t136, kind=dp) - real(2*t64*t484*t292, kind=dp) + t126*t677) + real(4*t437 &
796 *t152*t269, kind=dp) + t115*(-0.32e2_dp/0.15e2_dp*t717*t106*t144 + &
797 0.64e2_dp/0.15e2_dp*t497*t498*t34*real(t269, kind=dp) - 0.112e3_dp/0.15e2_dp &
798 *t503*t504*t34*t653 - 0.32e2_dp/0.15e2_dp*t142*t143*t280 &
799 + 0.32e2_dp/0.15e2_dp*t503*t498*real(t675, kind=dp) + real(2*t667* &
800 t147, kind=dp) - 0.2e1_dp*t517*t739 + 0.2e1_dp*real(t64, kind=dp)*real(t136, kind=dp)*t677 &
801 + real(2*t523*t800, kind=dp) - real(2*t150*t803, kind=dp)) + real(6*t533 &
802 *t156*t808, kind=dp) + t155*t677*t116*t118 + 0.2e1_dp*t155*t541 &
803 *real(t800, kind=dp) - 0.2e1_dp*t155*real(t156, kind=dp)*real(t803, kind=dp)) + 0.3e1_dp*t163 &
804 *t164*(real(2*t216*t173*t269, kind=dp) + t14*(-0.16e2_dp/0.15e2_dp &
805 *t61*t716*t104*t109 + 0.32e2_dp/0.15e2_dp*t167*t758 - 0.56e2_dp &
806 /0.15e2_dp*t167*t762 + real(2*t667*t170, kind=dp) - real(2*t64 &
807 *t568*t292, kind=dp)) + real(4*t437*t183*t269, kind=dp) + t115*(-0.32e2_dp &
808 /0.15e2_dp*real(t667, kind=dp)*real(t175, kind=dp)*real(t178, kind=dp) + 0.32e2_dp/0.15e2_dp &
809 *t581*t177*t143*real(t292, kind=dp) - 0.32e2_dp/0.15e2_dp*real(t64, kind=dp)* &
810 t34*t716*real(t178, kind=dp) + 0.64e2_dp/0.15e2_dp*t176*t590*t720 - 0.112e3_dp &
811 /0.15e2_dp*t176*t177*t723 + real(2*t129*t800, kind=dp) - real(2 &
812 *t181*t803, kind=dp)) - 0.64e2_dp/0.15e2_dp*real(t603, kind=dp)*real(t604, kind=dp)* &
813 REAL(t808, kind=dp) - 0.16e2_dp/0.15e2_dp*t115*t716*t187 - 0.56e2_dp/0.15e2_dp &
814 *t611*t612*t118*t653 - 0.32e2_dp/0.15e2_dp*t611*t498*real(t800, kind=dp) &
815 + 0.32e2_dp/0.15e2_dp*t611*real(t604, kind=dp)*real(t803, kind=dp)))*t199 &
816 + 0.4e1_dp/0.9e1_dp*t195*qndrho*t199)*clda)*sx
817 END IF
818
819 END SUBROUTINE xpbe_hole_t_c_lr_lda_calc_1
820
821! **************************************************************************************************
822!> \brief low level routine that calculates the energy derivatives in one point
823!> \param e_0 derivatives of the energy on the grid
824!> \param e_rho derivatives of the energy on the grid
825!> \param e_ndrho derivatives of the energy on the grid
826!> \param rho value of density on the grid
827!> \param ndrho value of gradient on the grid
828!> \param sscale functional parameters
829!> \param sx functional parameters
830!> \param R functional parameters
831!> \param order order of the derivatives
832!> \par History
833!> 01.2009 created [Manuel Guidon]
834!> \author Manuel Guidon
835! **************************************************************************************************
836 ELEMENTAL SUBROUTINE xpbe_hole_t_c_lr_lda_calc_2(e_0, e_rho, e_ndrho, &
837 rho, ndrho, sscale, sx, R, order)
