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xc_lyp.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 lyp correlation functional
10!> \par History
11!> 11.2003 created [fawzi]
12!> \author fawzi
13! **************************************************************************************************
14MODULE xc_lyp
15 USE bibliography, ONLY: lee1988,&
16 cite_reference
17 USE input_section_types, ONLY: section_vals_type,&
18 section_vals_val_get
19 USE kinds, ONLY: dp
20 USE mathconstants, ONLY: pi
21 USE xc_derivative_desc, ONLY: deriv_norm_drho,&
22 deriv_norm_drhoa,&
23 deriv_norm_drhob,&
24 deriv_rho,&
25 deriv_rhoa,&
26 deriv_rhob
27 USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
28 xc_dset_get_derivative
29 USE xc_derivative_types, ONLY: xc_derivative_get,&
30 xc_derivative_type
31 USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
32 USE xc_rho_set_types, ONLY: xc_rho_set_get,&
33 xc_rho_set_type
34#include "../base/base_uses.f90"
35
36 IMPLICIT NONE
37 PRIVATE
38
39 LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .true.
40 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_lyp'
41 REAL(kind=dp), PARAMETER, PRIVATE :: a = 0.04918_dp, b = 0.132_dp, &
42 c = 0.2533_dp, d = 0.349_dp
43
44 PUBLIC :: lyp_lda_info, lyp_lsd_info, lyp_lda_eval, lyp_lsd_eval
45CONTAINS
46
47! **************************************************************************************************
48!> \brief return various information on the functional
49!> \param reference string with the reference of the actual functional
50!> \param shortform string with the shortform of the functional name
51!> \param needs the components needed by this functional are set to
52!> true (does not set the unneeded components to false)
53!> \param max_deriv ...
54!> \par History
55!> 11.2003 created [fawzi]
56!> \author fawzi
57! **************************************************************************************************
58 SUBROUTINE lyp_lda_info(reference, shortform, needs, max_deriv)
59 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
60 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
61 INTEGER, INTENT(out), OPTIONAL :: max_deriv
62
63 IF (PRESENT(reference)) THEN
64 reference = "C. Lee, W. Yang, R.G. Parr, Phys. Rev. B, 37, 785 (1988) {LDA version}"
65 END IF
66 IF (PRESENT(shortform)) THEN
67 shortform = "Lee-Yang-Parr correlation energy functional (LDA)"
68 END IF
69 IF (PRESENT(needs)) THEN
70 needs%rho = .true.
71 needs%rho_1_3 = .true.
72 needs%norm_drho = .true.
73 END IF
74 IF (PRESENT(max_deriv)) max_deriv = 3
75
76 END SUBROUTINE lyp_lda_info
77
78! **************************************************************************************************
79!> \brief return various information on the functional
80!> \param reference string with the reference of the actual functional
81!> \param shortform string with the shortform of the functional name
82!> \param needs the components needed by this functional are set to
83!> true (does not set the unneeded components to false)
84!> \param max_deriv ...
85!> \par History
86!> 11.2003 created [fawzi]
87!> \author fawzi
88! **************************************************************************************************
89 SUBROUTINE lyp_lsd_info(reference, shortform, needs, max_deriv)
90 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
91 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
92 INTEGER, INTENT(out), OPTIONAL :: max_deriv
93
94 IF (PRESENT(reference)) THEN
95 reference = "C. Lee, W. Yang, R.G. Parr, Phys. Rev. B, 37, 785 (1988) {LSD version}"
96 END IF
97 IF (PRESENT(shortform)) THEN
98 shortform = "Lee-Yang-Parr correlation energy functional (LSD)"
99 END IF
100 IF (PRESENT(needs)) THEN
101 needs%rho_spin = .true.
102 needs%norm_drho_spin = .true.
103 needs%norm_drho = .true.
104 END IF
105 IF (PRESENT(max_deriv)) max_deriv = 2
106
107 END SUBROUTINE lyp_lsd_info
108
109! **************************************************************************************************
110!> \brief evaluates the lyp correlation functional for lda
111!> \param rho_set the density where you want to evaluate the functional
112!> \param deriv_set place where to store the functional derivatives (they are
113!> added to the derivatives)
114!> \param grad_deriv degree of the derivative that should be evaluated,
115!> if positive all the derivatives up to the given degree are evaluated,
116!> if negative only the given degree is calculated
117!> \param lyp_params input parameters (scaling)
118!> \par History
119!> 11.2003 created [fawzi]
120!> 01.2007 added scaling [Manuel Guidon]
121!> \author fawzi
122! **************************************************************************************************
123 SUBROUTINE lyp_lda_eval(rho_set, deriv_set, grad_deriv, lyp_params)
124 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
125 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
126 INTEGER, INTENT(in) :: grad_deriv
127 TYPE(section_vals_type), POINTER :: lyp_params
128
129 CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lda_eval'
130
131 INTEGER :: handle, npoints
132 INTEGER, DIMENSION(2, 3) :: bo
133 REAL(kind=dp) :: epsilon_norm_drho, epsilon_rho, sc
134 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndrho, &
135 e_ndrho_ndrho, e_ndrho_ndrho_rho, e_ndrho_rho, e_ndrho_rho_rho, e_rho, e_rho_rho, &
136 e_rho_rho_rho, norm_drho, rho, rho_1_3
137 TYPE(xc_derivative_type), POINTER :: deriv
138
139 CALL timeset(routinen, handle)
140
141 CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
142 CALL cite_reference(lee1988)
143
144 CALL xc_rho_set_get(rho_set, rho_1_3=rho_1_3, rho=rho, &
145 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho, &
146 drho_cutoff=epsilon_norm_drho)
147 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
148
149 dummy => rho
150
151 e_0 => dummy
152 e_rho => dummy
153 e_ndrho => dummy
154 e_rho_rho => dummy
155 e_ndrho_rho => dummy
156 e_ndrho_ndrho => dummy
157 e_rho_rho_rho => dummy
158 e_ndrho_rho_rho => dummy
159 e_ndrho_ndrho_rho => dummy
160
161 IF (grad_deriv >= 0) THEN
162 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
163 allocate_deriv=.true.)
164 CALL xc_derivative_get(deriv, deriv_data=e_0)
165 END IF
166 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
167 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
168 allocate_deriv=.true.)
169 CALL xc_derivative_get(deriv, deriv_data=e_rho)
170 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
171 allocate_deriv=.true.)
172 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
173 END IF
174 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
175 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
176 allocate_deriv=.true.)
177 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
178 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rho], &
179 allocate_deriv=.true.)
180 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho)
181 deriv => xc_dset_get_derivative(deriv_set, &
182 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
183 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
184 END IF
185 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
186 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
187 allocate_deriv=.true.)
188 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
189 deriv => xc_dset_get_derivative(deriv_set, &
190 [deriv_norm_drho, deriv_rho, deriv_rho], allocate_deriv=.true.)
191 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho)
192 deriv => xc_dset_get_derivative(deriv_set, &
193 [deriv_norm_drho, deriv_norm_drho, deriv_rho], allocate_deriv=.true.)
194 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho)
195!FM deriv => xc_dset_get_derivative(deriv_set,&
196!FM [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.,&
197!FM
198!FM call xc_derivative_get(deriv,deriv_data=e_ndrho_ndrho_ndrho)
199 END IF
200 IF (grad_deriv > 3 .OR. grad_deriv < -3) THEN
201 cpabort("derivatives bigger than 3 not implemented")
202 END IF
203
204!$OMP PARALLEL DEFAULT(NONE) &
205!$OMP SHARED(rho, rho_1_3, norm_drho, e_0, e_rho, e_ndrho) &
206!$OMP SHARED(e_rho_rho, e_ndrho_rho, e_ndrho_ndrho) &
207!$OMP SHARED(e_rho_rho_rho, e_ndrho_rho_rho) &
208!$OMP SHARED(e_ndrho_ndrho_rho, grad_deriv, npoints) &
209!$OMP SHARED(epsilon_rho, sc)
210
211 CALL lyp_lda_calc(rho=rho, rho_1_3=rho_1_3, norm_drho=norm_drho, &
212 e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_rho_rho=e_rho_rho, &
213 e_ndrho_rho=e_ndrho_rho, e_ndrho_ndrho=e_ndrho_ndrho, &
214 e_rho_rho_rho=e_rho_rho_rho, e_ndrho_rho_rho=e_ndrho_rho_rho, &
215 e_ndrho_ndrho_rho=e_ndrho_ndrho_rho, &
216 grad_deriv=grad_deriv, &
217 npoints=npoints, epsilon_rho=epsilon_rho, sc=sc)
218
219!$OMP END PARALLEL
220
221 CALL timestop(handle)
222 END SUBROUTINE lyp_lda_eval
223
224! **************************************************************************************************
225!> \brief evaluates the lyp correlation functional for lda
226!> \param rho the density where you want to evaluate the functional
227!> \param rho_1_3 ...
