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xc_xbecke88_long_range.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 longrange part of Becke 88 exchange functional
10!> \par History
11!> 01.2008 created [mguidon]
12!> \author Manuel Guidon
13! **************************************************************************************************
14MODULE xc_xbecke88_long_range
15 USE bibliography, ONLY: becke1988,&
16 cite_reference
17 USE cp_array_utils, ONLY: cp_3d_r_cp_type
18 USE input_section_types, ONLY: section_vals_type,&
19 section_vals_val_get
20 USE kinds, ONLY: dp
21 USE mathconstants, ONLY: pi,&
22 rootpi
23 USE xc_derivative_desc, ONLY: deriv_norm_drho,&
24 deriv_norm_drhoa,&
25 deriv_norm_drhob,&
26 deriv_rho,&
27 deriv_rhoa,&
28 deriv_rhob
29 USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
30 xc_dset_get_derivative
31 USE xc_derivative_types, ONLY: xc_derivative_get,&
32 xc_derivative_type
33 USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
34 USE xc_rho_set_types, ONLY: xc_rho_set_get,&
35 xc_rho_set_type
36#include "../base/base_uses.f90"
37
38 IMPLICIT NONE
39 PRIVATE
40
41 LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .true.
42 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_xbecke88_long_range'
43 REAL(kind=dp), PARAMETER :: beta = 0.0042_dp
44
45 PUBLIC :: xb88_lr_lda_info, xb88_lr_lsd_info, xb88_lr_lda_eval, xb88_lr_lsd_eval
46CONTAINS
47
48! **************************************************************************************************
49!> \brief return various information on the functional
50!> \param reference string with the reference of the actual functional
51!> \param shortform string with the shortform of the functional name
52!> \param needs the components needed by this functional are set to
53!> true (does not set the unneeded components to false)
54!> \param max_deriv ...
55!> \par History
56!> 01.2008 created [mguidon]
57!> \author Manuel Guidon
58! **************************************************************************************************
59 SUBROUTINE xb88_lr_lda_info(reference, shortform, needs, max_deriv)
60 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
61 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
62 INTEGER, INTENT(out), OPTIONAL :: max_deriv
63
64 IF (PRESENT(reference)) THEN
65 reference = "A. Becke, Phys. Rev. A 38, 3098 (1988) {LDA version}"
66 END IF
67 IF (PRESENT(shortform)) THEN
68 shortform = "Becke 1988 Exchange Functional (LDA)"
69 END IF
70 IF (PRESENT(needs)) THEN
71 needs%rho = .true.
72 needs%norm_drho = .true.
73 END IF
74 IF (PRESENT(max_deriv)) max_deriv = 3
75
76 END SUBROUTINE xb88_lr_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!> 01.2008 created [mguidon]
87!> \author Manuel Guidon
88! **************************************************************************************************
89 SUBROUTINE xb88_lr_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 = "A. Becke, Phys. Rev. A 38, 3098 (1988) {LSD version}"
96 END IF
97 IF (PRESENT(shortform)) THEN
98 shortform = "Becke 1988 Exchange Functional (LSD)"
99 END IF
100 IF (PRESENT(needs)) THEN
101 needs%rho_spin = .true.
102 needs%rho_spin_1_3 = .true.
103 needs%norm_drho_spin = .true.
104 END IF
105 IF (PRESENT(max_deriv)) max_deriv = 3
106
107 END SUBROUTINE xb88_lr_lsd_info
108
109! **************************************************************************************************
110!> \brief evaluates the becke 88 longrange exchange 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 xb88_lr_params input parameters (scaling)
118!> \par History
119!> 01.2008 created [mguidon]
120!> \author Manuel Guidon
121! **************************************************************************************************
122 SUBROUTINE xb88_lr_lda_eval(rho_set, deriv_set, grad_deriv, xb88_lr_params)
123 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
124 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
125 INTEGER, INTENT(in) :: grad_deriv
126 TYPE(section_vals_type), POINTER :: xb88_lr_params
127
128 CHARACTER(len=*), PARAMETER :: routinen = 'xb88_lr_lda_eval'
129
130 INTEGER :: handle, npoints
131 INTEGER, DIMENSION(2, 3) :: bo
132 REAL(kind=dp) :: epsilon_rho, omega, sx
133 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndrho, &
134 e_ndrho_ndrho, e_ndrho_ndrho_ndrho, e_ndrho_ndrho_rho, e_ndrho_rho, e_ndrho_rho_rho, &
135 e_rho, e_rho_rho, e_rho_rho_rho, norm_drho, rho
136 TYPE(xc_derivative_type), POINTER :: deriv
137
138 CALL timeset(routinen, handle)
139
140 CALL section_vals_val_get(xb88_lr_params, "scale_x", r_val=sx)
141 CALL section_vals_val_get(xb88_lr_params, "omega", r_val=omega)
142
143 CALL cite_reference(becke1988)
144
145 CALL xc_rho_set_get(rho_set, rho=rho, &
146 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho)
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 ! meaningful default for the arrays we don't need: let us make compiler
150 ! and debugger happy...
151 dummy => rho
152
153 e_0 => dummy
154 e_rho => dummy
155 e_ndrho => dummy
156 e_rho_rho => dummy
157 e_ndrho_rho => dummy
158 e_ndrho_ndrho => dummy
159 e_rho_rho_rho => dummy
160 e_ndrho_rho_rho => dummy
161 e_ndrho_ndrho_rho => dummy
162 e_ndrho_ndrho_ndrho => dummy
163
164 IF (grad_deriv >= 0) THEN
165 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
166 allocate_deriv=.true.)
167 CALL xc_derivative_get(deriv, deriv_data=e_0)
168 END IF
169 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
170 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
171 allocate_deriv=.true.)
172 CALL xc_derivative_get(deriv, deriv_data=e_rho)
173 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
174 allocate_deriv=.true.)
175 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
176 END IF
177 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
178 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
179 allocate_deriv=.true.)
180 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
181 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rho], &
182 allocate_deriv=.true.)
183 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho)
184 deriv => xc_dset_get_derivative(deriv_set, &
185 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
186 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
187 END IF
188 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
189 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
190 allocate_deriv=.true.)
191 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
192 deriv => xc_dset_get_derivative(deriv_set, &
193 [deriv_norm_drho, deriv_rho, deriv_rho], allocate_deriv=.true.)
194 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho)
195 deriv => xc_dset_get_derivative(deriv_set, &
196 [deriv_norm_drho, deriv_norm_drho, deriv_rho], allocate_deriv=.true.)
197 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho)
198 deriv => xc_dset_get_derivative(deriv_set, &
199 [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
200 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)
201 END IF
202 IF (grad_deriv > 3 .OR. grad_deriv < -3) THEN
203 cpabort("derivatives bigger than 3 not implemented")
204 END IF
205
206!$OMP PARALLEL DEFAULT(NONE) &
207!$OMP SHARED(rho, norm_drho, e_0, e_rho, e_ndrho, e_rho_rho) &
208!$OMP SHARED(e_ndrho_rho, e_ndrho_ndrho, e_rho_rho_rho) &
209!$OMP SHARED(e_ndrho_rho_rho, e_ndrho_ndrho_rho) &
210!$OMP SHARED(e_ndrho_ndrho_ndrho, grad_deriv, npoints) &
211!$OMP SHARED(epsilon_rho, sx, omega)
212
213 CALL xb88_lr_lda_calc(rho=rho, norm_drho=norm_drho, &
214 e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_rho_rho=e_rho_rho, &
215 e_ndrho_rho=e_ndrho_rho, e_ndrho_ndrho=e_ndrho_ndrho, &
216 e_rho_rho_rho=e_rho_rho_rho, e_ndrho_rho_rho=e_ndrho_rho_rho, &
217 e_ndrho_ndrho_rho=e_ndrho_ndrho_rho, &
218 e_ndrho_ndrho_ndrho=e_ndrho_ndrho_ndrho, grad_deriv=grad_deriv, &
219 npoints=npoints, epsilon_rho=epsilon_rho, &
220 sx=sx, omega=omega)
221
222!$OMP END PARALLEL
223
224 CALL timestop(handle)
225 END SUBROUTINE xb88_lr_lda_eval
226
227! **************************************************************************************************
228!> \brief low level calculation of the becke 88 exchange functional for lda
229!> \param rho alpha or beta spin density
230!> \param norm_drho || grad rho ||
231!> \param e_0 adds to it the local value of the functional
232!> \param e_rho derivative of the functional wrt. to the variables
233!> named where the * is.
234!> \param e_ndrho ...
235!> \param e_rho_rho ...
236!> \param e_ndrho_rho ...
237!> \param e_ndrho_ndrho ...
238!> \param e_rho_rho_rho ...
239!> \param e_ndrho_rho_rho ...
240!> \param e_ndrho_ndrho_rho ...
241!> \param e_ndrho_ndrho_ndrho ...
242!> \param grad_deriv ...
243!> \param npoints ...
244!> \param epsilon_rho ...
245!> \param sx scaling-parameter for exchange
246!> \param omega parameter for erfc
247!> \par History
248!> 01.2008 created [mguidon]
249!> \author Manuel Guidon
250!> \note
251!> - Just took the lsd code and scaled rho and ndrho by 1/2 (e_0 with 2.0)
252!> - Derivatives higher than 1 not tested