838 REAL(kind=dp), INTENT(INOUT) :: e_0, e_rho, e_ndrho
839 REAL(kind=dp), INTENT(IN) :: rho, ndrho, sscale, sx, r
840 INTEGER, INTENT(IN) :: order
841
842 REAL(kind=dp) :: p, pndrho, prho, q, qndrho, qrho, sndrho, srho, ssval, t1, t102, t106, t11, &
843 t110, t113, t115, t117, t118, t119, t12, t122, t125, t126, t127, t128, t13, t130, t133, &
844 t135, t138, t14, t140, t142, t143, t146, t150, t151, t152, t155, t158, t165, t17, t170, &
845 t172, t173, t174, t178, t179, t180, t183, t184, t185, t188, t19, t190, t191, t192, t193, &
846 t196, t197, t2, t200, t204, t207, t21, t211, t212, t213, t217, t22, t221, t225, t229, &
847 t232, t235, t236, t242, t248, t25, t264, t268, t27, t272, t276, t278, t280, t287, t289, &
848 t29, t292, t297, t299, t3, t305, t307, t31, t317, t320, t324
849 REAL(kind=dp) :: t327, t33, t330, t333, t334, t338, t34, t340, t344, t35, t352, t353, t358, &
850 t37, t38, t380, t39, t394, t398, t399, t4, t40, t401, t406, t407, t408, t41, t415, t435, &
851 t44, t45, t454, t46, t461, t48, t485, t496, t498, t5, t50, t51, t512, t52, t524, t525, &
852 t529, t53, t531, t54, t545, t56, t579, t58, t581, t586, t6, t60, t61, t64, t65, t7, t74, &
853 t75, t77, t79, t8, t81, t83, t84, t85, t86, t89, t91, t93, t94, t95, t97
854
855 IF (order >= 0) THEN
856 t1 = 3**(0.1e1_dp/0.3e1_dp)
857 t2 = t1**2
858 t3 = ndrho*t2
859 t4 = pi**2
860 t5 = t4*rho
861 t6 = t5**(0.1e1_dp/0.3e1_dp)
862 t7 = 0.1e1_dp/t6
863 t8 = 0.1e1_dp/rho
864 ssval = t3*t7*t8/0.6e1_dp
865
866 t11 = red(rho, ndrho)
867 t12 = t11**2
868 t13 = sscale**2
869 t14 = t12*t13
870 t17 = t12**2
871 t19 = t13**2
872 t21 = a1*t12*t13 + a2*t17*t19
873 t22 = t14*t21
874 t25 = t17*t11
875 t27 = t19*sscale
876 t29 = t17*t12
877 t31 = t19*t13
878 t33 = 1 + a3*t17*t19 + a4*t25*t27 + a5*t29*t31
879 t34 = 0.1e1_dp/t33
880 t35 = r**2
881 t37 = t6**2
882 t38 = t2*t37
883 t39 = t34*t35*t38
884 q = t22*t39
885 t40 = t21*t34
886 t41 = 0.1e1_dp/a
887 p = 0.9e1_dp/0.4e1_dp*t14*t40*t41
888 t44 = rho**(0.1e1_dp/0.3e1_dp)
889 t45 = t44*rho
890 t46 = exei(p, q)
891 t48 = expint(1, q)
892 t50 = t14*t40
893 t51 = d + t50
894 t52 = t51*t35
895 t53 = t52*t38
896 t54 = expint(1, t53)
897 t56 = t51**2
898 t58 = 0.1e1_dp/t56/t51
899 t60 = d*c
900 t61 = d**2
901 t64 = d*t21
902 t65 = t34*b
903 t74 = g1 + g2*t12*t13 + g3*t17*t19 + g4*t25*t27
904 t75 = e*t74
905 t77 = f1*t21
906 t79 = t77*t34 + f2
907 t81 = t40*c + 2*t64*t65 + 2*t75 + t60*t79
908 t83 = t17*t19
909 t84 = t21**2
910 t85 = t33**2
911 t86 = 0.1e1_dp/t85
912 t89 = c*t79
913 t91 = t84*t86*b + t40*t89
914 t93 = t35*t2
915 t94 = t61*c
916 t95 = d*e
917 t97 = e*t21
918 t102 = t34*c
919 t106 = 2*t97*t34 + 2*t95*t74 + 2*t64*t102 + t94*t79
920 t110 = t102*t79
921 t113 = c*t84
