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xc_lyp.F
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1!--------------------------------------------------------------------------------------------------!
2! CP2K: A general program to perform molecular dynamics simulations !
3! Copyright 2000-2026 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 maximum degree of the derivative that should be evaluated
115!> \param lyp_params input parameters (scaling)
116!> \par History
117!> 11.2003 created [fawzi]
118!> 01.2007 added scaling [Manuel Guidon]
119!> \author fawzi
120! **************************************************************************************************
121 SUBROUTINE lyp_lda_eval(rho_set, deriv_set, grad_deriv, lyp_params)
122 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
123 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
124 INTEGER, INTENT(in) :: grad_deriv
125 TYPE(section_vals_type), POINTER :: lyp_params
126
127 CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lda_eval'
128
129 INTEGER :: handle, npoints
130 INTEGER, DIMENSION(2, 3) :: bo
131 REAL(kind=dp) :: epsilon_norm_drho, epsilon_rho, sc
132 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndrho, &
133 e_ndrho_ndrho, e_ndrho_ndrho_rho, e_ndrho_rho, e_ndrho_rho_rho, e_rho, e_rho_rho, &
134 e_rho_rho_rho, norm_drho, rho, rho_1_3
135 TYPE(xc_derivative_type), POINTER :: deriv
136
137 CALL timeset(routinen, handle)
138
139 CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
140 CALL cite_reference(lee1988)
141
142 CALL xc_rho_set_get(rho_set, rho_1_3=rho_1_3, rho=rho, &
143 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho, &
144 drho_cutoff=epsilon_norm_drho)
145 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
146
147 dummy => rho
148
149 e_0 => dummy
150 e_rho => dummy
151 e_ndrho => dummy
152 e_rho_rho => dummy
153 e_ndrho_rho => dummy
154 e_ndrho_ndrho => dummy
155 e_rho_rho_rho => dummy
156 e_ndrho_rho_rho => dummy
157 e_ndrho_ndrho_rho => dummy
158
159 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
160 allocate_deriv=.true.)
161 CALL xc_derivative_get(deriv, deriv_data=e_0)
162 IF (grad_deriv >= 1) THEN
163 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
164 allocate_deriv=.true.)
165 CALL xc_derivative_get(deriv, deriv_data=e_rho)
166 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
167 allocate_deriv=.true.)
168 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
169 END IF
170 IF (grad_deriv >= 2) THEN
171 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
172 allocate_deriv=.true.)
173 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
174 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rho], &
175 allocate_deriv=.true.)
176 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho)
177 deriv => xc_dset_get_derivative(deriv_set, &
178 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
179 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
180 END IF
181 IF (grad_deriv >= 3) THEN
182 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
183 allocate_deriv=.true.)
184 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
185 deriv => xc_dset_get_derivative(deriv_set, &
186 [deriv_norm_drho, deriv_rho, deriv_rho], allocate_deriv=.true.)
187 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho)
188 deriv => xc_dset_get_derivative(deriv_set, &
189 [deriv_norm_drho, deriv_norm_drho, deriv_rho], allocate_deriv=.true.)
190 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho)
191!FM deriv => xc_dset_get_derivative(deriv_set,&
192!FM [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.,&
193!FM
194!FM call xc_derivative_get(deriv,deriv_data=e_ndrho_ndrho_ndrho)
195 END IF
196 IF (grad_deriv > 3) THEN
197 cpabort("derivatives bigger than 3 not implemented")
198 END IF
199
200!$OMP PARALLEL DEFAULT(NONE) &
201!$OMP SHARED(rho, rho_1_3, norm_drho, e_0, e_rho, e_ndrho) &
202!$OMP SHARED(e_rho_rho, e_ndrho_rho, e_ndrho_ndrho) &
203!$OMP SHARED(e_rho_rho_rho, e_ndrho_rho_rho) &
204!$OMP SHARED(e_ndrho_ndrho_rho, grad_deriv, npoints) &
205!$OMP SHARED(epsilon_rho, sc)
206
207 CALL lyp_lda_calc(rho=rho, rho_1_3=rho_1_3, norm_drho=norm_drho, &
208 e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_rho_rho=e_rho_rho, &
209 e_ndrho_rho=e_ndrho_rho, e_ndrho_ndrho=e_ndrho_ndrho, &
210 e_rho_rho_rho=e_rho_rho_rho, e_ndrho_rho_rho=e_ndrho_rho_rho, &
211 e_ndrho_ndrho_rho=e_ndrho_ndrho_rho, &
212 grad_deriv=grad_deriv, &
213 npoints=npoints, epsilon_rho=epsilon_rho, sc=sc)
214
215!$OMP END PARALLEL
216
217 CALL timestop(handle)
218 END SUBROUTINE lyp_lda_eval
219
220! **************************************************************************************************
221!> \brief evaluates the lyp correlation functional for lda
222!> \param rho the density where you want to evaluate the functional
223!> \param rho_1_3 ...
224!> \param norm_drho ...
225!> \param e_0 ...
226!> \param e_rho ...
227!> \param e_ndrho ...
228!> \param e_rho_rho ...
229!> \param e_ndrho_rho ...
230!> \param e_ndrho_ndrho ...
231!> \param e_rho_rho_rho ...
232!> \param e_ndrho_rho_rho ...
233!> \param e_ndrho_ndrho_rho ...
234!> \param grad_deriv maximum degree of the derivative that should be evaluated
235!> \param npoints ...
236!> \param epsilon_rho ...
