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xc_cs1.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 Calculate the CS1 Functional (Handy s improved LYP functional)
10!> \par History
11!> JGH (26.02.2003) : OpenMP enabled
12!> fawzi (04.2004) : adapted to the new xc interface
13!> \author JGH (16.03.2002)
14! **************************************************************************************************
15MODULE xc_cs1
16
17 USE kinds, ONLY: dp
18 USE xc_derivative_desc, ONLY: deriv_norm_drho,&
19 deriv_norm_drhoa,&
20 deriv_norm_drhob,&
21 deriv_rho,&
22 deriv_rhoa,&
23 deriv_rhob
24 USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
25 xc_dset_get_derivative
26 USE xc_derivative_types, ONLY: xc_derivative_get,&
27 xc_derivative_type
28 USE xc_functionals_utilities, ONLY: set_util
29 USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
30 USE xc_rho_set_types, ONLY: xc_rho_set_get,&
31 xc_rho_set_type
32#include "../base/base_uses.f90"
33
34 IMPLICIT NONE
35
36 PRIVATE
37
38 REAL(KIND=dp), PARAMETER :: f13 = 1.0_dp/3.0_dp, &
39 f23 = 2.0_dp*f13, &
40 f43 = 4.0_dp*f13, &
41 f53 = 5.0_dp*f13
42
43 PUBLIC :: cs1_lda_info, cs1_lda_eval, cs1_lsd_info, cs1_lsd_eval
44
45 REAL(KIND=dp) :: eps_rho
46 LOGICAL :: debug_flag
47 REAL(KIND=dp) :: fsig
48
49 REAL(KIND=dp), PARAMETER :: a = 0.04918_dp, &
50 b = 0.132_dp, &
51 c = 0.2533_dp, &
52 d = 0.349_dp
53
54 REAL(KIND=dp), PARAMETER :: c1 = 0.018897_dp, &
55 c2 = -0.155240_dp, &
56 c3 = 0.159068_dp, &
57 c4 = -0.007953_dp
58
59 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_cs1'
60
61CONTAINS
62
63! **************************************************************************************************
64!> \brief return various information on the functional
65!> \param reference string with the reference of the actual functional
66!> \param shortform string with the shortform of the functional name
67!> \param needs the components needed by this functional are set to
68!> true (does not set the unneeded components to false)
69!> \param max_deriv ...
70! **************************************************************************************************
71 SUBROUTINE cs1_lda_info(reference, shortform, needs, max_deriv)
72 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
73 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
74 INTEGER, INTENT(out), OPTIONAL :: max_deriv
75
76 IF (PRESENT(reference)) THEN
77 reference = "N.C. Handy and A.J. Cohen, J. Chem. Phys., 116, 5411 (2002) {LDA version}"
78 END IF
79 IF (PRESENT(shortform)) THEN
80 shortform = "CS1: Handy improved LYP correlation energy functional {LDA}"
81 END IF
82 IF (PRESENT(needs)) THEN
83 needs%rho = .true.
84 needs%rho_1_3 = .true.
85 needs%norm_drho = .true.
86 END IF
87 IF (PRESENT(max_deriv)) max_deriv = 3
88
89 END SUBROUTINE cs1_lda_info
90
91! **************************************************************************************************
92!> \brief return various information on the functional
93!> \param reference string with the reference of the actual functional
94!> \param shortform string with the shortform of the functional name
95!> \param needs the components needed by this functional are set to
96!> true (does not set the unneeded components to false)
97!> \param max_deriv ...
98! **************************************************************************************************
99 SUBROUTINE cs1_lsd_info(reference, shortform, needs, max_deriv)
100 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
101 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
102 INTEGER, INTENT(out), OPTIONAL :: max_deriv
103
104 IF (PRESENT(reference)) THEN
105 reference = "N.C. Handy and A.J. Cohen, J. Chem. Phys., 116, 5411 (2002)"
106 END IF
107 IF (PRESENT(shortform)) THEN
108 shortform = "CS1: Handy improved LYP correlation energy functional"
109 END IF
110 IF (PRESENT(needs)) THEN
111 needs%rho_spin = .true.
112 needs%rho_spin_1_3 = .true.
113 needs%norm_drho_spin = .true.
114 END IF
115 IF (PRESENT(max_deriv)) max_deriv = 1
116
117 END SUBROUTINE cs1_lsd_info
118
119! **************************************************************************************************
120!> \brief ...
121!> \param cutoff ...
122!> \param debug ...
123! **************************************************************************************************
124 SUBROUTINE cs1_init(cutoff, debug)
125
126 REAL(kind=dp), INTENT(IN) :: cutoff
127 LOGICAL, INTENT(IN), OPTIONAL :: debug
128
129 eps_rho = cutoff
130 CALL set_util(cutoff)
131
132 IF (PRESENT(debug)) THEN
133 debug_flag = debug
134 ELSE
135 debug_flag = .false.