922 t115 = 2*t75*t40 + 2*t64*t110 + t113*t86
923 t117 = t29*t31
924 t118 = t117*c
925 t119 = t79*t84
926 t122 = t94 + 2*t95 + t14*t106 + t83*t115 + t118*t119*t86
927 t125 = t35**2
928 t126 = t125*t1
929 t127 = t6*t5
930 t128 = t61*e
931 t130 = t34*e
932 t133 = t128*t74 + 2*t64*t130
933 t135 = t130*t74
934 t138 = e*t84
935 t140 = 2*t64*t135 + t138*t86
936 t142 = t117*e
937 t143 = t74*t84
938 t146 = t128 + t14*t133 + t83*t140 + t142*t143*t86
939 t150 = 2*e + t60 + t61*b + t14*t81 + t83*t91 + t93*t37* &
940 t122 + 3*t126*t127*t146
941 t151 = t58*t150
942 t152 = d*t35
943 t155 = exp(-t152*t38 - q)
944 t158 = -0.4e1_dp/0.9e1_dp*a*t46 + 0.4e1_dp/0.9e1_dp*a*t48 - 0.4e1_dp/ &
945 0.9e1_dp*a*t54 - 0.4e1_dp/0.9e1_dp*t151*t155
946 e_0 = e_0 + (t45*t158*clda)*sx
947 END IF
948 IF (order >= 1 .OR. order == -1) THEN
949 t165 = rho**2
950 srho = -t3/t127*t8*t4/0.18e2_dp - t3*t7/t165/0.6e1_dp
951 t170 = t2*t7
952 sndrho = t170*t8/0.6e1_dp
953 t172 = t11*t13
954 t173 = t172*t40
955 t174 = dsdrho(rho, ndrho)
956 t178 = 2*t173*t93*t37*t174
957 t179 = a1*t11
958 t180 = t13*t174
959 t183 = t12*t11
960 t184 = a2*t183
961 t185 = t19*t174
962 t188 = 2*t179*t180 + 4*t184*t185
963 t190 = t14*t188*t39
964 t191 = t21*t86
965 t192 = t14*t191
966 t193 = a3*t183
967 t196 = a4*t17
968 t197 = t27*t174
969 t200 = a5*t25
970 t204 = 4*t193*t185 + 5*t196*t197 + 6*t200*t31*t174
971 t207 = t192*t93*t37*t204
972 t211 = 0.2e1_dp/0.3e1_dp*t50*t93*t7*t4
973 qrho = t178 + t190 - t207 + t211
974 t212 = t172*t21
975 t213 = t34*t41
976 t217 = t188*t34
977 t221 = t86*t41
978 prho = 0.9e1_dp/0.2e1_dp*t212*t213*t174 + 0.9e1_dp/0.4e1_dp*t14*t217 &
979 *t41 - 0.9e1_dp/0.4e1_dp*t22*t221*t204
980 t225 = dsdndrho(rho)
981 t229 = t13*t225
982 t232 = t19*t225
983 t235 = 2*t179*t229 + 4*t184*t232
984 t236 = t235*t34
985 t242 = t27*t225
986 t248 = 4*t193*t232 + 5*t196*t242 + 6*t200*t31*t225
987 pndrho = 0.9e1_dp/0.2e1_dp*t212*t213*t225 + 0.9e1_dp/0.4e1_dp*t14* &
988 t236*t41 - 0.9e1_dp/0.4e1_dp*t22*t221*t248
989 qndrho = 2*t173*t93*t37*t225 + t14*t235*t39 - t192*t93 &
990 *t37*t248
991 t264 = dexeirho(p, q, prho, qrho)
992 t268 = exp(-q)
993 t272 = t268/t12/t13
994 t276 = 0.1e1_dp/t35
995 t278 = 0.1e1_dp/t37
996 t280 = 0.1e1_dp/t21*t33*t276*t1*t278
997 t287 = t191*t204
998 t289 = 2*t172*t40*t174 + t14*t217 - t14*t287
999 t292 = t170*t4
1000 t297 = exp(-t53)
1001 t299 = 0.1e1_dp/t51
1002 t305 = t56**2
1003 t307 = 0.1e1_dp/t305*t150
1004 t317 = d*t188
1005 t320 = t86*b
1006 t324 = g2*t11
1007 t327 = g3*t183
1008 t330 = g4*t17
1009 t333 = 2*t324*t180 + 4*t327*t185 + 5*t330*t197
1010 t334 = e*t333
1011 t338 = t86*t204
1012 t340 = f1*t188*t34 - t77*t338
1013 t344 = t183*t19
1014 t352 = 0.1e1_dp/t85/t33
1015 t353 = t84*t352