237!> \param sc scaling-parameter for correlation
238!> \par History
239!> 11.2003 created [fawzi]
240!> 01.2007 added scaling [Manuel Guidon]
241!> \author fawzi
242! **************************************************************************************************
243 SUBROUTINE lyp_lda_calc(rho, rho_1_3, norm_drho, &
244 e_0, e_rho, e_ndrho, e_rho_rho, e_ndrho_rho, &
245 e_ndrho_ndrho, e_rho_rho_rho, e_ndrho_rho_rho, e_ndrho_ndrho_rho, &
246 grad_deriv, npoints, epsilon_rho, sc)
247 INTEGER, INTENT(in) :: npoints, grad_deriv
248 REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: e_ndrho_ndrho_rho, e_ndrho_rho_rho, &
249 e_rho_rho_rho, e_ndrho_ndrho, &
250 e_ndrho_rho, e_rho_rho, e_ndrho, &
251 e_rho, e_0
252 REAL(kind=dp), DIMENSION(1:npoints), INTENT(in) :: norm_drho, rho_1_3, rho
253 REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
254
255 INTEGER :: ii
256 REAL(kind=dp) :: cf, epsilon_rho13, my_ndrho, my_rho, my_rho_1_3, t1, t102, t103, t105, &
257 t106, t11, t112, t123, t124, t127, t128, t13, t133, t134, t14, t161, t165, t166, t173, &
258 t176, t184, t185, t189, t192, t193, t196, t199, t2, t200, t201, t202, t203, t215, t22, &
259 t227, t228, t231, t245, t246, t248, t26, t265, t278, t279, t3, t332, t37, t38, t39, t4, &
260 t40, t41, t44, t45, t48, t5, t52, t6, t61, t62, t69, t7, t70, t77, t78, t80, t87, t88, &
261 t89, t93, t94, t95, t98, t99
262
263 epsilon_rho13 = epsilon_rho**(1.0_dp/3.0_dp)
264 cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
265 SELECT CASE (grad_deriv)
266 CASE (1)
267!$OMP DO
268 DO ii = 1, npoints
269 my_rho = rho(ii)
270 IF (my_rho > epsilon_rho) THEN
271 my_rho_1_3 = rho_1_3(ii)
272 my_ndrho = norm_drho(ii)
273 t1 = my_rho_1_3**2
274 t2 = t1*my_rho
275 t3 = 0.1e1_dp/t2
276 t4 = a*t3
277 t5 = my_rho**2
278 t6 = t5*my_rho
279 t7 = my_rho_1_3*t6
280 t11 = 0.1e1_dp/my_rho_1_3
281 t13 = exp(-c*t11)
282 t14 = b*t13
283 t22 = my_ndrho**2
284 t26 = my_rho_1_3*t22
285 t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
286 t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
287 & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
288 &*t26*c + 0.7e1_dp*t14*t22*c*d
289 t38 = my_rho_1_3 + d
290 t39 = t38**2
291 t40 = 0.1e1_dp/t39
292 t41 = t37*t40
293
294 e_0(ii) = e_0(ii) &
295 + (t4*t41/0.72e2_dp)*sc
296 t44 = 0.1e1_dp/t1/t5
297 t45 = a*t44
298 t48 = my_rho_1_3*t5
299 t52 = b*c
300 t61 = t13*cf
301 t62 = t61*d
302 t69 = 0.1e1_dp/t1
303 t70 = t69*t13
304 t77 = 0.1e1_dp/my_rho
305 t78 = t52*t77
306 t80 = t13*t22*d
307 t87 = c**2
308 t88 = b*t87
309 t89 = t77*t13
310 t93 = my_rho_1_3*my_rho
311 t94 = 0.1e1_dp/t93
312 t95 = t88*t94
313 t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
314 & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
315 0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
316 &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
317 t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
318 0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
319 0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
320 t80
321 t99 = t98*t40
322 t102 = 0.1e1_dp/t48
323 t103 = a*t102
324 t105 = 0.1e1_dp/t39/t38
325 t106 = t37*t105
326
327 e_rho(ii) = e_rho(ii) &
328 - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
329 & + t103*t106/0.108e3_dp)*sc
330
331 t112 = my_rho_1_3*my_ndrho
332 t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
333 &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
334 my_ndrho*c*d
335 t124 = t123*t40
336
337 e_ndrho(ii) = e_ndrho(ii) &
338 + (t4*t124/0.72e2_dp)*sc
339 END IF
340 END DO
341!$OMP END DO
342 CASE default
343!$OMP DO
344 DO ii = 1, npoints
345 my_rho = rho(ii)
346 IF (my_rho > epsilon_rho) THEN
347 my_rho_1_3 = rho_1_3(ii)
348 my_ndrho = norm_drho(ii)
349 t1 = my_rho_1_3**2
350 t2 = t1*my_rho
351 t3 = 0.1e1_dp/t2
352 t4 = a*t3
353 t5 = my_rho**2
354 t6 = t5*my_rho
355 t7 = my_rho_1_3*t6
356 t11 = 0.1e1_dp/my_rho_1_3
357 t13 = exp(-c*t11)
358 t14 = b*t13
359 t22 = my_ndrho**2
360 t26 = my_rho_1_3*t22
361 t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
362 t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
363 & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
364 &*t26*c + 0.7e1_dp*t14*t22*c*d
365 t38 = my_rho_1_3 + d
366 t39 = t38**2
367 t40 = 0.1e1_dp/t39
368 t41 = t37*t40
369
370 e_0(ii) = e_0(ii) &
371 + (t4*t41/0.72e2_dp)*sc
372
373 IF (grad_deriv > 0) THEN