228!> \param norm_drho ...
229!> \param e_0 ...
230!> \param e_rho ...
231!> \param e_ndrho ...
232!> \param e_rho_rho ...
233!> \param e_ndrho_rho ...
234!> \param e_ndrho_ndrho ...
235!> \param e_rho_rho_rho ...
236!> \param e_ndrho_rho_rho ...
237!> \param e_ndrho_ndrho_rho ...
238!> \param grad_deriv degree of the derivative that should be evaluated,
239!> if positive all the derivatives up to the given degree are evaluated,
240!> if negative only the given degree is calculated
241!> \param npoints ...
242!> \param epsilon_rho ...
243!> \param sc scaling-parameter for correlation
244!> \par History
245!> 11.2003 created [fawzi]
246!> 01.2007 added scaling [Manuel Guidon]
247!> \author fawzi
248! **************************************************************************************************
249 SUBROUTINE lyp_lda_calc(rho, rho_1_3, norm_drho, &
250 e_0, e_rho, e_ndrho, e_rho_rho, e_ndrho_rho, &
251 e_ndrho_ndrho, e_rho_rho_rho, e_ndrho_rho_rho, e_ndrho_ndrho_rho, &
252 grad_deriv, npoints, epsilon_rho, sc)
253 INTEGER, INTENT(in) :: npoints, grad_deriv
254 REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: e_ndrho_ndrho_rho, e_ndrho_rho_rho, &
255 e_rho_rho_rho, e_ndrho_ndrho, &
256 e_ndrho_rho, e_rho_rho, e_ndrho, &
257 e_rho, e_0
258 REAL(kind=dp), DIMENSION(1:npoints), INTENT(in) :: norm_drho, rho_1_3, rho
259 REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
260
261 INTEGER :: ii
262 REAL(kind=dp) :: cf, epsilon_rho13, my_ndrho, my_rho, my_rho_1_3, t1, t102, t103, t105, &
263 t106, t11, t112, t123, t124, t127, t128, t13, t133, t134, t14, t161, t165, t166, t173, &
264 t176, t184, t185, t189, t192, t193, t196, t199, t2, t200, t201, t202, t203, t215, t22, &
265 t227, t228, t231, t245, t246, t248, t26, t265, t278, t279, t3, t332, t37, t38, t39, t4, &
266 t40, t41, t44, t45, t48, t5, t52, t6, t61, t62, t69, t7, t70, t77, t78, t80, t87, t88, &
267 t89, t93, t94, t95, t98, t99
268
269 epsilon_rho13 = epsilon_rho**(1.0_dp/3.0_dp)
270 cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
271 SELECT CASE (grad_deriv)
272 CASE (1)
273!$OMP DO
274 DO ii = 1, npoints
275 my_rho = rho(ii)
276 IF (my_rho > epsilon_rho) THEN
277 my_rho_1_3 = rho_1_3(ii)
278 my_ndrho = norm_drho(ii)
279 t1 = my_rho_1_3**2
280 t2 = t1*my_rho
281 t3 = 0.1e1_dp/t2
282 t4 = a*t3
283 t5 = my_rho**2
284 t6 = t5*my_rho
285 t7 = my_rho_1_3*t6
286 t11 = 0.1e1_dp/my_rho_1_3
287 t13 = exp(-c*t11)
288 t14 = b*t13
289 t22 = my_ndrho**2
290 t26 = my_rho_1_3*t22
291 t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
292 t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
293 & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
294 &*t26*c + 0.7e1_dp*t14*t22*c*d
295 t38 = my_rho_1_3 + d
296 t39 = t38**2
297 t40 = 0.1e1_dp/t39
298 t41 = t37*t40
299
300 e_0(ii) = e_0(ii) &
301 + (t4*t41/0.72e2_dp)*sc
302 t44 = 0.1e1_dp/t1/t5
303 t45 = a*t44
304 t48 = my_rho_1_3*t5
305 t52 = b*c
306 t61 = t13*cf
307 t62 = t61*d
308 t69 = 0.1e1_dp/t1
309 t70 = t69*t13
310 t77 = 0.1e1_dp/my_rho
311 t78 = t52*t77
312 t80 = t13*t22*d
313 t87 = c**2
314 t88 = b*t87
315 t89 = t77*t13
316 t93 = my_rho_1_3*my_rho
317 t94 = 0.1e1_dp/t93
318 t95 = t88*t94
319 t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
320 & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
321 0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
322 &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
323 t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
324 0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
325 0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
326 t80
327 t99 = t98*t40
328 t102 = 0.1e1_dp/t48
329 t103 = a*t102
330 t105 = 0.1e1_dp/t39/t38
331 t106 = t37*t105
332
333 e_rho(ii) = e_rho(ii) &
334 - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
335 & + t103*t106/0.108e3_dp)*sc
336
337 t112 = my_rho_1_3*my_ndrho
338 t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
339 &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
340 my_ndrho*c*d
341 t124 = t123*t40
342
343 e_ndrho(ii) = e_ndrho(ii) &
344 + (t4*t124/0.72e2_dp)*sc
345 END IF
346 END DO
347!$OMP END DO
348 CASE default
349!$OMP DO
350 DO ii = 1, npoints
351 my_rho = rho(ii)
352 IF (my_rho > epsilon_rho) THEN
353 my_rho_1_3 = rho_1_3(ii)
354 my_ndrho = norm_drho(ii)
355 t1 = my_rho_1_3**2
356 t2 = t1*my_rho
357 t3 = 0.1e1_dp/t2
358 t4 = a*t3
359 t5 = my_rho**2
360 t6 = t5*my_rho
361 t7 = my_rho_1_3*t6
362 t11 = 0.1e1_dp/my_rho_1_3
363 t13 = exp(-c*t11)
364 t14 = b*t13
365 t22 = my_ndrho**2
366 t26 = my_rho_1_3*t22
367 t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
368 t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
369 & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
370 &*t26*c + 0.7e1_dp*t14*t22*c*d
371 t38 = my_rho_1_3 + d
372 t39 = t38**2
373 t40 = 0.1e1_dp/t39
374 t41 = t37*t40
375
376 IF (grad_deriv >= 0) THEN
377 e_0(ii) = e_0(ii) &
378 + (t4*t41/0.72e2_dp)*sc
379 END IF
380
381 t44 = 0.1e1_dp/t1/t5
382 t45 = a*t44
383 t48 = my_rho_1_3*t5
384 t52 = b*c
385 t61 = t13*cf
386 t62 = t61*d
387 t69 = 0.1e1_dp/t1
388 t70 = t69*t13
389 t77 = 0.1e1_dp/my_rho
390 t78 = t52*t77
391 t80 = t13*t22*d
392 t87 = c**2
393 t88 = b*t87
394 t89 = t77*t13
395 t93 = my_rho_1_3*my_rho
396 t94 = 0.1e1_dp/t93
397 t95 = t88*t94
398 t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
399 & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