136 END IF
137
138 fsig = 2.0_dp**f13
139
140 END SUBROUTINE cs1_init
141
142! **************************************************************************************************
143!> \brief ...
144!> \param rho_set ...
145!> \param deriv_set ...
146!> \param order ...
147! **************************************************************************************************
148 SUBROUTINE cs1_lda_eval(rho_set, deriv_set, order)
149 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
150 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
151 INTEGER, INTENT(in) :: order
152
153 CHARACTER(len=*), PARAMETER :: routinen = 'cs1_lda_eval'
154
155 INTEGER :: handle, m, npoints
156 INTEGER, DIMENSION(2, 3) :: bo
157 REAL(kind=dp) :: epsilon_rho
158 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: e_0, e_ndrho, e_ndrho_ndrho, &
159 e_ndrho_ndrho_ndrho, e_rho, e_rho_ndrho, e_rho_ndrho_ndrho, e_rho_rho, e_rho_rho_ndrho, &
160 e_rho_rho_rho, grho, rho, rho13
161 TYPE(xc_derivative_type), POINTER :: deriv
162
163 CALL timeset(routinen, handle)
164 NULLIFY (rho, rho13, grho, e_0, e_rho, e_ndrho, &
165 e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
166 e_rho_rho_rho, e_rho_rho_ndrho, e_rho_ndrho_ndrho, &
167 e_ndrho_ndrho_ndrho)
168
169 CALL xc_rho_set_get(rho_set, rho_1_3=rho13, rho=rho, &
170 norm_drho=grho, local_bounds=bo, rho_cutoff=epsilon_rho)
171 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
172 m = abs(order)
173 CALL cs1_init(epsilon_rho)
174
175 IF (order >= 0) THEN
176 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
177 allocate_deriv=.true.)
178 CALL xc_derivative_get(deriv, deriv_data=e_0)
179
180 CALL cs1_u_0(rho, grho, rho13, e_0, npoints)
181 END IF
182 IF (order >= 1 .OR. order == -1) THEN
183 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
184 allocate_deriv=.true.)
185 CALL xc_derivative_get(deriv, deriv_data=e_rho)
186 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
187 allocate_deriv=.true.)
188 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
189
190 CALL cs1_u_1(rho, grho, rho13, e_rho, e_ndrho, &
191 npoints)
192 END IF
193 IF (order >= 2 .OR. order == -2) THEN
194 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
195 allocate_deriv=.true.)
196 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
197 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_norm_drho], &
198 allocate_deriv=.true.)
199 CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho)
200 deriv => xc_dset_get_derivative(deriv_set, &
201 [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
202 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
203
204 CALL cs1_u_2(rho, grho, rho13, e_rho_rho, e_rho_ndrho, &
205 e_ndrho_ndrho, npoints)
206 END IF
207 IF (order >= 3 .OR. order == -3) THEN
208 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
209 allocate_deriv=.true.)
210 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
211 deriv => xc_dset_get_derivative(deriv_set, &
212 [deriv_rho, deriv_rho, deriv_norm_drho], allocate_deriv=.true.)
213 CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_ndrho)
214 deriv => xc_dset_get_derivative(deriv_set, &
215 [deriv_rho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
216 CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho_ndrho)
217 deriv => xc_dset_get_derivative(deriv_set, &
218 [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
219 CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)
220
221 CALL cs1_u_3(rho, grho, rho13, e_rho_rho_rho, e_rho_rho_ndrho, &
222 e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, npoints)
223 END IF
224 IF (order > 3 .OR. order < -3) THEN
225 cpabort("derivatives bigger than 3 not implemented")
226 END IF
227
228 CALL timestop(handle)
229 END SUBROUTINE cs1_lda_eval
230
231! **************************************************************************************************
232!> \brief ...
233!> \param rho_set ...
234!> \param deriv_set ...
235!> \param order ...
236! **************************************************************************************************
237 SUBROUTINE cs1_lsd_eval(rho_set, deriv_set, order)
238 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
239 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
240 INTEGER, INTENT(in) :: order
241
242 CHARACTER(len=*), PARAMETER :: routinen = 'cs1_lsd_eval'
243
244 INTEGER :: handle, npoints
245 INTEGER, DIMENSION(2, 3) :: bo
246 REAL(kind=dp) :: epsilon_rho
247 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
248 POINTER :: e_0, e_ndrhoa, e_ndrhob, e_rhoa, e_rhob, &
249 norm_drhoa, norm_drhob, rhoa, &
250 rhoa_1_3, rhob, rhob_1_3
251 TYPE(xc_derivative_type), POINTER :: deriv
252
253 CALL timeset(routinen, handle)
254
255 CALL xc_rho_set_get(rho_set, rhoa=rhoa, rhob=rhob, &
256 rhoa_1_3=rhoa_1_3, rhob_1_3=rhob_1_3, &
257 norm_drhoa=norm_drhoa, norm_drhob=norm_drhob, &
258 local_bounds=bo, rho_cutoff=epsilon_rho)
259 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
260 CALL cs1_init(epsilon_rho)
261
262 IF (order >= 0) THEN
263 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
264 allocate_deriv=.true.)