253! **************************************************************************************************
254 SUBROUTINE xb88_lr_lda_calc(rho, norm_drho, &
255 e_0, e_rho, e_ndrho, e_rho_rho, e_ndrho_rho, &
256 e_ndrho_ndrho, e_rho_rho_rho, e_ndrho_rho_rho, e_ndrho_ndrho_rho, &
257 e_ndrho_ndrho_ndrho, grad_deriv, npoints, epsilon_rho, sx, &
258 omega)
259 INTEGER, INTENT(in) :: npoints, grad_deriv
260 REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: e_ndrho_ndrho_ndrho, &
261 e_ndrho_ndrho_rho, e_ndrho_rho_rho, e_rho_rho_rho, e_ndrho_ndrho, e_ndrho_rho, e_rho_rho, &
262 e_ndrho, e_rho, e_0
263 REAL(kind=dp), DIMENSION(1:npoints), INTENT(in) :: norm_drho, rho
264 REAL(kind=dp), INTENT(in) :: epsilon_rho, sx, omega
265
266 INTEGER :: ii
267 REAL(kind=dp) :: cx, epsilon_rho43, my_epsilon_rho, my_ndrho, my_rho, t1, t10, t100, t1002, &
268 t1009, t101, t1013, t103, t104, t1044, t105, t1069, t109, t1091, t11, t1102, t112, t113, &
269 t1136, t1141, t1146, t1153, t1156, t116, t1163, t1167, t117, t1177, t118, t12, t122, &
270 t1220, t126, t127, t128, t1284, t130, t132, t133, t1334, t1341, t1345, t135, t136, t137, &
271 t1370, t1396, t140, t1400, t1404, t1405, t141, t1412, t143, t1449, t1456, t146, t1467, &
272 t147, t1472, t148, t151, t155, t1553, t16, t168, t169, t17, t172, t173, t176, t177, t18, &
273 t185, t186, t190, t196, t2, t200, t207, t21, t211, t212, t213
274 REAL(kind=dp) :: t216, t219, t22, t221, t222, t225, t226, t23, t230, t231, t232, t233, t237, &
275 t24, t241, t244, t245, t250, t251, t254, t255, t258, t259, t26, t264, t265, t27, t270, &
276 t271, t28, t281, t284, t285, t289, t29, t293, t297, t3, t30, t304, t31, t311, t312, t313, &
277 t316, t319, t321, t323, t325, t326, t328, t330, t335, t339, t34, t343, t346, t347, t351, &
278 t354, t358, t36, t365, t368, t37, t372, t377, t38, t382, t383, t384, t39, t393, t397, &
279 t40, t400, t401, t404, t405, t408, t41, t412, t413, t417, t418, t42, t428, t429, t43, &
280 t435, t44, t451, t452, t455, t457, t46, t460, t462, t463, t464
281 REAL(kind=dp) :: t465, t466, t467, t47, t470, t473, t478, t479, t48, t482, t486, t489, t49, &
282 t492, t496, t5, t501, t502, t505, t508, t51, t513, t514, t519, t52, t521, t525, t526, &
283 t529, t530, t533, t534, t536, t537, t539, t55, t562, t566, t570, t571, t572, t573, t574, &
284 t575, t576, t580, t586, t59, t590, t6, t60, t601, t605, t606, t613, t624, t628, t632, &
285 t639, t64, t640, t641, t657, t667, t669, t677, t68, t687, t69, t7, t71, t716, t72, t722, &
286 t735, t739, t746, t75, t76, t769, t77, t79, t791, t793, t8, t838, t84, t842, t846, t85, &
287 t857, t86, t860, t867, t87, t880, t90, t91, t933, t94, t95, t961
288 REAL(kind=dp) :: t98, t99, xx
289
290 my_epsilon_rho = epsilon_rho
291 epsilon_rho43 = my_epsilon_rho**(4.0_dp/3.0_dp)
292 cx = 1.5_dp*(3.0_dp/4.0_dp/pi)**(1.0_dp/3.0_dp)
293
294!$OMP DO
295 DO ii = 1, npoints
296 !! scale densities with 0.5 because code comes from LSD
297 my_rho = rho(ii)*0.5_dp
298 my_ndrho = norm_drho(ii)*0.5_dp
299 IF (my_rho > my_epsilon_rho) THEN
300 IF (grad_deriv >= 0) THEN
301 t1 = my_rho**(0.1e1_dp/0.3e1_dp)
302 t2 = t1*my_rho
303 t3 = 0.1e1_dp/t2
304 xx = my_ndrho*max(t3, epsilon_rho43)
305 t5 = my_ndrho**2
306 t6 = beta*t5
307 t7 = my_rho**2
308 t8 = t1**2
309 t10 = 0.1e1_dp/t8/t7
310 t11 = beta*my_ndrho
311 t12 = log(xx + sqrt(xx**0.2e1_dp + 0.1e1_dp))
312 t16 = 0.10e1_dp + 0.60e1_dp*t11*t3*t12
313 t17 = 0.1e1_dp/t16
314 t18 = t10*t17
315 t21 = 0.20e1_dp*cx + 0.20e1_dp*t6*t18
316 t22 = sqrt(t21)
317 t23 = t22*t21
318 t24 = my_rho*t23
319 t26 = rootpi
320 t27 = 0.1e1_dp/t26
321 t28 = 0.1e1_dp/omega
322 t29 = 0.1e1_dp/t22
323 t30 = t28*t29
324 t31 = t26*t1
325 t34 = erf(0.3000000000e1_dp*t30*t31)
326 t36 = omega*t22
327 t37 = 0.1e1_dp/t1
328 t38 = t27*t37
329 t39 = omega**2
330 t40 = 0.1e1_dp/t39
331 t41 = 0.1e1_dp/t21
332 t42 = t40*t41
333 t43 = pi*t8
334 t44 = t42*t43
335 t46 = exp(-0.8999999998e1_dp*t44)
336 t47 = t39*t21
337 t48 = 0.1e1_dp/pi
338 t49 = 0.1e1_dp/t8
339 t51 = t46 - 0.10e1_dp
340 t52 = t48*t49*t51
341 t55 = t46 - 0.15e1_dp - 0.5555555558e-1_dp*t47*t52
342 t59 = t26*t34 + 0.3333333334e0_dp*t36*t38*t55
343 t60 = t27*t59
344
345 !! Multiply with 2.0 because it code comes from LSD
346 e_0(ii) = e_0(ii) - 0.2222222224e0_dp*t24*omega*t60*sx*2.0_dp
347
348 END IF
349 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
350 t64 = t23*omega
351 t68 = my_rho*t22*omega
352 t69 = t7*my_rho
353 t71 = 0.1e1_dp/t8/t69
354 t72 = t71*t17
355 t75 = t16**2
356 t76 = 0.1e1_dp/t75
357 t77 = t10*t76
358 t79 = 0.1e1_dp/t1/t7
359 t84 = 1 + t5*t10
360 t85 = sqrt(t84)
361 t86 = 0.1e1_dp/t85
362 t87 = t71*t86
363 t90 = -0.8000000000e1_dp*t11*t79*t12 - 0.8000000000e1_dp*t6*t87
364 t91 = t77*t90
365 t94 = -0.5333333333e1_dp*t6*t72 - 0.20e1_dp*t6*t91
366 t95 = t60*t94
367 t98 = omega*t27
368 t99 = sqrt(0.3141592654e1_dp)
369 t100 = 0.1e1_dp/t99
370 t101 = t26*t100
371 t103 = exp(-0.9000000000e1_dp*t44)
372 t104 = 0.1e1_dp/t23
373 t105 = t28*t104
374 t109 = t26*t49
375 t112 = -0.1500000000e1_dp*t105*t31*t94 + 0.1000000000e1_dp*t30* &
376 t109
377 t113 = t103*t112
378 t116 = omega*t29
379 t117 = t116*t27
380 t118 = t37*t55
381 t122 = t27*t3
382 t126 = t21**2
383 t127 = 0.1e1_dp/t126
384 t128 = t40*t127
385 t130 = t128*t43*t94
386 t132 = pi*t37
387 t133 = t42*t132
388 t135 = 0.8999999998e1_dp*t130 - 0.5999999999e1_dp*t133
389 t136 = t135*t46
390 t137 = t39*t94
391 t140 = t8*my_rho
392 t141 = 0.1e1_dp/t140
393 t143 = t48*t141*t51
394 t146 = t47*t48
395 t147 = t49*t135
396 t148 = t147*t46
397 t151 = t136 - 0.5555555558e-1_dp*t137*t52 + 0.3703703705e-1_dp*t47 &
398 *t143 - 0.5555555558e-1_dp*t146*t148
399 t155 = real(2*t101*t113, kind=dp) + 0.1666666667e0_dp*t117*t118*t94 - &
400 0.1111111111e0_dp*t36*t122*t55 + 0.3333333334e0_dp*t36*t38* &
401 t151
402
403 e_rho(ii) = e_rho(ii) + (-0.2222222224e0_dp*t64*t60 - 0.3333333336e0_dp*t68*t95 - &
404 0.2222222224e0_dp*t24*t98*t155)*sx
405
406 t168 = 0.60e1_dp*beta*t3*t12 + 0.60e1_dp*t11*t10*t86
407 t169 = t77*t168
408 t172 = 0.40e1_dp*t11*t18 - 0.20e1_dp*t6*t169
409 t173 = t60*t172
410 t176 = pi*t100
411 t177 = t176*t103
412 t185 = t128*pi
413 t186 = t8*t172
414 t190 = t39*t172
415 t196 = 0.8999999998e1_dp*t185*t186*t46 - 0.5555555558e-1_dp*t190 &
416 *t52 - 0.5000000001e0_dp*t41*t172*t46
417 t200 = -0.3000000000e1_dp*t177*t105*t1*t172 + 0.1666666667e0_dp* &
418 t117*t118*t172 + 0.3333333334e0_dp*t36*t38*t196
419
420 e_ndrho(ii) = e_ndrho(ii) + (-0.3333333336e0_dp*t68*t173 - 0.2222222224e0_dp*t24*t98 &
421 *t200)*sx
422
423 END IF
424 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
425 t207 = t27*t155
426 t211 = my_rho*t29*omega
427 t212 = t94**2
428 t213 = t60*t212
429 t216 = t207*t94
430 t219 = t7**2
431 t221 = 0.1e1_dp/t8/t219
432 t222 = t221*t17
433 t225 = t71*t76
434 t226 = t225*t90
435 t230 = 0.1e1_dp/t75/t16
436 t231 = t10*t230
437 t232 = t90**2
438 t233 = t231*t232
439 t237 = 0.1e1_dp/t1/t69
440 t241 = t221*t86
441 t244 = t5**2
442 t245 = beta*t244
443 t250 = 0.1e1_dp/t85/t84
444 t251 = 0.1e1_dp/t1/t219/t69*t250
445 t254 = 0.1866666667e2_dp*t11*t237*t12 + 0.4000000000e2_dp*t6*t241 &
446 - 0.1066666667e2_dp*t245*t251
447 t255 = t77*t254
448 t258 = 0.1955555555e2_dp*t6*t222 + 0.1066666667e2_dp*t6*t226 + 0.40e1_dp &
449 *t6*t233 - 0.20e1_dp*t6*t255
450 t259 = t60*t258
451 t264 = 0.9000000000e1_dp*t130 - 0.6000000000e1_dp*t133
452 t265 = t264*t103
453 t270 = 0.1e1_dp/t22/t126
454 t271 = t28*t270
455 t281 = t26*t141
456 t284 = 0.2250000000e1_dp*t271*t31*t212 - 0.1000000000e1_dp*t105* &
457 t109*t94 - 0.1500000000e1_dp*t105*t31*t258 - 0.6666666667e0_dp &
458 *t30*t281
459 t285 = t103*t284
460 t289 = omega*t104*t27
461 t293 = t3*t55
462 t297 = t37*t151
463 t304 = t27*t79
464 t311 = t126*t21
465 t312 = 0.1e1_dp/t311
466 t313 = t40*t312
467 t316 = 0.1800000000e2_dp*t313*t43*t212
468 t319 = 0.1200000000e2_dp*t128*t132*t94
469 t321 = t128*t43*t258
470 t323 = pi*t3
471 t325 = 0.2000000000e1_dp*t42*t323
472 t326 = -t316 + t319 + 0.8999999998e1_dp*t321 + t325
473 t328 = t135**2
474 t330 = t39*t258
475 t335 = t137*t48
476 t339 = t48*t10*t51
477 t343 = t141*t135*t46
478 t346 = t49*t326
479 t347 = t346*t46
480 t351 = t49*t328*t46
481 t354 = t326*t46 + t328*t46 - 0.5555555558e-1_dp*t330*t52 + 0.7407407410e-1_dp &
482 *t137*t143 - 0.1111111112e0_dp*t335*t148 - 0.6172839508e-1_dp &
483 *t47*t339 + 0.7407407410e-1_dp*t146*t343 - 0.5555555558e-1_dp &
484 *t146*t347 - 0.5555555558e-1_dp*t146*t351
485 t358 = real(2*t101*t265*t112, kind=dp) + real(2*t101*t285, kind=dp) - 0.8333333335e-1_dp &
486 *t289*t118*t212 - 0.1111111111e0_dp*t117*t293*t94 &
487 + 0.3333333334e0_dp*t117*t297*t94 + 0.1666666667e0_dp*t117* &
488 t118*t258 + 0.1481481481e0_dp*t36*t304*t55 - 0.2222222222e0_dp* &
489 t36*t122*t151 + 0.3333333334e0_dp*t36*t38*t354
490
491 e_rho_rho(ii) = e_rho_rho(ii) + (-0.6666666672e0_dp*t36*t95 - 0.4444444448e0_dp*t64*t207 - &
492 0.1666666668e0_dp*t211*t213 - 0.6666666672e0_dp*t68*t216 - 0.3333333336e0_dp &
493 *t68*t259 - 0.2222222224e0_dp*t24*t98*t358)*sx
494
495 t365 = t27*t200
496 t368 = t94*t172
497 t372 = t365*t94
498 t377 = t225*t168
499 t382 = t6*t10
500 t383 = t230*t90
501 t384 = t383*t168
502 t393 = beta*t5*my_ndrho