374 t44 = 0.1e1_dp/t1/t5
375 t45 = a*t44
376 t48 = my_rho_1_3*t5
377 t52 = b*c
378 t61 = t13*cf
379 t62 = t61*d
380 t69 = 0.1e1_dp/t1
381 t70 = t69*t13
382 t77 = 0.1e1_dp/my_rho
383 t78 = t52*t77
384 t80 = t13*t22*d
385 t87 = c**2
386 t88 = b*t87
387 t89 = t77*t13
388 t93 = my_rho_1_3*my_rho
389 t94 = 0.1e1_dp/t93
390 t95 = t88*t94
391 t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
392 & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
393 0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
394 &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
395 t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
396 0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
397 0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
398 t80
399 t99 = t98*t40
400 t102 = 0.1e1_dp/t48
401 t103 = a*t102
402 t105 = 0.1e1_dp/t39/t38
403 t106 = t37*t105
404 t112 = my_rho_1_3*my_ndrho
405 t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
406 &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
407 my_ndrho*c*d
408 t124 = t123*t40
409
410 e_rho(ii) = e_rho(ii) &
411 - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
412 & + t103*t106/0.108e3_dp)*sc
413 e_ndrho(ii) = e_ndrho(ii) &
414 + (t4*t124/0.72e2_dp)*sc
415
416 IF (grad_deriv > 1) THEN
417 t127 = 0.1e1_dp/t1/t6
418 t128 = a*t127
419 t133 = 0.1e1_dp/t7
420 t134 = a*t133
421 t161 = t3*t13
422 t165 = 0.1e1_dp/t5
423 t166 = t165*t13
424 t173 = t52*t165
425 t176 = t88*t102
426 t184 = b*t87*c
427 t185 = t102*t13
428 t189 = t184*t44
429 t192 = -0.560e3_dp*t93 - 0.432e3_dp*my_rho*d - 0.128e3_dp&
430 & *t52*my_rho*t13*cf - 0.8e1_dp*t88*t1*t13* &
431 cf - 0.560e3_dp*t14*t93*cf - 0.112e3_dp*t52*t1&
432 & *t62 - 0.8e1_dp*t88*my_rho_1_3*t62 - 0.432e3_dp* &
433 t14*my_rho*cf*d - 0.14e2_dp/0.9e1_dp*t52* &
434 t161*t22 - 0.11e2_dp/0.9e1_dp*t88*t166*t22 - &
435 0.2e1_dp/0.3e1_dp*t14*t94*t22 - 0.20e2_dp/ &
436 0.9e1_dp*t173*t80 - 0.2e1_dp*t176*t80 - &
437 0.20e2_dp/0.9e1_dp*t14*t3*t22*d + 0.7e1_dp/ &
438 0.9e1_dp*t184*t185*t22 + 0.7e1_dp/0.9e1_dp* &
439 t189*t80
440 t193 = t192*t40
441 t196 = t98*t105
442 t199 = 0.1e1_dp/t6
443 t200 = a*t199
444 t201 = t39**2
445 t202 = 0.1e1_dp/t201
446 t203 = t37*t202
447 t215 = t13*my_ndrho*d
448 t227 = 0.20e2_dp/0.3e1_dp*t52*t70*my_ndrho + 0.4e1_dp* &
449 t14*t11*my_ndrho + 0.20e2_dp/0.3e1_dp*t78*t215&
450 & + 0.20e2_dp/0.3e1_dp*t14*t69*my_ndrho*d + &
451 0.14e2_dp/0.3e1_dp*t88*t89*my_ndrho + 0.14e2_dp &
452 &/0.3e1_dp*t95*t215
453 t228 = t227*t40
454 t231 = t123*t105
455 t245 = 0.6e1_dp*t14*t1 + 0.20e2_dp*t14*my_rho_1_3*d + &
456 0.14e2_dp*t14*my_rho_1_3*c + 0.14e2_dp*t14*c* &
457 d
458 t246 = t245*t40
459
460 e_rho_rho(ii) = e_rho_rho(ii) &
461 + (0.5e1_dp/0.81e2_dp*t128*t41 - 0.5e1_dp/0.108e3_dp&
462 & *t45*t99 + t134*t106/0.27e2_dp + t4*t193/ &
463 0.72e2_dp - t103*t196/0.54e2_dp + t200*t203/ &
464 0.108e3_dp)*sc
465 e_ndrho_rho(ii) = e_ndrho_rho(ii) &
466 - (0.5e1_dp/0.216e3_dp*t45*t124 - t4*t228/ &
467 0.72e2_dp + t103*t231/0.108e3_dp)*sc
468 e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii) &
469 + (t4*t246/0.72e2_dp)*sc
470
471 IF (grad_deriv > 2) THEN
472 t248 = t5**2
473 t265 = 0.1e1_dp/t248
474 t278 = t87**2
475 t279 = b*t278
476 t332 = -0.432e3_dp*d - 0.2240e4_dp/0.3e1_dp*my_rho_1_3 - &
477 0.74e2_dp/0.27e2_dp*t184*t127*t80 + 0.100e3_dp/ &
478 0.27e2_dp*t14*t44*t22*d + 0.7e1_dp/0.27e2_dp* &
479 t279*t127*t13*t22 - 0.8e1_dp/0.3e1_dp*t184* &
480 t70*cf - 0.2240e4_dp/0.3e1_dp*t14*my_rho_1_3* &
481 cf - 0.48e2_dp*t88*t11*t13*cf - 0.944e3_dp/ &
482 0.3e1_dp*t52*t61 - 0.40e2_dp*t88*t69*t62 - &
483 0.656e3_dp/0.3e1_dp*t52*t11*t62 + 0.7e1_dp/ &
484 0.27e2_dp*t279*t265*t80 + 0.64e2_dp/0.27e2_dp* &
485 t52*t44*t13*t22 - 0.8e1_dp/0.3e1_dp*t184*t77&
486 & *t62 - 0.432e3_dp*t14*cf*d + 0.52e2_dp/ &
487 0.27e2_dp*t88*t199*t13*t22 - 0.20e2_dp/ &
488 0.9e1_dp*t184*t133*t13*t22 + 0.8e1_dp/0.9e1_dp&
489 & *t14*t102*t22 + 0.100e3_dp/0.27e2_dp*t52*t199&
490 & *t80 + 0.106e3_dp/0.27e2_dp*t88*t133*t80
491
492 e_rho_rho_rho(ii) = e_rho_rho_rho(ii) &
493 - (0.55e2_dp/0.243e3_dp*a/t1/t248*t41 - 0.5e1_dp &
494 &/0.27e2_dp*t128*t99 + 0.40e2_dp/0.243e3_dp*a/ &
495 my_rho_1_3/t248*t106 + 0.5e1_dp/0.72e2_dp*t45* &
496 t193 - t134*t196/0.9e1_dp + 0.7e1_dp/0.108e3_dp* &
497 a*t265*t203 - t4*t332*t40/0.72e2_dp + t103* &
498 t192*t105/0.36e2_dp - t200*t98*t202/0.36e2_dp &
499 &+ t128*t37/t201/t38/0.81e2_dp)*sc