400 0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
401 &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
402 t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
403 0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
404 0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
405 t80
406 t99 = t98*t40
407 t102 = 0.1e1_dp/t48
408 t103 = a*t102
409 t105 = 0.1e1_dp/t39/t38
410 t106 = t37*t105
411 t112 = my_rho_1_3*my_ndrho
412 t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
413 &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
414 my_ndrho*c*d
415 t124 = t123*t40
416
417 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
418 e_rho(ii) = e_rho(ii) &
419 - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
420 & + t103*t106/0.108e3_dp)*sc
421 e_ndrho(ii) = e_ndrho(ii) &
422 + (t4*t124/0.72e2_dp)*sc
423 END IF
424
425 t127 = 0.1e1_dp/t1/t6
426 t128 = a*t127
427 t133 = 0.1e1_dp/t7
428 t134 = a*t133
429 t161 = t3*t13
430 t165 = 0.1e1_dp/t5
431 t166 = t165*t13
432 t173 = t52*t165
433 t176 = t88*t102
434 t184 = b*t87*c
435 t185 = t102*t13
436 t189 = t184*t44
437 t192 = -0.560e3_dp*t93 - 0.432e3_dp*my_rho*d - 0.128e3_dp&
438 & *t52*my_rho*t13*cf - 0.8e1_dp*t88*t1*t13* &
439 cf - 0.560e3_dp*t14*t93*cf - 0.112e3_dp*t52*t1&
440 & *t62 - 0.8e1_dp*t88*my_rho_1_3*t62 - 0.432e3_dp* &
441 t14*my_rho*cf*d - 0.14e2_dp/0.9e1_dp*t52* &
442 t161*t22 - 0.11e2_dp/0.9e1_dp*t88*t166*t22 - &
443 0.2e1_dp/0.3e1_dp*t14*t94*t22 - 0.20e2_dp/ &
444 0.9e1_dp*t173*t80 - 0.2e1_dp*t176*t80 - &
445 0.20e2_dp/0.9e1_dp*t14*t3*t22*d + 0.7e1_dp/ &
446 0.9e1_dp*t184*t185*t22 + 0.7e1_dp/0.9e1_dp* &
447 t189*t80
448 t193 = t192*t40
449 t196 = t98*t105
450 t199 = 0.1e1_dp/t6
451 t200 = a*t199
452 t201 = t39**2
453 t202 = 0.1e1_dp/t201
454 t203 = t37*t202
455 t215 = t13*my_ndrho*d
456 t227 = 0.20e2_dp/0.3e1_dp*t52*t70*my_ndrho + 0.4e1_dp* &
457 t14*t11*my_ndrho + 0.20e2_dp/0.3e1_dp*t78*t215&
458 & + 0.20e2_dp/0.3e1_dp*t14*t69*my_ndrho*d + &
459 0.14e2_dp/0.3e1_dp*t88*t89*my_ndrho + 0.14e2_dp &
460 &/0.3e1_dp*t95*t215
461 t228 = t227*t40
462 t231 = t123*t105
463 t245 = 0.6e1_dp*t14*t1 + 0.20e2_dp*t14*my_rho_1_3*d + &
464 0.14e2_dp*t14*my_rho_1_3*c + 0.14e2_dp*t14*c* &
465 d
466 t246 = t245*t40
467
468 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
469 e_rho_rho(ii) = e_rho_rho(ii) &
470 + (0.5e1_dp/0.81e2_dp*t128*t41 - 0.5e1_dp/0.108e3_dp&
471 & *t45*t99 + t134*t106/0.27e2_dp + t4*t193/ &
472 0.72e2_dp - t103*t196/0.54e2_dp + t200*t203/ &
473 0.108e3_dp)*sc
474 e_ndrho_rho(ii) = e_ndrho_rho(ii) &
475 - (0.5e1_dp/0.216e3_dp*t45*t124 - t4*t228/ &
476 0.72e2_dp + t103*t231/0.108e3_dp)*sc
477 e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii) &
478 + (t4*t246/0.72e2_dp)*sc
479 END IF
480
481 t248 = t5**2
482 t265 = 0.1e1_dp/t248
483 t278 = t87**2
484 t279 = b*t278
485 t332 = -0.432e3_dp*d - 0.2240e4_dp/0.3e1_dp*my_rho_1_3 - &
486 0.74e2_dp/0.27e2_dp*t184*t127*t80 + 0.100e3_dp/ &
487 0.27e2_dp*t14*t44*t22*d + 0.7e1_dp/0.27e2_dp* &
488 t279*t127*t13*t22 - 0.8e1_dp/0.3e1_dp*t184* &
489 t70*cf - 0.2240e4_dp/0.3e1_dp*t14*my_rho_1_3* &
490 cf - 0.48e2_dp*t88*t11*t13*cf - 0.944e3_dp/ &
491 0.3e1_dp*t52*t61 - 0.40e2_dp*t88*t69*t62 - &
492 0.656e3_dp/0.3e1_dp*t52*t11*t62 + 0.7e1_dp/ &
493 0.27e2_dp*t279*t265*t80 + 0.64e2_dp/0.27e2_dp* &
494 t52*t44*t13*t22 - 0.8e1_dp/0.3e1_dp*t184*t77&
495 & *t62 - 0.432e3_dp*t14*cf*d + 0.52e2_dp/ &
496 0.27e2_dp*t88*t199*t13*t22 - 0.20e2_dp/ &
497 0.9e1_dp*t184*t133*t13*t22 + 0.8e1_dp/0.9e1_dp&
498 & *t14*t102*t22 + 0.100e3_dp/0.27e2_dp*t52*t199&
499 & *t80 + 0.106e3_dp/0.27e2_dp*t88*t133*t80
500
501 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
502 e_rho_rho_rho(ii) = e_rho_rho_rho(ii) &
503 - (0.55e2_dp/0.243e3_dp*a/t1/t248*t41 - 0.5e1_dp &
504 &/0.27e2_dp*t128*t99 + 0.40e2_dp/0.243e3_dp*a/ &
505 my_rho_1_3/t248*t106 + 0.5e1_dp/0.72e2_dp*t45* &
506 t193 - t134*t196/0.9e1_dp + 0.7e1_dp/0.108e3_dp* &
507 a*t265*t203 - t4*t332*t40/0.72e2_dp + t103* &
508 t192*t105/0.36e2_dp - t200*t98*t202/0.36e2_dp &
509 &+ t128*t37/t201/t38/0.81e2_dp)*sc
510 e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii) &
511 + (0.5e1_dp/0.81e2_dp*t128*t124 - 0.5e1_dp/ &
512 0.108e3_dp*t45*t228 + t134*t231/0.27e2_dp + t4*&
513 & (-0.28e2_dp/0.9e1_dp*t52*t161*my_ndrho - &
514 0.22e2_dp/0.9e1_dp*t88*t166*my_ndrho - 0.4e1_dp &
515 &/0.3e1_dp*t14*t94*my_ndrho - 0.40e2_dp/0.9e1_dp &
516 &*t173*t215 - 0.4e1_dp*t176*t215 - 0.40e2_dp/ &
517 0.9e1_dp*t14*t3*my_ndrho*d + 0.14e2_dp/ &
518 0.9e1_dp*t184*t185*my_ndrho + 0.14e2_dp/0.9e1_dp&
519 & *t189*t215)*t40/0.72e2_dp - t103*t227*t105/ &
520 0.54e2_dp + t200*t123*t202/0.108e3_dp)*sc
521 e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii) &
522 - (0.5e1_dp/0.216e3_dp*t45*t246 - t4*(0.20e2_dp/ &
523 0.3e1_dp*t52*t70 + 0.4e1_dp*t14*t11 + 0.20e2_dp &
524 &/0.3e1_dp*t52*t89*d + 0.20e2_dp/0.3e1_dp*t14* &
525 t69*d + 0.14e2_dp/0.3e1_dp*t88*t89 + 0.14e2_dp/ &
526 0.3e1_dp*t88*t94*t13*d)*t40/0.72e2_dp + t103&
527 & *t245*t105/0.108e3_dp)*sc
528 END IF
529 END IF
530
531!FM t1 = my_rho_1_3 ** 2
532!FM t2 = t1 * my_rho
533!FM t3 = 0.1e1_dp / t2
534!FM t4 = a * t3
535!FM t5 = my_rho ** 2
536!FM t6 = t5 * my_rho
537!FM t7 = my_rho_1_3 * t6
538!FM t11 = 0.1e1_dp / my_rho_1_3
539!FM t13 = exp(-c * t11)
540!FM t14 = b * t13
541!FM t22 = my_ndrho ** 2
542!FM t26 = my_rho_1_3 * t22
543!FM t37 = -0.72e2_dp *( t7 - t14 *&
