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xc_tpss.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 tpss functional.
10!> \note
11!> The derivation of the formulaes is lengthly, and not fully trivial,
12!> so I have put it in doc/tpss.mw
13!> \par History
14!> 05.2004 created
15!> \author fawzi
16! **************************************************************************************************
17MODULE xc_tpss
18 USE bibliography, ONLY: tao2003,&
19 cite_reference
20 USE cp_log_handling, ONLY: cp_get_default_logger,&
21 cp_logger_type
22 USE input_section_types, ONLY: section_vals_type,&
23 section_vals_val_get
24 USE kinds, ONLY: dp
25 USE mathconstants, ONLY: pi
26 USE xc_derivative_desc, ONLY: deriv_norm_drho,&
27 deriv_rho,&
28 deriv_tau
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_tpss'
43
44 PUBLIC :: tpss_lda_info, tpss_lda_eval
45
46!***
47CONTAINS
48
49! **************************************************************************************************
50!> \brief return various information on the functional
51!> \param tpss_params ...
52!> \param reference string with the reference of the actual functional
53!> \param shortform string with the shortform of the functional name
54!> \param needs the components needed by this functional are set to
55!> true (does not set the unneeded components to false)
56!> \param max_deriv the highest derivative available
57!> \author fawzi
58! **************************************************************************************************
59 SUBROUTINE tpss_lda_info(tpss_params, reference, shortform, needs, max_deriv)
60 TYPE(section_vals_type), POINTER :: tpss_params
61 CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
62 TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
63 INTEGER, INTENT(out), OPTIONAL :: max_deriv
64
65 REAL(kind=dp) :: sc, sx
66
67 CALL section_vals_val_get(tpss_params, "SCALE_C", r_val=sc)
68 CALL section_vals_val_get(tpss_params, "SCALE_X", r_val=sx)
69
70 IF (PRESENT(reference)) THEN
71 IF (sx == 1._dp .AND. sc == 1._dp) THEN
72 reference = "J. Tao, J.P.Perdew, V.N.Staroverov, E.Scuseria PRL, 91, 146401 (2003) {LDA version}"
73 ELSE
74 WRITE (reference, "(a,'sx=',f5.3,'sc=',f5.3,' {LDA version}')") &
75 "J. Tao, J.P.Perdew, V.N.Staroverov, E.Scuseria PRL, 91, 146401 (2003)", &
76 sx, sc
77 END IF
78 END IF
79 IF (PRESENT(shortform)) THEN
80 IF (sx == 1._dp .AND. sc == 1._dp) THEN
81 shortform = "TPSS meta-GGA functional (LDA)"
82 ELSE
83 WRITE (shortform, "(a,'sx=',f5.3,'sc=',f5.3,' (LDA)')") &
84 "TPSS meta-GGA functional", &
85 sx, sc
86 END IF
87 END IF
88 IF (PRESENT(needs)) THEN
89 needs%rho = .true.
90 needs%tau = .true.
91 needs%norm_drho = .true.
92 END IF
93 IF (PRESENT(max_deriv)) max_deriv = 1
94
95 END SUBROUTINE tpss_lda_info
96
97! **************************************************************************************************
98!> \brief evaluates the tpss functional in the spin unpolarized (lda) case
99!> \param rho_set the density where you want to evaluate the functional
100!> \param deriv_set place where to store the functional derivatives (they are
101!> added to the derivatives)
102!> \param grad_deriv degree of the derivative that should be evaluated,
103!> if positive all the derivatives up to the given degree are evaluated,
104!> if negative only the given degree is calculated
105!> \param tpss_params ...
106!> \author fawzi
107! **************************************************************************************************
108 SUBROUTINE tpss_lda_eval(rho_set, deriv_set, grad_deriv, tpss_params)
109 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
110 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
111 INTEGER, INTENT(in) :: grad_deriv
112 TYPE(section_vals_type), POINTER :: tpss_params
113
114 CHARACTER(len=*), PARAMETER :: routinen = 'tpss_lda_eval'
115
116 INTEGER :: handle, non_coer, npoints
117 INTEGER, DIMENSION(2, 3) :: bo
118 REAL(kind=dp) :: epsilon_rho, epsilon_tau, scale_ec, &
119 scale_ex
120 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
121 POINTER :: dummy, e_0, e_ndrho, e_rho, e_tau, &
122 norm_drho, rho, tau
123 TYPE(cp_logger_type), POINTER :: logger
124 TYPE(xc_derivative_type), POINTER :: deriv
125
126 CALL timeset(routinen, handle)
127
128 CALL cite_reference(tao2003)
129
130 CALL xc_rho_set_get(rho_set, rho=rho, &
131 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho, &
132 tau=tau, tau_cutoff=epsilon_tau)
133 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
134
135 dummy => rho
136
137 e_0 => dummy
138 e_rho => dummy
139 e_ndrho => dummy
140 e_tau => dummy
141
142 IF (grad_deriv >= 0) THEN
143 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
144 allocate_deriv=.true.)
