Line data Source code
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 Calculate the several different kinetic energy functionals
10 : !> with a GGA form
11 : !> \par History
12 : !> JGH (26.02.2003) : OpenMP enabled
13 : !> fawzi (04.2004) : adapted to the new xc interface
14 : !> \author JGH (20.02.2002)
15 : ! **************************************************************************************************
16 : MODULE xc_ke_gga
17 :
18 : USE cp_array_utils, ONLY: cp_3d_r_cp_type
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_functionals_utilities, ONLY: calc_wave_vector,&
32 : set_util
33 : USE xc_input_constants, ONLY: ke_lc,&
34 : ke_llp,&
35 : ke_ol1,&
36 : ke_ol2,&
37 : ke_pbe,&
38 : ke_pw86,&
39 : ke_pw91,&
40 : ke_t92
41 : USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
42 : USE xc_rho_set_types, ONLY: xc_rho_set_get,&
43 : xc_rho_set_type
44 : #include "../base/base_uses.f90"
45 :
46 : IMPLICIT NONE
47 :
48 : PRIVATE
49 :
50 : REAL(KIND=dp), PARAMETER :: f13 = 1.0_dp/3.0_dp, &
51 : f23 = 2.0_dp*f13, &
52 : f43 = 4.0_dp*f13, &
53 : f53 = 5.0_dp*f13
54 :
55 : PUBLIC :: ke_gga_info, ke_gga_lda_eval, ke_gga_lsd_eval
56 :
57 : REAL(KIND=dp) :: cf, b, b_lda, b_lsd, flda, flsd, sfac, t13
58 : REAL(KIND=dp) :: fact, tact
59 : REAL(KIND=dp) :: eps_rho
60 :
61 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_ke_gga'
62 :
63 : CONTAINS
64 :
65 : ! **************************************************************************************************
66 : !> \brief ...
67 : !> \param cutoff ...
68 : ! **************************************************************************************************
69 1780 : SUBROUTINE ke_gga_init(cutoff)
70 :
71 : REAL(KIND=dp), INTENT(IN) :: cutoff
72 :
73 1780 : eps_rho = cutoff
74 1780 : CALL set_util(cutoff)
75 :
76 1780 : cf = 0.3_dp*(3.0_dp*pi*pi)**f23
77 1780 : flda = cf
78 1780 : flsd = flda*2.0_dp**f23
79 : ! the_factor 2^(1/3) for LDA is here
80 1780 : b_lda = 2.0_dp**f43*(3.0_dp*pi*pi)**(f13)
81 1780 : b_lsd = 2.0_dp*(3.0_dp*pi*pi)**(f13)
82 1780 : sfac = 1.0_dp/(2.0_dp*(3.0_dp*pi*pi)**f13)
83 1780 : t13 = 2.0_dp**f13
84 :
85 1780 : END SUBROUTINE ke_gga_init
86 :
87 : ! **************************************************************************************************
88 : !> \brief ...
89 : !> \param functional ...
90 : !> \param lsd ...
91 : !> \param reference ...
92 : !> \param shortform ...
93 : !> \param needs ...
94 : !> \param max_deriv ...
95 : ! **************************************************************************************************
96 2042 : SUBROUTINE ke_gga_info(functional, lsd, reference, shortform, needs, max_deriv)
97 : INTEGER, INTENT(in) :: functional
98 : LOGICAL, INTENT(in) :: lsd
99 : CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
100 : TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
101 : INTEGER, INTENT(out), OPTIONAL :: max_deriv
102 :
103 2042 : IF (PRESENT(reference)) THEN
104 0 : SELECT CASE (functional)
105 : CASE (ke_ol1)
106 : reference = "H. Ou-Yang and M. Levy, "// &
107 0 : "Intl. J. Quant. Chem. 40, 379 (1991); Functional 1"
108 : CASE (ke_ol2)
109 : reference = "H. Ou-Yang and M. Levy, "// &
110 0 : "Intl. J. Quant. Chem. 40, 379 (1991); Functional 2"
111 : CASE (ke_llp)
112 0 : reference = "H. Lee, C. Lee, R.G. Parr, Phys. Rev. A, 44, 768 (1991)"
113 : CASE (ke_pw86)
114 0 : reference = "J.P. Perdew and Y. Wang, Phys. Rev. B, 33, 8800 (1986)"
115 : CASE (ke_pw91)
116 0 : reference = "J.P. Perdew and Y. Wang, Electronic Structure of Solids 91"
117 : CASE (ke_lc)
118 0 : reference = "A. Lembarki and H. Chermette, Phys. Rev. A, 50, 5328 (1994)"
119 : CASE (ke_t92)
120 0 : reference = "A.J. Thakkar, Phys. Rev. A, 46, 6920 (1992)"
121 : CASE (ke_pbe)
122 0 : reference = "J.P.Perdew, K.Burke, M.Ernzerhof, Phys. Rev. Letter, 77, 3865 (1996)"
123 : END SELECT
124 0 : IF (.NOT. lsd) THEN
125 0 : IF (LEN_TRIM(reference) + 6 < LEN(reference)) THEN
126 0 : reference(LEN_TRIM(reference):LEN_TRIM(reference) + 6) = ' {spin unpolarized}'
127 : END IF
128 : END IF
129 : END IF
130 2042 : IF (PRESENT(shortform)) THEN
131 0 : SELECT CASE (functional)
132 : CASE (ke_ol1)
133 0 : shortform = "Ou-Yang-Levy Functional 1"
134 : CASE (ke_ol2)
135 0 : shortform = "Ou-Yang-Levy Functional 2"
136 : CASE (ke_llp)
137 0 : shortform = "Lee-Lee-Parr Functional"
138 : CASE (ke_pw86)
139 0 : shortform = "Perdew-Wang 1986 Functional (kinetic energy)"
140 : CASE (ke_pw91)
141 0 : shortform = "Perdew-Wang 1991 Functional (kinetic energy)"
142 : CASE (ke_lc)
143 0 : shortform = "Lembarki-Chermette kinetic energy functional"
144 : CASE (ke_t92)
145 0 : shortform = "Thakkar 1992 Functional"
146 : CASE (ke_pbe)
147 0 : shortform = "Perdew-Burke-Ernzerhof Functional (kinetic energy)"
148 : END SELECT
149 0 : IF (.NOT. lsd) THEN
150 0 : IF (LEN_TRIM(shortform) + 6 < LEN(shortform)) THEN
151 0 : shortform(LEN_TRIM(shortform):LEN_TRIM(shortform) + 6) = ' {spin unpolarized}'
152 : END IF
153 : END IF
154 : END IF
155 2042 : IF (PRESENT(needs)) THEN
156 2042 : IF (lsd) THEN
157 0 : needs%rho_spin = .TRUE.
158 0 : needs%rho_spin_1_3 = .TRUE.
159 0 : needs%norm_drho_spin = .TRUE.
160 : ELSE
161 2042 : needs%rho = .TRUE.
162 2042 : needs%rho_1_3 = .TRUE.
163 2042 : needs%norm_drho = .TRUE.
164 : END IF
165 : END IF
166 2042 : IF (PRESENT(max_deriv)) max_deriv = 3
167 :
168 2042 : END SUBROUTINE ke_gga_info
169 :
170 : ! **************************************************************************************************
171 : !> \brief ...
172 : !> \param functional ...
173 : !> \param rho_set ...
174 : !> \param deriv_set ...
175 : !> \param order ...