1016 t358 = t89*t204
1017 t380 = t86*c
1018 t394 = t64*t86
1019 t398 = c*t21
1020 t399 = t86*t188
1021 t401 = t352*t204
1022 t406 = t25*t31
1023 t407 = t406*c
1024 t408 = t86*t174
1025 t415 = t79*t21
1026 t435 = t86*e
1027 t454 = t406*e
1028 t461 = t74*t21
1029 e_rho = e_rho + (0.4e1_dp/0.3e1_dp*t44*t158*clda + t45*(-0.4e1_dp/0.9e1_dp* &
1030 a*t264 - 0.4e1_dp/0.27e2_dp*a*qrho*t272*t280 + 0.4e1_dp/0.27e2_dp &
1031 *a*(t289*t35*t38 + 0.2e1_dp/0.3e1_dp*t52*t292)*t297*t299 &
1032 *t276*t1*t278 + 0.4e1_dp/0.3e1_dp*t307*t155*t289 - 0.4e1_dp &
1033 /0.9e1_dp*t58*(real(2*t172*t81*t174, kind=dp) + real(t14*(t217 &
1034 *c - t191*c*t204 + 2*t317*t65 - 2*t64*t320*t204 + 2 &
1035 *t334 + t60*t340), kind=dp) + real(4*t344*t91*t174, kind=dp) + real(t83* &
1036 (2*t191*b*t188 - 2*t353*b*t204 + t217*t89 - t191*t358 &
1037 + t40*c*t340), kind=dp) + 0.2e1_dp/0.3e1_dp*t93*t7*t122*t4 + t93 &
1038 *t37*real(2*t172*t106*t174 + t14*(2*e*t188*t34 &
1039 - 2*t97*t338 + 2*t95*t333 + 2*t317*t102 - 2*t64*t380 &
1040 *t204 + t94*t340) + 4*t344*t115*t174 + t83*(2*t334 &
1041 *t40 + 2*t75*t217 - 2*t75*t287 + 2*t317*t110 - 2*t394 &
1042 *t358 + 2*t64*t102*t340 + 2*t398*t399 - 2*t113* &
1043 t401) + 6*t407*t119*t408 + t118*t340*t84*t86 + 2*t118 &
1044 *t415*t399 - 2*t118*t119*t401, kind=dp) + 0.4e1_dp*t126*t6*t146 &
1045 *t4 + 0.3e1_dp*t126*t127*real(2*t172*t133*t174 + t14 &
1046 *(t128*t333 + 2*t317*t130 - 2*t64*t435*t204) + 4*t344 &
1047 *t140*t174 + t83*(2*t317*t135 - 2*t394*t75*t204 &
1048 + 2*t64*t130*t333 + 2*t97*t399 - 2*t138*t401) + 6* &
1049 t454*t143*t408 + t142*t333*t84*t86 + 2*t142*t461*t399 &
1050 - 2*t142*t143*t401, kind=dp))*t155 - 0.4e1_dp/0.9e1_dp*t151*(-0.2e1_dp &
1051 /0.3e1_dp*t152*t292 - t178 - t190 + t207 - t211)*t155)* &
1052 clda)*sx
1053 t485 = dexeindrho(p, q, pndrho, qndrho)
1054 t496 = t191*t248
1055 t498 = 2*t172*t40*t225 + t14*t236 - t14*t496
1056 t512 = d*t235
1057 t524 = 2*t324*t229 + 4*t327*t232 + 5*t330*t242
1058 t525 = e*t524
1059 t529 = t86*t248
1060 t531 = f1*t235*t34 - t77*t529
1061 t545 = t89*t248
1062 t579 = t86*t235
1063 t581 = t352*t248
1064 t586 = t86*t225
1065 e_ndrho = e_ndrho + (t45*(-0.4e1_dp/0.9e1_dp*a*t485 - 0.4e1_dp/0.27e2_dp*a*qndrho &
1066 *t272*t280 + 0.4e1_dp/0.9e1_dp*a*t498*t297*t299 + 0.4e1_dp &
1067 /0.3e1_dp*t307*t155*t498 - 0.4e1_dp/0.9e1_dp*t58*real(2*t172 &
1068 *t81*t225 + t14*(t236*c - t191*c*t248 + 2*t512*t65 &
1069 - 2*t64*t320*t248 + 2*t525 + t60*t531) + 4*t344*t91 &
1070 *t225 + t83*(2*t191*b*t235 - 2*t353*b*t248 + t236 &
1071 *t89 - t191*t545 + t40*c*t531) + t93*t37*(2*t172* &
1072 t106*t225 + t14*(2*e*t235*t34 - 2*t97*t529 + 2*t95 &
1073 *t524 + 2*t512*t102 - 2*t64*t380*t248 + t94*t531) + &
1074 4*t344*t115*t225 + t83*(2*t525*t40 + 2*t75*t236 - &