145 CALL xc_derivative_get(deriv, deriv_data=e_0)
146 END IF
147 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
148 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
149 allocate_deriv=.true.)
150 CALL xc_derivative_get(deriv, deriv_data=e_rho)
151 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
152 allocate_deriv=.true.)
153 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
154 deriv => xc_dset_get_derivative(deriv_set, [deriv_tau], &
155 allocate_deriv=.true.)
156 CALL xc_derivative_get(deriv, deriv_data=e_tau)
157 END IF
158 IF (grad_deriv > 1 .OR. grad_deriv < -1) THEN
159 cpabort("derivatives bigger than 1 not implemented")
160 END IF
161
162 non_coer = 0
163 CALL section_vals_val_get(tpss_params, "SCALE_C", r_val=scale_ec)
164 CALL section_vals_val_get(tpss_params, "SCALE_X", r_val=scale_ex)
165
166!$OMP PARALLEL DEFAULT(NONE) &
167!$OMP SHARED(rho, tau, norm_drho, e_0, e_rho, e_ndrho, e_tau) &
168!$OMP SHARED(epsilon_rho, epsilon_tau, npoints, grad_deriv) &
169!$OMP SHARED(scale_ec, scale_ex) &
170!$OMP REDUCTION(+: non_coer)
171
172 CALL tpss_lda_calc(rho=rho, norm_drho=norm_drho, &
173 tau=tau, e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_tau=e_tau, &
174 grad_deriv=grad_deriv, npoints=npoints, epsilon_rho=epsilon_rho, &
175 epsilon_tau=epsilon_tau, scale_ec=scale_ec, scale_ex=scale_ex, non_coer=non_coer)
176
177!$OMP END PARALLEL
178
179 logger => cp_get_default_logger()
180 ! we could check if tau/grad were consistent, but don't do anything here
181 IF (non_coer > 0) THEN
182 non_coer = 0
183 END IF
184
185 CALL timestop(handle)
186 END SUBROUTINE tpss_lda_eval
187
188! **************************************************************************************************
189!> \brief low level calculation routine for the unpolarized (lda) tpss
190!> \param rho ...
191!> \param norm_drho ...
192!> \param tau ...
193!> \param e_0 ...
194!> \param e_rho ...
195!> \param e_ndrho ...
196!> \param e_tau ...
197!> \param npoints ...
198!> \param grad_deriv ...
199!> \param epsilon_rho ...
200!> \param epsilon_tau ...
201!> \param scale_ec ...
202!> \param scale_ex ...
203!> \param non_coer ...
204!> \author fawzi
205!> \note
206!> maple is nice, but if you want the uman readable version of the code
207!> look in doc/tpss.mw
208! **************************************************************************************************
209 SUBROUTINE tpss_lda_calc(rho, norm_drho, tau, e_0, e_rho, e_ndrho, e_tau, &
210 npoints, grad_deriv, epsilon_rho, epsilon_tau, &
211 scale_ec, scale_ex, non_coer)
212 REAL(kind=dp), DIMENSION(*), INTENT(in) :: rho, norm_drho, tau
213 REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_rho, e_ndrho, e_tau
214 INTEGER, INTENT(in) :: npoints, grad_deriv
215 REAL(kind=dp), INTENT(in) :: epsilon_rho, epsilon_tau, scale_ec, &