265 CALL xc_derivative_get(deriv, deriv_data=e_0)
266
267 CALL cs1_ss_0(rhoa, rhob, norm_drhoa, norm_drhob, &
268 rhoa_1_3, rhob_1_3, e_0, npoints)
269 END IF
270 IF (order >= 1 .OR. order == -1) THEN
271 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
272 allocate_deriv=.true.)
273 CALL xc_derivative_get(deriv, deriv_data=e_rhoa)
274 deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
275 allocate_deriv=.true.)
276 CALL xc_derivative_get(deriv, deriv_data=e_rhob)
277 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
278 allocate_deriv=.true.)
279 CALL xc_derivative_get(deriv, deriv_data=e_ndrhoa)
280 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
281 allocate_deriv=.true.)
282 CALL xc_derivative_get(deriv, deriv_data=e_ndrhob)
283
284 CALL cs1_ss_1(rhoa, rhob, norm_drhoa, norm_drhob, &
285 rhoa_1_3, rhob_1_3, e_rhoa, e_rhob, e_ndrhoa, e_ndrhob, &
286 npoints)
287 END IF
288 IF (order > 1 .OR. order < 1) THEN
289 cpabort("derivatives bigger than 3 not implemented")
290 END IF
291 CALL timestop(handle)
292 END SUBROUTINE cs1_lsd_eval
293
294! **************************************************************************************************
295!> \brief ...
296!> \param rho ...
297!> \param grho ...
298!> \param r13 ...
299!> \param e_0 ...
300!> \param npoints ...
301! **************************************************************************************************
302 SUBROUTINE cs1_u_0(rho, grho, r13, e_0, npoints)
303
304 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, r13
305 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_0
306 INTEGER, INTENT(in) :: npoints
307
308 INTEGER :: ip
309 REAL(kind=dp) :: c2p, c3p, c4p, cp, dpv, f1, f2, f3, f4, &
310 g, oc, ocp, od, odp, r, r3, x
311
312 dpv = fsig*d
313 cp = c*fsig*fsig
314 c2p = c2*fsig**4
315 c3p = -c3*0.25_dp
316 c4p = -c4*0.25_dp
317
318!$OMP PARALLEL DO DEFAULT(NONE) &
319!$OMP SHARED(npoints,rho,eps_rho,e_0,dpv,cp,c2p,c3p,c4p,r13,grho) &
320!$OMP PRIVATE(ip,r,r3,g,x,odp,ocp,od,oc,f1,f2,f3,f4)
321
322 DO ip = 1, npoints
323
324 IF (rho(ip) > eps_rho) THEN
325 r = rho(ip)
326 r3 = r13(ip)
327 g = grho(ip)
328 x = g/(r*r3)
329 odp = 1.0_dp/(r3 + dpv)
330 ocp = 1.0_dp/(r*r*r3*r3 + cp*g*g)
331 od = 1.0_dp/(r3 + d)
332 oc = 1.0_dp/(r*r*r3*r3 + c*g*g)
333 f1 = c1*r*r3*odp
334 f2 = c2p*g**4*r3*r*odp*ocp*ocp
335 f3 = c3p*r*r3*od
336 f4 = c4p*g**4*r3*r*od*oc*oc
337 e_0(ip) = e_0(ip) + f1 + f2 + f3 + f4
338 END IF
339
340 END DO
341
342!$OMP END PARALLEL DO
343
344 END SUBROUTINE cs1_u_0
345
346! **************************************************************************************************
347!> \brief ...
348!> \param rho ...
349!> \param grho ...
350!> \param r13 ...
351!> \param e_rho ...
352!> \param e_ndrho ...
353!> \param npoints ...