500 e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii) &
501 + (0.5e1_dp/0.81e2_dp*t128*t124 - 0.5e1_dp/ &
502 0.108e3_dp*t45*t228 + t134*t231/0.27e2_dp + t4*&
503 & (-0.28e2_dp/0.9e1_dp*t52*t161*my_ndrho - &
504 0.22e2_dp/0.9e1_dp*t88*t166*my_ndrho - 0.4e1_dp &
505 &/0.3e1_dp*t14*t94*my_ndrho - 0.40e2_dp/0.9e1_dp &
506 &*t173*t215 - 0.4e1_dp*t176*t215 - 0.40e2_dp/ &
507 0.9e1_dp*t14*t3*my_ndrho*d + 0.14e2_dp/ &
508 0.9e1_dp*t184*t185*my_ndrho + 0.14e2_dp/0.9e1_dp&
509 & *t189*t215)*t40/0.72e2_dp - t103*t227*t105/ &
510 0.54e2_dp + t200*t123*t202/0.108e3_dp)*sc
511 e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii) &
512 - (0.5e1_dp/0.216e3_dp*t45*t246 - t4*(0.20e2_dp/ &
513 0.3e1_dp*t52*t70 + 0.4e1_dp*t14*t11 + 0.20e2_dp &
514 &/0.3e1_dp*t52*t89*d + 0.20e2_dp/0.3e1_dp*t14* &
515 t69*d + 0.14e2_dp/0.3e1_dp*t88*t89 + 0.14e2_dp/ &
516 0.3e1_dp*t88*t94*t13*d)*t40/0.72e2_dp + t103&
517 & *t245*t105/0.108e3_dp)*sc
518 END IF
519 END IF
520 END IF
521 END IF
522 END DO
523
524!$OMP END DO
525
526 END SELECT
527 END SUBROUTINE lyp_lda_calc
528
529! **************************************************************************************************
530!> \brief evaluates the becke 88 exchange functional for lsd
531!> \param rho_set ...
532!> \param deriv_set ...
533!> \param grad_deriv ...
534!> \param lyp_params input parameter (scaling)
535!> \par History
536!> 11.2003 created [fawzi]
537!> 01.2007 added scaling [Manuel Guidon]
538!> \author fawzi
539! **************************************************************************************************
540 SUBROUTINE lyp_lsd_eval(rho_set, deriv_set, grad_deriv, lyp_params)
541 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
542 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
543 INTEGER, INTENT(in) :: grad_deriv
544 TYPE(section_vals_type), POINTER :: lyp_params
545
546 CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lsd_eval'
547
548 INTEGER :: handle, npoints
549 INTEGER, DIMENSION(2, 3) :: bo
550 REAL(kind=dp) :: epsilon_drho, epsilon_rho, sc
551 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndr, e_ndr_ndr, &
552 e_ndr_ra, e_ndr_rb, e_ndra, e_ndra_ndra, e_ndra_ra, e_ndra_rb, e_ndrb, e_ndrb_ndrb, &
553 e_ndrb_ra, e_ndrb_rb, e_ra, e_ra_ra, e_ra_rb, e_rb, e_rb_rb, norm_drho, norm_drhoa, &
554 norm_drhob, rhoa, rhob
555 TYPE(xc_derivative_type), POINTER :: deriv
556
557 CALL timeset(routinen, handle)
558 NULLIFY (deriv)
559
560 CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
561 CALL cite_reference(lee1988)
562
563 CALL xc_rho_set_get(rho_set, &
564 rhoa=rhoa, rhob=rhob, norm_drhoa=norm_drhoa, &
565 norm_drhob=norm_drhob, norm_drho=norm_drho, &
566 rho_cutoff=epsilon_rho, &
567 drho_cutoff=epsilon_drho, local_bounds=bo)
568 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
569
570 dummy => rhoa
571 e_0 => dummy
572 e_ra => dummy
573 e_rb => dummy
574 e_ndra_ra => dummy
575 e_ndra_rb => dummy
576 e_ndrb_ra => dummy
577 e_ndrb_rb => dummy
578 e_ndr_ndr => dummy
579 e_ndra_ndra => dummy
580 e_ndrb_ndrb => dummy
581 e_ndr => dummy
582 e_ndra => dummy
583 e_ndrb => dummy
584 e_ra_ra => dummy
585 e_ra_rb => dummy
586 e_rb_rb => dummy
587 e_ndr_ra => dummy
588 e_ndr_rb => dummy
589
590 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
591 allocate_deriv=.true.)
592 CALL xc_derivative_get(deriv, deriv_data=e_0)
593 IF (grad_deriv >= 1) THEN
594 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
595 allocate_deriv=.true.)
596 CALL xc_derivative_get(deriv, deriv_data=e_ra)
597 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
598 allocate_deriv=.true.)
599 CALL xc_derivative_get(deriv, deriv_data=e_rb)
600 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
601 allocate_deriv=.true.)
602 CALL xc_derivative_get(deriv, deriv_data=e_ndr)
603 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
604 allocate_deriv=.true.)
605 CALL xc_derivative_get(deriv, deriv_data=e_ndra)
606 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
607 allocate_deriv=.true.)
608 CALL xc_derivative_get(deriv, deriv_data=e_ndrb)
609 END IF
610 IF (grad_deriv >= 2) THEN
611 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhoa], &
612 allocate_deriv=.true.)
613 CALL xc_derivative_get(deriv, deriv_data=e_ra_ra)
614 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhob], &
615 allocate_deriv=.true.)