216 scale_ex
217 INTEGER, INTENT(inout) :: non_coer
218
219 INTEGER :: abs_grad_deriv, ii
220 LOGICAL :: t571, t639
221 REAL(kind=dp) :: a, a_1, a_2, a_s1, a_s1rho, a_s2, a_s2rho, alpha, alpha_1_1, alpha_1_2, &
222 alphanorm_drho, alpharho, alphatau, arho, b, beta, beta_1_1, beta_1_2, beta_2_1, &
223 beta_2_2, beta_3_1, beta_3_2, beta_4_1, beta_4_2, c, d, e_c_u_0, e_c_u_0rho, e_c_u_1_s1, &
224 e_c_u_1_s1rho, e_c_u_1_s2, e_c_u_1_s2rho, e_var, epsilon_cgga, epsilon_cgga_0_1, &
225 epsilon_cgga_1_0, epsilon_cggarho, epsilon_crevpkzb, epsilon_crevpkzbnorm_drho, &
226 epsilon_crevpkzbrho, epsilon_crevpkzbtau, ex_unif, fx, gamma_var, hnorm_drho, k_f_s1, &
227 k_f_s1rho, k_s, k_s_s1, k_s_s2, kappa, m, ma, manorm_drho, marho, mb, mbnorm_drho, mbrho
228 REAL(kind=dp) :: mu, my_ndrho, my_rho, my_tau, p, p_1, p_2, p_3, phi_s1, phi_s2, pnorm_drho, &
229 prho, rs, rs_s1, rs_s1rho, rs_s2, rs_s2rho, rsrho, t, t1, t100, t101, t111, t12, t13, &
230 t138, t14, t140, t143, t145, t146, t147, t151, t152, t16, t161, t168, t177, t186, t187, &
231 t189, t19, t190, t191, t193, t194, t196, t197, t198, t199, t2, t20, t201, t202, t204, &
232 t205, t208, t209, t21, t211, t212, t213, t215, t216, t218, t219, t22, t220, t221, t223, &
233 t224, t226, t227, t230, t231, t233, t234, t235, t238, t239, t241, t242, t243, t245, t246, &
234 t248, t249, t252, t253, t254, t256, t26, t260, t263, t264, t265
235 REAL(kind=dp) :: t267, t268, t269, t27, t271, t272, t274, t275, t276, t277, t278, t279, t28, &
236 t280, t281, t284, t286, t288, t29, t290, t291, t293, t294, t295, t299, t3, t301, t302, &
237 t303, t305, t307, t310, t313, t316, t319, t322, t325, t327, t328, t329, t331, t337, t340, &
238 t343, t344, t35, t351, t36, t370, t371, t376, t383, t385, t386, t39, t390, t391, t395, &
239 t396, t398, t4, t403, t404, t406, t41, t410, t411, t419, t42, t430, t437, t445, t450, &
240 t452, t464, t472, t475, t485, t489, t49, t490, t5, t505, t513, t517, t536, t541, t542, &
241 t546, t547, t549, t55, t554, t555, t557, t561, t562, t569, t574
242 REAL(kind=dp) :: t58, t585, t6, t60, t604, t609, t610, t614, t615, t617, t622, t623, t625, &
243 t629, t630, t637, t642, t645, t659, t67, t7, t71, t73, t77, t78, t79, t799, t80, t84, &
244 t85, t89, t9, t94, t95, t96, t_s1, t_s1norm_drho, t_s1rho, t_s2, t_s2norm_drho, t_s2rho, &
245 tau_w, tau_wnorm_drho, tau_wrho, tildeq_b, tildeq_bnorm_drho, tildeq_brho, tildeq_btau, &
246 tnorm_drho, trho, z, znorm_drho, zrho, ztau
247
248 IF (.false.) THEN
249 ! useful for testing, we just hack in a well defined functional of tau, ndrho and rho
250 ! and see that things converge properly with OT.
251!$OMP DO
252 DO ii = 1, npoints
253 my_tau = tau(ii)
254 my_rho = rho(ii)
255 my_ndrho = norm_drho(ii)
256 IF (grad_deriv >= 0) THEN
257 e_0(ii) = e_0(ii) + my_tau*my_ndrho*my_rho
258 END IF