354! **************************************************************************************************
355 SUBROUTINE cs1_u_1(rho, grho, r13, e_rho, e_ndrho, npoints)
356
357 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, r13
358 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho, e_ndrho
359 INTEGER, INTENT(in) :: npoints
360
361 INTEGER :: ip
362 REAL(kind=dp) :: c2p, c3p, c4p, cp, df1, df3, dgf2, dgf4, &
363 dpv, drf2, drf4, g, oc, ocp, od, odp, &
364 r, r3
365
366 dpv = fsig*d
367 cp = c*fsig*fsig
368 c2p = c2*fsig**4
369 c3p = -c3*0.25_dp
370 c4p = -c4*0.25_dp
371
372!$OMP PARALLEL DO DEFAULT(NONE) &
373!$OMP SHARED(npoints, rho, eps_rho, r13, grho, e_rho) &
374!$OMP SHARED(e_ndrho, dpv, cp, c2p, c3p, c4p) &
375!$OMP PRIVATE(ip, r, r3, g, odp, ocp, od, oc, df1) &
376!$OMP PRIVATE(drf2, dgf2, df3, drf4, dgf4)
377
378 DO ip = 1, npoints
379
380 IF (rho(ip) > eps_rho) THEN
381 r = rho(ip)
382 r3 = r13(ip)
383 g = grho(ip)
384 odp = 1.0_dp/(r3 + dpv)
385 ocp = 1.0_dp/(r*r*r3*r3 + cp*g*g)
386 od = 1.0_dp/(r3 + d)
387 oc = 1.0_dp/(r*r*r3*r3 + c*g*g)
388 df1 = c1*f13*r3*(3*r3 + 4*dpv)*odp*odp
389 drf2 = -f13*c2p*g**4*r3*(13*r**3 - 3*r3*cp*g*g + 12*r*r*r3*r3*dpv - &
390 4*dpv*cp*g*g)*odp**2*ocp**3
391 dgf2 = 4*c2p*g**3*r**4*odp*ocp**3
392 df3 = f13*r3*c3p*(3*r3 + 4*d)*od*od
393 drf4 = -f13*c4p*g**4*r3*(13*r**3 - 3*r3*c*g*g + 12*r*r*r3*r3*d - &
394 4*d*c*g*g)*od**2*oc**3
395 dgf4 = 4*c4p*g**3*r**4*od*oc**3
396 e_rho(ip) = e_rho(ip) + df1 + drf2 + df3 + drf4
397 e_ndrho(ip) = e_ndrho(ip) + dgf2 + dgf4
398 END IF
399
400 END DO
401
402!$OMP END PARALLEL DO
403
404 END SUBROUTINE cs1_u_1
405
406! **************************************************************************************************
407!> \brief ...
408!> \param rho ...
409!> \param grho ...
410!> \param r13 ...
411!> \param e_rho_rho ...
412!> \param e_rho_ndrho ...
413!> \param e_ndrho_ndrho ...
414!> \param npoints ...
415! **************************************************************************************************
416 SUBROUTINE cs1_u_2(rho, grho, r13, e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
417 npoints)
418
419 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, r13
420 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho_rho, e_rho_ndrho, e_ndrho_ndrho
421 INTEGER, INTENT(in) :: npoints
422
423 INTEGER :: ip
424 REAL(kind=dp) :: c2p, c3p, c4p, cp, d2f1, d2f3, d2gf2, &
425 d2gf4, d2rf2, d2rf4, dpv, drgf2, &
426 drgf4, g, oc, ocp, od, odp, r, r3
427
428 dpv = fsig*d
429 cp = c*fsig*fsig
430 c2p = c2*fsig**4
431 c3p = -c3*0.25_dp
432 c4p = -c4*0.25_dp
433
434!$OMP PARALLEL DO DEFAULT(NONE) &
435!$OMP SHARED(npoints, rho, eps_rho, r13, grho, e_rho_rho) &
436!$OMP SHARED(e_rho_ndrho, e_ndrho_ndrho, dpv, cp, c2p, c3p, c4p) &
437!$OMP PRIVATE(ip,r,r3,g,odp,ocp,od,oc,d2f1,d2rf2,drgf2,d2f3) &
438!$OMP PRIVATE(d2rf4,drgf4,d2gf2,d2gf4)
439
440 DO ip = 1, npoints
441
442 IF (rho(ip) > eps_rho) THEN