503 t397 = 0.1e1_dp/t1/t219/t7*t250
504 t400 = -0.8000000000e1_dp*beta*t79*t12 - 0.2400000000e2_dp*t11* &
505 t87 + 0.8000000000e1_dp*t393*t397
506 t401 = t77*t400
507 t404 = -0.1066666667e2_dp*t11*t72 + 0.5333333333e1_dp*t6*t377 - 0.40e1_dp &
508 *t11*t91 + 0.40e1_dp*t382*t384 - 0.20e1_dp*t6*t401
509 t405 = t60*t404
510 t408 = t207*t172
511 t412 = t26*pi*t100
512 t413 = t412*t128
513 t417 = t271*t26
514 t418 = t1*t94
515 t428 = 0.2250000000e1_dp*t417*t418*t172 - 0.1500000000e1_dp*t105 &
516 *t31*t404 - 0.5000000000e0_dp*t105*t109*t172
517 t429 = t103*t428
518 t435 = t37*t196
519 t451 = t313*pi
520 t452 = t8*t94
521 t455 = 0.1800000000e2_dp*t451*t452*t172
522 t457 = t128*t43*t404
523 t460 = t128*t132*t172
524 t462 = -t455 + 0.8999999998e1_dp*t457 + 0.5999999999e1_dp*t460
525 t463 = t462*t46
526 t464 = t135*t40
527 t465 = t464*t127
528 t466 = t172*t46
529 t467 = t43*t466
530 t470 = t39*t404
531 t473 = t94*t127
532 t478 = 0.1e1_dp/my_rho
533 t479 = t41*t478
534 t482 = t190*t48
535 t486 = t49*t462*t46
536 t489 = t41*t135
537 t492 = t463 + 0.8999999998e1_dp*t465*t467 - 0.5555555558e-1_dp*t470 &
538 *t52 - 0.5000000001e0_dp*t473*t466 + 0.3703703705e-1_dp*t190*t143 &
539 + 0.3333333334e0_dp*t479*t466 - 0.5555555558e-1_dp*t482*t148 &
540 - 0.5555555558e-1_dp*t146*t486 - 0.5000000001e0_dp*t489*t466
541 t496 = 0.1800000000e2_dp*t413*t186*t113 + real(2*t101*t429, kind=dp) &
542 - 0.8333333335e-1_dp*t289*t118*t368 + 0.1666666667e0_dp*t117*t435 &
543 *t94 + 0.1666666667e0_dp*t117*t118*t404 - 0.5555555555e-1_dp &
544 *t117*t293*t172 - 0.1111111111e0_dp*t36*t122*t196 + 0.1666666667e0_dp &
545 *t117*t297*t172 + 0.3333333334e0_dp*t36*t38*t492
546
547 e_ndrho_rho(ii) = e_ndrho_rho(ii) + (-0.3333333336e0_dp*t36*t173 - 0.2222222224e0_dp*t64*t365 - &
548 0.1666666668e0_dp*t211*t60*t368 - 0.3333333336e0_dp*t68*t372 &
549 - 0.3333333336e0_dp*t68*t405 - 0.3333333336e0_dp*t68*t408 - 0.2222222224e0_dp &
550 *t24*t98*t496)*sx
551
552 t501 = t172**2
553 t502 = t60*t501
554 t505 = t365*t172
555 t508 = beta*t10
556 t513 = t168**2
557 t514 = t231*t513
558 t519 = t219*my_rho
559 t521 = 0.1e1_dp/t1/t519
560 t525 = 0.120e2_dp*t508*t86 - 0.60e1_dp*t6*t521*t250
561 t526 = t77*t525
562 t529 = 0.40e1_dp*t508*t17 - 0.80e1_dp*t11*t169 + 0.40e1_dp*t6*t514 &
563 - 0.20e1_dp*t6*t526
564 t530 = t60*t529
565 t533 = pi**2
566 t534 = t533*t100
567 t536 = 0.1e1_dp/t39/omega
568 t537 = t534*t536
569 t539 = 0.1e1_dp/t22/t311
570 t562 = t8*t501
571 t566 = t8*t529
572 t570 = t39**2
573 t571 = 0.1e1_dp/t570
574 t572 = t126**2
575 t573 = 0.1e1_dp/t572
576 t574 = t571*t573
577 t575 = t574*t533
578 t576 = t2*t501
579 t580 = t39*t529
580 t586 = -0.2250000000e2_dp*t451*t562*t46 + 0.8999999998e1_dp*t185 &
581 *t566*t46 + 0.8099999996e2_dp*t575*t576*t46 - 0.5555555558e-1_dp &
582 *t580*t52 - 0.5000000001e0_dp*t41*t529*t46
583 t590 = -0.2700000000e2_dp*t537*t539*my_rho*t501*t103 + 0.4500000000e1_dp &
584 *t177*t271*t1*t501 - 0.3000000000e1_dp*t177*t105* &
585 t1*t529 - 0.8333333335e-1_dp*t289*t118*t501 + 0.3333333334e0_dp &
586 *t117*t435*t172 + 0.1666666667e0_dp*t117*t118*t529 + 0.3333333334e0_dp &
587 *t36*t38*t586
588
589 e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii) + (-0.1666666668e0_dp*t211*t502 - 0.6666666672e0_dp*t68*t505 &
590 - 0.3333333336e0_dp*t68*t530 - 0.2222222224e0_dp*t24*t98*t590) &
591 *sx
592
593 END IF
594 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
595 t601 = t27*t358
596 t605 = my_rho*t104*omega
597 t606 = t212*t94
598 t613 = t94*t258
599 t624 = 0.1e1_dp/t8/t519
600 t628 = t221*t76
601 t632 = t71*t230
602 t639 = t75**2
603 t640 = 0.1e1_dp/t639
604 t641 = t10*t640
605 t657 = t219**2
606 t667 = t84**2
607 t669 = 0.1e1_dp/t85/t667
608 t677 = -0.9125925923e2_dp*t6*t624*t17 - 0.5866666667e2_dp*t6*t628 &
609 *t90 - 0.3200000001e2_dp*t6*t632*t232 + 0.1600000000e2_dp*t6 &
610 *t225*t254 - 0.120e2_dp*t6*t641*t232*t90 + 0.120e2_dp*t382 &
611 *t383*t254 - 0.20e1_dp*t6*t77*(-0.6222222223e2_dp*t11/t1/ &
612 t219*t12 - 0.2115555556e3_dp*t6*t624*t86 + 0.1315555556e3_dp* &
613 t245/t1/t657*t250 - 0.4266666668e2_dp*beta*t244*t5/t657 &
614 /t69*t669)
615 t687 = t28*t539
616 t716 = t264**2
617 t722 = omega*t270*t27
618 t735 = t79*t55
619 t739 = t3*t151
620 t746 = t37*t354
621 t769 = t40*t573
622 t791 = 0.5400000000e2_dp*t769*t43*t606 - 0.3600000000e2_dp*t313* &
623 t132*t212 - 0.5400000000e2_dp*t451*t452*t258 - 0.6000000000e1_dp &
624 *t128*t323*t94 + 0.1800000000e2_dp*t128*t132*t258 + 0.8999999998e1_dp &
625 *t128*t43*t677 - 0.2666666667e1_dp*t42*pi*t79
626 t793 = t328*t135
627 t838 = real(3*t326*t135*t46, kind=dp) + real(t791*t46, kind=dp) + real(t793* &
628 t46, kind=dp) - 0.5555555558e-1_dp*t39*t677*t52 + 0.1111111112e0_dp*t330 &
629 *t143 - 0.1666666668e0_dp*t330*t48*t148 - 0.1851851853e0_dp*t137 &
630 *t339 + 0.2222222223e0_dp*t335*t343 - 0.1666666668e0_dp*t335* &
631 t347 - 0.1666666668e0_dp*t335*t351 + 0.1646090535e0_dp*t47*t48 &
632 *t71*t51 - 0.1851851853e0_dp*real(t146, kind=dp)*real(t10, kind=dp)*real(t135, kind=dp) &
633 *real(t46, kind=dp) + 0.1111111112e0_dp*real(t146, kind=dp)*real(t141, kind=dp)*real(t326, kind=dp) &
634 *real(t46, kind=dp) + 0.1111111112e0_dp*real(t146, kind=dp)*real(t141, kind=dp)*real(t328, kind=dp) &
635 *real(t46, kind=dp) - 0.5555555558e-1_dp*real(t146, kind=dp)*real(t49, kind=dp)*real(t791, kind=dp) &
636 *real(t46, kind=dp) - 0.1666666668e0_dp*real(t146, kind=dp)*real(t346, kind=dp)*real(t136, kind=dp) &
637 - 0.5555555558e-1_dp*real(t146, kind=dp)*real(t49, kind=dp)*real(t793, kind=dp)* &
638 REAL(t46, kind=dp)
639 t842 = 0.2e1_dp*t101*(-t316 + t319 + 0.9000000000e1_dp*t321 + t325) &
640 *t103*t112 + 0.2e1_dp*t101*t103*(-0.5625000000e1_dp*t687*t31 &
641 *t606 + 0.2250000000e1_dp*t271*t109*t212 + 0.6750000000e1_dp* &
642 t417*t418*t258 + 0.1000000000e1_dp*t105*t281*t94 - 0.1500000000e1_dp &
643 *t105*t109*t258 - 0.1500000000e1_dp*t105*t31*t677 &
644 + 0.1111111111e1_dp*t30*t26*t10) + 0.4e1_dp*t101*t265*t284 + &
645 0.2e1_dp*t101*t716*t103*t112 + 0.1250000000e0_dp*t722*t118 &
646 *t606 + 0.8333333333e-1_dp*t289*t293*t212 - 0.2500000000e0_dp*t289 &
647 *t297*t212 - 0.2500000000e0_dp*t289*t118*t613 + 0.2222222222e0_dp &
648 *t117*t735*t94 - 0.3333333333e0_dp*t117*t739*t94 - &
649 0.1666666667e0_dp*t117*t293*t258 + 0.5000000001e0_dp*t117*t746 &
650 *t94 + 0.5000000001e0_dp*t117*t297*t258 + 0.1666666667e0_dp*t117 &
651 *t118*t677 - 0.3456790122e0_dp*t36*t27*t237*t55 + 0.4444444444e0_dp &
652 *t36*t304*t151 - 0.3333333333e0_dp*t36*t122*t354 &
653 + 0.3333333334e0_dp*t36*t38*t838
654 t846 = -0.5000000004e0_dp*t116*t213 - 0.2000000001e1_dp*t36*t216 &
655 - 0.1000000001e1_dp*t36*t259 - 0.6666666672e0_dp*t64*t601 + 0.8333333340e-1_dp &
656 *t605*t60*t606 - 0.5000000004e0_dp*t211*t207*t212 &
657 - 0.5000000004e0_dp*t211*t60*t613 - 0.1000000001e1_dp*t68* &
658 t601*t94 - 0.1000000001e1_dp*t68*t207*t258 - 0.3333333336e0_dp* &
659 t68*t60*t677 - 0.2222222224e0_dp*t24*t98*t842
660
661 e_rho_rho_rho(ii) = e_rho_rho_rho(ii) + t846*sx
662
663 t857 = t27*t496
664 t860 = t212*t172
665 t867 = t94*t404
666 t880 = t258*t172
667 t933 = 0.3911111110e2_dp*t11*t222 - 0.1955555555e2_dp*t6*t628*t168 &
668 + 0.2133333334e2_dp*t11*t226 - 0.2133333334e2_dp*t6*t71*t384 &
669 + 0.1066666667e2_dp*t6*t225*t400 + 0.80e1_dp*t11*t233 - 0.120e2_dp &
670 *t382*t640*t232*t168 + 0.80e1_dp*t382*t383*t400 - 0.40e1_dp &
671 *t11*t255 + 0.40e1_dp*t382*t230*t254*t168 - 0.20e1_dp* &
672 t6*t77*(0.1866666667e2_dp*beta*t237*t12 + 0.9866666667e2_dp* &
673 t11*t241 - 0.8266666668e2_dp*t393*t251 + 0.3200000001e2_dp*beta &
674 *t244*my_ndrho/t657/t7*t669)
675 t961 = t687*t26
676 t1002 = t3*t196
677 t1009 = 0.2e1_dp*t101*(-t455 + 0.9000000000e1_dp*t457 + 0.6000000000e1_dp &
678 *t460)*t103*t112 + 0.1800000000e2_dp*t412*t264*t40*t127 &
679 *t8*t172*t103*t112 + 0.2e1_dp*t101*t265*t428 + 0.1800000000e2_dp &
680 *t413*t186*t285 + 0.2e1_dp*t101*t103*(-0.5625000000e1_dp &
681 *t961*t1*t212*t172 + 0.4500000000e1_dp*t417*t418*t404 &
682 + 0.1500000000e1_dp*t417*t49*t94*t172 - 0.1000000000e1_dp* &
683 t105*t109*t404 + 0.2250000000e1_dp*t417*t1*t258*t172 - 0.1500000000e1_dp &
684 *t105*t31*t933 + 0.3333333334e0_dp*t105*t281* &
685 t172) + 0.1250000000e0_dp*t722*t118*t860 - 0.8333333335e-1_dp*t289 &
686 *t435*t212 - 0.1666666667e0_dp*t289*t118*t867 + 0.5555555555e-1_dp &
687 *t289*t293*t368 - 0.1111111111e0_dp*t117*t1002*t94 &
688 - 0.1111111111e0_dp*t117*t293*t404
689 t1013 = t37*t492
690 t1044 = t769*pi
691 t1069 = 0.5400000000e2_dp*t1044*t8*t212*t172 - 0.3600000000e2_dp &
692 *t451*t452*t404 - 0.2400000000e2_dp*t451*t37*t94*t172 + &
693 0.1200000000e2_dp*t128*t132*t404 - 0.1800000000e2_dp*t451*t8* &
694 t258*t172 + 0.8999999998e1_dp*t128*t43*t933 - 0.2000000000e1_dp &
695 *t128*t323*t172
696 t1091 = t127*t172*t46
697 t1102 = t1069*t46 + 0.8999999998e1_dp*t326*t40*t127*t467 + real(2 &
698 *t136*t462, kind=dp) + 0.8999999998e1_dp*t328*t40*t127*t467 - &
699 0.5555555558e-1_dp*t39*t933*t52 - 0.5000000001e0_dp*t258*t127 &
700 *t466 + 0.7407407410e-1_dp*t470*t143 + 0.6666666668e0_dp*t94*t478 &
701 *t1091 - 0.1111111112e0_dp*t470*t48*t148 - 0.1111111112e0_dp &
702 *t335*t486 - 0.1000000001e1_dp*t94*t135*t1091