259 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
260 e_rho(ii) = e_rho(ii) + my_tau*my_ndrho
261 e_ndrho(ii) = e_ndrho(ii) + my_tau*my_rho
262 e_tau(ii) = e_tau(ii) + my_rho*my_ndrho
263 END IF
264 END DO
265!$OMP END DO
266 RETURN
267 END IF
268
269 abs_grad_deriv = abs(grad_deriv)
270
271 kappa = 0.804e0_dp
272 beta = 0.66725e-1_dp
273 mu = 0.21951e0_dp
274 gamma_var = (0.1e1_dp - log(0.2e1_dp))/pi**2
275 b = 0.4e0_dp
276 c = 0.159096e1_dp
277 e_var = 0.1537e1_dp
278 d = 0.28e1_dp
279 p_1 = 0.10e1_dp
280 a_1 = 0.31091e-1_dp
281 alpha_1_1 = 0.21370e0_dp
282 beta_1_1 = 0.75957e1_dp
283 beta_2_1 = 0.35876e1_dp
284 beta_3_1 = 0.16382e1_dp
285 beta_4_1 = 0.49294e0_dp
286 p_2 = 0.10e1_dp
287 a_2 = 0.15545e-1_dp
288 alpha_1_2 = 0.20548e0_dp
289 beta_1_2 = 0.141189e2_dp
290 beta_2_2 = 0.61977e1_dp
291 beta_3_2 = 0.33662e1_dp
292 beta_4_2 = 0.62517e0_dp
293 p_3 = 0.10e1_dp
294
295 t1 = 3._dp**(0.1e1_dp/0.3e1_dp)
296 t2 = 4._dp**(0.1e1_dp/0.3e1_dp)
297 t3 = t2**2
298 t4 = t1*t3
299 t5 = 2._dp**(0.1e1_dp/0.3e1_dp)
300 t6 = 0.1e1_dp/pi
301 t12 = t5**2
302
303!$OMP DO
304
305 DO ii = 1, npoints
306 my_tau = tau(ii)
307 my_rho = rho(ii)
308 IF (my_rho > epsilon_rho .AND. my_tau > epsilon_tau) THEN
309 my_ndrho = norm_drho(ii)
310
311 t7 = 0.1e1_dp/my_rho
312 t254 = my_ndrho**2
313 tau_w = t254*t7/0.8e1_dp
314
315 IF (my_tau < tau_w) THEN
316 ! enforce z=norm_rho**2/(8._dp*rho*tau) <1
317 m = 0.5_dp*t254 + 4.0_dp*my_rho*my_tau
318 my_tau = m/8._dp/my_rho
319 my_ndrho = sqrt(m)
320 t254 = m
321 non_coer = non_coer + 1
322 END IF
323
324 t9 = (t6*t7)**(0.1e1_dp/0.3e1_dp)
325 rs_s1 = t4*t5*t9/0.4e1_dp
326 phi_s1 = t12/0.2e1_dp
327 t13 = t1*t12
328 t14 = pi**2
329 t16 = (t14*my_rho)**(0.1e1_dp/0.3e1_dp)
330 k_f_s1 = t13*t16/0.2e1_dp
331 t19 = sqrt(k_f_s1*t6)
332 k_s_s1 = 0.2e1_dp*t19
333 t20 = 0.1e1_dp/phi_s1
334 t21 = my_ndrho*t20
335 t22 = 0.1e1_dp/k_s_s1
336 t_s1 = t21*t22*t7/0.2e1_dp
337 rs_s2 = rs_s1
338 phi_s2 = phi_s1
339 t26 = sqrt(k_f_s1*t6)
340 k_s_s2 = 0.2e1_dp*t26
341 t27 = 0.1e1_dp/phi_s2
342 t28 = my_ndrho*t27
343 t29 = 0.1e1_dp/k_s_s2
344 t_s2 = t28*t29*t7/0.2e1_dp
345 t35 = 0.1e1_dp/a_1
346 t36 = sqrt(rs_s2)
347 t39 = t36*rs_s2
348 t41 = p_1 + 0.1e1_dp
349 t42 = rs_s2**t41
350 t49 = log(0.1e1_dp + t35/(beta_1_1*t36 + beta_2_1*rs_s2 + &
351 beta_3_1*t39 + beta_4_1*t42)/0.2e1_dp)
352 t55 = sqrt(rs_s1)
353 t58 = t55*rs_s1
354 t60 = rs_s1**t41
355 t67 = log(0.1e1_dp + t35/(beta_1_1*t55 + beta_2_1*rs_s1 + &
356 beta_3_1*t58 + beta_4_1*t60)/0.2e1_dp)
357 t71 = 0.1e1_dp + alpha_1_2*rs_s2
358 t73 = 0.1e1_dp/a_2
359 t77 = p_2 + 0.1e1_dp
360 t78 = rs_s2**t77
361 t79 = beta_4_2*t78
362 t80 = beta_1_2*t36 + beta_2_2*rs_s2 + beta_3_2*t39 + t79
363 t84 = 0.1e1_dp + t73/t80/0.2e1_dp
364 t85 = log(t84)
365 e_c_u_1_s2 = -0.2e1_dp*a_2*t71*t85
366 t89 = 0.1e1_dp + alpha_1_2*rs_s1
367 t94 = rs_s1**t77