616 CALL xc_derivative_get(deriv, deriv_data=e_ra_rb)
617 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob, deriv_rhob], &
618 allocate_deriv=.true.)
619 CALL xc_derivative_get(deriv, deriv_data=e_rb_rb)
620 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhoa], &
621 allocate_deriv=.true.)
622 CALL xc_derivative_get(deriv, deriv_data=e_ndr_ra)
623 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhob], &
624 allocate_deriv=.true.)
625 CALL xc_derivative_get(deriv, deriv_data=e_ndr_rb)
626 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhoa], &
627 allocate_deriv=.true.)
628 CALL xc_derivative_get(deriv, deriv_data=e_ndra_ra)
629 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhob], &
630 allocate_deriv=.true.)
631 CALL xc_derivative_get(deriv, deriv_data=e_ndra_rb)
632 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob, deriv_rhob], &
633 allocate_deriv=.true.)
634 CALL xc_derivative_get(deriv, deriv_data=e_ndrb_rb)
635 deriv => xc_dset_get_derivative(deriv_set, &
636 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
637 CALL xc_derivative_get(deriv, deriv_data=e_ndr_ndr)
638 deriv => xc_dset_get_derivative(deriv_set, &
639 [deriv_norm_drhoa, deriv_norm_drhoa], allocate_deriv=.true.)
640 CALL xc_derivative_get(deriv, deriv_data=e_ndra_ndra)
641 deriv => xc_dset_get_derivative(deriv_set, &
642 [deriv_norm_drhob, deriv_norm_drhob], allocate_deriv=.true.)
643 CALL xc_derivative_get(deriv, deriv_data=e_ndrb_ndrb)
644 END IF
645
646!$OMP PARALLEL DEFAULT(NONE) &
647!$OMP SHARED(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob) &
648!$OMP SHARED(e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra) &
649!$OMP SHARED(e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb) &
650!$OMP SHARED(e_ndr, e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb) &
651!$OMP SHARED(e_ndr_ra, e_ndr_rb, grad_deriv) &
652!$OMP SHARED(npoints, epsilon_rho, sc)
653
654 CALL lyp_lsd_calc( &
655 rhoa=rhoa, rhob=rhob, norm_drho=norm_drho, norm_drhoa=norm_drhoa, &
656 norm_drhob=norm_drhob, e_0=e_0, e_ra=e_ra, e_rb=e_rb, &
657 e_ndra_ra=e_ndra_ra, e_ndra_rb=e_ndra_rb, e_ndrb_ra&
658 &=e_ndrb_ra, e_ndrb_rb=e_ndrb_rb, e_ndr_ndr=e_ndr_ndr, &
659 e_ndra_ndra=e_ndra_ndra, e_ndrb_ndrb=e_ndrb_ndrb, e_ndr=e_ndr, &
660 e_ndra=e_ndra, e_ndrb=e_ndrb, e_ra_ra=e_ra_ra, &
661 e_ra_rb=e_ra_rb, e_rb_rb=e_rb_rb, e_ndr_ra=e_ndr_ra, &
662 e_ndr_rb=e_ndr_rb, &
663 grad_deriv=grad_deriv, npoints=npoints, &
664 epsilon_rho=epsilon_rho, sc=sc)
665
666!$OMP END PARALLEL
667
668 CALL timestop(handle)
669 END SUBROUTINE lyp_lsd_eval
670
671! **************************************************************************************************
672!> \brief low level calculation of the becke 88 exchange functional for lsd
673!> \param rhoa alpha spin density
674!> \param rhob beta spin density
675!> \param norm_drho || grad rhoa + grad rhob ||
676!> \param norm_drhoa || grad rhoa ||
677!> \param norm_drhob || grad rhob ||
678!> \param e_0 adds to it the local value of the functional
679!> \param e_ra e_*: derivative of the functional wrt. to the variables
680!> named where the * is.
681!> \param e_rb ...
682!> \param e_ndra_ra ...
683!> \param e_ndra_rb ...
684!> \param e_ndrb_ra ...
685!> \param e_ndrb_rb ...
686!> \param e_ndr_ndr ...
687!> \param e_ndra_ndra ...
688!> \param e_ndrb_ndrb ...
689!> \param e_ndr ...
690!> \param e_ndra ...
691!> \param e_ndrb ...
692!> \param e_ra_ra ...
693!> \param e_ra_rb ...
694!> \param e_rb_rb ...
695!> \param e_ndr_ra ...
696!> \param e_ndr_rb ...
697!> \param grad_deriv ...
698!> \param npoints ...
699!> \param epsilon_rho ...