544!FM & t7 * cf - t6 * d * (1.0_dp+ t14 * cf)) + t14 *(t22*(0.3e1_dp &
545!FM & * t1 + 0.7e1_dp * c * d)&
546!FM + 0.10e2_dp * t26 * d + 0.7e1_dp &
547!FM &* t26 * c )
548!FM t38 = my_rho_1_3 + d
549!FM t39 = t38 ** 2
550!FM t40 = 0.1e1_dp / t39
551!FM t41 = t37 * t40
552!FM
553!FM IF (grad_deriv>=0.AND.my_rho>epsilon_rho) THEN
554!FM e_0(ii) = e_0(ii)&
555!FM + t4 * t41 / 0.72e2_dp
556!FM END IF
557!FM
558!FM t44 = 0.1e1_dp / (t1 * t5)
559!FM t45 = a * t44
560!FM t48 = my_rho_1_3 * t5
561!FM t52 = b * c
562!FM t61 = t13 * cf
563!FM t62 = t61 * d
564!FM t69 = 0.1e1_dp / t1
565!FM t70 = t69 * t13
566!FM t77 = 0.1e1_dp / my_rho
567!FM t78 = t52 * t77
568!FM t80 = t13 * t22 * d
569!FM t87 = c ** 2
570!FM t88 = b * t87
571!FM t89 = t77 * t13
572!FM t93 = my_rho_1_3 * my_rho
573!FM t94 = 0.1e1_dp / t93
574!FM t95 = t88 * t94
575!FM t98 = -0.216e3_dp * t5 *d -0.240e3_dp * t48(1.0_dp+ t14 * cf) -&
576!FM & 0.24e2_dp * t52 * (t2 * t62 +t13*t5*cf) &
577!FM - 0.216e3_dp * t14 * t5 * cf &
578!FM &* d + t22 *(0.10e2_dp / 0.3e1_dp * t52 * t70 + 0.2e1_dp *&
579!FM & t14 * t11 + 0.10e2_dp / 0.3e1_dp * t14 * t69 * d + 0.7e1_dp /&
580!FM & 0.3e1_dp * t88 * t89 ) +(0.10e2_dp / 0.3e1_dp * t78 +&
581!FM & 0.7e1_dp / 0.3e1_dp * t95 ) *&
582!FM & t80
583!FM t99 = t98 * t40
584!FM t102 = 0.1e1_dp / t48
585!FM t103 = a * t102
586!FM t105 = 0.1e1_dp / (t39 * t38)
587!FM t106 = t37 * t105
588!FM t112 = my_rho_1_3 * my_ndrho
589!FM t123 = t14 *(0.6e1_dp t1 * my_ndrho + t112 * 0.20e2_dp &
590!FM &* d + 0.14e2_dp * c *(t112 + t14 *&
591!FM & my_ndrho * d))
592!FM t124 = t123 * t40
593!FM
594!FM IF (grad_deriv>=1.OR.grad_deriv==-1) THEN
595!FM e_rho(ii) = e_rho(ii) &
596!FM -0.5e1_dp / 0.216e3_dp * t45 * t41 + t4 * t99 / 0.72e2_dp&
597!FM & - t103 * t106 / 0.108e3_dp
598!FM e_ndrho(ii) = e_ndrho(ii)&
599!FM +t4 * t124 / 0.72e2_dp
600!FM END IF
601!FM
602!FM t127 = 0.1e1_dp / (t1 * t6)
603!FM t128 = a * t127
604!FM t133 = 0.1e1_dp / t7
605!FM t134 = a * t133
606!FM t161 = t3 * t13
607!FM t165 = 0.1e1_dp / t5
608!FM t166 = t165 * t13
609!FM t173 = t52 * t165
610!FM t176 = t88 * t102
611!FM t184 = b * t87 * c
612!FM t185 = t102 * t13
613!FM t189 = t184 * t44
614!FM t192 = -0.560e3_dp * t93 - 0.432e3_dp * my_rho * d +cf*(&
615!FM -t13*(0.128e3_dp&
616!FM & * t52 * my_rho + 0.8e1_dp * t88 * t1 )&
617!FM & - 0.560e3_dp * t14 * t93 ) - 0.112e3_dp * t52 * t1&
618!FM & * t62 - 0.8e1_dp * t88 * my_rho_1_3 * t62 - 0.432e3_dp *&
619!FM & t14 * my_rho * cf * d - 0.14e2_dp / 0.9e1_dp * t52 *&
620!FM & t161 * t22 - 0.11e2_dp / 0.9e1_dp * t88 * t166 * t22 -&
621!FM & 0.2e1_dp / 0.3e1_dp * t14 * t94 * t22 - 0.20e2_dp /&
622!FM & 0.9e1_dp * t173 * t80 - 0.2e1_dp * t176 * t80 -&
623!FM & 0.20e2_dp / 0.9e1_dp * t14 * t3 * t22 * d + 0.7e1_dp /&
624!FM & 0.9e1_dp * t184 * t185 * t22 + 0.7e1_dp / 0.9e1_dp *&
625!FM & t189 * t80
626!FM t193 = t192 * t40
627!FM t196 = t98 * t105
628!FM t199 = 0.1e1_dp / t6
629!FM t200 = a * t199
630!FM t201 = t39 ** 2
631!FM t202 = 0.1e1_dp / t201
632!FM t203 = t37 * t202
633!FM t215 = t13 * my_ndrho * d
634!FM t227 = 0.20e2_dp / 0.3e1_dp * t52 * t70 * my_ndrho + 0.4e1_dp *&
635!FM & t14 * t11 * my_ndrho + 0.20e2_dp / 0.3e1_dp * t78 * t215&
636!FM & + 0.20e2_dp / 0.3e1_dp * t14 * t69 * my_ndrho * d +&
637!FM & 0.14e2_dp / 0.3e1_dp * t88 * t89 * my_ndrho + 0.14e2_dp &
638!FM &/ 0.3e1_dp * t95 * t215
639!FM t228 = t227 * t40
640!FM t231 = t123 * t105
641!FM t245 = 0.6e1_dp * t14 * t1 + 0.20e2_dp * t14 * my_rho_1_3 * d +&
642!FM & 0.14e2_dp * t14 * my_rho_1_3 * c + 0.14e2_dp * t14 * c *&
643!FM & d
644!FM t246 = t245 * t40
645!FM
646!FM IF (grad_deriv>=2 .OR.grad_deriv==-2) THEN
647!FM e_rho_rho(ii) = e_rho_rho(ii)&
648!FM +0.5e1_dp / 0.81e2_dp * t128 * t41 - 0.5e1_dp / 0.108e3_dp&
649!FM & * t45 * t99 + t134 * t106 / 0.27e2_dp + t4 * t193 /&
650!FM & 0.72e2_dp - t103 * t196 / 0.54e2_dp + t200 * t203 /&
651!FM & 0.108e3_dp
652!FM e_ndrho_rho(ii) = e_ndrho_rho(ii)&
653!FM -0.5e1_dp / 0.216e3_dp * t45 * t124 + t4 * t228 /&
654!FM & 0.72e2_dp - t103 * t231 / 0.108e3_dp
655!FM e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii)&
656!FM +t4 * t246 / 0.72e2_dp
657!FM END IF
658!FM
659!FM t248 = t5 ** 2
660!FM t265 = 0.1e1_dp / t248
661!FM t278 = t87 ** 2
662!FM t279 = b * t278
663!FM t332 = -0.432e3_dp * d - 0.2240e4_dp / 0.3e1_dp * my_rho_1_3 -&
664!FM & 0.74e2_dp / 0.27e2_dp * t184 * t127 * t80 + 0.100e3_dp /&
665!FM & 0.27e2_dp * t14 * t44 * t22 * d + 0.7e1_dp / 0.27e2_dp *&
666!FM & t279 * t127 * t13 * t22 - 0.8e1_dp / 0.3e1_dp * t184 *&
667!FM & t70 * cf - 0.2240e4_dp / 0.3e1_dp * t14 * my_rho_1_3 *&
668!FM & cf - 0.48e2_dp * t88 * t11 * t13 * cf - 0.944e3_dp /&
669!FM & 0.3e1_dp * t52 * t61 - 0.40e2_dp * t88 * t69 * t62 -&
670!FM & 0.656e3_dp / 0.3e1_dp * t52 * t11 * t62 + 0.7e1_dp /&
671!FM & 0.27e2_dp * t279 * t265 * t80 + 0.64e2_dp / 0.27e2_dp *&
672!FM & t52 * t44 * t13 * t22 - 0.8e1_dp / 0.3e1_dp * t184 * t77&
673!FM & * t62 - 0.432e3_dp * t14 * cf * d + 0.52e2_dp /&
674!FM & 0.27e2_dp * t88 * t199 * t13 * t22 - 0.20e2_dp /&
675!FM & 0.9e1_dp * t184 * t133 * t13 * t22 + 0.8e1_dp / 0.9e1_dp&
676!FM & * t14 * t102 * t22 + 0.100e3_dp / 0.27e2_dp * t52 * t199&
677!FM & * t80 + 0.106e3_dp / 0.27e2_dp * t88 * t133 * t80
678!FM
679!FM IF (grad_deriv>=3 .OR. grad_deriv==-3) THEN
680!FM e_rho_rho_rho(ii) = e_rho_rho_rho(ii)&
681!FM -0.55e2_dp / 0.243e3_dp * a / t1 / t248 * t41 + 0.5e1_dp &
682!FM &/ 0.27e2_dp * t128 * t99 - 0.40e2_dp / 0.243e3_dp * a /&