368 t95 = beta_4_2*t94
369 t96 = beta_1_2*t55 + beta_2_2*rs_s1 + beta_3_2*t58 + t95
370 t100 = 0.1e1_dp + t73/t96/0.2e1_dp
371 t101 = log(t100)
372 e_c_u_1_s1 = -0.2e1_dp*a_2*t89*t101
373 t111 = p_3 + 1._dp
374 rs = t4*t9/0.4e1_dp
375 t138 = 0.1e1_dp + alpha_1_1*rs
376 t140 = sqrt(rs)
377 t143 = t140*rs
378 t145 = rs**t41
379 t146 = beta_4_1*t145
380 t147 = beta_1_1*t140 + beta_2_1*rs + beta_3_1*t143 + t146
381 t151 = 0.1e1_dp + t35/t147/0.2e1_dp
382 t152 = log(t151)
383 e_c_u_0 = -0.2e1_dp*a_1*t138*t152
384 t161 = rs**t77
385 t168 = log(0.1e1_dp + t73/(beta_1_2*t140 + beta_2_2*rs + &
386 beta_3_2*t143 + beta_4_2*t161)/0.2e1_dp)
387 t177 = rs**t111
388 t186 = 0.1e1_dp/gamma_var
389 t187 = beta*t186
390 t189 = phi_s1**2
391 t190 = t189*phi_s1
392 t191 = 0.1e1_dp/t190
393 t193 = exp(-e_c_u_1_s1*t186*t191)
394 t194 = t193 - 0.1e1_dp
395 a_s1 = t187/t194
396 t196 = gamma_var*t190
397 t197 = t_s1**2
398 t198 = a_s1*t197
399 t199 = 0.1e1_dp + t198
400 t201 = a_s1**2
401 t202 = t197**2
402 t204 = 0.1e1_dp + t198 + t201*t202
403 t205 = 0.1e1_dp/t204
404 t208 = 0.1e1_dp + t187*t197*t199*t205
405 t209 = log(t208)
406 epsilon_cgga_1_0 = e_c_u_1_s1 + t196*t209
407 t211 = phi_s2**2
408 t212 = t211*phi_s2
409 t213 = 0.1e1_dp/t212
410 t215 = exp(-e_c_u_1_s2*t186*t213)
411 t216 = t215 - 0.1e1_dp
412 a_s2 = t187/t216
413 t218 = gamma_var*t212
414 t219 = t_s2**2
415 t220 = a_s2*t219
416 t221 = t220 + 0.1e1_dp
417 t223 = a_s2**2
418 t224 = t219**2
419 t226 = 0.1e1_dp + t220 + t223*t224
420 t227 = 0.1e1_dp/t226
421 t230 = 0.1e1_dp + t187*t219*t221*t227
422 t231 = log(t230)
423 epsilon_cgga_0_1 = e_c_u_1_s2 + t218*t231
424 t233 = sqrt(t1*t16*t6)
425 k_s = 0.2e1_dp*t233
426 t234 = 0.1e1_dp/k_s
427 t235 = my_ndrho*t234
428 t = t235*t7/0.2e1_dp
429 t238 = exp(-e_c_u_0*t186)
430 t239 = -0.1e1_dp + t238
431 a = t187/t239
432 t241 = t**2
433 t242 = a*t241
434 t243 = 0.1e1_dp + t242
435 t245 = a**2
436 t246 = t241**2
437 t248 = 0.1e1_dp + t242 + t245*t246
438 t249 = 0.1e1_dp/t248
439 t252 = 0.1e1_dp + t187*t241*t243*t249
440 t253 = log(t252)
441 epsilon_cgga = e_c_u_0 + gamma_var*t253
442 ma = max(epsilon_cgga_1_0, epsilon_cgga)
443 mb = max(epsilon_cgga_0_1, epsilon_cgga)
444 t256 = tau_w**2
445 t260 = ma/0.2e1_dp + mb/0.2e1_dp
446 t263 = 0.53e0_dp*epsilon_cgga*t256 - 0.153e1_dp*t256*t260
447 t264 = my_tau**2
448 t265 = 0.1e1_dp/t264
449 epsilon_crevpkzb = epsilon_cgga + t263*t265
450 t267 = my_rho*epsilon_crevpkzb
451 t268 = d*epsilon_crevpkzb
452 t269 = t256*tau_w
453 t271 = 0.1e1_dp/t264/my_tau
454 t272 = t269*t271
455 t274 = 0.1e1_dp + t268*t272
456 t275 = t254*t1
457 t276 = t14**(0.1e1_dp/0.3e1_dp)
458 t277 = t276**2
459 t278 = 0.1e1_dp/t277
460 t279 = my_rho**2
461 t280 = my_rho**(0.1e1_dp/0.3e1_dp)
462 t281 = t280**2
463 t284 = t278/t281/t279
464 p = t275*t284/0.12e2_dp
465 t286 = 0.1e1_dp/my_tau