700!> \param sc scaling parameter for correlation
701!> \par History
702!> 01.2004 created [fawzi]
703!> \author fawzi
704! **************************************************************************************************
705 SUBROUTINE lyp_lsd_calc(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob, &
706 e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, &
707 e_ndra_ndra, e_ndrb_ndrb, e_ndr, &
708 e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb, &
709 grad_deriv, npoints, epsilon_rho, sc)
710 REAL(kind=dp), DIMENSION(*), INTENT(in) :: rhoa, rhob, norm_drho, norm_drhoa, &
711 norm_drhob
712 REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, &
713 e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb, e_ndr, e_ndra, e_ndrb, &
714 e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb
715 INTEGER, INTENT(in) :: grad_deriv, npoints
716 REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
717
718 INTEGER :: ii
719 REAL(kind=dp) :: cf, my_ndrho, my_ndrhoa, my_ndrhob, my_rho, my_rhoa, my_rhob, t1, t100, &
720 t101, t102, t103, t104, t107, t108, t109, t112, t115, t118, t12, t120, t124, t129, t13, &
721 t130, t132, t135, t138, t14, t140, t142, t145, t15, t153, t155, t159, t16, t164, t168, &
722 t17, t171, t176, t18, t181, t182, t185, t189, t194, t195, t198, t2, t20, t202, t205, &
723 t206, t21, t210, t214, t215, t218, t22, t222, t228, t23, t232, t236, t238, t24, t243, &
724 t249, t25, t252, t253, t255, t257, t26, t260, t265, t268, t27, t270, t29, t3, t30, t304, &
725 t31, t310, t313, t316, t319, t322, t326, t329, t332, t334, t341, t35
726 REAL(kind=dp) :: t354, t356, t360, t363, t37, t373, t376, t381, t39, t391, t4, t40, t408, &
727 t41, t415, t419, t422, t430, t44, t445, t449, t45, t452, t46, t467, t47, t48, t483, t487, &
728 t49, t490, t5, t50, t505, t515, t519, t52, t520, t54, t56, t57, t6, t61, t62, t64, t66, &
729 t7, t72, t75, t78, t8, t82, t85, t86, t87, t88, t90, t92, t94, t95, t98, t99
730
731 cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
732
733!$OMP DO
734
735 DO ii = 1, npoints
736 my_rhoa = max(rhoa(ii), 0.0_dp)
737 my_rhob = max(rhob(ii), 0.0_dp)
738 my_rho = my_rhoa + my_rhob
739 IF (my_rho > epsilon_rho) THEN
740 my_ndrho = norm_drho(ii)
741 my_ndrhoa = norm_drhoa(ii)
742 my_ndrhob = norm_drhob(ii)
743
744 t1 = my_rho**(0.1e1_dp/0.3e1_dp)
745 t2 = 0.1e1_dp/t1
746 t3 = d*t2
747 t4 = 0.1e1_dp + t3
748 t5 = 0.1e1_dp/t4
749 t6 = a*t5
750 t7 = my_rhoa*my_rhob
751 t8 = 0.1e1_dp/my_rho
752 t12 = a*b
753 t13 = c*t2
754 t14 = exp(-t13)
755 t15 = t12*t14
756 t16 = my_rho**2
757 t17 = t16*my_rho
758 t18 = t1**2
759 t20 = 0.1e1_dp/t18/t17
760 t21 = t5*t20
761 t22 = 2**(0.1e1_dp/0.3e1_dp)
762 t23 = t22**2
763 t24 = t23*cf
764 t25 = my_rhoa**2
765 t26 = my_rhoa**(0.1e1_dp/0.3e1_dp)
766 t27 = t26**2
767 t29 = my_rhob**2
768 t30 = my_rhob**(0.1e1_dp/0.3e1_dp)
769 t31 = t30**2
770 t35 = 0.8e1_dp*t24*(t27*t25 + t31*t29)
771 t37 = t3*t5
772 t39 = 0.47e2_dp/0.18e2_dp - 0.7e1_dp/0.18e2_dp*t13 - &
773 0.7e1_dp/0.18e2_dp*t37
774 t40 = my_ndrho**2
775 t41 = t39*t40
776 t44 = 0.5e1_dp/0.2e1_dp - t13/0.18e2_dp - t37/0.18e2_dp
777 t45 = my_ndrhoa**2
778 t46 = my_ndrhob**2
779 t47 = t45 + t46
780 t48 = t44*t47
781 t49 = t13 + t37 - 0.11e2_dp
782 t50 = my_rhoa*t8
783 t52 = my_rhob*t8
784 t54 = t50*t45 + t52*t46
785 t56 = t49*t54/0.9e1_dp
786 t57 = t35 + t41 - t48 - t56
787 t61 = 0.2e1_dp/0.3e1_dp*t16
788 t62 = t61 - t25
789 t64 = t61 - t29
790 t66 = t7*t57 - 0.2e1_dp/0.3e1_dp*t16*t40 + t62*t46 + &
791 t64*t45
792
793 IF (my_rho > epsilon_rho) THEN
794 e_0(ii) = e_0(ii) &
795 - (0.4e1_dp*t6*t7*t8 + t15*t21*t66)*sc
796 END IF
797 !--------
798
799 IF (grad_deriv /= 0) THEN
800 t72 = t27*my_rhoa
801 t75 = t49*t8
802 t78 = 0.64e2_dp/0.3e1_dp*t24*t72 - t75*t45/0.9e1_dp
803 t82 = my_rhob*t57 + t7*t78 - 0.2e1_dp*my_rhoa*t46
804 t85 = t4**2
805 t86 = 0.1e1_dp/t85
806 t87 = a*t86
807 t88 = t87*my_rhoa
808 t90 = 0.1e1_dp/t1/t16
809 t92 = my_rhob*t90*d