1075 2*t75*t496 + 2*t512*t110 - 2*t394*t545 + 2*t64*t102 &
1076 *t531 + 2*t398*t579 - 2*t113*t581) + 6*t407*t119* &
1077 t586 + t118*t531*t84*t86 + 2*t118*t415*t579 - 2*t118 &
1078 *t119*t581) + 3*t126*t127*(2*t172*t133*t225 + t14 &
1079 *(t128*t524 + 2*t512*t130 - 2*t64*t435*t248) + 4*t344 &
1080 *t140*t225 + t83*(2*t512*t135 - 2*t394*t75*t248 &
1081 + 2*t64*t130*t524 + 2*t97*t579 - 2*t138*t581) + 6* &
1082 t454*t143*t586 + t142*t524*t84*t86 + 2*t142*t461*t579 &
1083 - 2*t142*t143*t581), kind=dp)*t155 + 0.4e1_dp/0.9e1_dp*t151*qndrho &
1084 *t155)*clda)*sx
1085 END IF
1086
1087 END SUBROUTINE xpbe_hole_t_c_lr_lda_calc_2
1088
1089! **************************************************************************************************
1090!> \brief These functions evaluate products exp(x)*Ei(x) and pi*exp(x)*erfc(sqrt(x)),
1091!> as well as their derivatives with respect to various combinations of
1092!> rho and norm_drho.
1093!> \param P = 9/4*s^2*H/A
1094!> \param Q = s^2*H*R^2*kf^2
1095!> \return ...
1096!> \par History
1097!> 01.2009 created [Manuel Guidon]
1098!> \author Manuel Guidon
1099!> \note
1100!> - In order to avoid numerical instabilities, these routines use Taylor-
1101!> expansions for the above core-products for large arguments.
1102!> - red calculates the reduced gradient in a save way (i.e. using a fixed
1103!> cutoff EPS_RHO)
1104! **************************************************************************************************
1105 ELEMENTAL FUNCTION exei(P, Q)
1106 REAL(dp), INTENT(IN) :: p, q
1107 REAL(dp) :: exei
1108
1109 REAL(dp) :: q2, q3, q4, tmp
1110
1111 exei = 0.0_dp
1112 IF (p < expcutoff) THEN
1113 !Use exact product
1114 IF (p + q < 0.5_dp) THEN
1115 tmp = -euler - log(p + q) + p + q
1116 tmp = tmp - 0.25_dp*(p + q)**2 + 1.0_dp/18.0_dp*(p + q)**3 - 1.0_dp/96.0_dp*(p + q)**4
1117 tmp = tmp + 1.0_dp/600.0_dp*(p + q)**5
1118 exei = exp(p)*tmp
1119 ELSE
1120 exei = exp(p)*expint(1, q + p)
1121 END IF
1122 ELSE
1123 !Use approximation
1124 tmp = 1.0_dp/p
1125 ! *** 1st order
1126 exei = tmp
1127 ! *** 2nd order
1128 tmp = tmp/p
1129 exei = exei - (q + 1.0_dp)*tmp
1130 ! *** 3rd order
1131 tmp = tmp/p
1132 q2 = q*q
1133 exei = exei + (2.0_dp*q + q2 + 2.0_dp)*tmp
1134 ! *** 4th order
1135 tmp = tmp/p
1136 q3 = q2*q
1137 exei = exei - (3.0_dp*q2 + 6.0_dp*q + q3 + 6.0_dp)*tmp
1138 ! *** 5th order
1139 tmp = tmp/p
1140 q4 = q3*q
1141 exei = exei + (24.0_dp + 4.0_dp*q3 + q4 + 12.0_dp*q2 + 24.0_dp*q)*tmp
1142
1143 ! *** scaling factor
1144 exei = exp(-q)*exei
1145 END IF
1146 END FUNCTION exei
1147
1148! **************************************************************************************************
1149!> \brief ...