443 r = rho(ip)
444 r3 = r13(ip)
445 g = grho(ip)
446 odp = 1.0_dp/(r3 + dpv)
447 ocp = 1.0_dp/(r*r*r3*r3 + cp*g*g)
448 od = 1.0_dp/(r3 + d)
449 oc = 1.0_dp/(r*r*r3*r3 + c*g*g)
450 d2f1 = c1*f23*f13*dpv*r3/r*(r3 + 2*dpv)*odp**3
451 d2rf2 = c2p*f13*f23*g**4*r3/r*(193*dpv*r**5*r3*r3 + 90*dpv*dpv*r**5*r3 &
452 - 88*g*g*cp*r**3*r3 - 100*dpv*dpv*cp*g*g*r*r*r3*r3 &
453 + 2*dpv*dpv*cp*cp*g**4 - 190*g*g*r**3*cp*dpv + g**4*r3*cp*cp*dpv &
454 + 104*r**6)*odp**3*ocp**4
455 drgf2 = c2p*f43*g**3*r*r*r3*(-13*r**3*r3*r3 + 11*cp*r*g*g - 12*dpv*r**3*r3 &
456 + 12*r3*r3*dpv*cp*g*g)*odp*odp*ocp**4
457 d2gf2 = -12*c2p*g*g*r**4*(cp*g*g - r*r*r3*r3)*odp*ocp**4
458 d2f3 = f13*f23*c3p*d*r3/r*(r3 + 2*d)*od**3
459 d2rf4 = c4p*f13*f23*g**4*r3/r*(193*d*r**5*r3*r3 + 90*d*d*r**5*r3 &
460 - 88*g*g*c*r**3*r3 - 100*d*d*c*g*g*r*r*r3*r3 &
461 + 2*d*d*c*c*g**4 - 190*g*g*r**3*c*d + g**4*r3*c*c*d &
462 + 104*r**6)*od**3*oc**4
463 drgf4 = c4p*f43*g**3*r*r*r3*(-13*r**3*r3*r3 + 11*c*r*g*g - 12*d*r**3*r3 &
464 + 12*r3*r3*d*c*g*g)*od*od*oc**4
465 d2gf4 = -12*c4p*g*g*r**4*(c*g*g - r*r*r3*r3)*od*oc**4
466 e_rho_rho(ip) = e_rho_rho(ip) + d2f1 + d2rf2 + d2f3 + d2rf4
467 e_rho_ndrho(ip) = e_rho_ndrho(ip) + drgf2 + drgf4
468 e_ndrho_ndrho(ip) = e_ndrho_ndrho(ip) + d2gf2 + d2gf4
469 END IF
470
471 END DO
472
473!$OMP END PARALLEL DO
474
475 END SUBROUTINE cs1_u_2
476
477! **************************************************************************************************
478!> \brief ...
479!> \param rho ...
480!> \param grho ...
481!> \param r13 ...
482!> \param e_rho_rho_rho ...
483!> \param e_rho_rho_ndrho ...
484!> \param e_rho_ndrho_ndrho ...
485!> \param e_ndrho_ndrho_ndrho ...
486!> \param npoints ...
487! **************************************************************************************************
488 SUBROUTINE cs1_u_3(rho, grho, r13, e_rho_rho_rho, e_rho_rho_ndrho, &
489 e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, npoints)
490
491 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, r13
492 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho_rho_rho, e_rho_rho_ndrho, &
493 e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho
494 INTEGER, INTENT(in) :: npoints
495
496 INTEGER :: ip
497 REAL(kind=dp) :: c2p, c3p, c4p, cp, d2rgf2, d2rgf4, d3f1, d3f3, d3gf2, d3gf4, d3rf2, d3rf4, &
498 dpv, dr2gf2, dr2gf4, g, oc, ocp, od, odp, r, r3, t1, t10, t11, t13, t15, t16, t17, t19, &
499 t2, t22, t23, t26, t29, t3, t32, t33, t37, t4, t44, t45, t50, t51, t52, t58, t6, t61, t7, &
500 t74, t76, t77, t8, t80, t81, t82, t9
501
502 dpv = fsig*d
503 cp = c*fsig*fsig
504 c2p = c2*fsig**4
505 c3p = -c3*0.25_dp
506 c4p = -c4*0.25_dp
507
508!$OMP PARALLEL DO DEFAULT(NONE) &
509!$OMP SHARED(npoints, rho, eps_rho, r13, grho, e_rho_rho_rho) &
510!$OMP SHARED(e_rho_rho_ndrho, e_rho_ndrho_ndrho) &
511!$OMP SHARED(e_ndrho_ndrho_ndrho, dpv, cp, c2p, c3p, c4p) &
512!$OMP PRIVATE(ip,r,r3,g,odp,ocp,od,oc,d3f1,d3rF2,d2rgF2) &