703 t1136 = -0.6172839508e-1_dp*t190*t339 - 0.5555555556e0_dp*t41/t7 &
704 *t466 + 0.7407407410e-1_dp*t482*t343 + 0.7407407410e-1_dp*t146* &
705 t141*t462*t46 + 0.6666666668e0_dp*t479*t135*t172*t46 - 0.5555555558e-1_dp &
706 *t482*t347 - 0.5555555558e-1_dp*t146*t49*t1069 &
707 *t46 - 0.5000000001e0_dp*t41*t326*t466 - 0.5555555558e-1_dp*t482 &
708 *t351 - 0.1111111112e0_dp*t146*t147*t463 - 0.5000000001e0_dp* &
709 t41*t328*t466
710 t1141 = -0.1666666667e0_dp*t289*t297*t368 + 0.3333333334e0_dp*t117 &
711 *t1013*t94 + 0.3333333334e0_dp*t117*t297*t404 - 0.8333333335e-1_dp &
712 *t289*t118*t880 + 0.1666666667e0_dp*t117*t435*t258 + &
713 0.1666666667e0_dp*t117*t118*t933 + 0.7407407405e-1_dp*t117*t735 &
714 *t172 + 0.1481481481e0_dp*t36*t304*t196 - 0.1111111111e0_dp* &
715 t117*t739*t172 - 0.2222222222e0_dp*t36*t122*t492 + 0.1666666667e0_dp &
716 *t117*t746*t172 + 0.3333333334e0_dp*t36*t38*(t1102 &
717 + t1136)
718 t1146 = -0.3333333336e0_dp*t117*t59*t94*t172 - 0.6666666672e0_dp &
719 *t36*t372 - 0.6666666672e0_dp*t36*t405 - 0.6666666672e0_dp*t36 &
720 *t408 - 0.4444444448e0_dp*t64*t857 + 0.8333333340e-1_dp*t605*t60 &
721 *t860 - 0.1666666668e0_dp*t211*t365*t212 - 0.3333333336e0_dp* &
722 t211*t60*t867 - 0.3333333336e0_dp*t211*t207*t368 - 0.6666666672e0_dp &
723 *t68*t857*t94 - 0.6666666672e0_dp*t68*t207*t404 - 0.1666666668e0_dp &
724 *t211*t60*t880 - 0.3333333336e0_dp*t68*t365* &
725 t258 - 0.3333333336e0_dp*t68*t60*t933 - 0.3333333336e0_dp*t68* &
726 t601*t172 - 0.2222222224e0_dp*t24*t98*(t1009 + t1141)
727
728 e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii) + t1146*sx
729
730 t1153 = t27*t590
731 t1156 = t94*t501
732 t1163 = t404*t172
733 t1167 = t94*t529
734 t1177 = beta*t71
735 t1220 = -0.1066666667e2_dp*t1177*t17 + 0.2133333334e2_dp*t11*t377 &
736 - 0.1066666667e2_dp*t6*t632*t513 + 0.5333333333e1_dp*t6*t225 &
737 *t525 - 0.40e1_dp*t508*t76*t90 + 0.160e2_dp*t11*t10*t384 - &
738 0.80e1_dp*t11*t401 - 0.120e2_dp*t382*t640*t90*t513 + 0.80e1_dp &
739 *t382*t230*t400*t168 + 0.40e1_dp*t382*t383*t525 - 0.20e1_dp &
740 *t6*t77*(-0.3200000000e2_dp*t1177*t86 + 0.4800000000e2_dp*t6 &
741 *t397 - 0.2400000000e2_dp*t245/t657/my_rho*t669)
742 t1284 = t37*t586
743 t1334 = 0.5400000000e2_dp*t1044*t452*t501 - 0.3600000000e2_dp*t451 &
744 *t8*t404*t172 - 0.1800000000e2_dp*t451*t452*t529 + 0.8999999998e1_dp &
745 *t128*t43*t1220 - 0.1200000000e2_dp*t313*t132*t501 &
746 + 0.5999999999e1_dp*t128*t132*t529
747 t1341 = t501*t46
748 t1345 = t529*t46
749 t1370 = t40*pi
750 t1396 = t1334*t46 + 0.1800000000e2_dp*t462*t40*t127*t467 - 0.2250000000e2_dp &
751 *t464*t312*t43*t1341 + 0.8999999998e1_dp*t465 &
752 *t43*t1345 - 0.1000000000e1_dp*t404*t127*t466 + 0.8099999996e2_dp &
753 *t135*t571*t573*t533*t2*t1341 - 0.5555555558e-1_dp*t39 &
754 *t1220*t52 - 0.5000000001e0_dp*t473*t1345 + 0.3333333334e0_dp* &
755 t479*t1345 + 0.1000000000e1_dp*t94*t312*t1341 - 0.4500000000e1_dp &
756 *t94*t573*t501*t1370*t8*t46 + 0.3703703705e-1_dp*t580 &
757 *t143 + 0.3000000000e1_dp*t312*t37*t501*t1370*t46 - 0.5555555558e-1_dp &
758 *t580*t48*t148 - 0.1111111112e0_dp*t482*t486 - 0.5555555558e-1_dp &
759 *t146*t49*t1334*t46 - 0.1000000000e1_dp*t41* &
760 t462*t466 - 0.5000000001e0_dp*t489*t1345
761 t1400 = -0.3600000000e2_dp*t412*t313*t562*t113 + 0.1800000000e2_dp &
762 *t413*t566*t113 + 0.3600000000e2_dp*t413*t186*t429 + 0.1620000000e3_dp &
763 *t26*t533*t100*t574*t576*t113 + 0.2e1_dp*t101 &
764 *t103*(-0.5625000000e1_dp*t961*t418*t501 + 0.4500000000e1_dp &
765 *t417*t1*t404*t172 + 0.2250000000e1_dp*t417*t418*t529 - &
766 0.1500000000e1_dp*t105*t31*t1220 + 0.7500000000e0_dp*t271*t109 &
767 *t501 - 0.5000000000e0_dp*t105*t109*t529) + 0.1250000000e0_dp* &
768 t722*t118*t1156 - 0.1666666667e0_dp*t289*t435*t368 - 0.1666666667e0_dp &
769 *t289*t118*t1163 - 0.8333333335e-1_dp*t289*t118*t1167 &
770 + 0.1666666667e0_dp*t117*t1284*t94 + 0.3333333334e0_dp*t117 &
771 *t435*t404 + 0.1666666667e0_dp*t117*t118*t1220 + 0.2777777778e-1_dp &
772 *t289*t293*t501 - 0.1111111111e0_dp*t117*t1002*t172 &
773 - 0.5555555555e-1_dp*t117*t293*t529 - 0.1111111111e0_dp*t36*t122 &
774 *t586 - 0.8333333335e-1_dp*t289*t297*t501 + 0.3333333334e0_dp &
775 *t117*t1013*t172 + 0.1666666667e0_dp*t117*t297*t529 + 0.3333333334e0_dp &
776 *t36*t38*t1396
777 t1404 = -0.1666666668e0_dp*t116*t502 - 0.6666666672e0_dp*t36*t505 &
778 - 0.3333333336e0_dp*t36*t530 - 0.2222222224e0_dp*t64*t1153 + 0.8333333340e-1_dp &
779 *t605*t60*t1156 - 0.3333333336e0_dp*t211*t365 &
780 *t368 - 0.3333333336e0_dp*t211*t60*t1163 - 0.1666666668e0_dp*t211 &
781 *t60*t1167 - 0.3333333336e0_dp*t68*t1153*t94 - 0.6666666672e0_dp &
782 *t68*t365*t404 - 0.3333333336e0_dp*t68*t60*t1220 - 0.1666666668e0_dp &
783 *t211*t207*t501 - 0.6666666672e0_dp*t68*t857* &
784 t172 - 0.3333333336e0_dp*t68*t207*t529 - 0.2222222224e0_dp*t24* &
785 t98*t1400
786
787 e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii) + t1404*sx
788
789 t1405 = t501*t172
790 t1412 = t172*t529
791 t1449 = -0.120e2_dp*t508*t76*t168 + 0.240e2_dp*t11*t514 - 0.120e2_dp &
792 *t11*t526 - 0.120e2_dp*t6*t641*t513*t168 + 0.120e2_dp*t382 &
793 *t230*t168*t525 - 0.20e1_dp*t6*t77*(-0.240e2_dp*beta*t521 &
794 *t250*my_ndrho + 0.180e2_dp*t393/t657*t669)
795 t1456 = t1405*t103
796 t1467 = t533*pi
797 t1472 = t572*t21
798 t1553 = 0.1350000000e3_dp*t537/t22/t572*my_rho*t1456 - 0.8100000000e2_dp &
799 *t534*t536*t539*my_rho*t172*t103*t529 - 0.2430000000e3_dp &
800 *t1467*t100/t570/omega/t22/t1472*t140*t1456 - &
801 0.1125000000e2_dp*t177*t687*t1*t1405 + 0.1350000000e2_dp*t176 &
802 *t103*t28*t270*t1*t1412 - 0.3000000000e1_dp*t177*t105* &
803 t1*t1449 + 0.1250000000e0_dp*t722*t118*t1405 - 0.2500000000e0_dp &
804 *t289*t435*t501 - 0.2500000000e0_dp*t289*t118*t1412 + 0.5000000001e0_dp &
805 *t117*t1284*t172 + 0.5000000001e0_dp*t117*t435 &
806 *t529 + 0.1666666667e0_dp*t117*t118*t1449 + 0.3333333334e0_dp*t36 &
807 *t38*(0.6750000000e2_dp*t1044*t8*t1405*t46 - 0.6750000000e2_dp &
808 *t451*t186*t1345 - 0.5264999998e3_dp*t571/t1472*t533 &
809 *t2*t1405*t46 + 0.8999999998e1_dp*t185*t8*t1449*t46 + 0.2429999999e3_dp &
810 *t575*t2*t529*t466 + 0.7289999995e3_dp/t570/t39 &
811 /t572/t126*t1467*t7*t1405*t46 - 0.5555555558e-1_dp*t39 &
812 *t1449*t52 - 0.5000000001e0_dp*t41*t1449*t46)
813
814 e_ndrho_ndrho_ndrho(ii) = e_ndrho_ndrho_ndrho(ii) + (0.8333333340e-1_dp*t605*t60*t1405 - &
815 0.5000000004e0_dp*t211*t365*t501 - 0.5000000004e0_dp*t211*t60*t1412 - 0.1000000001e1_dp &
816 *t68*t1153*t172 - 0.1000000001e1_dp*t68*t365*t529 - 0.3333333336e0_dp &
817 *t68*t60*t1449 - 0.2222222224e0_dp*t24*t98*t1553) &
818 *sx
819
820 END IF
821 END IF
822 END DO
823!$OMP END DO
824
825 END SUBROUTINE xb88_lr_lda_calc
826
827! **************************************************************************************************
828!> \brief evaluates the becke 88 longrange exchange functional for lsd
829!> \param rho_set ...
830!> \param deriv_set ...
831!> \param grad_deriv ...
832!> \param xb88_lr_params ...
833!> \par History
834!> 01.2008 created [mguidon]
835!> \author Manuel Guidon
836! **************************************************************************************************
837 SUBROUTINE xb88_lr_lsd_eval(rho_set, deriv_set, grad_deriv, xb88_lr_params)
838 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
839 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
840 INTEGER, INTENT(in) :: grad_deriv
841 TYPE(section_vals_type), POINTER :: xb88_lr_params
842
843 CHARACTER(len=*), PARAMETER :: routinen = 'xb88_lr_lsd_eval'
844
845 INTEGER :: handle, i, ispin, npoints
846 INTEGER, DIMENSION(2, 3) :: bo
847 REAL(kind=dp) :: epsilon_rho, omega, sx
848 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
849 POINTER :: dummy, e_0
850 TYPE(cp_3d_r_cp_type), DIMENSION(2) :: e_ndrho, e_ndrho_ndrho, e_ndrho_ndrho_ndrho, &
851 e_ndrho_ndrho_rho, e_ndrho_rho, e_ndrho_rho_rho, e_rho, e_rho_rho, e_rho_rho_rho, &
852 norm_drho, rho
853 TYPE(xc_derivative_type), POINTER :: deriv
854
855 CALL timeset(routinen, handle)
856
857 CALL cite_reference(becke1988)
858
859 NULLIFY (deriv)
860 DO i = 1, 2
861 NULLIFY (norm_drho(i)%array, rho(i)%array)
862 END DO
863
864 CALL section_vals_val_get(xb88_lr_params, "scale_x", r_val=sx)
865 CALL section_vals_val_get(xb88_lr_params, "omega", r_val=omega)
866
867 CALL xc_rho_set_get(rho_set, &
868 rhoa=rho(1)%array, &
869 rhob=rho(2)%array, norm_drhoa=norm_drho(1)%array, &
870 norm_drhob=norm_drho(2)%array, rho_cutoff=epsilon_rho, &
871 local_bounds=bo)
872 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
873
874 ! meaningful default for the arrays we don't need: let us make compiler
875 ! and debugger happy...
876 dummy => rho(1)%array
877
878 e_0 => dummy
879 DO i = 1, 2
880 e_rho(i)%array => dummy
881 e_ndrho(i)%array => dummy
882 e_rho_rho(i)%array => dummy
883 e_ndrho_rho(i)%array => dummy
884 e_ndrho_ndrho(i)%array => dummy
885 e_rho_rho_rho(i)%array => dummy
886 e_ndrho_rho_rho(i)%array => dummy
887 e_ndrho_ndrho_rho(i)%array => dummy
888 e_ndrho_ndrho_ndrho(i)%array => dummy
889 END DO
890
891 IF (grad_deriv >= 0) THEN
892 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
893 allocate_deriv=.true.)