1150!> \param P ...
1151!> \param Q ...
1152!> \param dPrho ...
1153!> \param dQrho ...
1154!> \return ...
1155! **************************************************************************************************
1156 ELEMENTAL FUNCTION dexeirho(P, Q, dPrho, dQrho)
1157 REAL(dp), INTENT(IN) :: p, q, dprho, dqrho
1158 REAL(dp) :: dexeirho
1159
1160 dexeirho = dprho*exei(p, q) - (dprho + dqrho)/(p + q)*exp(-q)
1161 END FUNCTION dexeirho
1162
1163! **************************************************************************************************
1164!> \brief ...
1165!> \param P ...
1166!> \param Q ...
1167!> \param dPndrho ...
1168!> \param dQndrho ...
1169!> \return ...
1170! **************************************************************************************************
1171 ELEMENTAL FUNCTION dexeindrho(P, Q, dPndrho, dQndrho)
1172 REAL(dp), INTENT(IN) :: p, q, dpndrho, dqndrho
1173 REAL(dp) :: dexeindrho
1174
1175 dexeindrho = dpndrho*exei(p, q) - (dpndrho + dqndrho)/(p + q)*exp(-q)
1176 END FUNCTION dexeindrho
1177
1178! **************************************************************************************************
1179!> \brief ...
1180!> \param rho ...
1181!> \param ndrho ...
1182!> \return ...
1183! **************************************************************************************************
1184 ELEMENTAL FUNCTION red(rho, ndrho)
1185 REAL(dp), INTENT(IN) :: rho, ndrho
1186 REAL(dp) :: red
1187
1188 red = 1.0_dp/6.0_dp*ndrho*3.0_dp**(2.0_dp/3.0_dp)
1189 red = red/(pi**(2.0_dp/3.0_dp))
1190 red = red*max(1.0_dp/rho**(4.0_dp/3.0_dp), eps_rho)
1191 END FUNCTION red
1192
1193! **************************************************************************************************
1194!> \brief ...
1195!> \param rho ...
1196!> \param ndrho ...
1197!> \return ...
1198! **************************************************************************************************
1199 ELEMENTAL FUNCTION dsdrho(rho, ndrho)
1200 REAL(dp), INTENT(IN) :: rho, ndrho
1201 REAL(dp) :: dsdrho
1202
1203 dsdrho = -2.0_dp/9.0_dp*ndrho*3.0**(2.0_dp/3.0_dp)
1204 dsdrho = dsdrho/(pi**(2.0_dp/3.0_dp))
1205 dsdrho = dsdrho*max(1.0_dp/rho**(7.0_dp/3.0_dp), eps_rho)
1206 END FUNCTION dsdrho
1207
1208! **************************************************************************************************
1209!> \brief ...
1210!> \param rho ...
1211!> \return ...
1212! **************************************************************************************************
1213 ELEMENTAL FUNCTION dsdndrho(rho)
1214 REAL(dp), INTENT(IN) :: rho
1215 REAL(dp) :: dsdndrho
1216
1217 dsdndrho = 1.0_dp/6.0_dp*3.0_dp**(2.0_dp/3.0_dp)
1218 dsdndrho = dsdndrho/(pi**(2.0_dp/3.0_dp))
1219 dsdndrho = dsdndrho*max(1.0_dp/rho**(4.0_dp/3.0_dp), eps_rho)
1220 END FUNCTION dsdndrho
1221
1222! **************************************************************************************************
1223!> \brief computes the exponential integral
1224!> En(x) = Int(exp(-x*t)/t^n,t=1..infinity) x>0, n=0,1,..