176 : ! **************************************************************************************************
177 1780 : SUBROUTINE ke_gga_lda_eval(functional, rho_set, deriv_set, order)
178 :
179 : INTEGER, INTENT(IN) :: functional
180 : TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
181 : TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
182 : INTEGER, INTENT(IN) :: order
183 :
184 : CHARACTER(LEN=*), PARAMETER :: routineN = 'ke_gga_lda_eval'
185 :
186 : INTEGER :: handle, npoints
187 : INTEGER, DIMENSION(2, 3) :: bo
188 : REAL(KIND=dp) :: drho_cutoff, rho_cutoff
189 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: s
190 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: fs
191 1780 : REAL(KIND=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: e_0, e_ndrho, e_ndrho_ndrho, &
192 1780 : e_ndrho_ndrho_ndrho, e_rho, e_rho_ndrho, e_rho_ndrho_ndrho, e_rho_rho, e_rho_rho_ndrho, &
193 1780 : e_rho_rho_rho, grho, rho, rho13
194 : TYPE(xc_derivative_type), POINTER :: deriv
195 :
196 1780 : CALL timeset(routineN, handle)
197 1780 : NULLIFY (rho, rho13, e_0, e_rho, e_ndrho, &
198 1780 : e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
199 1780 : e_rho_rho_rho, e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho)
200 :
201 : CALL xc_rho_set_get(rho_set, rho_1_3=rho13, rho=rho, &
202 : norm_drho=grho, local_bounds=bo, rho_cutoff=rho_cutoff, &
203 1780 : drho_cutoff=drho_cutoff)
204 1780 : npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
205 1780 : CALL ke_gga_init(rho_cutoff)
206 :
207 5340 : ALLOCATE (s(npoints))
208 7120 : ALLOCATE (fs(npoints, order + 1))
209 :
210 : ! s = norm_drho/(rho^(4/3)*2*(pi*pi*3)^(1/3))
211 1780 : CALL calc_wave_vector("p", rho, grho, s)
212 :
213 1780 : fact = flda
214 : ! Definition of s has changed
215 1780 : b = b_lda
216 : ! tact = t13
217 1780 : tact = 1.0_dp
218 :
219 1780 : SELECT CASE (functional)
220 : CASE (ke_ol1)
221 0 : CALL efactor_ol1(s, fs, order)
222 0 : CPABORT("OL1 functional currently not working properly")
223 : CASE (ke_ol2)
224 0 : CALL efactor_ol2(s, fs, order)
225 0 : CPABORT("OL2 functional currently not working properly")
226 : CASE (ke_llp)
227 736 : CALL efactor_llp(s, fs, order)
228 : CASE (ke_pw86)
229 54 : CALL efactor_pw86(s, fs, order)
230 : CASE (ke_pw91)
231 54 : CALL efactor_pw91(s, fs, order, 1)
232 : CASE (ke_lc)
233 54 : CALL efactor_pw91(s, fs, order, 2)
234 : CASE (ke_t92)
235 294 : CALL efactor_t92(s, fs, order)
236 : CASE (ke_pbe)
237 588 : CALL efactor_pbex(s, fs, order, 1)
238 : CASE DEFAULT
239 1780 : CPABORT("Unsupported functional")
240 : END SELECT
241 :
242 : deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
243 1780 : allocate_deriv=.TRUE.)
244 1780 : CALL xc_derivative_get(deriv, deriv_data=e_0)
245 :
246 1780 : CALL kex_p_0(rho, rho13, fs, e_0, npoints)
247 :
248 1780 : IF (order >= 1) THEN
249 : deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
250 1780 : allocate_deriv=.TRUE.)
251 1780 : CALL xc_derivative_get(deriv, deriv_data=e_rho)
252 : deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
253 1780 : allocate_deriv=.TRUE.)
254 1780 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
255 :
256 : CALL kex_p_1(rho, rho13, s, fs, e_rho=e_rho, e_ndrho=e_ndrho, &
257 1780 : npoints=npoints)
258 : END IF
259 1780 : IF (order >= 2) THEN
260 : deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
261 138 : allocate_deriv=.TRUE.)
262 138 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
263 : deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_norm_drho], &
264 138 : allocate_deriv=.TRUE.)
265 138 : CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho)
266 : deriv => xc_dset_get_derivative(deriv_set, &
267 138 : [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.)
268 138 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
269 :
270 : CALL kex_p_2(rho, rho13, s, fs, e_rho_rho=e_rho_rho, &
271 138 : e_rho_ndrho=e_rho_ndrho, e_ndrho_ndrho=e_ndrho_ndrho, npoints=npoints)
272 : END IF
273 1780 : IF (order >= 3) THEN
274 : deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
275 0 : allocate_deriv=.TRUE.)
276 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
277 : deriv => xc_dset_get_derivative(deriv_set, &
278 0 : [deriv_rho, deriv_rho, deriv_norm_drho], allocate_deriv=.TRUE.)
279 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_ndrho)
280 : deriv => xc_dset_get_derivative(deriv_set, &
281 0 : [deriv_rho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.)
282 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho_ndrho)
283 : deriv => xc_dset_get_derivative(deriv_set, &
284 0 : [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.)
285 0 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)
286 :
287 : CALL kex_p_3(rho, rho13, s, fs, e_rho_rho_rho=e_rho_rho_rho, &
288 : e_rho_rho_ndrho=e_rho_rho_ndrho, e_rho_ndrho_ndrho=e_rho_ndrho_ndrho, &
289 0 : e_ndrho_ndrho_ndrho=e_ndrho_ndrho_ndrho, npoints=npoints)
290 : END IF
291 1780 : IF (order > 3) THEN
292 0 : CPABORT("derivatives bigger than 3 not implemented")
293 : END IF
294 :
295 1780 : DEALLOCATE (s)
296 1780 : DEALLOCATE (fs)
297 :
298 1780 : CALL timestop(handle)
299 :
300 1780 : END SUBROUTINE ke_gga_lda_eval
301 :
302 : ! **************************************************************************************************
303 : !> \brief ...
304 : !> \param functional ...
305 : !> \param rho_set ...
306 : !> \param deriv_set ...
307 : !> \param order ...
308 : ! **************************************************************************************************
309 0 : SUBROUTINE ke_gga_lsd_eval(functional, rho_set, deriv_set, order)
310 :
311 : INTEGER, INTENT(IN) :: functional
312 : TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
313 : TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
314 : INTEGER, INTENT(IN), OPTIONAL :: order
315 :
316 : CHARACTER(len=*), PARAMETER :: routineN = 'ke_gga_lsd_eval'
317 : INTEGER, DIMENSION(2), PARAMETER :: &
318 : norm_drho_spin_name = [deriv_norm_drhoa, deriv_norm_drhob], &
319 : rho_spin_name = [deriv_rhoa, deriv_rhob]
320 :
321 : INTEGER :: handle, ispin, npoints
322 : INTEGER, DIMENSION(2, 3) :: bo
323 : REAL(KIND=dp) :: rho_cutoff
324 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: s
325 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: fs
326 0 : REAL(KIND=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: e_0, e_ndrho, e_ndrho_ndrho, &
327 0 : e_ndrho_ndrho_ndrho, e_rho, e_rho_ndrho, e_rho_ndrho_ndrho, e_rho_rho, e_rho_rho_ndrho, &
328 0 : e_rho_rho_rho
329 0 : TYPE(cp_3d_r_cp_type), DIMENSION(2) :: norm_drho, rho, rho_1_3
330 : TYPE(xc_derivative_type), POINTER :: deriv
331 :
332 0 : CALL timeset(routineN, handle)
333 0 : NULLIFY (e_0, e_ndrho, e_ndrho_ndrho, e_ndrho_ndrho_ndrho, e_rho_ndrho_ndrho, &
334 0 : e_rho_ndrho, e_rho_rho_ndrho, e_rho, e_rho_rho, e_rho_rho_rho)
335 0 : DO ispin = 1, 2
336 0 : NULLIFY (norm_drho(ispin)%array, rho(ispin)%array, rho_1_3(ispin)%array)
337 : END DO
338 :
339 : CALL xc_rho_set_get(rho_set, rhoa_1_3=rho_1_3(1)%array, &
340 : rhob_1_3=rho_1_3(2)%array, rhoa=rho(1)%array, &
341 : rhob=rho(2)%array, norm_drhoa=norm_drho(1)%array, &
342 : norm_drhob=norm_drho(2)%array, rho_cutoff=rho_cutoff, &
343 0 : local_bounds=bo)
344 0 : npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
345 0 : CALL ke_gga_init(rho_cutoff)
346 :
347 0 : ALLOCATE (s(npoints))
348 0 : ALLOCATE (fs(npoints, order + 1))
349 :
350 0 : fact = flsd
351 0 : b = b_lsd
352 0 : tact = 1.0_dp
353 :
354 0 : DO ispin = 1, 2
355 :
356 0 : CALL calc_wave_vector("p", rho(ispin)%array, norm_drho(ispin)%array, s)
357 :
358 0 : SELECT CASE (functional)
359 : CASE (ke_ol1)
360 0 : CALL efactor_ol1(s, fs, order)
361 : CASE (ke_ol2)
362 0 : CALL efactor_ol2(s, fs, order)
363 : CASE (ke_llp)
364 0 : CALL efactor_llp(s, fs, order)
365 : CASE (ke_pw86)
366 0 : tact = (1.0_dp/2.0_dp)**(1.0_dp/3.0_dp)
367 0 : CALL efactor_pw86(s, fs, order, f2_lsd=tact)
368 0 : tact = 1.0_dp
369 : CASE (ke_pbe)
370 0 : tact = (1.0_dp/2.0_dp)**(1.0_dp/3.0_dp)
371 0 : CALL efactor_pbex(s, fs, order, 1, f2_lsd=tact)
372 0 : tact = 1.0_dp
373 : CASE (ke_pw91)
374 0 : tact = (1.0_dp/2.0_dp)**(1.0_dp/3.0_dp)
375 0 : CALL efactor_pw91(s, fs, order, 1, f2_lsd=tact)
376 0 : tact = 1.0_dp
377 : CASE (ke_lc)
378 0 : tact = (1.0_dp/2.0_dp)**(1.0_dp/3.0_dp)
379 0 : CALL efactor_pw91(s, fs, order, 2, f2_lsd=tact)
380 0 : tact = 1.0_dp
381 : CASE (ke_t92)
382 0 : CALL efactor_t92(s, fs, order)
383 : CASE DEFAULT
384 0 : CPABORT("Unsupported functional")
385 : END SELECT
386 :
387 : deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
388 0 : allocate_deriv=.TRUE.)