810 t94 = 0.4e1_dp/0.3e1_dp*t88*t92
811 t95 = 0.1e1_dp/t16
812 t98 = 0.4e1_dp*t6*t7*t95
813 t99 = t12*c
814 t100 = t16**2
815 t101 = t100*my_rho
816 t102 = 0.1e1_dp/t101
817 t103 = t102*t14
818 t104 = t5*t66
819 t107 = t99*t103*t104/0.3e1_dp
820 t108 = t86*t102
821 t109 = t66*d
822 t112 = t15*t108*t109/0.3e1_dp
823 t115 = t5/t18/t100
824 t118 = 0.11e2_dp/0.3e1_dp*t15*t115*t66
825 t120 = 0.1e1_dp/t1/my_rho
826 t124 = d**2
827 t129 = c*t120 + d*t120*t5 - t124/t18/my_rho*t86
828 t130 = 0.7e1_dp/0.54e2_dp*t129
829 t132 = t129/0.54e2_dp
830 t135 = -t129/0.3e1_dp
831 t138 = my_rhoa*t95
832 t140 = my_rhob*t95
833 t142 = -t138*t45 - t140*t46
834 t145 = t130*t40 - t132*t47 - t135*t54/0.9e1_dp - t49* &
835 t142/0.9e1_dp
836 t153 = t7*t145 - 0.4e1_dp/0.3e1_dp*my_rho*t40 + &
837 0.4e1_dp/0.3e1_dp*my_rho*t46 + 0.4e1_dp/0.3e1_dp&
838 & *my_rho*t45
839 t155 = t15*t21*t153
840
841 e_ra(ii) = e_ra(ii) &
842 - (0.4e1_dp*t6*t52 + t15*t21*t82 + t94 - t98 + &
843 t107 + t112 - t118 + t155)*sc
844
845 t159 = t31*my_rhob
846 t164 = 0.64e2_dp/0.3e1_dp*t24*t159 - t75*t46/0.9e1_dp
847 t168 = my_rhoa*t57 + t7*t164 - 0.2e1_dp*my_rhob*t45
848
849 e_rb(ii) = e_rb(ii) &
850 - (0.4e1_dp*t6*t50 + t15*t21*t168 + t94 - t98 + &
851 t107 + t112 - t118 + t155)*sc
852
853 t171 = t39*my_ndrho
854 t176 = 0.2e1_dp*t7*t171 - 0.4e1_dp/0.3e1_dp*t16*my_ndrho
855
856 e_ndr(ii) = e_ndr(ii) &
857 - (t15*t21*t176)*sc
858
859 t181 = t49*my_rhoa
860 t182 = t8*my_ndrhoa
861 t185 = -0.2e1_dp*t44*my_ndrhoa - 0.2e1_dp/0.9e1_dp*t181*t182
862 t189 = t7*t185 + 0.2e1_dp*t64*my_ndrhoa
863
864 e_ndra(ii) = e_ndra(ii) &
865 - (t15*t21*t189)*sc
866
867 t194 = t49*my_rhob
868 t195 = t8*my_ndrhob
869 t198 = -0.2e1_dp*t44*my_ndrhob - 0.2e1_dp/0.9e1_dp*t194*t195
870 t202 = t7*t198 + 0.2e1_dp*t62*my_ndrhob
871
872 e_ndrb(ii) = e_ndrb(ii) &
873 - (t15*t21*t202)*sc
874
875 IF (grad_deriv > 1) THEN
876 t205 = t100*t16
877 t206 = 0.1e1_dp/t205
878 t210 = 0.26e2_dp/0.9e1_dp*t99*t206*t14*t104
879 t214 = 0.2e1_dp/0.3e1_dp*t99*t103*t5*t153
880 t215 = c**2
881 t218 = 0.1e1_dp/t1/t205
882 t222 = t12*t215*t218*t14*t104/0.9e1_dp
883 t228 = 0.2e1_dp/0.9e1_dp*t12*c*t218*t14*t86*t109
884 t232 = 0.26e2_dp/0.9e1_dp*t15*t86*t206*t109
885 t236 = 0.2e1_dp/0.3e1_dp*t15*t108*t153*d
886 t238 = 0.1e1_dp/t85/t4
887 t243 = 0.2e1_dp/0.9e1_dp*t15*t238*t218*t66*t124
888 t249 = 0.154e3_dp/0.9e1_dp*t15*t5/t18/t101*t66
889 t252 = 0.22e2_dp/0.3e1_dp*t15*t115*t153
890 t253 = t6*t140
891 t255 = t87*t92
892 t257 = c*t90
893 t260 = d*t90*t5
894 t265 = t124/t18/t16*t86
895 t268 = 0.1e1_dp/t17
896 t270 = t124*d*t268*t238
897 t304 = t15*t21*(t7*((-0.14e2_dp/0.81e2_dp*t257 - &
898 0.14e2_dp/0.81e2_dp*t260 + 0.7e1_dp/0.27e2_dp* &
899 t265 - 0.7e1_dp/0.81e2_dp*t270)*t40 - (-0.2e1_dp/ &
900 0.81e2_dp*t257 - 0.2e1_dp/0.81e2_dp*t260 + t265/ &
901 0.27e2_dp - t270/0.81e2_dp)*t47 - (0.4e1_dp/ &
902 0.9e1_dp*t257 + 0.4e1_dp/0.9e1_dp*t260 - 0.2e1_dp &
903 &/0.3e1_dp*t265 + 0.2e1_dp/0.9e1_dp*t270)*t54/ &
904 0.9e1_dp - 0.2e1_dp/0.9e1_dp*t135*t142 - t49*&
905 & (0.2e1_dp*my_rhoa*t268*t45 + 0.2e1_dp*my_rhob* &
906 t268*t46)/0.9e1_dp) - 0.4e1_dp/0.3e1_dp*t40 + &
907 0.4e1_dp/0.3e1_dp*t46 + 0.4e1_dp/0.3e1_dp*t45)
908 t310 = 0.40e2_dp/0.9e1_dp*t88*my_rhob/t1/t17*d
909 t313 = my_rhob*t20
910 t316 = 0.8e1_dp/0.9e1_dp*a*t238*my_rhoa*t313*t124
911 t319 = 0.8e1_dp*t6*t7*t268
912 t322 = t99*t103*t5*t82
913 t326 = t15*t108*t82*d
914 t329 = t15*t115*t82
915 t332 = t135*t8
916 t334 = t49*t95
917 t341 = t15*t21*(my_rhob*t145 + t7*(-t332*t45/ &
918 0.9e1_dp + t334*t45/0.9e1_dp))
919
920 e_ra_ra(ii) = e_ra_ra(ii) &
921 + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
922 t252 + 0.8e1_dp*t253 - 0.8e1_dp/0.3e1_dp*t255 - &
923 t304 + t310 - t316 - t319 - 0.2e1_dp/0.3e1_dp*t322 - &
924 0.2e1_dp/0.3e1_dp*t326 + 0.22e2_dp/0.3e1_dp*t329&
925 & - 0.2e1_dp*t341 - t15*t21*(0.2e1_dp*my_rhob* &
926 t78 + 0.320e3_dp/0.9e1_dp*t72*my_rhob*t24 - &
927 0.2e1_dp*t46))*sc
928
929 t354 = t99*t103*t5*t168