894 CALL xc_derivative_get(deriv, deriv_data=e_0)
895 END IF
896 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
897 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
898 allocate_deriv=.true.)
899 CALL xc_derivative_get(deriv, deriv_data=e_rho(1)%array)
900 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
901 allocate_deriv=.true.)
902 CALL xc_derivative_get(deriv, deriv_data=e_rho(2)%array)
903 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
904 allocate_deriv=.true.)
905 CALL xc_derivative_get(deriv, deriv_data=e_ndrho(1)%array)
906 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
907 allocate_deriv=.true.)
908 CALL xc_derivative_get(deriv, deriv_data=e_ndrho(2)%array)
909 END IF
910 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
911 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhoa], &
912 allocate_deriv=.true.)
913 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho(1)%array)
914 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob, deriv_rhob], &
915 allocate_deriv=.true.)
916 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho(2)%array)
917 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhoa], &
918 allocate_deriv=.true.)
919 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho(1)%array)
920 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob, deriv_rhob], &
921 allocate_deriv=.true.)
922 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho(2)%array)
923 deriv => xc_dset_get_derivative(deriv_set, &
924 [deriv_norm_drhoa, deriv_norm_drhoa], allocate_deriv=.true.)
925 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho(1)%array)
926 deriv => xc_dset_get_derivative(deriv_set, &
927 [deriv_norm_drhob, deriv_norm_drhob], allocate_deriv=.true.)
928 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho(2)%array)
929 END IF
930 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
931 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhoa, deriv_rhoa], &
932 allocate_deriv=.true.)
933 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho(1)%array)
934 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob, deriv_rhob, deriv_rhob], &
935 allocate_deriv=.true.)
936 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho(2)%array)
937 deriv => xc_dset_get_derivative(deriv_set, &
938 [deriv_norm_drhoa, deriv_rhoa, deriv_rhoa], allocate_deriv=.true.)
939 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho(1)%array)
940 deriv => xc_dset_get_derivative(deriv_set, &
941 [deriv_norm_drhob, deriv_rhob, deriv_rhob], allocate_deriv=.true.)
942 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho(2)%array)
943 deriv => xc_dset_get_derivative(deriv_set, &
944 [deriv_norm_drhoa, deriv_norm_drhoa, deriv_rhoa], allocate_deriv=.true.)
945 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho(1)%array)
946 deriv => xc_dset_get_derivative(deriv_set, &
947 [deriv_norm_drhob, deriv_norm_drhob, deriv_rhob], allocate_deriv=.true.)
948 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho(2)%array)
949 deriv => xc_dset_get_derivative(deriv_set, &
950 [deriv_norm_drhoa, deriv_norm_drhoa, deriv_norm_drhoa], allocate_deriv=.true.)
951 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho(1)%array)
952 deriv => xc_dset_get_derivative(deriv_set, &
953 [deriv_norm_drhob, deriv_norm_drhob, deriv_norm_drhob], allocate_deriv=.true.)
954 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho(2)%array)
955 END IF
956 IF (grad_deriv > 3 .OR. grad_deriv < -3) THEN
957 cpabort("derivatives bigger than 3 not implemented")
958 END IF
959
960 DO ispin = 1, 2
961
962!$OMP PARALLEL DEFAULT(NONE) &
963!$OMP SHARED(rho, norm_drho, e_0, e_rho, e_ndrho) &
964!$OMP SHARED(e_rho_rho, e_ndrho_rho, e_ndrho_ndrho) &
965!$OMP SHARED(e_rho_rho_rho, e_ndrho_rho_rho) &
966!$OMP SHARED(e_ndrho_ndrho_rho, e_ndrho_ndrho_ndrho) &
967!$OMP SHARED(grad_deriv, npoints, epsilon_rho, sx, omega) &
968!$OMP SHARED(ispin)
969
970 CALL xb88_lr_lsd_calc( &
971 rho_spin=rho(ispin)%array, &
972 norm_drho_spin=norm_drho(ispin)%array, &
973 e_0=e_0, &
974 e_rho_spin=e_rho(ispin)%array, &
975 e_ndrho_spin=e_ndrho(ispin)%array, &
976 e_rho_rho_spin=e_rho_rho(ispin)%array, &
977 e_ndrho_rho_spin=e_ndrho_rho(ispin)%array, &
978 e_ndrho_ndrho_spin=e_ndrho_ndrho(ispin)%array, &
979 e_rho_rho_rho_spin=e_rho_rho_rho(ispin)%array, &
980 e_ndrho_rho_rho_spin=e_ndrho_rho_rho(ispin)%array, &
981 e_ndrho_ndrho_rho_spin=e_ndrho_ndrho_rho(ispin)%array, &
982 e_ndrho_ndrho_ndrho_spin=e_ndrho_ndrho_ndrho(ispin)%array, &
983 grad_deriv=grad_deriv, npoints=npoints, &
984 epsilon_rho=epsilon_rho, &
985 sx=sx, omega=omega)
986
987!$OMP END PARALLEL
988
989 END DO
990
991 CALL timestop(handle)
992
993 END SUBROUTINE xb88_lr_lsd_eval
994
995! **************************************************************************************************
996!> \brief low level calculation of the becke 88 exchange functional for lsd
997!> \param rho_spin alpha or beta spin density
998!> \param norm_drho_spin || grad rho_spin ||
999!> \param e_0 adds to it the local value of the functional
1000!> \param e_rho_spin e_*_spin derivative of the functional wrt. to the variables
1001!> named where the * is. Everything wrt. to the spin of the arguments.
1002!> \param e_ndrho_spin ...
1003!> \param e_rho_rho_spin ...
1004!> \param e_ndrho_rho_spin ...
1005!> \param e_ndrho_ndrho_spin ...
1006!> \param e_rho_rho_rho_spin ...
1007!> \param e_ndrho_rho_rho_spin ...
1008!> \param e_ndrho_ndrho_rho_spin ...
1009!> \param e_ndrho_ndrho_ndrho_spin ...
1010!> \param grad_deriv ...
1011!> \param npoints ...
1012!> \param epsilon_rho ...
1013!> \param sx scaling-parameter for exchange
1014!> \param omega ...
1015!> \par History
1016!> 01.2008 created [mguidon]
1017!> \author Manuel Guidon
1018!> \note
1019!> - Derivatives higher than one not tested
1020! **************************************************************************************************
1021 SUBROUTINE xb88_lr_lsd_calc(rho_spin, norm_drho_spin, e_0, &
1022 e_rho_spin, e_ndrho_spin, e_rho_rho_spin, e_ndrho_rho_spin, &
1023 e_ndrho_ndrho_spin, e_rho_rho_rho_spin, e_ndrho_rho_rho_spin, &
1024 e_ndrho_ndrho_rho_spin, &
1025 e_ndrho_ndrho_ndrho_spin, grad_deriv, npoints, epsilon_rho, sx, &
1026 omega)
1027 REAL(kind=dp), DIMENSION(*), INTENT(in) :: rho_spin, norm_drho_spin
1028 REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_rho_spin, e_ndrho_spin, e_rho_rho_spin, &
1029 e_ndrho_rho_spin, e_ndrho_ndrho_spin, e_rho_rho_rho_spin, e_ndrho_rho_rho_spin, &
1030 e_ndrho_ndrho_rho_spin, e_ndrho_ndrho_ndrho_spin
1031 INTEGER, INTENT(in) :: grad_deriv, npoints
1032 REAL(kind=dp), INTENT(in) :: epsilon_rho, sx, omega
1033
1034 INTEGER :: ii
1035 REAL(kind=dp) :: cx, epsilon_rho43, my_epsilon_rho, ndrho, rho, t1, t10, t100, t1002, t1009, &
1036 t101, t1013, t103, t104, t1044, t105, t1069, t109, t1091, t11, t1102, t112, t113, t1136, &
1037 t1141, t1146, t1153, t1156, t116, t1163, t1167, t117, t1177, t118, t12, t122, t1220, &
1038 t126, t127, t128, t1284, t130, t132, t133, t1334, t1341, t1345, t135, t136, t137, t1370, &
1039 t1396, t140, t1400, t1404, t1405, t141, t1412, t143, t1449, t1456, t146, t1467, t147, &
1040 t1472, t148, t151, t155, t1553, t16, t168, t169, t17, t172, t173, t176, t177, t18, t185, &
1041 t186, t190, t196, t2, t200, t207, t21, t211, t212, t213, t216
1042 REAL(kind=dp) :: t219, t22, t221, t222, t225, t226, t23, t230, t231, t232, t233, t237, t24, &
1043 t241, t244, t245, t250, t251, t254, t255, t258, t259, t26, t264, t265, t27, t270, t271, &
1044 t28, t281, t284, t285, t289, t29, t293, t297, t3, t30, t304, t31, t311, t312, t313, t316, &
1045 t319, t321, t323, t325, t326, t328, t330, t335, t339, t34, t343, t346, t347, t351, t354, &
1046 t358, t36, t365, t368, t37, t372, t377, t38, t382, t383, t384, t39, t393, t397, t40, &
1047 t400, t401, t404, t405, t408, t41, t412, t413, t417, t418, t42, t428, t429, t43, t435, &
1048 t44, t451, t452, t455, t457, t46, t460, t462, t463, t464, t465
1049 REAL(kind=dp) :: t466, t467, t47, t470, t473, t478, t479, t48, t482, t486, t489, t49, t492, &
1050 t496, t5, t501, t502, t505, t508, t51, t513, t514, t519, t52, t521, t525, t526, t529, &
1051 t530, t533, t534, t536, t537, t539, t55, t562, t566, t570, t571, t572, t573, t574, t575, &
1052 t576, t580, t586, t59, t590, t6, t60, t601, t605, t606, t613, t624, t628, t632, t639, &
1053 t64, t640, t641, t657, t667, t669, t677, t68, t687, t69, t7, t71, t716, t72, t722, t735, &
1054 t739, t746, t75, t76, t769, t77, t79, t791, t793, t8, t838, t84, t842, t846, t85, t857, &
1055 t86, t860, t867, t87, t880, t90, t91, t933, t94, t95, t961, t98
1056 REAL(kind=dp) :: t99, xx
1057
1058 my_epsilon_rho = 0.5_dp*epsilon_rho
1059 epsilon_rho43 = my_epsilon_rho**(4.0_dp/3.0_dp)
1060 cx = 1.5_dp*(3.0_dp/4.0_dp/pi)**(1.0_dp/3.0_dp)
1061
1062!$OMP DO