389 0 : CALL xc_derivative_get(deriv, deriv_data=e_0)
390 :
391 : CALL kex_p_0(rho(ispin)%array, rho_1_3(ispin)%array, fs, &
392 0 : e_0=e_0, npoints=npoints)
393 0 : IF (order >= 1) THEN
394 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin)], &
395 0 : allocate_deriv=.TRUE.)
396 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho)
397 : deriv => xc_dset_get_derivative(deriv_set, [norm_drho_spin_name(ispin)], &
398 0 : allocate_deriv=.TRUE.)
399 0 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
400 :
401 : CALL kex_p_1(rho=rho(ispin)%array, &
402 : r13=rho_1_3(ispin)%array, s=s, fs=fs, e_rho=e_rho, &
403 0 : e_ndrho=e_ndrho, npoints=npoints)
404 : END IF
405 0 : IF (order >= 2) THEN
406 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin), &
407 0 : rho_spin_name(ispin)], allocate_deriv=.TRUE.)
408 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
409 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin), &
410 0 : norm_drho_spin_name(ispin)], allocate_deriv=.TRUE.)
411 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho)
412 : deriv => xc_dset_get_derivative(deriv_set, [norm_drho_spin_name(ispin), &
413 0 : norm_drho_spin_name(ispin)], allocate_deriv=.TRUE.)
414 0 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
415 :
416 : CALL kex_p_2(rho(ispin)%array, rho_1_3(ispin)%array, &
417 0 : s, fs, e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, npoints)
418 : END IF
419 0 : IF (order >= 3) THEN
420 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin), &
421 : rho_spin_name(ispin), rho_spin_name(ispin)], &
422 0 : allocate_deriv=.TRUE.)
423 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
424 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin), &
425 : rho_spin_name(ispin), norm_drho_spin_name(ispin)], &
426 0 : allocate_deriv=.TRUE.)
427 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_ndrho)
428 : deriv => xc_dset_get_derivative(deriv_set, [rho_spin_name(ispin), &
429 : norm_drho_spin_name(ispin), norm_drho_spin_name(ispin)], &
430 0 : allocate_deriv=.TRUE.)
431 0 : CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho_ndrho)
432 : deriv => xc_dset_get_derivative(deriv_set, [norm_drho_spin_name(ispin), &
433 : norm_drho_spin_name(ispin), norm_drho_spin_name(ispin)], &
434 0 : allocate_deriv=.TRUE.)
435 0 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)
436 :
437 : CALL kex_p_3(rho(ispin)%array, &
438 : rho_1_3(ispin)%array, s, fs, e_rho_rho_rho, e_rho_rho_ndrho, &
439 0 : e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, npoints)
440 : END IF
441 0 : IF (order > 3) THEN
442 0 : CPABORT("derivatives bigger than 3 not implemented")
443 : END IF
444 :
445 : END DO
446 :
447 0 : DEALLOCATE (s)
448 0 : DEALLOCATE (fs)
449 0 : CALL timestop(handle)
450 0 : END SUBROUTINE ke_gga_lsd_eval
451 :
452 : ! **************************************************************************************************
453 : !> \brief ...
454 : !> \param rho ...
455 : !> \param r13 ...
456 : !> \param fs ...
457 : !> \param e_0 ...
458 : !> \param npoints ...
459 : ! **************************************************************************************************
460 1780 : SUBROUTINE kex_p_0(rho, r13, fs, e_0, npoints)
461 :
462 : REAL(KIND=dp), DIMENSION(*), INTENT(IN) :: rho, r13
463 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: fs
464 : REAL(KIND=dp), DIMENSION(*), INTENT(INOUT) :: e_0
465 : INTEGER, INTENT(in) :: npoints
466 :
467 : INTEGER :: ip
468 :
469 : !$OMP PARALLEL DO DEFAULT(NONE) &
470 : !$OMP SHARED(npoints, rho, e_0, fact, r13, fs, eps_rho) &
471 1780 : !$OMP PRIVATE(ip)
472 :
473 : DO ip = 1, npoints
474 :
475 : IF (rho(ip) > eps_rho) THEN
476 : e_0(ip) = e_0(ip) + fact*r13(ip)*r13(ip)*rho(ip)*fs(ip, 1)
477 : END IF
478 :
479 : END DO
480 :
481 : !$OMP END PARALLEL DO
482 :
483 1780 : END SUBROUTINE kex_p_0
484 :
485 : ! **************************************************************************************************
486 : !> \brief ...
487 : !> \param rho ...
488 : !> \param r13 ...
489 : !> \param s ...
490 : !> \param fs ...
491 : !> \param e_rho ...
492 : !> \param e_ndrho ...
493 : !> \param npoints ...
494 : ! **************************************************************************************************
495 1780 : SUBROUTINE kex_p_1(rho, r13, s, fs, e_rho, e_ndrho, npoints)
496 :
497 : REAL(KIND=dp), DIMENSION(*), INTENT(IN) :: rho, r13, s
498 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: fs
499 : REAL(KIND=dp), DIMENSION(*), INTENT(INOUT) :: e_rho, e_ndrho
500 : INTEGER, INTENT(in) :: npoints
501 :
502 : INTEGER :: ip
503 : REAL(KIND=dp) :: a0, a1, sx, sy
504 :
505 : !$OMP PARALLEL DO DEFAULT(NONE) &
506 : !$OMP SHARED(npoints, rho, eps_rho, fact, r13, sfac, tact) &
507 : !$OMP SHARED(fs, e_rho, e_ndrho, s) &
508 1780 : !$OMP PRIVATE(ip,a0,a1,sx,sy)
509 :
510 : DO ip = 1, npoints
511 :
512 : IF (rho(ip) > eps_rho) THEN
513 :
514 : a0 = fact*r13(ip)*r13(ip)*rho(ip)
515 : a1 = f53*fact*r13(ip)*r13(ip)
516 : sx = -f43*s(ip)/rho(ip)
517 : sy = sfac*tact/(r13(ip)*rho(ip))
518 : e_rho(ip) = e_rho(ip) + a1*fs(ip, 1) + a0*fs(ip, 2)*sx
519 : e_ndrho(ip) = e_ndrho(ip) + a0*fs(ip, 2)*sy
520 :
521 : END IF
522 :
523 : END DO
524 :
525 : !$OMP END PARALLEL DO
526 :
527 1780 : END SUBROUTINE kex_p_1
528 :
529 : ! **************************************************************************************************
530 : !> \brief ...
531 : !> \param rho ...
532 : !> \param r13 ...
533 : !> \param s ...
534 : !> \param fs ...
535 : !> \param e_rho_rho ...
536 : !> \param e_rho_ndrho ...
537 : !> \param e_ndrho_ndrho ...
538 : !> \param npoints ...