513!$OMP PRIVATE(dr2gF2,d3gF2,d3F3,d3rF4,d2rgF4,dr2gF4,d3gF4) &
514!$OMP PRIVATE(t1, t2, t3, t4, t6, t7, t8, t9, t10, t11, t13) &
515!$OMP PRIVATE(t15, t16, t17, t19, t22, t23, t26, t29, t32) &
516!$OMP PRIVATE(t33, t37, t44, t45, t50, t51, t52, t58, t61) &
517!$OMP PRIVATE(t74, t76, t77, t80, t81, t82)
518
519 DO ip = 1, npoints
520
521 IF (rho(ip) > eps_rho) THEN
522 r = rho(ip)
523 r3 = r13(ip)
524 g = grho(ip)
525 odp = 1.0_dp/(r3 + dpv)
526 ocp = 1.0_dp/(r*r*r3*r3 + cp*g*g)
527 od = 1.0_dp/(r3 + d)
528 oc = 1.0_dp/(r*r*r3*r3 + c*g*g)
529 d3f1 = -c1*f23*f13*f13*dpv*r3/(r*r)*(11*dpv*r3 + 4*dpv*dpv + 4*r/r3)*odp**4
530 t1 = g**2; t2 = t1**2; t3 = r3; t4 = t3**2; t8 = dpv**2; t9 = t8*dpv
531 t10 = cp**2; t11 = t10*cp; t13 = t2*t1; t16 = r**2; t17 = t4*t16
532 t19 = t10*t2; t22 = t16**2; t23 = t22**2; t32 = t22*t16; t37 = t16*r
533 t58 = t22*r; t61 = cp*t1
534 t74 = 4*t9*t11*t13 + 668*t17*t9*t19 + 5524*t4*t23*dpv + 5171*t3*t23*t8 + &
535 1620*t23*t9 - 3728*t3*t32*cp*t1 + 440*t4*t37*t10*t2 + 1500*t2*t3*t37*dpv*t10 &
536 + 4*t13*t4*dpv*t11 + 1737*t37*t8*t19 + 11*t3*t8*t11*t13 - 3860*t3*t58*t9*t61 + &
537 1976*t23*r - 11535*t4*t58*t8*t61 - 11412*t1*t32*cp*dpv
538 t76 = (t3 + dpv)**2; t77 = t76**2; t80 = t17 + t61; t81 = t80**2; t82 = t81**2
539 d3rf2 = -f23*f13*f13*c2p*t2/t4/r*t74/t77/t82/t80
540 t4 = t3*r; t6 = r**2; t7 = t6**2; t8 = t7*t6; t9 = dpv**2; t15 = t1**2
541 t17 = cp**2; t23 = t3**2; t26 = t6*r; t29 = cp*t1; t33 = t17*t15; t44 = t3 + dpv
542 t45 = t44**2; t50 = t23*t6 + t29; t51 = t50**2; t52 = t51**2
543 d2rgf2 = c2p*f23*f43*t1*g*t4*(90*t8*t9 + 193*t3*t8*dpv + 44*t15*t4*t17 - 236*t1 &
544 *t7*cp + 104*t23*t8 - 240*t3*t26*t9*t29 + 54*t23*t9*t33 - 478*t23*t26*dpv*t29 &
545 + 97*r*dpv*t33)/t45/t44/t52/t50
546 dr2gf2 = -4*c2p*g*g*r*r*r3*(-40*r**3*r3*dpv*cp*g*g + 12*r3*r3*dpv*cp*cp*g**4 &
547 + 13*r**6*r3 - 40*r**3*r3*r3*cp*g*g + 11*r*cp*cp*g**4 + 12*r**6*dpv) &
548 *odp*odp*ocp**5
549 d3gf2 = c2p*24*g*r**3*r3*(r**6 - 5*cp*g*g*r**3*r3 + 2*cp*cp*g**4*r3*r3)*odp*ocp**5
550 d3f3 = -f23*f13*f13*c3p*d*r3/(r*r)*(11*d*r3 + 4*d*d + 4*r3*r3)*od**4
551 t1 = g**2; t2 = t1**2; t3 = r3; t4 = t3**2; t8 = d**2; t9 = t8*d
552 t10 = c**2; t11 = t10*c; t13 = t2*t1; t16 = r**2; t17 = t4*t16
553 t19 = t10*t2; t22 = t16**2; t23 = t22**2; t32 = t22*t16; t37 = t16*r
554 t58 = t22*r; t61 = c*t1
555 t74 = 4*t9*t11*t13 + 668*t17*t9*t19 + 5524*t4*t23*d + 5171*t3*t23*t8 + &
556 1620*t23*t9 - 3728*t3*t32*c*t1 + 440*t4*t37*t10*t2 + 1500*t2*t3*t37*d*t10 &
557 + 4*t13*t4*d*t11 + 1737*t37*t8*t19 + 11*t3*t8*t11*t13 - 3860*t3*t58*t9*t61 + &
558 1976*t23*r - 11535*t4*t58*t8*t61 - 11412*t1*t32*c*d
559 t76 = (t3 + d)**2; t77 = t76**2; t80 = t17 + t61; t81 = t80**2; t82 = t81**2
560 d3rf4 = -f23*f13*f13*c4p*t2/t4/r*t74/t77/t82/t80
561 t4 = t3*r; t6 = r**2; t7 = t6**2; t8 = t7*t6; t9 = d**2; t15 = t1**2
562 t17 = c**2; t23 = t3**2; t26 = t6*r; t29 = c*t1; t33 = t17*t15; t44 = t3 + d