1063 DO ii = 1, npoints
1064 rho = rho_spin(ii)
1065 ndrho = norm_drho_spin(ii)
1066 IF (rho > my_epsilon_rho) THEN
1067 IF (grad_deriv >= 0) THEN
1068 t1 = rho**(0.1e1_dp/0.3e1_dp)
1069 t2 = t1*rho
1070 t3 = 0.1e1_dp/t2
1071 xx = ndrho*max(t3, epsilon_rho43)
1072 t5 = ndrho**2
1073 t6 = beta*t5
1074 t7 = rho**2
1075 t8 = t1**2
1076 t10 = 0.1e1_dp/t8/t7
1077 t11 = beta*ndrho
1078 t12 = log(xx + sqrt(xx**0.2e1_dp + 0.1e1_dp))
1079 t16 = 0.10e1_dp + 0.60e1_dp*t11*t3*t12
1080 t17 = 0.1e1_dp/t16
1081 t18 = t10*t17
1082 t21 = 0.20e1_dp*cx + 0.20e1_dp*t6*t18
1083 t22 = sqrt(t21)
1084 t23 = t22*t21
1085 t24 = rho*t23
1086 t26 = rootpi
1087 t27 = 0.1e1_dp/t26
1088 t28 = 0.1e1_dp/omega
1089 t29 = 0.1e1_dp/t22
1090 t30 = t28*t29
1091 t31 = t26*t1
1092 t34 = erf(0.3000000000e1_dp*t30*t31)
1093 t36 = omega*t22
1094 t37 = 0.1e1_dp/t1
1095 t38 = t27*t37
1096 t39 = omega**2
1097 t40 = 0.1e1_dp/t39
1098 t41 = 0.1e1_dp/t21
1099 t42 = t40*t41
1100 t43 = pi*t8
1101 t44 = t42*t43
1102 t46 = exp(-0.8999999998e1_dp*t44)
1103 t47 = t39*t21
1104 t48 = 0.1e1_dp/pi
1105 t49 = 0.1e1_dp/t8
1106 t51 = t46 - 0.10e1_dp
1107 t52 = t48*t49*t51
1108 t55 = t46 - 0.15e1_dp - 0.5555555558e-1_dp*t47*t52
1109 t59 = t26*t34 + 0.3333333334e0_dp*t36*t38*t55
1110 t60 = t27*t59
1111
1112 e_0(ii) = e_0(ii) - 0.2222222224e0_dp*t24*omega*t60*sx
1113
1114 END IF
1115 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1116 t64 = t23*omega
1117 t68 = rho*t22*omega
1118 t69 = t7*rho
1119 t71 = 0.1e1_dp/t8/t69
1120 t72 = t71*t17
1121 t75 = t16**2
1122 t76 = 0.1e1_dp/t75
1123 t77 = t10*t76
1124 t79 = 0.1e1_dp/t1/t7
1125 t84 = 1 + t5*t10
1126 t85 = sqrt(t84)
1127 t86 = 0.1e1_dp/t85
1128 t87 = t71*t86
1129 t90 = -0.8000000000e1_dp*t11*t79*t12 - 0.8000000000e1_dp*t6*t87
1130 t91 = t77*t90
1131 t94 = -0.5333333333e1_dp*t6*t72 - 0.20e1_dp*t6*t91
1132 t95 = t60*t94
1133 t98 = omega*t27
1134 t99 = sqrt(0.3141592654e1_dp)
1135 t100 = 0.1e1_dp/t99
1136 t101 = t26*t100
1137 t103 = exp(-0.9000000000e1_dp*t44)
1138 t104 = 0.1e1_dp/t23
1139 t105 = t28*t104
1140 t109 = t26*t49
1141 t112 = -0.1500000000e1_dp*t105*t31*t94 + 0.1000000000e1_dp*t30* &
1142 t109
1143 t113 = t103*t112
1144 t116 = omega*t29
1145 t117 = t116*t27
1146 t118 = t37*t55
1147 t122 = t27*t3
1148 t126 = t21**2
1149 t127 = 0.1e1_dp/t126
1150 t128 = t40*t127
1151 t130 = t128*t43*t94
1152 t132 = pi*t37
1153 t133 = t42*t132
1154 t135 = 0.8999999998e1_dp*t130 - 0.5999999999e1_dp*t133
1155 t136 = t135*t46
1156 t137 = t39*t94
1157 t140 = t8*rho
1158 t141 = 0.1e1_dp/t140
1159 t143 = t48*t141*t51
1160 t146 = t47*t48
1161 t147 = t49*t135
1162 t148 = t147*t46
1163 t151 = t136 - 0.5555555558e-1_dp*t137*t52 + 0.3703703705e-1_dp*t47 &
1164 *t143 - 0.5555555558e-1_dp*t146*t148
1165 t155 = real(2*t101*t113, kind=dp) + 0.1666666667e0_dp*t117*t118*t94 - &
1166 0.1111111111e0_dp*t36*t122*t55 + 0.3333333334e0_dp*t36*t38* &
1167 t151
1168
1169 e_rho_spin(ii) = e_rho_spin(ii) + (-0.2222222224e0_dp*t64*t60 - 0.3333333336e0_dp*t68*t95 - &
1170 0.2222222224e0_dp*t24*t98*t155)*sx
1171
1172 t168 = 0.60e1_dp*beta*t3*t12 + 0.60e1_dp*t11*t10*t86
1173 t169 = t77*t168
1174 t172 = 0.40e1_dp*t11*t18 - 0.20e1_dp*t6*t169
1175 t173 = t60*t172
1176 t176 = pi*t100
1177 t177 = t176*t103
1178 t185 = t128*pi
1179 t186 = t8*t172
1180 t190 = t39*t172
1181 t196 = 0.8999999998e1_dp*t185*t186*t46 - 0.5555555558e-1_dp*t190 &
1182 *t52 - 0.5000000001e0_dp*t41*t172*t46
1183 t200 = -0.3000000000e1_dp*t177*t105*t1*t172 + 0.1666666667e0_dp* &
1184 t117*t118*t172 + 0.3333333334e0_dp*t36*t38*t196
1185
1186 e_ndrho_spin(ii) = e_ndrho_spin(ii) + (-0.3333333336e0_dp*t68*t173 - 0.2222222224e0_dp*t24*t98 &
1187 *t200)*sx
1188
1189 END IF
1190 IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1191 t207 = t27*t155
1192 t211 = rho*t29*omega
1193 t212 = t94**2
1194 t213 = t60*t212
1195 t216 = t207*t94
1196 t219 = t7**2
1197 t221 = 0.1e1_dp/t8/t219
1198 t222 = t221*t17
1199 t225 = t71*t76
1200 t226 = t225*t90
1201 t230 = 0.1e1_dp/t75/t16
1202 t231 = t10*t230
1203 t232 = t90**2
1204 t233 = t231*t232
1205 t237 = 0.1e1_dp/t1/t69
1206 t241 = t221*t86
1207 t244 = t5**2
1208 t245 = beta*t244
1209 t250 = 0.1e1_dp/t85/t84
1210 t251 = 0.1e1_dp/t1/t219/t69*t250
1211 t254 = 0.1866666667e2_dp*t11*t237*t12 + 0.4000000000e2_dp*t6*t241 &
1212 - 0.1066666667e2_dp*t245*t251
1213 t255 = t77*t254
1214 t258 = 0.1955555555e2_dp*t6*t222 + 0.1066666667e2_dp*t6*t226 + 0.40e1_dp &
1215 *t6*t233 - 0.20e1_dp*t6*t255
1216 t259 = t60*t258
1217 t264 = 0.9000000000e1_dp*t130 - 0.6000000000e1_dp*t133
1218 t265 = t264*t103
1219 t270 = 0.1e1_dp/t22/t126
1220 t271 = t28*t270
1221 t281 = t26*t141
1222 t284 = 0.2250000000e1_dp*t271*t31*t212 - 0.1000000000e1_dp*t105* &
1223 t109*t94 - 0.1500000000e1_dp*t105*t31*t258 - 0.6666666667e0_dp &
1224 *t30*t281
1225 t285 = t103*t284
1226 t289 = omega*t104*t27
1227 t293 = t3*t55
1228 t297 = t37*t151
1229 t304 = t27*t79
1230 t311 = t126*t21
1231 t312 = 0.1e1_dp/t311
1232 t313 = t40*t312
1233 t316 = 0.1800000000e2_dp*t313*t43*t212
1234 t319 = 0.1200000000e2_dp*t128*t132*t94
1235 t321 = t128*t43*t258
1236 t323 = pi*t3
1237 t325 = 0.2000000000e1_dp*t42*t323
1238 t326 = -t316 + t319 + 0.8999999998e1_dp*t321 + t325
1239 t328 = t135**2
1240 t330 = t39*t258
1241 t335 = t137*t48
1242 t339 = t48*t10*t51
1243 t343 = t141*t135*t46
1244 t346 = t49*t326
1245 t347 = t346*t46
1246 t351 = t49*t328*t46
1247 t354 = t326*t46 + t328*t46 - 0.5555555558e-1_dp*t330*t52 + 0.7407407410e-1_dp &
1248 *t137*t143 - 0.1111111112e0_dp*t335*t148 - 0.6172839508e-1_dp &
1249 *t47*t339 + 0.7407407410e-1_dp*t146*t343 - 0.5555555558e-1_dp &
1250 *t146*t347 - 0.5555555558e-1_dp*t146*t351
1251 t358 = real(2*t101*t265*t112, kind=dp) + real(2*t101*t285, kind=dp) - 0.8333333335e-1_dp &
1252 *t289*t118*t212 - 0.1111111111e0_dp*t117*t293*t94 &
1253 + 0.3333333334e0_dp*t117*t297*t94 + 0.1666666667e0_dp*t117* &
1254 t118*t258 + 0.1481481481e0_dp*t36*t304*t55 - 0.2222222222e0_dp* &
1255 t36*t122*t151 + 0.3333333334e0_dp*t36*t38*t354
1256
1257 e_rho_rho_spin(ii) = e_rho_rho_spin(ii) + (-0.6666666672e0_dp*t36*t95 - 0.4444444448e0_dp*t64*t207 - &
1258 0.1666666668e0_dp*t211*t213 - 0.6666666672e0_dp*t68*t216 - 0.3333333336e0_dp &
1259 *t68*t259 - 0.2222222224e0_dp*t24*t98*t358)*sx
1260
1261 t365 = t27*t200
1262 t368 = t94*t172
1263 t372 = t365*t94
1264 t377 = t225*t168
1265 t382 = t6*t10
1266 t383 = t230*t90
1267 t384 = t383*t168
1268 t393 = beta*t5*ndrho
1269 t397 = 0.1e1_dp/t1/t219/t7*t250
1270 t400 = -0.8000000000e1_dp*beta*t79*t12 - 0.2400000000e2_dp*t11* &
1271 t87 + 0.8000000000e1_dp*t393*t397
1272 t401 = t77*t400
1273 t404 = -0.1066666667e2_dp*t11*t72 + 0.5333333333e1_dp*t6*t377 - 0.40e1_dp &
1274 *t11*t91 + 0.40e1_dp*t382*t384 - 0.20e1_dp*t6*t401
1275 t405 = t60*t404
1276 t408 = t207*t172
1277 t412 = t26*pi*t100
1278 t413 = t412*t128
1279 t417 = t271*t26
1280 t418 = t1*t94
1281 t428 = 0.2250000000e1_dp*t417*t418*t172 - 0.1500000000e1_dp*t105 &
1282 *t31*t404 - 0.5000000000e0_dp*t105*t109*t172
1283 t429 = t103*t428
1284 t435 = t37*t196
1285 t451 = t313*pi
1286 t452 = t8*t94
1287 t455 = 0.1800000000e2_dp*t451*t452*t172
1288 t457 = t128*t43*t404
1289 t460 = t128*t132*t172
1290 t462 = -t455 + 0.8999999998e1_dp*t457 + 0.5999999999e1_dp*t460
1291 t463 = t462*t46
1292 t464 = t135*t40
1293 t465 = t464*t127
1294 t466 = t172*t46
1295 t467 = t43*t466
1296 t470 = t39*t404
1297 t473 = t94*t127
1298 t478 = 0.1e1_dp/rho
1299 t479 = t41*t478
1300 t482 = t190*t48
1301 t486 = t49*t462*t46
1302 t489 = t41*t135
1303 t492 = t463 + 0.8999999998e1_dp*t465*t467 - 0.5555555558e-1_dp*t470 &
1304 *t52 - 0.5000000001e0_dp*t473*t466 + 0.3703703705e-1_dp*t190*t143 &
1305 + 0.3333333334e0_dp*t479*t466 - 0.5555555558e-1_dp*t482*t148 &
1306 - 0.5555555558e-1_dp*t146*t486 - 0.5000000001e0_dp*t489*t466
1307 t496 = 0.1800000000e2_dp*t413*t186*t113 + real(2*t101*t429, kind=dp) &
1308 - 0.8333333335e-1_dp*t289*t118*t368 + 0.1666666667e0_dp*t117*t435 &
1309 *t94 + 0.1666666667e0_dp*t117*t118*t404 - 0.5555555555e-1_dp &
1310 *t117*t293*t172 - 0.1111111111e0_dp*t36*t122*t196 + 0.1666666667e0_dp &
1311 *t117*t297*t172 + 0.3333333334e0_dp*t36*t38*t492
1312
1313 e_ndrho_rho_spin(ii) = e_ndrho_rho_spin(ii) + (-0.3333333336e0_dp*t36*t173 - 0.2222222224e0_dp*t64*t365 - &
1314 0.1666666668e0_dp*t211*t60*t368 - 0.3333333336e0_dp*t68*t372 &
1315 - 0.3333333336e0_dp*t68*t405 - 0.3333333336e0_dp*t68*t408 - 0.2222222224e0_dp &
1316 *t24*t98*t496)*sx
1317
1318 t501 = t172**2
1319 t502 = t60*t501
1320 t505 = t365*t172
1321 t508 = beta*t10
1322 t513 = t168**2
1323 t514 = t231*t513
1324 t519 = t219*rho
1325 t521 = 0.1e1_dp/t1/t519
1326 t525 = 0.120e2_dp*t508*t86 - 0.60e1_dp*t6*t521*t250
1327 t526 = t77*t525
1328 t529 = 0.40e1_dp*t508*t17 - 0.80e1_dp*t11*t169 + 0.40e1_dp*t6*t514 &
1329 - 0.20e1_dp*t6*t526
1330 t530 = t60*t529
1331 t533 = pi**2
1332 t534 = t533*t100
1333 t536 = 0.1e1_dp/t39/omega
1334 t537 = t534*t536