539 : ! **************************************************************************************************
540 138 : SUBROUTINE kex_p_2(rho, r13, s, fs, e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
541 : npoints)
542 :
543 : REAL(KIND=dp), DIMENSION(*), INTENT(IN) :: rho, r13, s
544 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: fs
545 : REAL(KIND=dp), DIMENSION(*), INTENT(INOUT) :: e_rho_rho, e_rho_ndrho, e_ndrho_ndrho
546 : INTEGER, INTENT(in) :: npoints
547 :
548 : INTEGER :: ip
549 : REAL(KIND=dp) :: a0, a1, a2, sx, sxx, sxy, sy
550 :
551 : !$OMP PARALLEL DO DEFAULT(NONE) &
552 : !$OMP SHARED (npoints, rho, eps_rho, fact, r13) &
553 : !$OMP SHARED (e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, fs) &
554 : !$OMP SHARED(s, sfac, tact) &
555 138 : !$OMP PRIVATE(ip,a0,a1,a2,sx,sy,sxx,sxy)
556 :
557 : DO ip = 1, npoints
558 :
559 : IF (rho(ip) > eps_rho) THEN
560 :
561 : a0 = fact*r13(ip)*r13(ip)*rho(ip)
562 : a1 = f53*fact*r13(ip)*r13(ip)
563 : a2 = f23*f53*fact/r13(ip)
564 : sx = -f43*s(ip)/rho(ip)
565 : sy = sfac*tact/(r13(ip)*rho(ip))
566 : sxx = 28.0_dp/9.0_dp*s(ip)/(rho(ip)*rho(ip))
567 : sxy = -f43*sfac*tact/(r13(ip)*rho(ip)*rho(ip))
568 : e_rho_rho(ip) = e_rho_rho(ip) + a2*fs(ip, 1) + 2.0_dp*a1*fs(ip, 2)*sx + &
569 : a0*fs(ip, 3)*sx*sx + a0*fs(ip, 2)*sxx
570 : e_rho_ndrho(ip) = e_rho_ndrho(ip) + a1*fs(ip, 2)*sy + a0*fs(ip, 3)*sx*sy + &
571 : a0*fs(ip, 2)*sxy
572 : e_ndrho_ndrho(ip) = e_ndrho_ndrho(ip) + a0*fs(ip, 3)*sy*sy
573 :
574 : END IF
575 :
576 : END DO
577 :
578 : !$OMP END PARALLEL DO
579 :
580 138 : END SUBROUTINE kex_p_2
581 :
582 : ! **************************************************************************************************
583 : !> \brief ...
584 : !> \param rho ...
585 : !> \param r13 ...
586 : !> \param s ...
587 : !> \param fs ...
588 : !> \param e_rho_rho_rho ...
589 : !> \param e_rho_rho_ndrho ...
590 : !> \param e_rho_ndrho_ndrho ...
591 : !> \param e_ndrho_ndrho_ndrho ...
592 : !> \param npoints ...
593 : ! **************************************************************************************************
594 0 : SUBROUTINE kex_p_3(rho, r13, s, fs, e_rho_rho_rho, e_rho_rho_ndrho, &
595 : e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, npoints)
596 :
597 : REAL(KIND=dp), DIMENSION(*), INTENT(IN) :: rho, r13, s
598 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: fs
599 : REAL(KIND=dp), DIMENSION(*), INTENT(inout) :: e_rho_rho_rho, e_rho_rho_ndrho, &
600 : e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho
601 : INTEGER, INTENT(in) :: npoints
602 :
603 : INTEGER :: ip
604 : REAL(KIND=dp) :: a0, a1, a2, a3, sx, sxx, sxxx, sxxy, &
605 : sxy, sy
606 :
607 : !$OMP PARALLEL DO DEFAULT(NONE) &
608 : !$OMP SHARED(npoints, rho, eps_rho, fact, r13) &
609 : !$OMP SHARED(s, sfac, tact, fs, e_rho_rho_rho) &
610 : !$OMP SHARED(e_rho_rho_ndrho, e_rho_ndrho_ndrho) &
611 : !$OMP SHARED(e_ndrho_ndrho_ndrho) &
612 0 : !$OMP PRIVATE(ip,a0,a1,a2,a3,sx,sy,sxx,sxy,sxxx,sxxy)
613 :
614 : DO ip = 1, npoints
615 :
616 : IF (rho(ip) > eps_rho) THEN
617 :
618 : a0 = fact*r13(ip)*r13(ip)*rho(ip)
619 : a1 = f53*fact*r13(ip)*r13(ip)
620 : a2 = f23*f53*fact/r13(ip)
621 : a3 = -f13*f23*f53*fact/(r13(ip)*rho(ip))
622 : sx = -f43*s(ip)/rho(ip)
623 : sy = sfac*tact/(r13(ip)*rho(ip))
624 : sxx = 28.0_dp/9.0_dp*s(ip)/(rho(ip)*rho(ip))
625 : sxy = -f43*sfac*tact/(r13(ip)*rho(ip)*rho(ip))
626 : sxxx = -280.0_dp/27.0_dp*s(ip)/(rho(ip)*rho(ip)*rho(ip))
627 : sxxy = 28.0_dp/9.0_dp*sfac*tact/(r13(ip)*rho(ip)*rho(ip)*rho(ip))
628 : e_rho_rho_rho(ip) = e_rho_rho_rho(ip) + a3*fs(ip, 1) + 3.0_dp*a2*fs(ip, 2)*sx + &
629 : 3.0_dp*a1*fs(ip, 3)*sx*sx + 3.0_dp*a1*fs(ip, 2)*sxx + &
630 : a0*fs(ip, 4)*sx*sx*sx + 3.0_dp*a0*fs(ip, 3)*sx*sxx + &
631 : a0*fs(ip, 2)*sxxx
632 : e_rho_rho_ndrho(ip) = e_rho_rho_ndrho(ip) + a2*fs(ip, 2)*sy + 2.0_dp*a1*fs(ip, 3)*sx*sy + &
633 : 2.0_dp*a1*fs(ip, 2)*sxy + a0*fs(ip, 4)*sx*sx*sy + &
634 : 2.0_dp*a0*fs(ip, 3)*sx*sxy + a0*fs(ip, 3)*sxx*sy + &
635 : a0*fs(ip, 2)*sxxy
636 : e_rho_ndrho_ndrho(ip) = e_rho_ndrho_ndrho(ip) + a1*fs(ip, 3)*sy*sy + a0*fs(ip, 4)*sx*sy*sy + &
637 : 2.0_dp*a0*fs(ip, 3)*sxy*sy
638 : e_ndrho_ndrho_ndrho(ip) = e_ndrho_ndrho_ndrho(ip) + a0*fs(ip, 4)*sy*sy*sy
639 :
640 : END IF
641 :
642 : END DO
643 :
644 : !$OMP END PARALLEL DO
645 :
646 0 : END SUBROUTINE kex_p_3
647 :
648 : ! Enhancement Factors
649 : ! **************************************************************************************************
650 : !> \brief ...
651 : !> \param s ...
652 : !> \param fs ...
653 : !> \param m ...
654 : ! **************************************************************************************************
655 0 : SUBROUTINE efactor_ol1(s, fs, m)
656 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
657 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
658 : INTEGER, INTENT(IN) :: m
659 :
660 : INTEGER :: ip
661 : REAL(KIND=dp) :: t1, t2
662 :
663 0 : t1 = b*b/(72.0_dp*cf)
664 0 : t2 = 0.001878_dp*b
665 :
666 : !$OMP PARALLEL DO DEFAULT(NONE) &
667 : !$OMP SHARED(s, m, fs, t1, t2) &
668 0 : !$OMP PRIVATE(ip)
669 :
670 : DO ip = 1, SIZE(s)
671 : SELECT CASE (m)
672 : CASE (0)
673 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)
674 : CASE (1)
675 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)
676 : fs(ip, 2) = 2.0_dp*t1*s(ip) + t2
677 : CASE (2:3)
678 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)
679 : fs(ip, 2) = 2.0_dp*t1*s(ip) + t2
680 : fs(ip, 3) = 2.0_dp*t1
681 : CASE DEFAULT
682 : CPABORT("Illegal order.")
683 : END SELECT
684 : END DO
685 :
686 : !$OMP END PARALLEL DO
687 :
688 0 : IF (m == 3) fs(:, 4) = 0.0_dp
689 :
690 0 : END SUBROUTINE efactor_ol1
691 : ! **************************************************************************************************
692 : !> \brief ...
693 : !> \param s ...
694 : !> \param fs ...
695 : !> \param m ...