683!FM & my_rho_1_3 / t248 * t106 - 0.5e1_dp / 0.72e2_dp * t45 *&
684!FM & t193 + t134 * t196 / 0.9e1_dp - 0.7e1_dp / 0.108e3_dp *&
685!FM & a * t265 * t203 + t4 * t332 * t40 / 0.72e2_dp - t103 *&
686!FM & t192 * t105 / 0.36e2_dp + t200 * t98 * t202 / 0.36e2_dp &
687!FM &- t128 * t37 / t201 / t38 / 0.81e2_dp
688!FM e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii)&
689!FM +0.5e1_dp / 0.81e2_dp * t128 * t124 - 0.5e1_dp /&
690!FM & 0.108e3_dp * t45 * t228 + t134 * t231 / 0.27e2_dp + t4 *&
691!FM & (-0.28e2_dp / 0.9e1_dp * t52 * t161 * my_ndrho -&
692!FM & 0.22e2_dp / 0.9e1_dp * t88 * t166 * my_ndrho - 0.4e1_dp &
693!FM &/ 0.3e1_dp * t14 * t94 * my_ndrho - 0.40e2_dp / 0.9e1_dp &
694!FM &* t173 * t215 - 0.4e1_dp * t176 * t215 - 0.40e2_dp /&
695!FM & 0.9e1_dp * t14 * t3 * my_ndrho * d + 0.14e2_dp /&
696!FM & 0.9e1_dp * t184 * t185 * my_ndrho + 0.14e2_dp / 0.9e1_dp&
697!FM & * t189 * t215) * t40 / 0.72e2_dp - t103 * t227 * t105 /&
698!FM & 0.54e2_dp + t200 * t123 * t202 / 0.108e3_dp
699!FM e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii)&
700!FM -0.5e1_dp / 0.216e3_dp * t45 * t246 + t4 * (0.20e2_dp /&
701!FM & 0.3e1_dp * t52 * t70 + 0.4e1_dp * t14 * t11 + 0.20e2_dp &
702!FM &/ 0.3e1_dp * t52 * t89 * d + 0.20e2_dp / 0.3e1_dp * t14 *&
703!FM & t69 * d + 0.14e2_dp / 0.3e1_dp * t88 * t89 + 0.14e2_dp /&
704!FM & 0.3e1_dp * t88 * t94 * t13 * d) * t40 / 0.72e2_dp - t103&
705!FM & * t245 * t105 / 0.108e3_dp
706!FM END IF
707
708 END DO
709
710!$OMP END DO
711
712 END SELECT
713 END SUBROUTINE lyp_lda_calc
714
715! **************************************************************************************************
716!> \brief evaluates the becke 88 exchange functional for lsd
717!> \param rho_set ...
718!> \param deriv_set ...
719!> \param grad_deriv ...
720!> \param lyp_params input parameter (scaling)
721!> \par History
722!> 11.2003 created [fawzi]
723!> 01.2007 added scaling [Manuel Guidon]
724!> \author fawzi
725! **************************************************************************************************
726 SUBROUTINE lyp_lsd_eval(rho_set, deriv_set, grad_deriv, lyp_params)
727 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
728 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
729 INTEGER, INTENT(in) :: grad_deriv
730 TYPE(section_vals_type), POINTER :: lyp_params
731
732 CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lsd_eval'
733
734 INTEGER :: handle, npoints
735 INTEGER, DIMENSION(2, 3) :: bo
736 REAL(kind=dp) :: epsilon_drho, epsilon_rho, sc
737 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndr, e_ndr_ndr, &
738 e_ndr_ra, e_ndr_rb, e_ndra, e_ndra_ndra, e_ndra_ra, e_ndra_rb, e_ndrb, e_ndrb_ndrb, &
739 e_ndrb_ra, e_ndrb_rb, e_ra, e_ra_ra, e_ra_rb, e_rb, e_rb_rb, norm_drho, norm_drhoa, &
740 norm_drhob, rhoa, rhob
741 TYPE(xc_derivative_type), POINTER :: deriv
742
743 CALL timeset(routinen, handle)
744 NULLIFY (deriv)
745
746 CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
747 CALL cite_reference(lee1988)
748
749 CALL xc_rho_set_get(rho_set, &
750 rhoa=rhoa, rhob=rhob, norm_drhoa=norm_drhoa, &
751 norm_drhob=norm_drhob, norm_drho=norm_drho, &
752 rho_cutoff=epsilon_rho, &
753 drho_cutoff=epsilon_drho, local_bounds=bo)
754 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
755
756 dummy => rhoa
757 e_0 => dummy
758 e_ra => dummy
759 e_rb => dummy
760 e_ndra_ra => dummy
761 e_ndra_rb => dummy
762 e_ndrb_ra => dummy
763 e_ndrb_rb => dummy
764 e_ndr_ndr => dummy
765 e_ndra_ndra => dummy
766 e_ndrb_ndrb => dummy
767 e_ndr => dummy
768 e_ndra => dummy
769 e_ndrb => dummy
770 e_ra_ra => dummy
771 e_ra_rb => dummy
772 e_rb_rb => dummy
773 e_ndr_ra => dummy
774 e_ndr_rb => dummy
775
776 IF (grad_deriv >= 0) THEN
777 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
778 allocate_deriv=.true.)
779 CALL xc_derivative_get(deriv, deriv_data=e_0)
780 END IF
781 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
782 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
783 allocate_deriv=.true.)
784 CALL xc_derivative_get(deriv, deriv_data=e_ra)
785 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
786 allocate_deriv=.true.)
787 CALL xc_derivative_get(deriv, deriv_data=e_rb)
788 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
789 allocate_deriv=.true.)
790 CALL xc_derivative_get(deriv, deriv_data=e_ndr)
791 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
792 allocate_deriv=.true.)
793 CALL xc_derivative_get(deriv, deriv_data=e_ndra)
794 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
795 allocate_deriv=.true.)
796 CALL xc_derivative_get(deriv, deriv_data=e_ndrb)
797 END IF
798 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
799 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhoa], &
800 allocate_deriv=.true.)
801 CALL xc_derivative_get(deriv, deriv_data=e_ra_ra)
802 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhob], &
803 allocate_deriv=.true.)
804 CALL xc_derivative_get(deriv, deriv_data=e_ra_rb)
805 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob, deriv_rhob], &
806 allocate_deriv=.true.)
807 CALL xc_derivative_get(deriv, deriv_data=e_rb_rb)
808 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhoa], &
809 allocate_deriv=.true.)
810 CALL xc_derivative_get(deriv, deriv_data=e_ndr_ra)
811 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhob], &
812 allocate_deriv=.true.)