1335 t539 = 0.1e1_dp/t22/t311
1336 t562 = t8*t501
1337 t566 = t8*t529
1338 t570 = t39**2
1339 t571 = 0.1e1_dp/t570
1340 t572 = t126**2
1341 t573 = 0.1e1_dp/t572
1342 t574 = t571*t573
1343 t575 = t574*t533
1344 t576 = t2*t501
1345 t580 = t39*t529
1346 t586 = -0.2250000000e2_dp*t451*t562*t46 + 0.8999999998e1_dp*t185 &
1347 *t566*t46 + 0.8099999996e2_dp*t575*t576*t46 - 0.5555555558e-1_dp &
1348 *t580*t52 - 0.5000000001e0_dp*t41*t529*t46
1349 t590 = -0.2700000000e2_dp*t537*t539*rho*t501*t103 + 0.4500000000e1_dp &
1350 *t177*t271*t1*t501 - 0.3000000000e1_dp*t177*t105* &
1351 t1*t529 - 0.8333333335e-1_dp*t289*t118*t501 + 0.3333333334e0_dp &
1352 *t117*t435*t172 + 0.1666666667e0_dp*t117*t118*t529 + 0.3333333334e0_dp &
1353 *t36*t38*t586
1354
1355 e_ndrho_ndrho_spin(ii) = e_ndrho_ndrho_spin(ii) + (-0.1666666668e0_dp*t211*t502 - 0.6666666672e0_dp*t68*t505 &
1356 - 0.3333333336e0_dp*t68*t530 - 0.2222222224e0_dp*t24*t98*t590) &
1357 *sx
1358
1359 END IF
1360 IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
1361 t601 = t27*t358
1362 t605 = rho*t104*omega
1363 t606 = t212*t94
1364 t613 = t94*t258
1365 t624 = 0.1e1_dp/t8/t519
1366 t628 = t221*t76
1367 t632 = t71*t230
1368 t639 = t75**2
1369 t640 = 0.1e1_dp/t639
1370 t641 = t10*t640
1371 t657 = t219**2
1372 t667 = t84**2
1373 t669 = 0.1e1_dp/t85/t667
1374 t677 = -0.9125925923e2_dp*t6*t624*t17 - 0.5866666667e2_dp*t6*t628 &
1375 *t90 - 0.3200000001e2_dp*t6*t632*t232 + 0.1600000000e2_dp*t6 &
1376 *t225*t254 - 0.120e2_dp*t6*t641*t232*t90 + 0.120e2_dp*t382 &
1377 *t383*t254 - 0.20e1_dp*t6*t77*(-0.6222222223e2_dp*t11/t1/ &
1378 t219*t12 - 0.2115555556e3_dp*t6*t624*t86 + 0.1315555556e3_dp* &
1379 t245/t1/t657*t250 - 0.4266666668e2_dp*beta*t244*t5/t657 &
1380 /t69*t669)
1381 t687 = t28*t539
1382 t716 = t264**2
1383 t722 = omega*t270*t27
1384 t735 = t79*t55
1385 t739 = t3*t151
1386 t746 = t37*t354
1387 t769 = t40*t573
1388 t791 = 0.5400000000e2_dp*t769*t43*t606 - 0.3600000000e2_dp*t313* &
1389 t132*t212 - 0.5400000000e2_dp*t451*t452*t258 - 0.6000000000e1_dp &
1390 *t128*t323*t94 + 0.1800000000e2_dp*t128*t132*t258 + 0.8999999998e1_dp &
1391 *t128*t43*t677 - 0.2666666667e1_dp*t42*pi*t79
1392 t793 = t328*t135
1393 t838 = real(3*t326*t135*t46, kind=dp) + real(t791*t46, kind=dp) + real(t793* &
1394 t46, kind=dp) - 0.5555555558e-1_dp*t39*t677*t52 + 0.1111111112e0_dp*t330 &
1395 *t143 - 0.1666666668e0_dp*t330*t48*t148 - 0.1851851853e0_dp*t137 &
1396 *t339 + 0.2222222223e0_dp*t335*t343 - 0.1666666668e0_dp*t335* &
1397 t347 - 0.1666666668e0_dp*t335*t351 + 0.1646090535e0_dp*t47*t48 &
1398 *t71*t51 - 0.1851851853e0_dp*real(t146, kind=dp)*real(t10, kind=dp)*real(t135, kind=dp) &
1399 *real(t46, kind=dp) + 0.1111111112e0_dp*real(t146, kind=dp)*real(t141, kind=dp)*real(t326, kind=dp) &
1400 *real(t46, kind=dp) + 0.1111111112e0_dp*real(t146, kind=dp)*real(t141, kind=dp)*real(t328, kind=dp) &
1401 *real(t46, kind=dp) - 0.5555555558e-1_dp*real(t146, kind=dp)*real(t49, kind=dp)*real(t791, kind=dp) &
1402 *real(t46, kind=dp) - 0.1666666668e0_dp*real(t146, kind=dp)*real(t346, kind=dp)*real(t136, kind=dp) &
1403 - 0.5555555558e-1_dp*real(t146, kind=dp)*real(t49, kind=dp)*real(t793, kind=dp)* &
1404 REAL(t46, kind=dp)
1405 t842 = 0.2e1_dp*t101*(-t316 + t319 + 0.9000000000e1_dp*t321 + t325) &
1406 *t103*t112 + 0.2e1_dp*t101*t103*(-0.5625000000e1_dp*t687*t31 &
1407 *t606 + 0.2250000000e1_dp*t271*t109*t212 + 0.6750000000e1_dp* &
1408 t417*t418*t258 + 0.1000000000e1_dp*t105*t281*t94 - 0.1500000000e1_dp &
1409 *t105*t109*t258 - 0.1500000000e1_dp*t105*t31*t677 &
1410 + 0.1111111111e1_dp*t30*t26*t10) + 0.4e1_dp*t101*t265*t284 + &
1411 0.2e1_dp*t101*t716*t103*t112 + 0.1250000000e0_dp*t722*t118 &
1412 *t606 + 0.8333333333e-1_dp*t289*t293*t212 - 0.2500000000e0_dp*t289 &
1413 *t297*t212 - 0.2500000000e0_dp*t289*t118*t613 + 0.2222222222e0_dp &
1414 *t117*t735*t94 - 0.3333333333e0_dp*t117*t739*t94 - &
1415 0.1666666667e0_dp*t117*t293*t258 + 0.5000000001e0_dp*t117*t746 &
1416 *t94 + 0.5000000001e0_dp*t117*t297*t258 + 0.1666666667e0_dp*t117 &
1417 *t118*t677 - 0.3456790122e0_dp*t36*t27*t237*t55 + 0.4444444444e0_dp &
1418 *t36*t304*t151 - 0.3333333333e0_dp*t36*t122*t354 &
1419 + 0.3333333334e0_dp*t36*t38*t838
1420 t846 = -0.5000000004e0_dp*t116*t213 - 0.2000000001e1_dp*t36*t216 &
1421 - 0.1000000001e1_dp*t36*t259 - 0.6666666672e0_dp*t64*t601 + 0.8333333340e-1_dp &
1422 *t605*t60*t606 - 0.5000000004e0_dp*t211*t207*t212 &
1423 - 0.5000000004e0_dp*t211*t60*t613 - 0.1000000001e1_dp*t68* &
1424 t601*t94 - 0.1000000001e1_dp*t68*t207*t258 - 0.3333333336e0_dp* &
1425 t68*t60*t677 - 0.2222222224e0_dp*t24*t98*t842
1426
1427 e_rho_rho_rho_spin(ii) = e_rho_rho_rho_spin(ii) + t846*sx
1428
1429 t857 = t27*t496
1430 t860 = t212*t172
1431 t867 = t94*t404
1432 t880 = t258*t172
1433 t933 = 0.3911111110e2_dp*t11*t222 - 0.1955555555e2_dp*t6*t628*t168 &
1434 + 0.2133333334e2_dp*t11*t226 - 0.2133333334e2_dp*t6*t71*t384 &
1435 + 0.1066666667e2_dp*t6*t225*t400 + 0.80e1_dp*t11*t233 - 0.120e2_dp &
1436 *t382*t640*t232*t168 + 0.80e1_dp*t382*t383*t400 - 0.40e1_dp &
1437 *t11*t255 + 0.40e1_dp*t382*t230*t254*t168 - 0.20e1_dp* &
1438 t6*t77*(0.1866666667e2_dp*beta*t237*t12 + 0.9866666667e2_dp* &
1439 t11*t241 - 0.8266666668e2_dp*t393*t251 + 0.3200000001e2_dp*beta &
1440 *t244*ndrho/t657/t7*t669)
1441 t961 = t687*t26
1442 t1002 = t3*t196
1443 t1009 = 0.2e1_dp*t101*(-t455 + 0.9000000000e1_dp*t457 + 0.6000000000e1_dp &
1444 *t460)*t103*t112 + 0.1800000000e2_dp*t412*t264*t40*t127 &
1445 *t8*t172*t103*t112 + 0.2e1_dp*t101*t265*t428 + 0.1800000000e2_dp &
1446 *t413*t186*t285 + 0.2e1_dp*t101*t103*(-0.5625000000e1_dp &
1447 *t961*t1*t212*t172 + 0.4500000000e1_dp*t417*t418*t404 &
1448 + 0.1500000000e1_dp*t417*t49*t94*t172 - 0.1000000000e1_dp* &
1449 t105*t109*t404 + 0.2250000000e1_dp*t417*t1*t258*t172 - 0.1500000000e1_dp &
1450 *t105*t31*t933 + 0.3333333334e0_dp*t105*t281* &
1451 t172) + 0.1250000000e0_dp*t722*t118*t860 - 0.8333333335e-1_dp*t289 &
1452 *t435*t212 - 0.1666666667e0_dp*t289*t118*t867 + 0.5555555555e-1_dp &
1453 *t289*t293*t368 - 0.1111111111e0_dp*t117*t1002*t94 &
1454 - 0.1111111111e0_dp*t117*t293*t404
1455 t1013 = t37*t492
1456 t1044 = t769*pi
1457 t1069 = 0.5400000000e2_dp*t1044*t8*t212*t172 - 0.3600000000e2_dp &
1458 *t451*t452*t404 - 0.2400000000e2_dp*t451*t37*t94*t172 + &
1459 0.1200000000e2_dp*t128*t132*t404 - 0.1800000000e2_dp*t451*t8* &
1460 t258*t172 + 0.8999999998e1_dp*t128*t43*t933 - 0.2000000000e1_dp &
1461 *t128*t323*t172
1462 t1091 = t127*t172*t46
1463 t1102 = t1069*t46 + 0.8999999998e1_dp*t326*t40*t127*t467 + real(2 &
1464 *t136*t462, kind=dp) + 0.8999999998e1_dp*t328*t40*t127*t467 - &
1465 0.5555555558e-1_dp*t39*t933*t52 - 0.5000000001e0_dp*t258*t127 &
1466 *t466 + 0.7407407410e-1_dp*t470*t143 + 0.6666666668e0_dp*t94*t478 &
1467 *t1091 - 0.1111111112e0_dp*t470*t48*t148 - 0.1111111112e0_dp &
1468 *t335*t486 - 0.1000000001e1_dp*t94*t135*t1091
1469 t1136 = -0.6172839508e-1_dp*t190*t339 - 0.5555555556e0_dp*t41/t7 &
1470 *t466 + 0.7407407410e-1_dp*t482*t343 + 0.7407407410e-1_dp*t146* &
1471 t141*t462*t46 + 0.6666666668e0_dp*t479*t135*t172*t46 - 0.5555555558e-1_dp &
1472 *t482*t347 - 0.5555555558e-1_dp*t146*t49*t1069 &
1473 *t46 - 0.5000000001e0_dp*t41*t326*t466 - 0.5555555558e-1_dp*t482 &
1474 *t351 - 0.1111111112e0_dp*t146*t147*t463 - 0.5000000001e0_dp* &
1475 t41*t328*t466
1476 t1141 = -0.1666666667e0_dp*t289*t297*t368 + 0.3333333334e0_dp*t117 &
1477 *t1013*t94 + 0.3333333334e0_dp*t117*t297*t404 - 0.8333333335e-1_dp &
1478 *t289*t118*t880 + 0.1666666667e0_dp*t117*t435*t258 + &
1479 0.1666666667e0_dp*t117*t118*t933 + 0.7407407405e-1_dp*t117*t735 &
1480 *t172 + 0.1481481481e0_dp*t36*t304*t196 - 0.1111111111e0_dp* &
1481 t117*t739*t172 - 0.2222222222e0_dp*t36*t122*t492 + 0.1666666667e0_dp &
1482 *t117*t746*t172 + 0.3333333334e0_dp*t36*t38*(t1102 &
1483 + t1136)
1484 t1146 = -0.3333333336e0_dp*t117*t59*t94*t172 - 0.6666666672e0_dp &
1485 *t36*t372 - 0.6666666672e0_dp*t36*t405 - 0.6666666672e0_dp*t36 &
1486 *t408 - 0.4444444448e0_dp*t64*t857 + 0.8333333340e-1_dp*t605*t60 &
1487 *t860 - 0.1666666668e0_dp*t211*t365*t212 - 0.3333333336e0_dp* &
1488 t211*t60*t867 - 0.3333333336e0_dp*t211*t207*t368 - 0.6666666672e0_dp &
1489 *t68*t857*t94 - 0.6666666672e0_dp*t68*t207*t404 - 0.1666666668e0_dp &
1490 *t211*t60*t880 - 0.3333333336e0_dp*t68*t365* &
1491 t258 - 0.3333333336e0_dp*t68*t60*t933 - 0.3333333336e0_dp*t68* &
1492 t601*t172 - 0.2222222224e0_dp*t24*t98*(t1009 + t1141)
1493
1494 e_ndrho_rho_rho_spin(ii) = e_ndrho_rho_rho_spin(ii) + t1146*sx
1495
1496 t1153 = t27*t590
1497 t1156 = t94*t501
1498 t1163 = t404*t172
1499 t1167 = t94*t529
1500 t1177 = beta*t71
1501 t1220 = -0.1066666667e2_dp*t1177*t17 + 0.2133333334e2_dp*t11*t377 &
1502 - 0.1066666667e2_dp*t6*t632*t513 + 0.5333333333e1_dp*t6*t225 &
1503 *t525 - 0.40e1_dp*t508*t76*t90 + 0.160e2_dp*t11*t10*t384 - &