466 z = tau_w*t286
467 t288 = 0.1e1_dp/z - 0.1e1_dp
468 alpha = 0.5e1_dp/0.3e1_dp*p*t288
469 t290 = alpha - 0.1e1_dp
470 t291 = b*alpha
471 t293 = 0.1e1_dp + t291*t290
472 t294 = sqrt(t293)
473 t295 = 0.1e1_dp/t294
474 tildeq_b = 0.9e1_dp/0.20e2_dp*t290*t295 + 0.2e1_dp/0.3e1_dp*p
475 t299 = z**2
476 t301 = 0.1e1_dp + t299
477 t302 = t301**2
478 t303 = 0.1e1_dp/t302
479 t305 = 0.10e2_dp/0.81e2_dp + c*t299*t303
480 t307 = tildeq_b**2
481 t310 = p**2
482 t313 = sqrt(0.18e2_dp*t299 + 0.50e2_dp*t310)
483 t316 = 0.1e1_dp/kappa
484 t319 = sqrt(e_var)
485 t322 = e_var*mu
486 t325 = t305*p + 0.146e3_dp/0.2025e4_dp*t307 - 0.73e2_dp/ &
487 0.4050e4_dp*tildeq_b*t313 + 0.100e3_dp/0.6561e4_dp*t316* &
488 t310 + 0.4e1_dp/0.45e2_dp*t319*t299 + t322*t310*p
489 t327 = 0.1e1_dp + t319*p
490 t328 = t327**2
491 t329 = 0.1e1_dp/t328
492 t331 = 0.1e1_dp + t325*t329*t316
493 fx = 0.1e1_dp + kappa - kappa/t331
494 ex_unif = -0.3e1_dp/0.4e1_dp*t1*t16*t6
495 t337 = my_rho*ex_unif
496
497 IF (grad_deriv >= 0) THEN
498 e_0(ii) = e_0(ii) + &
499 scale_ec*t267*t274 + scale_ex*t337*fx
500 END IF
501
502 IF (abs_grad_deriv > 0) THEN
503 t340 = t9**2
504 t343 = 0.1e1_dp/t279
505 t344 = 0.1e1_dp/t340*t6*t343
506 rsrho = -t4*t344/0.12e2_dp
507 t351 = t147**2
508 e_c_u_0rho = -0.2e1_dp*a_1*alpha_1_1*rsrho*t152 + t138/ &
509 t351*(beta_1_1/t140*rsrho/0.2e1_dp + beta_2_1*rsrho + &
510 0.3e1_dp/0.2e1_dp*beta_3_1*t140*rsrho + t146*t41*rsrho/ &
511 rs)/t151
512 t370 = t16**2
513 t371 = 0.1e1_dp/t370
514 t376 = k_s**2
515 trho = -my_ndrho/t376*t7/t233*t1*t371*t14*t6 &
516 /0.6e1_dp - t235*t343/0.2e1_dp
517 t383 = gamma_var**2
518 t385 = beta/t383
519 t386 = t239**2
520 arho = t385/t386*e_c_u_0rho*t238
521 t390 = t187*t
522 t391 = t243*t249
523 t395 = arho*t241
524 t396 = a*t
525 t398 = 0.2e1_dp*t396*trho
526 t403 = t187*t241
527 t404 = t248**2
528 t406 = t243/t404
529 t410 = t241*t
530 t411 = t245*t410
531 t419 = 0.1e1_dp/t252
532 epsilon_cggarho = e_c_u_0rho + gamma_var*(0.2e1_dp*t390*t391 &
533 *trho + t187*t241*(t395 + t398)*t249 - t403*t406*(t395 + &
534 t398 + 0.2e1_dp*a*t246*arho + 0.4e1_dp*t411*trho))*t419
535 tau_wrho = -t254*t343/0.8e1_dp
536 prho = -0.2e1_dp/0.9e1_dp*t275*t278/t281/t279/my_rho
537 zrho = tau_wrho*t286
538 t430 = p/t299
539 alpharho = 0.5e1_dp/0.3e1_dp*prho*t288 - 0.5e1_dp/0.3e1_dp &
540 *t430*zrho
541 t437 = t290/t294/t293
542 tildeq_brho = 0.9e1_dp/0.20e2_dp*alpharho*t295 - 0.9e1_dp/ &
543 0.40e2_dp*t437*(b*alpharho*t290 + t291*alpharho) + &
544 0.2e1_dp/0.3e1_dp*prho
545 t445 = c*z
546 t450 = c*t299*z
547 t452 = 0.1e1_dp/t302/t301
548 t464 = tildeq_b/t313
549 t472 = t316*p
550 t475 = t319*z
551 t485 = t325/t328/t327
552 t489 = t331**2
553 t490 = 0.1e1_dp/t489
554 rs_s1rho = -t4*t5*t344/0.12e2_dp
555 k_f_s1rho = t13*t371*t14/0.6e1_dp
556 t505 = k_s_s1**2
557 t_s1rho = -t21/t505*t7/t19*k_f_s1rho*t6/0.2e1_dp - t21 &