813 CALL xc_derivative_get(deriv, deriv_data=e_ndr_rb)
814 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhoa], &
815 allocate_deriv=.true.)
816 CALL xc_derivative_get(deriv, deriv_data=e_ndra_ra)
817 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhob], &
818 allocate_deriv=.true.)
819 CALL xc_derivative_get(deriv, deriv_data=e_ndra_rb)
820 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob, deriv_rhob], &
821 allocate_deriv=.true.)
822 CALL xc_derivative_get(deriv, deriv_data=e_ndrb_rb)
823 deriv => xc_dset_get_derivative(deriv_set, &
824 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
825 CALL xc_derivative_get(deriv, deriv_data=e_ndr_ndr)
826 deriv => xc_dset_get_derivative(deriv_set, &
827 [deriv_norm_drhoa, deriv_norm_drhoa], allocate_deriv=.true.)
828 CALL xc_derivative_get(deriv, deriv_data=e_ndra_ndra)
829 deriv => xc_dset_get_derivative(deriv_set, &
830 [deriv_norm_drhob, deriv_norm_drhob], allocate_deriv=.true.)
831 CALL xc_derivative_get(deriv, deriv_data=e_ndrb_ndrb)
832 END IF
833
834!$OMP PARALLEL DEFAULT(NONE) &
835!$OMP SHARED(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob) &
836!$OMP SHARED(e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra) &
837!$OMP SHARED(e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb) &
838!$OMP SHARED(e_ndr, e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb) &
839!$OMP SHARED(e_ndr_ra, e_ndr_rb, grad_deriv) &
840!$OMP SHARED(npoints, epsilon_rho, sc)
841
842 CALL lyp_lsd_calc( &
843 rhoa=rhoa, rhob=rhob, norm_drho=norm_drho, norm_drhoa=norm_drhoa, &
844 norm_drhob=norm_drhob, e_0=e_0, e_ra=e_ra, e_rb=e_rb, &
845 e_ndra_ra=e_ndra_ra, e_ndra_rb=e_ndra_rb, e_ndrb_ra&
846 &=e_ndrb_ra, e_ndrb_rb=e_ndrb_rb, e_ndr_ndr=e_ndr_ndr, &
847 e_ndra_ndra=e_ndra_ndra, e_ndrb_ndrb=e_ndrb_ndrb, e_ndr=e_ndr, &
848 e_ndra=e_ndra, e_ndrb=e_ndrb, e_ra_ra=e_ra_ra, &
849 e_ra_rb=e_ra_rb, e_rb_rb=e_rb_rb, e_ndr_ra=e_ndr_ra, &
850 e_ndr_rb=e_ndr_rb, &
851 grad_deriv=grad_deriv, npoints=npoints, &
852 epsilon_rho=epsilon_rho, sc=sc)
853
854!$OMP END PARALLEL
855
856 CALL timestop(handle)
857 END SUBROUTINE lyp_lsd_eval
858
859! **************************************************************************************************
860!> \brief low level calculation of the becke 88 exchange functional for lsd
861!> \param rhoa alpha spin density
862!> \param rhob beta spin density
863!> \param norm_drho || grad rhoa + grad rhob ||
864!> \param norm_drhoa || grad rhoa ||
865!> \param norm_drhob || grad rhob ||
866!> \param e_0 adds to it the local value of the functional
867!> \param e_ra e_*: derivative of the functional wrt. to the variables
868!> named where the * is.
869!> \param e_rb ...
870!> \param e_ndra_ra ...
871!> \param e_ndra_rb ...
872!> \param e_ndrb_ra ...
873!> \param e_ndrb_rb ...
874!> \param e_ndr_ndr ...
875!> \param e_ndra_ndra ...
876!> \param e_ndrb_ndrb ...
877!> \param e_ndr ...
878!> \param e_ndra ...
879!> \param e_ndrb ...
880!> \param e_ra_ra ...
881!> \param e_ra_rb ...
882!> \param e_rb_rb ...
883!> \param e_ndr_ra ...
884!> \param e_ndr_rb ...
885!> \param grad_deriv ...
886!> \param npoints ...
887!> \param epsilon_rho ...
888!> \param sc scaling parameter for correlation
889!> \par History
890!> 01.2004 created [fawzi]
891!> \author fawzi
892! **************************************************************************************************
893 SUBROUTINE lyp_lsd_calc(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob, &
894 e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, &
895 e_ndra_ndra, e_ndrb_ndrb, e_ndr, &
896 e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb, &
897 grad_deriv, npoints, epsilon_rho, sc)
898 REAL(kind=dp), DIMENSION(*), INTENT(in) :: rhoa, rhob, norm_drho, norm_drhoa, &
899 norm_drhob
900 REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, &
901 e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb, e_ndr, e_ndra, e_ndrb, &
902 e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb
903 INTEGER, INTENT(in) :: grad_deriv, npoints
904 REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
905
906 INTEGER :: ii
907 REAL(kind=dp) :: cf, my_ndrho, my_ndrhoa, my_ndrhob, my_rho, my_rhoa, my_rhob, t1, t100, &
908 t101, t102, t103, t104, t107, t108, t109, t112, t115, t118, t12, t120, t124, t129, t13, &
909 t130, t132, t135, t138, t14, t140, t142, t145, t15, t153, t155, t159, t16, t164, t168, &
910 t17, t171, t176, t18, t181, t182, t185, t189, t194, t195, t198, t2, t20, t202, t205, &
911 t206, t21, t210, t214, t215, t218, t22, t222, t228, t23, t232, t236, t238, t24, t243, &
912 t249, t25, t252, t253, t255, t257, t26, t260, t265, t268, t27, t270, t29, t3, t30, t304, &
913 t31, t310, t313, t316, t319, t322, t326, t329, t332, t334, t341, t35
914 REAL(kind=dp) :: t354, t356, t360, t363, t37, t373, t376, t381, t39, t391, t4, t40, t408, &
915 t41, t415, t419, t422, t430, t44, t445, t449, t45, t452, t46, t467, t47, t48, t483, t487, &
916 t49, t490, t5, t50, t505, t515, t519, t52, t520, t54, t56, t57, t6, t61, t62, t64, t66, &
917 t7, t72, t75, t78, t8, t82, t85, t86, t87, t88, t90, t92, t94, t95, t98, t99
918
919 cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
920
921!$OMP DO
922
923 DO ii = 1, npoints
924 my_rhoa = max(rhoa(ii), 0.0_dp)
925 my_rhob = max(rhob(ii), 0.0_dp)
926 my_rho = my_rhoa + my_rhob
927 IF (my_rho > epsilon_rho) THEN
928 my_ndrho = norm_drho(ii)
929 my_ndrhoa = norm_drhoa(ii)
930 my_ndrhob = norm_drhob(ii)
931
932 t1 = my_rho**(0.1e1_dp/0.3e1_dp)