930 t356 = t6*t138
931 t360 = t87*my_rhoa*t90*d
932 t363 = t15*t115*t168
933 t373 = t15*t21*(my_rhoa*t145 + t7*(-t332*t46/ &
934 0.9e1_dp + t334*t46/0.9e1_dp))
935 t376 = t15*t108*t168*d
936
937 e_rb_rb(ii) = e_rb_rb(ii) &
938 + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
939 t252 - t304 + t310 - t316 - t319 + 0.8e1_dp*t356 - &
940 0.8e1_dp/0.3e1_dp*t360 + 0.22e2_dp/0.3e1_dp* &
941 t363 - 0.2e1_dp*t373 - 0.2e1_dp/0.3e1_dp*t354 - &
942 0.2e1_dp/0.3e1_dp*t376 - t15*t21*(0.2e1_dp* &
943 my_rhoa*t164 + 0.320e3_dp/0.9e1_dp*my_rhoa* &
944 t159*t24 - 0.2e1_dp*t45))*sc
945
946 t381 = -t354/0.3e1_dp + 0.4e1_dp*t356 - 0.4e1_dp/0.3e1_dp&
947 & *t360 + 0.11e2_dp/0.3e1_dp*t363 - t373 - t341 - &
948 t376/0.3e1_dp + t310 - 0.4e1_dp*t6*t8 + 0.4e1_dp* &
949 t253 + t210 - t214 - t222
950 t391 = -t228 + t232 - t236 - t243 - t249 + t252 - 0.4e1_dp/ &
951 0.3e1_dp*t255 - t304 - t316 - t319 - t322/0.3e1_dp - &
952 t326/0.3e1_dp + 0.11e2_dp/0.3e1_dp*t329 - t15* &
953 t21*(t35 + t41 - t48 - t56 + my_rhob*t164 + my_rhoa &
954 &*t78)
955
956 e_ra_rb(ii) = e_ra_rb(ii) &
957 + (t381 + t391)*sc
958
959 t408 = t12*t14*t5
960 t415 = t99*t103*t5*t176/0.3e1_dp
961 t419 = t15*t108*t176*d/0.3e1_dp
962 t422 = 0.11e2_dp/0.3e1_dp*t15*t115*t176
963 t430 = t15*t21*(0.2e1_dp*t7*t130*my_ndrho - 0.8e1_dp &
964 &/0.3e1_dp*my_rho*my_ndrho)
965
966 e_ndr_ra(ii) = e_ndr_ra(ii) &
967 - (0.2e1_dp*t408*t313*t171 + t415 + t419 - t422 + &
968 t430)*sc
969 e_ndr_rb(ii) = e_ndr_rb(ii) &
970 - (0.2e1_dp*t408*t20*my_rhoa*t171 + t415 + t419 - &
971 t422 + t430)*sc
972
973 t445 = t99*t103*t5*t189/0.3e1_dp
974 t449 = t15*t108*t189*d/0.3e1_dp
975 t452 = 0.11e2_dp/0.3e1_dp*t15*t115*t189
976 t467 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhoa - &
977 0.2e1_dp/0.9e1_dp*t135*my_rhoa*t182 + 0.2e1_dp/ &
978 0.9e1_dp*t181*t95*my_ndrhoa) + 0.8e1_dp/0.3e1_dp&
979 & *my_rho*my_ndrhoa)
980
981 e_ndra_ra(ii) = e_ndra_ra(ii) &
982 - (t15*t21*(my_rhob*t185 - 0.2e1_dp/0.9e1_dp*t7&
983 & *t75*my_ndrhoa) + t445 + t449 - t452 + t467)*sc
984 e_ndra_rb(ii) = e_ndra_rb(ii) &
985 - (t15*t21*(my_rhoa*t185 - 0.4e1_dp*my_rhob* &
986 my_ndrhoa) + t445 + t449 - t452 + t467)*sc
987
988 t483 = t99*t103*t5*t202/0.3e1_dp
989 t487 = t15*t108*t202*d/0.3e1_dp
990 t490 = 0.11e2_dp/0.3e1_dp*t15*t115*t202
991 t505 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhob - &
992 0.2e1_dp/0.9e1_dp*t135*my_rhob*t195 + 0.2e1_dp/ &
993 0.9e1_dp*t194*t95*my_ndrhob) + 0.8e1_dp/0.3e1_dp&
994 & *my_rho*my_ndrhob)
995
996 e_ndrb_ra(ii) = e_ndrb_ra(ii) &
997 - (t15*t21*(my_rhob*t198 - 0.4e1_dp*my_rhoa* &
998 my_ndrhob) + t483 + t487 - t490 + t505)*sc
999 e_ndrb_rb(ii) = e_ndrb_rb(ii) &
1000 - (t15*t21*(my_rhoa*t198 - 0.2e1_dp/0.9e1_dp*t7&
1001 & *t75*my_ndrhob) + t483 + t487 - t490 + t505)*sc
1002
1003 t515 = 0.4e1_dp/0.3e1_dp*t16
1004
1005 e_ndr_ndr(ii) = e_ndr_ndr(ii) &
1006 - (t15*t21*(0.2e1_dp*t7*t39 - t515))*sc
1007
1008 t519 = t13/0.9e1_dp
1009 t520 = t37/0.9e1_dp
1010
1011 e_ndra_ndra(ii) = e_ndra_ndra(ii) &
1012 - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1013 &/0.9e1_dp*t181*t8) + t515 - 0.2e1_dp*t29))*sc
1014
1015 e_ndrb_ndrb(ii) = e_ndrb_ndrb(ii) &
1016 - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1017 &/0.9e1_dp*t194*t8) + t515 - 0.2e1_dp*t25))*sc
1018 END IF
1019 END IF
1020 END IF
1021 END DO
1022!$OMP END DO
1023
1024 END SUBROUTINE lyp_lsd_calc
1025
1026END MODULE xc_lyp
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition bibliography.F:21
bibliography::lee1988
integer, save, public lee1988
Definition bibliography.F:36
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:1052
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:65
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:541
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:122
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:127
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:48
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