558 *t22*t343/0.2e1_dp
559 t513 = a_2*alpha_1_2
560 t517 = t96**2
561 e_c_u_1_s1rho = -0.2e1_dp*t513*rs_s1rho*t101 + t89/t517* &
562 (beta_1_2/t55*rs_s1rho/0.2e1_dp + beta_2_2*rs_s1rho + &
563 0.3e1_dp/0.2e1_dp*beta_3_2*t55*rs_s1rho + t95*t77* &
564 rs_s1rho/rs_s1)/t100
565 t536 = t194**2
566 a_s1rho = t385/t536*e_c_u_1_s1rho*t191*t193
567 t541 = t187*t_s1
568 t542 = t199*t205
569 t546 = a_s1rho*t197
570 t547 = a_s1*t_s1
571 t549 = 0.2e1_dp*t547*t_s1rho
572 t554 = t187*t197
573 t555 = t204**2
574 t557 = t199/t555
575 t561 = t197*t_s1
576 t562 = t201*t561
577 t569 = 0.1e1_dp/t208
578 t571 = epsilon_cgga .LT. epsilon_cgga_1_0
579 IF (t571) THEN
580 marho = e_c_u_1_s1rho + t196*(0.2e1_dp*t541*t542 &
581 *t_s1rho + t187*t197*(t546 + t549)*t205 - t554*t557*(t546 &
582 + t549 + 0.2e1_dp*a_s1*t202*a_s1rho + 0.4e1_dp*t562* &
583 t_s1rho))*t569
584 ELSE
585 marho = epsilon_cggarho
586 END IF
587 rs_s2rho = rs_s1rho
588 t574 = k_s_s2**2
589 t_s2rho = -t28/t574*t7/t26*k_f_s1rho*t6/0.2e1_dp - t28 &
590 *t29*t343/0.2e1_dp
591 t585 = t80**2
592 e_c_u_1_s2rho = -0.2e1_dp*t513*rs_s2rho*t85 + t71/t585*( &
593 beta_1_2/t36*rs_s2rho/0.2e1_dp + beta_2_2*rs_s2rho + &
594 0.3e1_dp/0.2e1_dp*beta_3_2*t36*rs_s2rho + t79*t77* &
595 rs_s2rho/rs_s2)/t84
596 t604 = t216**2
597 a_s2rho = t385/t604*e_c_u_1_s2rho*t213*t215
598 t609 = t187*t_s2
599 t610 = t221*t227
600 t614 = a_s2rho*t219
601 t615 = a_s2*t_s2
602 t617 = 0.2e1_dp*t615*t_s2rho
603 t622 = t187*t219
604 t623 = t226**2
605 t625 = t221/t623
606 t629 = t219*t_s2
607 t630 = t223*t629
608 t637 = 0.1e1_dp/t230
609 t639 = epsilon_cgga .LT. epsilon_cgga_0_1
610 IF (t639) THEN
611 mbrho = e_c_u_1_s2rho + t218*(0.2e1_dp*t609*t610 &
612 *t_s2rho + t187*t219*(t614 + t617)*t227 - t622*t625*(t614 &
613 + t617 + 0.2e1_dp*a_s2*t224*a_s2rho + 0.4e1_dp*t630* &
614 t_s2rho))*t637
615 ELSE
616 mbrho = epsilon_cggarho
617 END IF
618 t642 = epsilon_cgga*tau_w
619 t645 = tau_w*t260
620 epsilon_crevpkzbrho = epsilon_cggarho + (0.53e0_dp* &
621 epsilon_cggarho*t256 + 0.106e1_dp*t642*tau_wrho - 0.306e1_dp* &
622 t645*tau_wrho - 0.153e1_dp*t256*(marho/0.2e1_dp + mbrho/ &
623 0.2e1_dp))*t265
624 t659 = t256*t271
625
626 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
627 e_rho(ii) = e_rho(ii) + &
628 scale_ec*(epsilon_crevpkzb*t274 + my_rho* &
629 epsilon_crevpkzbrho*t274 + t267*(d*epsilon_crevpkzbrho*t272 &
630 + 0.3e1_dp*t268*t659*tau_wrho)) + scale_ex*(ex_unif*fx - &
631 my_rho*pi*t1*t371*fx/0.4e1_dp + t337* &
632 t490*(((0.2e1_dp*t445*t303*zrho - 0.4e1_dp*t450*t452* &
633 zrho)*p + t305*prho + 0.292e3_dp/0.2025e4_dp*tildeq_b* &
634 tildeq_brho - 0.73e2_dp/0.4050e4_dp*tildeq_brho*t313 - &
635 0.73e2_dp/0.8100e4_dp*t464*(0.36e2_dp*z*zrho + 0.100e3_dp &
636 *p*prho) + 0.200e3_dp/0.6561e4_dp*t472*prho + 0.8e1_dp/ &
637 0.45e2_dp*t475*zrho + 0.3e1_dp*t322*t310*prho)*t329 - &