563 t45 = t44**2; t50 = t23*t6 + t29; t51 = t50**2; t52 = t51**2
564 d2rgf4 = c4p*f23*f43*t1*g*t4*(90*t8*t9 + 193*t3*t8*d + 44*t15*t4*t17 - 236*t1 &
565 *t7*c + 104*t23*t8 - 240*t3*t26*t9*t29 + 54*t23*t9*t33 - 478*t23*t26*d*t29 &
566 + 97*r*d*t33)/t45/t44/t52/t50
567 dr2gf4 = -4*c4p*g*g*r*r*r3*(-40*r**3*r3*d*c*g*g + 12*r3*r3*d*c*c*g**4 &
568 + 13*r**6*r3 - 40*r**3*r3*r3*c*g*g + 11*r*c*c*g**4 + 12*r**6*d) &
569 *od*od*oc**5
570 d3gf4 = c4p*24*g*r**3*r3*(r**6 - 5*c*g*g*r**3*r3 + 2*c*c*g**4*r3*r3)*od*oc**5
571 e_rho_rho_rho(ip) = e_rho_rho_rho(ip) + d3f1 + d3rf2 + d3f3 + d3rf4
572 e_rho_rho_ndrho(ip) = e_rho_rho_ndrho(ip) + d2rgf2 + d2rgf4
573 e_rho_ndrho_ndrho(ip) = e_rho_ndrho_ndrho(ip) + dr2gf2 + dr2gf4
574 e_ndrho_ndrho_ndrho(ip) = e_ndrho_ndrho_ndrho(ip) + d3gf2 + d3gf4
575 END IF
576
577 END DO
578
579!$OMP END PARALLEL DO
580
581 END SUBROUTINE cs1_u_3
582
583! **************************************************************************************************
584!> \brief ...
585!> \param rhoa ...
586!> \param rhob ...
587!> \param grhoa ...
588!> \param grhob ...
589!> \param r13a ...
590!> \param r13b ...
591!> \param e_0 ...
592!> \param npoints ...
593! **************************************************************************************************
594 SUBROUTINE cs1_ss_0(rhoa, rhob, grhoa, grhob, r13a, r13b, e_0, &
595 npoints)
596
597 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rhoa, rhob, grhoa, grhob, r13a, r13b
598 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_0
599 INTEGER, INTENT(in) :: npoints
600
601 INTEGER :: ip
602 REAL(kind=dp) :: f1a, f1b, f2a, f2b, ga, gb, oca, ocb, &
603 oda, odb, r3a, r3b, ra, rb, xa, xb
604
605!FM IF ( .NOT. debug_flag ) CPABORT("Routine not tested")
606
607 cpwarn("not tested!")
608
609!$OMP PARALLEL DO DEFAULT(NONE) &
610!$OMP SHARED(npoints, rhoa, eps_rho, r13a, grhoa, rhob) &
611!$OMP SHARED(r13b, grhob, e_0) &
612!$OMP PRIVATE(ip, f1a, f2a, ra, r3a, ga, xa, oda, oca) &
613!$OMP PRIVATE( f1b, f2b, rb, r3b, gb, xb, odb, ocb)
614
615 DO ip = 1, npoints
616
617 IF (rhoa(ip) < eps_rho) THEN
618 f1a = 0.0_dp
619 f2a = 0.0_dp
620 ELSE
621 ra = rhoa(ip)
622 r3a = r13a(ip)
623 ga = grhoa(ip)
624 xa = ga/(ra*r3a)
625 oda = 1.0_dp/(r3a + d)
626 oca = 1.0_dp/(ra*ra*r3a*r3a + c*ga*ga)
627 f1a = c1*ra*r3a*oda
628 f2a = c2*ga**4*r3a*ra*oda*oca*oca
629 END IF
630 IF (rhob(ip) < eps_rho) THEN
631 f1b = 0.0_dp
632 f2b = 0.0_dp
633 ELSE
634 rb = rhob(ip)
635 r3b = r13b(ip)
636 gb = grhob(ip)
637 xb = gb/(rb*r3b)
638 odb = 1.0_dp/(r3b + d)
639 ocb = 1.0_dp/(rb*rb*r3b*r3b + c*gb*gb)
640 f1b = c1*rb*r3b*odb
641 f2b = c2*gb**4*r3b*rb*odb*ocb*ocb
642 END IF
643
644 e_0(ip) = e_0(ip) + f1a + f1b + f2a + f2b
645
646 END DO
647
648!$OMP END PARALLEL DO
649
650 END SUBROUTINE cs1_ss_0
651
652! **************************************************************************************************
653!> \brief ...
654!> \param rhoa ...
655!> \param rhob ...