696 : ! **************************************************************************************************
697 0 : SUBROUTINE efactor_ol2(s, fs, m)
698 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
699 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
700 : INTEGER, INTENT(IN) :: m
701 :
702 : INTEGER :: ip
703 : REAL(KIND=dp) :: t1, t2, t3, y
704 :
705 0 : t1 = b*b/(72.0_dp*cf)
706 0 : t2 = 0.0245_dp*b
707 0 : t3 = 2.0_dp**f53*b
708 :
709 : !$OMP PARALLEL DO DEFAULT(NONE) &
710 : !$OMP SHARED(s, m, t1, t2, t3, fs) &
711 0 : !$OMP PRIVATE(ip,y)
712 :
713 : DO ip = 1, SIZE(s)
714 : y = 1.0_dp/(1.0_dp + t3*s(ip))
715 : SELECT CASE (m)
716 : CASE (0)
717 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)*y
718 : CASE (1)
719 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)*y
720 : fs(ip, 2) = 2.0_dp*t1*s(ip) + t2*y*y
721 : CASE (2)
722 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)*y
723 : fs(ip, 2) = 2.0_dp*t1*s(ip) + t2*y*y
724 : fs(ip, 3) = 2.0_dp*(t1 - t2*t3*y*y*y)
725 : CASE (3)
726 : fs(ip, 1) = 1.0_dp + t1*s(ip)*s(ip) + t2*s(ip)*y
727 : fs(ip, 2) = 2.0_dp*t1*s(ip) + t2*y*y
728 : fs(ip, 3) = 2.0_dp*(t1 - t2*t3*y*y*y)
729 : fs(ip, 4) = 6.0_dp*t2*t3*t3*y*y*y*y
730 : CASE DEFAULT
731 : CPABORT("Illegal order.")
732 : END SELECT
733 : END DO
734 :
735 : !$OMP END PARALLEL DO
736 :
737 0 : END SUBROUTINE efactor_ol2
738 : ! **************************************************************************************************
739 : !> \brief ...
740 : !> \param s ...
741 : !> \param fs ...
742 : !> \param m ...
743 : ! **************************************************************************************************
744 736 : SUBROUTINE efactor_llp(s, fs, m)
745 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
746 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
747 : INTEGER, INTENT(IN) :: m
748 :
749 : INTEGER :: ip
750 : REAL(KIND=dp) :: as, bs, p, q, sas, sbs, t1, t10, t11, t12, t133, t16, t17, t19, t2, t20, &
751 : t22, t23, t26, t28, t29, t3, t30, t33, t36, t39, t4, t40, t42, t43, t45, t46, t47, t49, &
752 : t5, t50, t54, t55, t7, t71, t8, t9, x, ys
753 :
754 736 : p = 0.0044188_dp*b*b
755 736 : q = 0.0253_dp*b
756 :
757 : !$OMP PARALLEL DO DEFAULT(NONE) &
758 : !$OMP SHARED(s, m, fs, p, q, b) &
759 : !$OMP PRIVATE(ip,x,bs,sbs,as,sas,ys,t2,t4,t5,t8,t9,t10,t12) &
760 : !$OMP PRIVATE(t1,t3,t7,t11,t16,t17,t20,t22,t23,t26,t30,t33) &
761 : !$OMP PRIVATE(t40,t42,t43,t45,t46,t47,t49,t50,t71,t133) &
762 736 : !$OMP PRIVATE(t19,t28,t29,t36,t39,t54,t55)
763 :
764 : DO ip = 1, SIZE(s)
765 : x = s(ip)
766 : bs = b*x
767 : sbs = SQRT(bs*bs + 1.0_dp)
768 : as = LOG(bs + sbs)
769 : sas = x*as
770 : ys = 1.0_dp/(1.0_dp + q*sas)
771 : SELECT CASE (m)
772 : CASE (0)
773 : fs(ip, 1) = 1.0_dp + p*x*x*ys
774 : CASE (1)
775 : fs(ip, 1) = 1.0_dp + p*x*x*ys
776 : t2 = q*x
777 : t4 = b**2
778 : t5 = x**2
779 : t8 = SQRT(1.0_dp + t4*t5)
780 : t9 = b*x + t8
781 : t10 = LOG(t9)
782 : t12 = 1.0_dp + t2*t10
783 : t17 = t12**2
784 : fs(ip, 2) = 2.0_dp*p*x/t12 - p*t5/t17*(q*t10 + t2*(b + 1.0_dp/t8*t4*x)/t9)
785 :
786 : CASE (2)
787 : fs(ip, 1) = 1.0_dp + p*x*x*ys
788 : ! first der
789 : t2 = q*x
790 : t4 = b**2
791 : t5 = x**2
792 : t8 = SQRT(1.0_dp + t4*t5)
793 : t9 = b*x + t8
794 : t10 = LOG(t9)
795 : t12 = 1.0_dp + t2*t10
796 : t17 = t12**2
797 : fs(ip, 2) = 2.0_dp*p*x/t12 - p*t5/t17*(q*t10 + t2*(b + 1.0_dp/t8*t4*x)/t9)
798 :
799 : ! second der
800 : t1 = q*x
801 : t3 = b**2
802 : t4 = x**2
803 : t7 = SQRT(1.0_dp + t3*t4)
804 : t8 = b*x + t7
805 : t9 = LOG(t8)
806 : t11 = 1.0_dp + t1*t9
807 : t16 = t11**2
808 : t17 = 1.0_dp/t16
809 : t20 = 1.0_dp/t7*t3
810 : t22 = b + t20*x
811 : t23 = 1/t8
812 : t26 = q*t9 + t1*t22*t23
813 : t30 = p*t4
814 : t33 = t26**2
815 : t40 = t7**2
816 : t43 = t3**2
817 : t49 = t22**2
818 : t50 = t8**2
819 : fs(ip, 3) = 2.0_dp*p/t11 - 4.0_dp*p*x*t17*t26 + 2.0_dp*t30/t16/ &
820 : t11*t33 - t30*t17*(2.0_dp*q*t22*t23 + t1* &
821 : (-1.0_dp/t40/t7*t43*t4 + t20)*t23 - t1*t49/t50)
822 :
823 : CASE (3)
824 :
825 : fs(ip, 1) = 1.0_dp + p*x*x*ys
826 : ! first der
827 : t2 = q*x
828 : t4 = b**2
829 : t5 = x**2
830 : t8 = SQRT(1.0_dp + t4*t5)
831 : t9 = b*x + t8
832 : t10 = LOG(t9)
833 : t12 = 1.0_dp + t2*t10
834 : t17 = t12**2
835 : fs(ip, 2) = 2.0_dp*p*x/t12 - p*t5/t17*(q*t10 + t2*(b + 1.0_dp/t8*t4*x)/t9)
836 :
837 : ! second der
838 : t1 = q*x
839 : t3 = b**2
840 : t4 = x**2
841 : t7 = SQRT(1.0_dp + t3*t4)
842 : t8 = b*x + t7
843 : t9 = LOG(t8)
844 : t11 = 1.0_dp + t1*t9
845 : t16 = t11**2
846 : t17 = 1.0_dp/t16
847 : t20 = 1.0_dp/t7*t3
848 : t22 = b + t20*x
849 : t23 = 1/t8
850 : t26 = q*t9 + t1*t22*t23
851 : t30 = p*t4
852 : t33 = t26**2
853 : t40 = t7**2
854 : t43 = t3**2
855 : t49 = t22**2
856 : t50 = t8**2
857 : fs(ip, 3) = 2.0_dp*p/t11 - 4.0_dp*p*x*t17*t26 + 2.0_dp*t30/t16/ &
858 : t11*t33 - t30*t17*(2.0_dp*q*t22*t23 + t1* &
859 : (-1.0_dp/t40/t7*t43*t4 + t20)*t23 - t1*t49/t50)
860 :
861 : t1 = q*x
862 : t3 = b**2
863 : t4 = x**2
864 : t7 = SQRT(1 + t3*t4)
865 : t8 = b*x + t7
866 : t9 = LOG(t8)
867 : t11 = 1.0_dp + t1*t9
868 : t12 = t11**2
869 : t133 = 1.0_dp/t12
870 : t17 = 1.0_dp/t7*t3
871 : t19 = b + t17*x
872 : t20 = 1.0_dp/t8
873 : t23 = q*t9 + t1*t19*t20
874 : t26 = p*x
875 : t28 = 1.0_dp/t12/t11
876 : t29 = t23**2
877 : t36 = t7**2
878 : t39 = t3**2
879 : t40 = 1.0_dp/t36/t7*t39
880 : t42 = -t40*t4 + t17
881 : t45 = t19**2
882 : t46 = t8**2
883 : t47 = 1.0_dp/t46
884 : t50 = 2.0_dp*q*t19*t20 + t1*t42*t20 - t1*t45*t47
885 : t54 = p*t4
886 : t55 = t12**2
887 : t71 = t36**2
888 : fs(ip, 4) = &
889 : -6.0_dp*p*t133*t23 + 12.0_dp*t26*t28*t29 - &
890 : 6.0_dp*t26*t133*t50 - 6.0_dp*t54/t55*t29*t23 + &
891 : 6.0_dp*t54*t28*t23*t50 - t54*t133* &
892 : (3.0_dp*q*t42*t20 - 3.0_dp*q*t45*t47 + 3.0_dp*t1* &
893 : (1.0_dp/t71/t7*t39*t3*t4*x - t40*x)*t20 - &
894 : 3.0_dp*t1*t42*t47*t19 + 2.0_dp*t1*t45*t19/t46/t8)
895 :
896 : CASE DEFAULT
897 : CPABORT("Illegal order.")