1225!> Note: Ei(-x) = -E1(x)
1226!> \param n ...
1227!> \param x ...
1228!> \return ...
1229!> \par History
1230!> 05.2007 Created
1231!> \author Manuel Guidon (adapted from Numerical recipies, cleaner version of mathlib)
1232! **************************************************************************************************
1233 ELEMENTAL FUNCTION expint(n, x)
1234 INTEGER, INTENT(IN) :: n
1235 REAL(dp), INTENT(IN) :: x
1236 REAL(dp) :: expint
1237
1238 INTEGER, PARAMETER :: maxit = 100
1239 REAL(dp), PARAMETER :: eps = 6.e-14_dp, euler = 0.5772156649015328606065120_dp, &
1240 fpmin = tiny(0.0_dp)
1241
1242 INTEGER :: i, ii, nm1
1243 REAL(dp) :: a, b, c, d, del, fact, h, psi
1244
1245 nm1 = n - 1
1246
1247 IF (n .LT. 0 .OR. x .LT. 0.0_dp .OR. (x .EQ. 0.0_dp .AND. (n .EQ. 0 .OR. n .EQ. 1))) THEN
1248 expint = huge(1.0_dp)
1249 ELSE IF (n .EQ. 0) THEN !Special case.
1250 expint = exp(-x)/x
1251 ELSE IF (x .EQ. 0.0_dp) THEN !Another special case.
1252 expint = 1.0_dp/nm1
1253 ELSE IF (x .GT. 1.0_dp) THEN !Lentz's algorithm (5.2).
1254 b = x + n
1255 c = 1.0_dp/fpmin
1256 d = 1.0_dp/b
1257 h = d
1258 DO i = 1, maxit
1259 a = -i*(nm1 + i)
1260 b = b + 2.0_dp
1261 d = 1.0_dp/(a*d + b)
1262 c = b + a/c
1263 del = c*d
1264 h = h*del
1265 IF (abs(del - 1.0_dp) .LT. eps .OR. i == maxit) THEN
1266 expint = h*exp(-x)
1267 RETURN
1268 END IF
1269 END DO
1270 ELSE !Evaluate series.
1271 IF (nm1 .NE. 0) THEN !Set first term.
1272 expint = 1.0_dp/nm1
1273 ELSE
1274 expint = -log(x) - euler
1275 END IF
1276 fact = 1.0_dp
1277 DO i = 1, maxit
1278 fact = -fact*x/i
1279 IF (i .NE. nm1) THEN
1280 del = -fact/(i - nm1)
1281 ELSE
1282 psi = -euler !Compute I(n).
1283 DO ii = 1, nm1
1284 psi = psi + 1.0_dp/ii
1285 END DO
1286 del = fact*(-log(x) + psi)
1287 END IF
1288 expint = expint + del
1289 IF (abs(del) .LT. abs(expint)*eps) RETURN
1290 END DO
1291 END IF
1292 RETURN
1293 END FUNCTION expint
1294
1295END MODULE xc_xpbe_hole_t_c_lr
1296
input_section_types
objects that represent the structure of input sections and the data contained in an input section
Definition input_section_types.F:15
input_section_types::section_vals_val_get
subroutine, public section_vals_val_get(section_vals, keyword_name, i_rep_section, i_rep_val, n_rep_val, val, l_val, i_val, r_val, c_val, l_vals, i_vals, r_vals, c_vals, explicit)
returns the requested value
Definition input_section_types.F:1040
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
mathconstants::euler
real(kind=dp), parameter, public euler
Definition mathconstants.F:119
mathconstants::rootpi
real(kind=dp), parameter, public rootpi
Definition mathconstants.F:114
xc_derivative_desc
Module with functions to handle derivative descriptors. derivative description are strings have the f...