656!> \param grhoa ...
657!> \param grhob ...
658!> \param r13a ...
659!> \param r13b ...
660!> \param e_rhoa ...
661!> \param e_rhob ...
662!> \param e_ndrhoa ...
663!> \param e_ndrhob ...
664!> \param npoints ...
665! **************************************************************************************************
666 SUBROUTINE cs1_ss_1(rhoa, rhob, grhoa, grhob, r13a, r13b, e_rhoa, &
667 e_rhob, e_ndrhoa, e_ndrhob, npoints)
668
669 REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rhoa, rhob, grhoa, grhob, r13a, r13b
670 REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rhoa, e_rhob, e_ndrhoa, e_ndrhob
671 INTEGER, INTENT(in) :: npoints
672
673 INTEGER :: ip
674 REAL(kind=dp) :: df1a, df1b, dgf2a, dgf2b, drf2a, drf2b, &
675 ga, gb, oca, ocb, oda, odb, r3a, r3b, &
676 ra, rb
677
678 cpwarn("not tested!")
679
680!$OMP PARALLEL DO DEFAULT(NONE) &
681!$OMP SHARED(npoints, rhoa, eps_rho, r13a, grhoa, rhob) &
682!$OMP SHARED(grhob, e_rhoa, e_ndrhoa, e_rhob, e_ndrhob,r13b) &
683!$OMP PRIVATE(ip, df1a, drf2a, dgf2a, ra, r3a, ga, oda, oca) &
684!$OMP PRIVATE( df1b, drf2b, dgf2b, rb, r3b, gb, odb, ocb)
685
686 DO ip = 1, npoints
687
688 IF (rhoa(ip) < eps_rho) THEN
689 df1a = 0.0_dp
690 drf2a = 0.0_dp
691 dgf2a = 0.0_dp
692 ELSE
693 ra = rhoa(ip)
694 r3a = r13a(ip)
695 ga = grhoa(ip)
696 oda = 1.0_dp/(r3a + d)
697 oca = 1.0_dp/(ra*ra*r3a*r3a + c*ga*ga)
698 df1a = c1*f13*r3a*(3*r3a + 4*d)*oda*oda
699
700 drf2a = -f13*c2*ga**4*r3a*(13*ra**3 - 3*r3a*c*ga*ga + 12*ra*ra*r3a*r3a*d - &
701 4*d*c*ga*ga)*oda**2*oca**3
702
703 dgf2a = 4*c2*ga**3*ra**4*oda*oca**3
704
705 END IF
706 IF (rhob(ip) < eps_rho) THEN
707 df1b = 0.0_dp
708 drf2b = 0.0_dp
709 dgf2b = 0.0_dp
710 ELSE
711 rb = rhob(ip)
712 r3b = r13b(ip)
713 gb = grhob(ip)
714 odb = 1.0_dp/(r3b + d)
715 ocb = 1.0_dp/(rb*rb*r3b*r3b + c*gb*gb)
716 df1b = c1*f13*r3b*(3*r3b + 4*d)*odb*odb
717
718 drf2b = -f13*c2*gb**4*r3b*(13*rb**3 - 3*r3b*c*gb*gb + 12*rb*rb*r3b*r3b*d - &
719 4*d*c*gb*gb)*odb**2*ocb**3
720
721 dgf2b = 4*c2*gb**3*rb**4*odb*ocb**3
722
723 END IF
724
725 e_rhoa(ip) = e_rhoa(ip) + df1a + drf2a
726 e_ndrhoa(ip) = e_ndrhoa(ip) + dgf2a
727 e_rhob(ip) = e_rhob(ip) + df1b + drf2b
728 e_ndrhob(ip) = e_ndrhob(ip) + dgf2b
729
730 END DO
731
732!$OMP END PARALLEL DO
733
734 END SUBROUTINE cs1_ss_1
735
736END MODULE xc_cs1
737
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
xc_cs1
Calculate the CS1 Functional (Handy s improved LYP functional)
Definition xc_cs1.F:15
xc_cs1::cs1_lda_eval
subroutine, public cs1_lda_eval(rho_set, deriv_set, order)
...
Definition xc_cs1.F:149
xc_cs1::cs1_lsd_eval
subroutine, public cs1_lsd_eval(rho_set, deriv_set, order)
...
Definition xc_cs1.F:238
xc_cs1::cs1_lsd_info
subroutine, public cs1_lsd_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_cs1.F:100
xc_cs1::cs1_lda_info
subroutine, public cs1_lda_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_cs1.F:72
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_functionals_utilities
Utility routines for the functional calculations.
Definition xc_functionals_utilities.F:15
xc_functionals_utilities::set_util
subroutine, public set_util(cutoff)
...
Definition xc_functionals_utilities.F:54
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_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