898 : END SELECT
899 : END DO
900 :
901 : !$OMP END PARALLEL DO
902 :
903 736 : END SUBROUTINE efactor_llp
904 : ! **************************************************************************************************
905 : !> \brief ...
906 : !> \param s ...
907 : !> \param fs ...
908 : !> \param m ...
909 : !> \param f2_lsd ...
910 : ! **************************************************************************************************
911 54 : SUBROUTINE efactor_pw86(s, fs, m, f2_lsd)
912 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
913 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
914 : INTEGER, INTENT(IN) :: m
915 : REAL(dp), OPTIONAL :: f2_lsd
916 :
917 : INTEGER :: ip
918 : REAL(KIND=dp) :: f15, ff, p0, p1, p15, p2, p3, s1, s2, &
919 : s4, s6, t1, t2, t3
920 :
921 54 : t1 = 1.296_dp
922 54 : t2 = 14.0_dp
923 54 : t3 = 0.2_dp
924 54 : f15 = 1.0_dp/15.0_dp
925 54 : ff = 1.0_dp
926 54 : IF (PRESENT(f2_lsd)) ff = f2_lsd
927 :
928 : !$OMP PARALLEL DO DEFAULT(NONE) &
929 : !$OMP SHARED(s, fs, m, t1, t2, t3, f15, ff) &
930 54 : !$OMP PRIVATE(ip, s1, s2, s4, s6, p0, p1, p2, p3, p15)
931 :
932 : DO ip = 1, SIZE(s)
933 : s1 = s(ip)*ff
934 : s2 = s1*s1
935 : s4 = s2*s2
936 : s6 = s2*s4
937 : SELECT CASE (m)
938 : CASE (0)
939 : p0 = 1.0_dp + t1*s2 + t2*s4 + t3*s6
940 : fs(ip, 1) = p0**f15
941 : CASE (1)
942 : p0 = 1.0_dp + t1*s2 + t2*s4 + t3*s6
943 : p1 = s1*ff*(2.0_dp*t1 + 4.0_dp*t2*s2 + 6.0_dp*t3*s4)
944 : p15 = p0**f15
945 : fs(ip, 1) = p15
946 : fs(ip, 2) = f15*p1*p15/p0
947 : CASE (2)
948 : p0 = 1.0_dp + t1*s2 + t2*s4 + t3*s6
949 : p1 = s1*ff*(2.0_dp*t1 + 4.0_dp*t2*s2 + 6.0_dp*t3*s4)
950 : p2 = ff*ff*(2.0_dp*t1 + 12.0_dp*t2*s2 + 30.0_dp*t3*s4)
951 : p15 = p0**f15
952 : fs(ip, 1) = p15
953 : fs(ip, 2) = f15*p1*p15/p0
954 : fs(ip, 3) = f15*p15/p0*(p2 - 14.0_dp/15.0_dp*p1*p1/p0)
955 : CASE (3)
956 : p0 = 1.0_dp + t1*s2 + t2*s4 + t3*s6
957 : p1 = s1*ff*(2.0_dp*t1 + 4.0_dp*t2*s2 + 6.0_dp*t3*s4)
958 : p2 = ff*ff*(2.0_dp*t1 + 12.0_dp*t2*s2 + 30.0_dp*t3*s4)
959 : p3 = s1*ff*ff*ff*(24.0_dp*t2 + 120.0_dp*t3*s2)
960 : p15 = p0**f15
961 : fs(ip, 1) = p15
962 : fs(ip, 2) = f15*p1*p15/p0
963 : fs(ip, 3) = f15*p15/p0*(p2 - 14.0_dp/15.0_dp*p1*p1/p0)
964 : fs(ip, 4) = f15*p15/p0*(-14.0_dp*f15*p1*p1/p0 + 14.0_dp*14.0_dp*f15*p1*p1*p1/p0/p0 + &
965 : p3 - 14.0_dp*p2*p1/p0 + 14.0_dp*p1*p1/p0/p0)
966 : CASE DEFAULT
967 : CPABORT("Illegal order.")
968 : END SELECT
969 : END DO
970 :
971 : !$OMP END PARALLEL DO
972 :
973 54 : END SUBROUTINE efactor_pw86
974 : ! **************************************************************************************************
975 : !> \brief ...
976 : !> \param s ...
977 : !> \param fs ...
978 : !> \param m ...
979 : ! **************************************************************************************************
980 294 : SUBROUTINE efactor_t92(s, fs, m)
981 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
982 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
983 : INTEGER, INTENT(IN) :: m
984 :
985 : INTEGER :: ip
986 : REAL(KIND=dp) :: a1, a2, as, asp, asp2, asp3, bs, p, q, &
987 : s1, s2, sas, sbs, sbs3, sbs5, t0, w1, &
988 : x, ys
989 :
990 294 : p = 0.0055_dp*b*b
991 294 : q = 0.0253_dp*b
992 294 : a1 = 0.072_dp*b
993 294 : a2 = 2.0_dp**f53*b
994 :
995 : !$OMP PARALLEL DO DEFAULT(NONE) &
996 : !$OMP SHARED(s, fs, m, p, q, a1, a2, b) &
997 : !$OMP PRIVATE(ip, x, bs, sbs, sas, ys, asp, sbs3, asp2, sbs5) &
998 294 : !$OMP PRIVATE(asp3, as, s2, s1, t0, w1)
999 :
1000 : DO ip = 1, SIZE(s)
1001 : x = s(ip)
1002 : bs = b*x
1003 : sbs = SQRT(bs*bs + 1.0_dp)
1004 : as = LOG(bs + sbs)
1005 : sas = x*as
1006 : ys = 1.0_dp/(1.0_dp + q*sas)
1007 : SELECT CASE (m)
1008 : CASE (0)
1009 : fs(ip, 1) = 1.0_dp + p*x*x*ys - a1*x/(1 + a2*x)
1010 : CASE (1)
1011 : asp = as + bs/sbs
1012 : fs(ip, 1) = 1.0_dp + p*x*x*ys - a1*x/(1 + a2*x)
1013 : fs(ip, 2) = 2.0_dp*p*x*ys - p*q*x*x*asp*ys*ys - a1/(1 + a2*x)**2
1014 : CASE (2)
1015 : asp = as + bs/sbs
1016 : sbs3 = sbs*sbs*sbs
1017 : asp2 = 2.0_dp*b/sbs - b*bs*bs/sbs3
1018 : fs(ip, 1) = 1.0_dp + p*x*x*ys - a1*x/(1 + a2*x)
1019 : fs(ip, 2) = 2.0_dp*p*x*ys - p*q*x*x*asp*ys*ys - a1/(1 + a2*x)**2
1020 : fs(ip, 3) = 2.0_dp*p*ys - p*q*x*(4.0_dp*asp + x*asp2)*ys*ys + &
1021 : 2.0_dp*p*q*q*x*x*asp*asp*ys*ys*ys + 2.0_dp*a1*a2/(1 + a2*x)**3
1022 : CASE (3)
1023 : asp = as + bs/sbs
1024 : sbs3 = sbs*sbs*sbs
1025 : sbs5 = sbs3*sbs*sbs
1026 : asp2 = 2.0_dp*b/sbs - b*bs*bs/sbs3
1027 : asp3 = -4.0_dp*b*b*bs/sbs3 + 3.0_dp*b*b*bs*bs*bs/sbs5
1028 : w1 = (4.0_dp*asp + x*asp2)
1029 : fs(ip, 1) = 1.0_dp + p*x*x*ys - a1*x/(1 + a2*x)
1030 : fs(ip, 2) = 2.0_dp*p*x*ys - p*q*x*x*asp*ys*ys - a1/(1 + a2*x)**2
1031 : fs(ip, 3) = 2.0_dp*p*ys - p*q*x*w1*ys*ys + &