Definition xc_derivative_desc.F:26
xc_derivative_desc::deriv_norm_drho
integer, parameter, public deriv_norm_drho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_norm_drhoa
integer, parameter, public deriv_norm_drhoa
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rhob
integer, parameter, public deriv_rhob
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rhoa
integer, parameter, public deriv_rhoa
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rho
integer, parameter, public deriv_rho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_norm_drhob
integer, parameter, public deriv_norm_drhob
Definition xc_derivative_desc.F:35
xc_derivative_set_types
represent a group ofunctional derivatives
Definition xc_derivative_set_types.F:14
xc_derivative_set_types::xc_dset_get_derivative
type(xc_derivative_type) function, pointer, public xc_dset_get_derivative(derivative_set, description, allocate_deriv)
returns the requested xc_derivative
Definition xc_derivative_set_types.F:66
xc_derivative_types
Provides types for the management of the xc-functionals and their derivatives.
Definition xc_derivative_types.F:12
xc_derivative_types::xc_derivative_get
subroutine, public xc_derivative_get(deriv, split_desc, order, deriv_data, accept_null_data)
returns various information on the given derivative
Definition xc_derivative_types.F:103
xc_rho_cflags_types
contains the structure
Definition xc_rho_cflags_types.F:14
xc_rho_set_types
contains the structure
Definition xc_rho_set_types.F:14
xc_rho_set_types::xc_rho_set_get
subroutine, public xc_rho_set_get(rho_set, can_return_null, rho, drho, norm_drho, rhoa, rhob, norm_drhoa, norm_drhob, rho_1_3, rhoa_1_3, rhob_1_3, laplace_rho, laplace_rhoa, laplace_rhob, drhoa, drhob, rho_cutoff, drho_cutoff, tau_cutoff, tau, tau_a, tau_b, local_bounds)
returns the various attributes of rho_set
Definition xc_rho_set_types.F:281
xc_xpbe_hole_t_c_lr
Calculates the exchange energy for the pbe hole model in a truncated coulomb potential,...
Definition xc_xpbe_hole_t_c_lr.F:17
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_info
subroutine, public xpbe_hole_t_c_lr_lda_info(reference, shortform, needs, max_deriv)
returns various information on the functional
Definition xc_xpbe_hole_t_c_lr.F:91
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_calc_1
elemental subroutine, public xpbe_hole_t_c_lr_lda_calc_1(e_0, e_rho, e_ndrho, rho, ndrho, sscale, sx, r, order)
low level routine that calculates the energy derivatives in one point
Definition xc_xpbe_hole_t_c_lr.F:471
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_eval
subroutine, public xpbe_hole_t_c_lr_lda_eval(rho_set, deriv_set, order, params)
evaluates the pbe-hole exchange in a truncated coulomb potential
Definition xc_xpbe_hole_t_c_lr.F:154
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_calc_2
elemental subroutine, public xpbe_hole_t_c_lr_lda_calc_2(e_0, e_rho, e_ndrho, rho, ndrho, sscale, sx, r, order)
low level routine that calculates the energy derivatives in one point
Definition xc_xpbe_hole_t_c_lr.F:838
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lsd_eval
subroutine, public xpbe_hole_t_c_lr_lsd_eval(rho_set, deriv_set, order, params)
evaluates the pbe-hole exchange in a truncated coulomb potential
Definition xc_xpbe_hole_t_c_lr.F:304
xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lsd_info
subroutine, public xpbe_hole_t_c_lr_lsd_info(reference, shortform, needs, max_deriv)
returns various information on the functional
Definition xc_xpbe_hole_t_c_lr.F:121
input_section_types::section_vals_type
stores the values of a section
Definition input_section_types.F:126
xc_derivative_set_types::xc_derivative_set_type
A derivative set contains the different derivatives of a xc-functional in form of a linked list.
Definition xc_derivative_set_types.F:49
xc_derivative_types::xc_derivative_type
represent a derivative of a functional
Definition xc_derivative_types.F:32
xc_rho_cflags_types::xc_rho_cflags_type
contains a flag for each component of xc_rho_set, so that you can use it to tell which components you...
Definition xc_rho_cflags_types.F:48
xc_rho_set_types::xc_rho_set_type
represent a density, with all the representation and data needed to perform a functional evaluation
Definition xc_rho_set_types.F:78