933 t2 = 0.1e1_dp/t1
934 t3 = d*t2
935 t4 = 0.1e1_dp + t3
936 t5 = 0.1e1_dp/t4
937 t6 = a*t5
938 t7 = my_rhoa*my_rhob
939 t8 = 0.1e1_dp/my_rho
940 t12 = a*b
941 t13 = c*t2
942 t14 = exp(-t13)
943 t15 = t12*t14
944 t16 = my_rho**2
945 t17 = t16*my_rho
946 t18 = t1**2
947 t20 = 0.1e1_dp/t18/t17
948 t21 = t5*t20
949 t22 = 2**(0.1e1_dp/0.3e1_dp)
950 t23 = t22**2
951 t24 = t23*cf
952 t25 = my_rhoa**2
953 t26 = my_rhoa**(0.1e1_dp/0.3e1_dp)
954 t27 = t26**2
955 t29 = my_rhob**2
956 t30 = my_rhob**(0.1e1_dp/0.3e1_dp)
957 t31 = t30**2
958 t35 = 0.8e1_dp*t24*(t27*t25 + t31*t29)
959 t37 = t3*t5
960 t39 = 0.47e2_dp/0.18e2_dp - 0.7e1_dp/0.18e2_dp*t13 - &
961 0.7e1_dp/0.18e2_dp*t37
962 t40 = my_ndrho**2
963 t41 = t39*t40
964 t44 = 0.5e1_dp/0.2e1_dp - t13/0.18e2_dp - t37/0.18e2_dp
965 t45 = my_ndrhoa**2
966 t46 = my_ndrhob**2
967 t47 = t45 + t46
968 t48 = t44*t47
969 t49 = t13 + t37 - 0.11e2_dp
970 t50 = my_rhoa*t8
971 t52 = my_rhob*t8
972 t54 = t50*t45 + t52*t46
973 t56 = t49*t54/0.9e1_dp
974 t57 = t35 + t41 - t48 - t56
975 t61 = 0.2e1_dp/0.3e1_dp*t16
976 t62 = t61 - t25
977 t64 = t61 - t29
978 t66 = t7*t57 - 0.2e1_dp/0.3e1_dp*t16*t40 + t62*t46 + &
979 t64*t45
980
981 IF (grad_deriv >= 0 .AND. my_rho > epsilon_rho) THEN
982 e_0(ii) = e_0(ii) &
983 - (0.4e1_dp*t6*t7*t8 + t15*t21*t66)*sc
984 END IF
985 !--------
986
987 t72 = t27*my_rhoa
988 t75 = t49*t8
989 t78 = 0.64e2_dp/0.3e1_dp*t24*t72 - t75*t45/0.9e1_dp
990 t82 = my_rhob*t57 + t7*t78 - 0.2e1_dp*my_rhoa*t46
991 t85 = t4**2
992 t86 = 0.1e1_dp/t85
993 t87 = a*t86
994 t88 = t87*my_rhoa
995 t90 = 0.1e1_dp/t1/t16
996 t92 = my_rhob*t90*d
997 t94 = 0.4e1_dp/0.3e1_dp*t88*t92
998 t95 = 0.1e1_dp/t16
999 t98 = 0.4e1_dp*t6*t7*t95
1000 t99 = t12*c
1001 t100 = t16**2
1002 t101 = t100*my_rho
1003 t102 = 0.1e1_dp/t101
1004 t103 = t102*t14
1005 t104 = t5*t66
1006 t107 = t99*t103*t104/0.3e1_dp
1007 t108 = t86*t102
1008 t109 = t66*d
1009 t112 = t15*t108*t109/0.3e1_dp
1010 t115 = t5/t18/t100
1011 t118 = 0.11e2_dp/0.3e1_dp*t15*t115*t66
1012 t120 = 0.1e1_dp/t1/my_rho
1013 t124 = d**2
1014 t129 = c*t120 + d*t120*t5 - t124/t18/my_rho*t86
1015 t130 = 0.7e1_dp/0.54e2_dp*t129
1016 t132 = t129/0.54e2_dp
1017 t135 = -t129/0.3e1_dp
1018 t138 = my_rhoa*t95
1019 t140 = my_rhob*t95
1020 t142 = -t138*t45 - t140*t46
1021 t145 = t130*t40 - t132*t47 - t135*t54/0.9e1_dp - t49* &
1022 t142/0.9e1_dp
1023 t153 = t7*t145 - 0.4e1_dp/0.3e1_dp*my_rho*t40 + &
1024 0.4e1_dp/0.3e1_dp*my_rho*t46 + 0.4e1_dp/0.3e1_dp&
1025 & *my_rho*t45
1026 t155 = t15*t21*t153
1027
1028 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1029 e_ra(ii) = e_ra(ii) &
1030 - (0.4e1_dp*t6*t52 + t15*t21*t82 + t94 - t98 + &
1031 t107 + t112 - t118 + t155)*sc
1032 END IF
1033
1034 t159 = t31*my_rhob
1035 t164 = 0.64e2_dp/0.3e1_dp*t24*t159 - t75*t46/0.9e1_dp
1036 t168 = my_rhoa*t57 + t7*t164 - 0.2e1_dp*my_rhob*t45
1037
1038 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1039 e_rb(ii) = e_rb(ii) &
1040 - (0.4e1_dp*t6*t50 + t15*t21*t168 + t94 - t98 + &
1041 t107 + t112 - t118 + t155)*sc
1042 END IF
1043
1044 t171 = t39*my_ndrho
1045 t176 = 0.2e1_dp*t7*t171 - 0.4e1_dp/0.3e1_dp*t16*my_ndrho
1046
1047 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1048 e_ndr(ii) = e_ndr(ii) &
1049 - (t15*t21*t176)*sc
1050 END IF
1051
1052 t181 = t49*my_rhoa
1053 t182 = t8*my_ndrhoa
1054 t185 = -0.2e1_dp*t44*my_ndrhoa - 0.2e1_dp/0.9e1_dp*t181*t182
1055 t189 = t7*t185 + 0.2e1_dp*t64*my_ndrhoa
1056
1057 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1058 e_ndra(ii) = e_ndra(ii) &
1059 - (t15*t21*t189)*sc
1060 END IF
1061
1062 t194 = t49*my_rhob
1063 t195 = t8*my_ndrhob
1064 t198 = -0.2e1_dp*t44*my_ndrhob - 0.2e1_dp/0.9e1_dp*t194*t195
1065 t202 = t7*t198 + 0.2e1_dp*t62*my_ndrhob
1066
1067 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1068 e_ndrb(ii) = e_ndrb(ii) &
1069 - (t15*t21*t202)*sc
1070 END IF
1071 !-------
1072
1073 t205 = t100*t16
1074 t206 = 0.1e1_dp/t205
1075 t210 = 0.26e2_dp/0.9e1_dp*t99*t206*t14*t104
1076 t214 = 0.2e1_dp/0.3e1_dp*t99*t103*t5*t153
1077 t215 = c**2
1078 t218 = 0.1e1_dp/t1/t205
1079 t222 = t12*t215*t218*t14*t104/0.9e1_dp
1080 t228 = 0.2e1_dp/0.9e1_dp*t12*c*t218*t14*t86*t109
1081 t232 = 0.26e2_dp/0.9e1_dp*t15*t86*t206*t109
1082 t236 = 0.2e1_dp/0.3e1_dp*t15*t108*t153*d
1083 t238 = 0.1e1_dp/t85/t4
1084 t243 = 0.2e1_dp/0.9e1_dp*t15*t238*t218*t66*t124
1085 t249 = 0.154e3_dp/0.9e1_dp*t15*t5/t18/t101*t66
1086 t252 = 0.22e2_dp/0.3e1_dp*t15*t115*t153
1087 t253 = t6*t140
1088 t255 = t87*t92
1089 t257 = c*t90
1090 t260 = d*t90*t5
1091 t265 = t124/t18/t16*t86
1092 t268 = 0.1e1_dp/t17
1093 t270 = t124*d*t268*t238
1094 t304 = t15*t21*(t7*((-0.14e2_dp/0.81e2_dp*t257 - &
1095 0.14e2_dp/0.81e2_dp*t260 + 0.7e1_dp/0.27e2_dp* &
1096 t265 - 0.7e1_dp/0.81e2_dp*t270)*t40 - (-0.2e1_dp/ &
1097 0.81e2_dp*t257 - 0.2e1_dp/0.81e2_dp*t260 + t265/ &
1098 0.27e2_dp - t270/0.81e2_dp)*t47 - (0.4e1_dp/ &
1099 0.9e1_dp*t257 + 0.4e1_dp/0.9e1_dp*t260 - 0.2e1_dp &
1100 &/0.3e1_dp*t265 + 0.2e1_dp/0.9e1_dp*t270)*t54/ &
1101 0.9e1_dp - 0.2e1_dp/0.9e1_dp*t135*t142 - t49*&
1102 & (0.2e1_dp*my_rhoa*t268*t45 + 0.2e1_dp*my_rhob* &
1103 t268*t46)/0.9e1_dp) - 0.4e1_dp/0.3e1_dp*t40 + &
1104 0.4e1_dp/0.3e1_dp*t46 + 0.4e1_dp/0.3e1_dp*t45)
1105 t310 = 0.40e2_dp/0.9e1_dp*t88*my_rhob/t1/t17*d
1106 t313 = my_rhob*t20
1107 t316 = 0.8e1_dp/0.9e1_dp*a*t238*my_rhoa*t313*t124
1108 t319 = 0.8e1_dp*t6*t7*t268
1109 t322 = t99*t103*t5*t82
1110 t326 = t15*t108*t82*d
1111 t329 = t15*t115*t82
1112 t332 = t135*t8
1113 t334 = t49*t95