1032 : 2.0_dp*p*q*q*x*x*asp*asp*ys*ys*ys + 2.0_dp*a1*a2/(1 + a2*x)**3
1033 :
1034 : s2 = -6*p/(1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**2*(q*LOG(b*x + SQRT(1 + b**2*x**2)) + &
1035 : q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)/(b*x + SQRT(1 + b**2*x**2))) + 12*p*x/ &
1036 : (1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**3*(q*LOG(b*x + SQRT(1 + b**2*x**2)) + &
1037 : q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)/(b*x + SQRT(1 + b**2*x**2)))**2
1038 : s1 = s2 - 6*p*x/(1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**2*(2*q*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)/ &
1039 : (b*x + SQRT(1 + b**2*x**2)) + q*x*(-1/SQRT(1 + b**2*x**2)**3*b**4*x**2 + 1/SQRT(1 + b**2*x**2)*b**2)/ &
1040 : (b*x + SQRT(1 + b**2*x**2)) - q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)**2/ &
1041 : (b*x + SQRT(1 + b**2*x**2))**2) - 6*p*x**2/(1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**4 &
1042 : *(q*LOG(b*x + SQRT(1 + b**2*x**2)) + q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)/(b*x + SQRT(1 + b**2*x**2)))**3
1043 : s2 = s1 + 6*p*x**2/(1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**3*(q*LOG(b*x + SQRT(1 + b**2*x**2)) + &
1044 : q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)/(b*x + SQRT(1 + b**2*x**2)))*(2*q*(b + 1/SQRT(1 + b**2*x**2)*b**2*x) &
1045 : /(b*x + SQRT(1 + b**2*x**2)) + q*x*(-1/SQRT(1 + b**2*x**2)**3*b**4*x**2 + 1/SQRT(1 + b**2*x**2)* &
1046 : b**2)/(b*x + SQRT(1 + b**2*x**2)) - q*x*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)**2/(b*x + SQRT(1 + b**2*x**2))**2)
1047 : t0 = s2 - p*x**2/(1 + q*x*LOG(b*x + SQRT(1 + b**2*x**2)))**2*(3*q*(-1/SQRT(1 + b**2*x**2)**3*b**4*x**2 + &
1048 : 1/SQRT(1 + b**2*x**2)*b**2)/(b*x + SQRT(1 + b**2*x**2)) - 3*q*(b + 1/SQRT(1 + b**2*x**2)*b**2*x)**2/ &
1049 : (b*x + SQRT(1 + b**2*x**2))**2 + q*x*(3/SQRT(1 + b**2*x**2)**5*b**6*x**3 - 3/SQRT(1 + b**2*x**2)**3*b**4*x)/ &
1050 : (b*x + SQRT(1 + b**2*x**2)) - 3*q*x*(-1/SQRT(1 + b**2*x**2)**3*b**4*x**2 + 1/SQRT(1 + b**2*x**2)*b**2)/ &
1051 : (b*x + SQRT(1 + b**2*x**2))**2*(b + 1/SQRT(1 + b**2*x**2)*b**2*x) + 2*q*x*(b + 1/SQRT(1 + b**2*x**2)* &
1052 : b**2*x)**3/(b*x + SQRT(1 + b**2*x**2))**3) - 6*a1/(1 + a2*x)**3*a2**2 + 6*a1*x/(1 + a2*x)**4*a2**3
1053 :
1054 : fs(ip, 4) = t0
1055 :
1056 : CASE DEFAULT
1057 : CPABORT("Illegal order")
1058 : END SELECT
1059 : END DO
1060 :
1061 : !$OMP END PARALLEL DO
1062 :
1063 294 : END SUBROUTINE efactor_t92
1064 : ! **************************************************************************************************
1065 : !> \brief ...
1066 : !> \param s ...
1067 : !> \param fs ...
1068 : !> \param m ...
1069 : !> \param pset ...
1070 : !> \param f2_lsd ...
1071 : ! **************************************************************************************************
1072 588 : SUBROUTINE efactor_pbex(s, fs, m, pset, f2_lsd)
1073 :
1074 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
1075 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
1076 : INTEGER, INTENT(IN) :: m, pset
1077 : REAL(dp), OPTIONAL :: f2_lsd
1078 :
1079 : REAL(KIND=dp), PARAMETER :: kappa1 = 0.804_dp, kappa2 = 1.245_dp, &
1080 : mu = 0.2195149727645171_dp
1081 :
1082 : INTEGER :: ip
1083 : REAL(KIND=dp) :: f0, mk, x, x2, y
1084 :
1085 : IF (pset == 1) mk = mu/kappa1
1086 588 : IF (pset == 2) mk = mu/kappa2
1087 :
1088 588 : f0 = 1.0_dp/tact
1089 588 : IF (PRESENT(f2_lsd)) f0 = f2_lsd
1090 :
1091 : !$OMP PARALLEL DO DEFAULT(NONE) &
1092 : !$OMP SHARED(s, m, fs, f0, mk) &
1093 588 : !$OMP PRIVATE(ip,x,x2,y)
1094 :
1095 : DO ip = 1, SIZE(s)
1096 : x = s(ip)*f0
1097 : x2 = x*x
1098 : y = 1.0_dp/(1.0_dp + mk*x2)
1099 : SELECT CASE (m)
1100 : CASE (0)
1101 : fs(ip, 1) = 1.0_dp + mu*x2*y
1102 : CASE (1)
1103 : fs(ip, 1) = 1.0_dp + mu*x2*y
1104 : fs(ip, 2) = 2.0_dp*mu*x*y*y*f0
1105 : CASE (2)
1106 : fs(ip, 1) = 1.0_dp + mu*x2*y
1107 : fs(ip, 2) = 2.0_dp*mu*x*y*y*f0
1108 : fs(ip, 3) = -2.0_dp*mu*(3.0_dp*mk*x2 - 1.0_dp)*y*y*y*f0*f0
1109 : CASE (3)
1110 : fs(ip, 1) = 1.0_dp + mu*x2*y
1111 : fs(ip, 2) = 2.0_dp*mu*x*y*y*f0
1112 : fs(ip, 3) = -2.0_dp*mu*(3.0_dp*mk*x2 - 1.0_dp)*y*y*y*f0*f0
1113 : fs(ip, 4) = 24.0_dp*mu*mk*x*(mk*x2 - 1.0_dp)*y*y*y*y*f0*f0*f0
1114 : CASE DEFAULT
1115 : CPABORT("Illegal order.")
1116 : END SELECT
1117 : END DO
1118 :
1119 : !$OMP END PARALLEL DO
1120 :
1121 588 : END SUBROUTINE efactor_pbex
1122 :
1123 : ! **************************************************************************************************
1124 : !> \brief ...
1125 : !> \param s ...
1126 : !> \param fs ...
1127 : !> \param m ...
1128 : !> \param pset ...
1129 : !> \param f2_lsd ...