1504 0.80e1_dp*t11*t401 - 0.120e2_dp*t382*t640*t90*t513 + 0.80e1_dp &
1505 *t382*t230*t400*t168 + 0.40e1_dp*t382*t383*t525 - 0.20e1_dp &
1506 *t6*t77*(-0.3200000000e2_dp*t1177*t86 + 0.4800000000e2_dp*t6 &
1507 *t397 - 0.2400000000e2_dp*t245/t657/rho*t669)
1508 t1284 = t37*t586
1509 t1334 = 0.5400000000e2_dp*t1044*t452*t501 - 0.3600000000e2_dp*t451 &
1510 *t8*t404*t172 - 0.1800000000e2_dp*t451*t452*t529 + 0.8999999998e1_dp &
1511 *t128*t43*t1220 - 0.1200000000e2_dp*t313*t132*t501 &
1512 + 0.5999999999e1_dp*t128*t132*t529
1513 t1341 = t501*t46
1514 t1345 = t529*t46
1515 t1370 = t40*pi
1516 t1396 = t1334*t46 + 0.1800000000e2_dp*t462*t40*t127*t467 - 0.2250000000e2_dp &
1517 *t464*t312*t43*t1341 + 0.8999999998e1_dp*t465 &
1518 *t43*t1345 - 0.1000000000e1_dp*t404*t127*t466 + 0.8099999996e2_dp &
1519 *t135*t571*t573*t533*t2*t1341 - 0.5555555558e-1_dp*t39 &
1520 *t1220*t52 - 0.5000000001e0_dp*t473*t1345 + 0.3333333334e0_dp* &
1521 t479*t1345 + 0.1000000000e1_dp*t94*t312*t1341 - 0.4500000000e1_dp &
1522 *t94*t573*t501*t1370*t8*t46 + 0.3703703705e-1_dp*t580 &
1523 *t143 + 0.3000000000e1_dp*t312*t37*t501*t1370*t46 - 0.5555555558e-1_dp &
1524 *t580*t48*t148 - 0.1111111112e0_dp*t482*t486 - 0.5555555558e-1_dp &
1525 *t146*t49*t1334*t46 - 0.1000000000e1_dp*t41* &
1526 t462*t466 - 0.5000000001e0_dp*t489*t1345
1527 t1400 = -0.3600000000e2_dp*t412*t313*t562*t113 + 0.1800000000e2_dp &
1528 *t413*t566*t113 + 0.3600000000e2_dp*t413*t186*t429 + 0.1620000000e3_dp &
1529 *t26*t533*t100*t574*t576*t113 + 0.2e1_dp*t101 &
1530 *t103*(-0.5625000000e1_dp*t961*t418*t501 + 0.4500000000e1_dp &
1531 *t417*t1*t404*t172 + 0.2250000000e1_dp*t417*t418*t529 - &
1532 0.1500000000e1_dp*t105*t31*t1220 + 0.7500000000e0_dp*t271*t109 &
1533 *t501 - 0.5000000000e0_dp*t105*t109*t529) + 0.1250000000e0_dp* &
1534 t722*t118*t1156 - 0.1666666667e0_dp*t289*t435*t368 - 0.1666666667e0_dp &
1535 *t289*t118*t1163 - 0.8333333335e-1_dp*t289*t118*t1167 &
1536 + 0.1666666667e0_dp*t117*t1284*t94 + 0.3333333334e0_dp*t117 &
1537 *t435*t404 + 0.1666666667e0_dp*t117*t118*t1220 + 0.2777777778e-1_dp &
1538 *t289*t293*t501 - 0.1111111111e0_dp*t117*t1002*t172 &
1539 - 0.5555555555e-1_dp*t117*t293*t529 - 0.1111111111e0_dp*t36*t122 &
1540 *t586 - 0.8333333335e-1_dp*t289*t297*t501 + 0.3333333334e0_dp &
1541 *t117*t1013*t172 + 0.1666666667e0_dp*t117*t297*t529 + 0.3333333334e0_dp &
1542 *t36*t38*t1396
1543 t1404 = -0.1666666668e0_dp*t116*t502 - 0.6666666672e0_dp*t36*t505 &
1544 - 0.3333333336e0_dp*t36*t530 - 0.2222222224e0_dp*t64*t1153 + 0.8333333340e-1_dp &
1545 *t605*t60*t1156 - 0.3333333336e0_dp*t211*t365 &
1546 *t368 - 0.3333333336e0_dp*t211*t60*t1163 - 0.1666666668e0_dp*t211 &
1547 *t60*t1167 - 0.3333333336e0_dp*t68*t1153*t94 - 0.6666666672e0_dp &
1548 *t68*t365*t404 - 0.3333333336e0_dp*t68*t60*t1220 - 0.1666666668e0_dp &
1549 *t211*t207*t501 - 0.6666666672e0_dp*t68*t857* &
1550 t172 - 0.3333333336e0_dp*t68*t207*t529 - 0.2222222224e0_dp*t24* &
1551 t98*t1400
1552
1553 e_ndrho_ndrho_rho_spin(ii) = e_ndrho_ndrho_rho_spin(ii) + t1404*sx
1554
1555 t1405 = t501*t172
1556 t1412 = t172*t529
1557 t1449 = -0.120e2_dp*t508*t76*t168 + 0.240e2_dp*t11*t514 - 0.120e2_dp &
1558 *t11*t526 - 0.120e2_dp*t6*t641*t513*t168 + 0.120e2_dp*t382 &
1559 *t230*t168*t525 - 0.20e1_dp*t6*t77*(-0.240e2_dp*beta*t521 &
1560 *t250*ndrho + 0.180e2_dp*t393/t657*t669)
1561 t1456 = t1405*t103
1562 t1467 = t533*pi
1563 t1472 = t572*t21
1564 t1553 = 0.1350000000e3_dp*t537/t22/t572*rho*t1456 - 0.8100000000e2_dp &
1565 *t534*t536*t539*rho*t172*t103*t529 - 0.2430000000e3_dp &
1566 *t1467*t100/t570/omega/t22/t1472*t140*t1456 - &
1567 0.1125000000e2_dp*t177*t687*t1*t1405 + 0.1350000000e2_dp*t176 &
1568 *t103*t28*t270*t1*t1412 - 0.3000000000e1_dp*t177*t105* &
1569 t1*t1449 + 0.1250000000e0_dp*t722*t118*t1405 - 0.2500000000e0_dp &
1570 *t289*t435*t501 - 0.2500000000e0_dp*t289*t118*t1412 + 0.5000000001e0_dp &
1571 *t117*t1284*t172 + 0.5000000001e0_dp*t117*t435 &
1572 *t529 + 0.1666666667e0_dp*t117*t118*t1449 + 0.3333333334e0_dp*t36 &
1573 *t38*(0.6750000000e2_dp*t1044*t8*t1405*t46 - 0.6750000000e2_dp &
1574 *t451*t186*t1345 - 0.5264999998e3_dp*t571/t1472*t533 &
1575 *t2*t1405*t46 + 0.8999999998e1_dp*t185*t8*t1449*t46 + 0.2429999999e3_dp &
1576 *t575*t2*t529*t466 + 0.7289999995e3_dp/t570/t39 &
1577 /t572/t126*t1467*t7*t1405*t46 - 0.5555555558e-1_dp*t39 &
1578 *t1449*t52 - 0.5000000001e0_dp*t41*t1449*t46)
1579
1580 e_ndrho_ndrho_ndrho_spin(ii) = e_ndrho_ndrho_ndrho_spin(ii) + (0.8333333340e-1_dp*t605*t60*t1405 - &
1581 0.5000000004e0_dp*t211*t365*t501 - 0.5000000004e0_dp*t211*t60*t1412 - 0.1000000001e1_dp &
1582 *t68*t1153*t172 - 0.1000000001e1_dp*t68*t365*t529 - 0.3333333336e0_dp &
1583 *t68*t60*t1449 - 0.2222222224e0_dp*t24*t98*t1553) &
1584 *sx
1585
1586 END IF
1587 END IF
1588 END DO
1589!$OMP END DO
1590
1591 END SUBROUTINE xb88_lr_lsd_calc
1592
1593END MODULE xc_xbecke88_long_range
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition bibliography.F:28
bibliography::becke1988
integer, save, public becke1988
Definition bibliography.F:43
cp_array_utils
various utilities that regard array of different kinds: output, allocation,... maybe it is not a good...
Definition cp_array_utils.F:18
input_section_types
objects that represent the structure of input sections and the data contained in an input section
Definition input_section_types.F:15
input_section_types::section_vals_val_get
subroutine, public section_vals_val_get(section_vals, keyword_name, i_rep_section, i_rep_val, n_rep_val, val, l_val, i_val, r_val, c_val, l_vals, i_vals, r_vals, c_vals, explicit)
returns the requested value
Definition input_section_types.F:1040
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
mathconstants::rootpi
real(kind=dp), parameter, public rootpi
Definition mathconstants.F:114
xc_derivative_desc
Module with functions to handle derivative descriptors. derivative description are strings have the f...
Definition xc_derivative_desc.F:26
xc_derivative_desc::deriv_norm_drho
integer, parameter, public deriv_norm_drho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_norm_drhoa
integer, parameter, public deriv_norm_drhoa
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rhob
integer, parameter, public deriv_rhob
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rhoa
integer, parameter, public deriv_rhoa
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rho
integer, parameter, public deriv_rho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_norm_drhob
integer, parameter, public deriv_norm_drhob
Definition xc_derivative_desc.F:35
xc_derivative_set_types
represent a group ofunctional derivatives
Definition xc_derivative_set_types.F:14
xc_derivative_set_types::xc_dset_get_derivative
type(xc_derivative_type) function, pointer, public xc_dset_get_derivative(derivative_set, description, allocate_deriv)
returns the requested xc_derivative
Definition xc_derivative_set_types.F:66
xc_derivative_types
Provides types for the management of the xc-functionals and their derivatives.
Definition xc_derivative_types.F:12
xc_derivative_types::xc_derivative_get
subroutine, public xc_derivative_get(deriv, split_desc, order, deriv_data, accept_null_data)
returns various information on the given derivative
Definition xc_derivative_types.F:103
xc_rho_cflags_types
contains the structure
Definition xc_rho_cflags_types.F:14
xc_rho_set_types
contains the structure
Definition xc_rho_set_types.F:14
xc_rho_set_types::xc_rho_set_get
subroutine, public xc_rho_set_get(rho_set, can_return_null, rho, drho, norm_drho, rhoa, rhob, norm_drhoa, norm_drhob, rho_1_3, rhoa_1_3, rhob_1_3, laplace_rho, laplace_rhoa, laplace_rhob, drhoa, drhob, rho_cutoff, drho_cutoff, tau_cutoff, tau, tau_a, tau_b, local_bounds)
returns the various attributes of rho_set
Definition xc_rho_set_types.F:281
xc_xbecke88_long_range
calculates the longrange part of Becke 88 exchange functional
Definition xc_xbecke88_long_range.F:14
xc_xbecke88_long_range::xb88_lr_lda_eval
subroutine, public xb88_lr_lda_eval(rho_set, deriv_set, grad_deriv, xb88_lr_params)
evaluates the becke 88 longrange exchange functional for lda
Definition xc_xbecke88_long_range.F:123
xc_xbecke88_long_range::xb88_lr_lsd_info
subroutine, public xb88_lr_lsd_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_xbecke88_long_range.F:90
xc_xbecke88_long_range::xb88_lr_lda_info
subroutine, public xb88_lr_lda_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_xbecke88_long_range.F:60
xc_xbecke88_long_range::xb88_lr_lsd_eval
subroutine, public xb88_lr_lsd_eval(rho_set, deriv_set, grad_deriv, xb88_lr_params)
evaluates the becke 88 longrange exchange functional for lsd
Definition xc_xbecke88_long_range.F:838
cp_array_utils::cp_3d_r_cp_type
represent a pointer to a contiguous 3d array
Definition cp_array_utils.F:149
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