1114 t341 = t15*t21*(my_rhob*t145 + t7*(-t332*t45/ &
1115 0.9e1_dp + t334*t45/0.9e1_dp))
1116
1117 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1118 e_ra_ra(ii) = e_ra_ra(ii) &
1119 + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
1120 t252 + 0.8e1_dp*t253 - 0.8e1_dp/0.3e1_dp*t255 - &
1121 t304 + t310 - t316 - t319 - 0.2e1_dp/0.3e1_dp*t322 - &
1122 0.2e1_dp/0.3e1_dp*t326 + 0.22e2_dp/0.3e1_dp*t329&
1123 & - 0.2e1_dp*t341 - t15*t21*(0.2e1_dp*my_rhob* &
1124 t78 + 0.320e3_dp/0.9e1_dp*t72*my_rhob*t24 - &
1125 0.2e1_dp*t46))*sc
1126 END IF
1127
1128 t354 = t99*t103*t5*t168
1129 t356 = t6*t138
1130 t360 = t87*my_rhoa*t90*d
1131 t363 = t15*t115*t168
1132 t373 = t15*t21*(my_rhoa*t145 + t7*(-t332*t46/ &
1133 0.9e1_dp + t334*t46/0.9e1_dp))
1134 t376 = t15*t108*t168*d
1135
1136 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1137 e_rb_rb(ii) = e_rb_rb(ii) &
1138 + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
1139 t252 - t304 + t310 - t316 - t319 + 0.8e1_dp*t356 - &
1140 0.8e1_dp/0.3e1_dp*t360 + 0.22e2_dp/0.3e1_dp* &
1141 t363 - 0.2e1_dp*t373 - 0.2e1_dp/0.3e1_dp*t354 - &
1142 0.2e1_dp/0.3e1_dp*t376 - t15*t21*(0.2e1_dp* &
1143 my_rhoa*t164 + 0.320e3_dp/0.9e1_dp*my_rhoa* &
1144 t159*t24 - 0.2e1_dp*t45))*sc
1145 END IF
1146
1147 t381 = -t354/0.3e1_dp + 0.4e1_dp*t356 - 0.4e1_dp/0.3e1_dp&
1148 & *t360 + 0.11e2_dp/0.3e1_dp*t363 - t373 - t341 - &
1149 t376/0.3e1_dp + t310 - 0.4e1_dp*t6*t8 + 0.4e1_dp* &
1150 t253 + t210 - t214 - t222
1151 t391 = -t228 + t232 - t236 - t243 - t249 + t252 - 0.4e1_dp/ &
1152 0.3e1_dp*t255 - t304 - t316 - t319 - t322/0.3e1_dp - &
1153 t326/0.3e1_dp + 0.11e2_dp/0.3e1_dp*t329 - t15* &
1154 t21*(t35 + t41 - t48 - t56 + my_rhob*t164 + my_rhoa &
1155 &*t78)
1156
1157 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1158 e_ra_rb(ii) = e_ra_rb(ii) &
1159 + (t381 + t391)*sc
1160 END IF
1161
1162 t408 = t12*t14*t5
1163 t415 = t99*t103*t5*t176/0.3e1_dp
1164 t419 = t15*t108*t176*d/0.3e1_dp
1165 t422 = 0.11e2_dp/0.3e1_dp*t15*t115*t176
1166 t430 = t15*t21*(0.2e1_dp*t7*t130*my_ndrho - 0.8e1_dp &
1167 &/0.3e1_dp*my_rho*my_ndrho)
1168
1169 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1170 e_ndr_ra(ii) = e_ndr_ra(ii) &
1171 - (0.2e1_dp*t408*t313*t171 + t415 + t419 - t422 + &
1172 t430)*sc
1173 e_ndr_rb(ii) = e_ndr_rb(ii) &
1174 - (0.2e1_dp*t408*t20*my_rhoa*t171 + t415 + t419 - &
1175 t422 + t430)*sc
1176 END IF
1177
1178 t445 = t99*t103*t5*t189/0.3e1_dp
1179 t449 = t15*t108*t189*d/0.3e1_dp
1180 t452 = 0.11e2_dp/0.3e1_dp*t15*t115*t189
1181 t467 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhoa - &
1182 0.2e1_dp/0.9e1_dp*t135*my_rhoa*t182 + 0.2e1_dp/ &
1183 0.9e1_dp*t181*t95*my_ndrhoa) + 0.8e1_dp/0.3e1_dp&
1184 & *my_rho*my_ndrhoa)
1185
1186 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1187 e_ndra_ra(ii) = e_ndra_ra(ii) &
1188 - (t15*t21*(my_rhob*t185 - 0.2e1_dp/0.9e1_dp*t7&
1189 & *t75*my_ndrhoa) + t445 + t449 - t452 + t467)*sc
1190 e_ndra_rb(ii) = e_ndra_rb(ii) &
1191 - (t15*t21*(my_rhoa*t185 - 0.4e1_dp*my_rhob* &
1192 my_ndrhoa) + t445 + t449 - t452 + t467)*sc
1193 END IF
1194
1195 t483 = t99*t103*t5*t202/0.3e1_dp
1196 t487 = t15*t108*t202*d/0.3e1_dp
1197 t490 = 0.11e2_dp/0.3e1_dp*t15*t115*t202
1198 t505 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhob - &
1199 0.2e1_dp/0.9e1_dp*t135*my_rhob*t195 + 0.2e1_dp/ &
1200 0.9e1_dp*t194*t95*my_ndrhob) + 0.8e1_dp/0.3e1_dp&
1201 & *my_rho*my_ndrhob)
1202
1203 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1204 e_ndrb_ra(ii) = e_ndrb_ra(ii) &
1205 - (t15*t21*(my_rhob*t198 - 0.4e1_dp*my_rhoa* &
1206 my_ndrhob) + t483 + t487 - t490 + t505)*sc
1207 e_ndrb_rb(ii) = e_ndrb_rb(ii) &
1208 - (t15*t21*(my_rhoa*t198 - 0.2e1_dp/0.9e1_dp*t7&
1209 & *t75*my_ndrhob) + t483 + t487 - t490 + t505)*sc
1210 END IF
1211
1212 t515 = 0.4e1_dp/0.3e1_dp*t16
1213
1214 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1215 e_ndr_ndr(ii) = e_ndr_ndr(ii) &
1216 - (t15*t21*(0.2e1_dp*t7*t39 - t515))*sc
1217 END IF
1218
1219 t519 = t13/0.9e1_dp
1220 t520 = t37/0.9e1_dp
1221
1222 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1223 e_ndra_ndra(ii) = e_ndra_ndra(ii) &
1224 - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1225 &/0.9e1_dp*t181*t8) + t515 - 0.2e1_dp*t29))*sc
1226
1227 e_ndrb_ndrb(ii) = e_ndrb_ndrb(ii) &
1228 - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1229 &/0.9e1_dp*t194*t8) + t515 - 0.2e1_dp*t25))*sc
1230 END IF
1231 END IF
1232 END DO
1233!$OMP END DO
1234
1235 END SUBROUTINE lyp_lsd_calc
1236
1237END MODULE xc_lyp
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition bibliography.F:28
bibliography::lee1988
integer, save, public lee1988
Definition bibliography.F:43
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
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_lyp
calculates the lyp correlation functional
Definition xc_lyp.F:14
xc_lyp::lyp_lda_info
subroutine, public lyp_lda_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_lyp.F:59
xc_lyp::lyp_lsd_eval
subroutine, public lyp_lsd_eval(rho_set, deriv_set, grad_deriv, lyp_params)
evaluates the becke 88 exchange functional for lsd
Definition xc_lyp.F:727
xc_lyp::lyp_lsd_info
subroutine, public lyp_lsd_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_lyp.F:90
xc_lyp::lyp_lda_eval
subroutine, public lyp_lda_eval(rho_set, deriv_set, grad_deriv, lyp_params)
evaluates the lyp correlation functional for lda
Definition xc_lyp.F:124
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
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