1130 : ! **************************************************************************************************
1131 108 : SUBROUTINE efactor_pw91(s, fs, m, pset, f2_lsd)
1132 : REAL(KIND=dp), DIMENSION(:), INTENT(IN) :: s
1133 : REAL(KIND=dp), DIMENSION(:, :), INTENT(OUT) :: fs
1134 : INTEGER, INTENT(IN) :: m, pset
1135 : REAL(dp), OPTIONAL :: f2_lsd
1136 :
1137 : INTEGER :: ip
1138 : REAL(dp) :: ff, t1, t10, t101, t106, t109, t111, t113, t119, t12, t123, t124, t13, t14, t15, &
1139 : t16, t17, t18, t19, t2, t20, t21, t22, t23, t25, t26, t27, t28, t29, t3, t30, t31, t33, &
1140 : t35, t37, t38, t39, t4, t40, t44, t47, t48, t5, t50, t51, t53, t55, t56, t57, t58, t59, &
1141 : t6, t60, t64, t65, t69, t7, t70, t71, t73, t77, t78, t8, t80, t82, t9, t90, t93, t94, &
1142 : t96, t98
1143 : REAL(KIND=dp) :: a1, a2, a3, a4, a5, bb, o, pa(6, 2), x
1144 :
1145 : ! parameter set 1: Perdew-Wang
1146 : ! parameter set 2: Lembarki-Chermette
1147 :
1148 : pa(1:6, 1) = [0.19645_dp, 0.2743_dp, &
1149 : 0.1508_dp, 100.0_dp, &
1150 756 : 7.7956_dp, 0.004_dp]
1151 : pa(1:6, 2) = [0.093907_dp, 0.26608_dp, &
1152 : 0.0809615_dp, 100.0_dp, &
1153 756 : 76.320_dp, 0.57767e-4_dp]
1154 108 : o = 1.0_dp
1155 108 : ff = 1.0_dp
1156 108 : IF (PRESENT(f2_lsd)) ff = f2_lsd
1157 108 : a1 = pa(1, pset)*FF
1158 108 : a2 = pa(2, pset)*ff*ff
1159 108 : a3 = pa(3, pset)*ff*ff
1160 108 : a4 = pa(4, pset)*ff*ff
1161 108 : bb = pa(5, pset)*ff
1162 : ! it should be valid also for lsd
1163 108 : a5 = pa(6, pset)*ff*ff*ff*ff
1164 :
1165 : !$OMP PARALLEL DEFAULT(NONE) &
1166 : !$OMP SHARED(s, fs, m, a1, a2, a3, a4, a5, bb, pa, o, ff) &
1167 : !$OMP PRIVATE(x,t1,t10,t101,t106,t109,t111,t113,t119,t12,t123) &
1168 : !$OMP PRIVATE(t124,t13,t14,t15,t16,t17,t18,t19,t2,t20,t21,t22) &
1169 : !$OMP PRIVATE(t23,t25,t26,t27,t28,t29,t3,t30,t31,t33,t35,t37) &
1170 : !$OMP PRIVATE(t38,t39,t4,t40,t44,t47,t48,t5,t50,t51,t53,t55) &
1171 : !$OMP PRIVATE(t56,t57,t58,t59,t6,t60,t64,t65,t69,t7,t70,t71) &
1172 108 : !$OMP PRIVATE(t73,t77,t78,t8,t80,t82,t9,t90,t93,t94,t96,t98,ip)
1173 :
1174 : IF (m >= 0) THEN
1175 : !$OMP DO
1176 : DO ip = 1, SIZE(s)
1177 : x = s(ip)
1178 : t3 = bb**2
1179 : t4 = x**2
1180 : t7 = SQRT(o + t3*t4)
1181 : t9 = LOG(bb*x + t7)
1182 : t10 = a1*x*t9
1183 : t12 = EXP(-a4*t4)
1184 : t17 = t4**2
1185 : fs(ip, 1) = (o + t10 + (a2 - a3*t12)*t4)/(o + t10 + a5*t17)
1186 : END DO
1187 : !$OMP END DO
1188 : END IF
1189 : IF (m >= 1) THEN
1190 : !$OMP DO
1191 : DO ip = 1, SIZE(s)
1192 : x = s(ip)
1193 : t2 = bb**2
1194 : t3 = x**2
1195 : t6 = SQRT(o + t2*t3)
1196 : t7 = bb*x + t6
1197 : t8 = LOG(t7)
1198 : t9 = a1*t8
1199 : t10 = a1*x
1200 : t17 = t10*(bb + 1/t6*t2*x)/t7
1201 : t19 = t3*x
1202 : t21 = EXP(-a4*t3)
1203 : t26 = a2 - a3*t21
1204 : t30 = t10*t8
1205 : t31 = t3**2
1206 : t33 = o + t30 + a5*t31
1207 : t38 = t33**2
1208 : fs(ip, 2) = &
1209 : (t9 + t17 + 2._dp*a3*a4*t19*t21 + 2._dp*t26*x)/ &
1210 : t33 - (o + t30 + t26*t3)/t38*(t9 + t17 + 4._dp*a5*t19)
1211 : END DO
1212 : !$OMP END DO
1213 : END IF
1214 : IF (m >= 2) THEN
1215 : !$OMP DO
1216 : DO ip = 1, SIZE(s)
1217 : x = s(ip)
1218 : t1 = bb**2
1219 : t2 = x**2
1220 : t5 = SQRT(o + t1*t2)
1221 : t7 = o/t5*t1
1222 : t9 = bb + t7*x
1223 : t12 = bb*x + t5
1224 : t13 = o/t12
1225 : t15 = 2._dp*a1*t9*t13
1226 : t16 = a1*x
1227 : t17 = t5**2
1228 : t20 = t1**2
1229 : t25 = t16*(-o/t17/t5*t20*t2 + t7)*t13
1230 : t26 = t9**2
1231 : t27 = t12**2
1232 : t30 = t16*t26/t27
1233 : t31 = a3*a4
1234 : t33 = EXP(-a4*t2)
1235 : t37 = a4**2
1236 : t39 = t2**2
1237 : t44 = a3*t33
1238 : t47 = LOG(t12)
1239 : t48 = t16*t47
1240 : t50 = o + t48 + a5*t39
1241 : t53 = a1*t47
1242 : t55 = t16*t9*t13
1243 : t56 = t2*x
1244 : t60 = a2 - t44
1245 : t64 = t50**2
1246 : t65 = o/t64
1247 : t69 = t53 + t55 + 4._dp*a5*t56
1248 : t73 = o + t48 + t60*t2
1249 : t77 = t69**2
1250 : fs(ip, 3) = &
1251 : (t15 + t25 - t30 + 10._dp*t31*t2*t33 - 4._dp*a3*t37*t39*t33 + &
1252 : 2._dp*a2 - 2._dp*t44)/t50 - 2._dp* &
1253 : (t53 + t55 + 2._dp*t31*t56*t33 + 2._dp*t60*x)* &
1254 : t65*t69 + 2._dp*t73/t64/t50*t77 - t73*t65*(t15 + t25 - t30 + 12._dp*a5*t2)
1255 : END DO
1256 : !$OMP END DO
1257 : END IF
1258 : IF (m >= 3) THEN
1259 : !$OMP DO
1260 : DO ip = 1, SIZE(s)
1261 : x = s(ip)
1262 : t1 = bb**2
1263 : t2 = x**2
1264 : t5 = SQRT(0.1e1_dp + t1*t2)
1265 : t6 = t5**2
1266 : t9 = t1**2
1267 : t10 = 1/t6/t5*t9
1268 : t13 = 1/t5*t1
1269 : t14 = -t10*t2 + t13
1270 : t17 = bb*x + t5
1271 : t18 = 1/t17
1272 : t20 = 3*a1*t14*t18
1273 : t22 = bb + t13*x
1274 : t23 = t22**2
1275 : t25 = t17**2
1276 : t26 = 1/t25
1277 : t28 = 3*a1*t23*t26
1278 : t29 = a1*x
1279 : t30 = t6**2
1280 : t35 = t2*x
1281 : t40 = 3*t29*(1/t30/t5*t1*t9*t35 - t10*x)*t18
1282 : t44 = 3*t29*t14*t26*t22
1283 : t50 = 2*t29*t23*t22/t25/t17
1284 : t51 = a3*a4
1285 : t53 = EXP(-a4*t2)
1286 : t57 = a4**2
1287 : t58 = a3*t57
1288 : t59 = t35*t53
1289 : t64 = t2**2
1290 : t70 = LOG(t17)
1291 : t71 = t29*t70
1292 : t73 = 0.1e1_dp + t71 + a5*t64
1293 : t78 = 2*a1*t22*t18
1294 : t80 = t29*t14*t18
1295 : t82 = t29*t23*t26
1296 : t90 = a3*t53
1297 : t93 = t73**2
1298 : t94 = 1/t93
1299 : t96 = a1*t70
1300 : t98 = t29*t18*t22
1301 : t101 = t96 + t98 + 4*a5*t35
1302 : t106 = a2 - t90
1303 : t109 = t96 + t98 + 2*t51*t59 + 2*t106*x
1304 : t111 = 1/t93/t73
1305 : t113 = t101**2
1306 : t119 = t78 + t80 - t82 + 12*a5*t2
1307 : t123 = 0.1e1_dp + t71 + t106*t2
1308 : t124 = t93**2
1309 : fs(ip, 4) = &
1310 : (t20 - t28 + t40 - t44 + t50 + 24*t51*x*t53 - 36._dp*t58*t59 + 8._dp*a3*t57*a4*t64* &
1311 : x*t53)/t73 - 3._dp*(t78 + t80 - t82 + 10._dp*t51*t2*t53 - &
1312 : 4._dp*t58*t64*t53 + 2._dp*a2 - 2._dp*t90)*t94*t101 + &
1313 : 6._dp*t109*t111*t113 - 3._dp*t109*t94*t119 - 6*t123/t124*t113*t101 + &
1314 : 6._dp*t123*t111*t101*t119 - t123*t94*(t20 - t28 + t40 - t44 + t50 + 24._dp*a5*x)
1315 : END DO
1316 : !$OMP END DO
1317 : END IF
1318 :
1319 : !$OMP END PARALLEL
1320 :
1321 108 : END SUBROUTINE efactor_pw91
1322 :
1323 : END MODULE xc_ke_gga
1324 :
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