638 0.2e1_dp*t485*t319*prho))
639 END IF
640
641 tnorm_drho = t234*t7/0.2e1_dp
642 hnorm_drho = gamma_var*(0.2e1_dp*t390*t391*tnorm_drho + &
643 0.2e1_dp*t187*t410*a*tnorm_drho*t249 - t403*t406*( &
644 0.2e1_dp*t396*tnorm_drho + 0.4e1_dp*t411*tnorm_drho))*t419
645 tau_wnorm_drho = my_ndrho*t7/0.4e1_dp
646 pnorm_drho = my_ndrho*t1*t284/0.6e1_dp
647 znorm_drho = tau_wnorm_drho*t286
648 alphanorm_drho = 0.5e1_dp/0.3e1_dp*pnorm_drho*t288 - &
649 0.5e1_dp/0.3e1_dp*t430*znorm_drho
650 tildeq_bnorm_drho = 0.9e1_dp/0.20e2_dp*alphanorm_drho*t295 - &
651 0.9e1_dp/0.40e2_dp*t437*(b*alphanorm_drho*t290 + t291* &
652 alphanorm_drho) + 0.2e1_dp/0.3e1_dp*pnorm_drho
653 t_s1norm_drho = t20*t22*t7/0.2e1_dp
654 IF (t571) THEN
655 manorm_drho = t196*(0.2e1_dp*t541*t542* &
656 t_s1norm_drho + 0.2e1_dp*t187*t561*a_s1*t_s1norm_drho*t205 &
657 - t554*t557*(0.2e1_dp*t547*t_s1norm_drho + 0.4e1_dp*t562 &
658 *t_s1norm_drho))*t569
659 ELSE
660 manorm_drho = hnorm_drho
661 END IF
662 t_s2norm_drho = t27*t29*t7/0.2e1_dp
663 IF (t639) THEN
664 mbnorm_drho = t218*(0.2e1_dp*t609*t610* &
665 t_s2norm_drho + 0.2e1_dp*t187*t629*a_s2*t_s2norm_drho*t227 &
666 - t622*t625*(0.2e1_dp*t615*t_s2norm_drho + 0.4e1_dp*t630 &
667 *t_s2norm_drho))*t637
668 ELSE
669 mbnorm_drho = hnorm_drho
670 END IF
671 epsilon_crevpkzbnorm_drho = hnorm_drho + (0.53e0_dp*hnorm_drho* &
672 t256 + 0.106e1_dp*t642*tau_wnorm_drho - 0.306e1_dp*t645* &
673 tau_wnorm_drho - 0.153e1_dp*t256*(manorm_drho/0.2e1_dp + &
674 mbnorm_drho/0.2e1_dp))*t265
675
676 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
677 e_ndrho(ii) = e_ndrho(ii) + &
678 scale_ec*(my_rho*epsilon_crevpkzbnorm_drho* &
679 t274 + t267*(d*epsilon_crevpkzbnorm_drho*t272 + 0.3e1_dp* &
680 t268*t659*tau_wnorm_drho)) + scale_ex*t337*t490*((( &
681 0.2e1_dp*t445*t303*znorm_drho - 0.4e1_dp*t450*t452* &
682 znorm_drho)*p + t305*pnorm_drho + 0.292e3_dp/0.2025e4_dp* &
683 tildeq_b*tildeq_bnorm_drho - 0.73e2_dp/0.4050e4_dp* &
684 tildeq_bnorm_drho*t313 - 0.73e2_dp/0.8100e4_dp*t464*( &
685 0.36e2_dp*z*znorm_drho + 0.100e3_dp*p*pnorm_drho) + &
686 0.200e3_dp/0.6561e4_dp*t472*pnorm_drho + 0.8e1_dp/0.45e2_dp &
687 *t475*znorm_drho + 0.3e1_dp*t322*t310*pnorm_drho)*t329 - &
688 0.2e1_dp*t485*t319*pnorm_drho)
689 END IF
690
691 epsilon_crevpkzbtau = -0.2e1_dp*t263*t271
692 t799 = t264**2
693 ztau = -tau_w*t265
694 alphatau = -0.5e1_dp/0.3e1_dp*t430*ztau
695 tildeq_btau = 0.9e1_dp/0.20e2_dp*alphatau*t295 - 0.9e1_dp/ &
696 0.40e2_dp*t437*(b*alphatau*t290 + t291*alphatau)
697
698 IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
699 e_tau(ii) = e_tau(ii) + &
700 scale_ec*(my_rho*epsilon_crevpkzbtau*t274 + t267* &
701 (d*epsilon_crevpkzbtau*t272 - 0.3e1_dp*t268*t269/t799)) + &
702 scale_ex*t337*t490*((0.2e1_dp*t445*t303*ztau - 0.4e1_dp &
703 *t450*t452*ztau)*p + 0.292e3_dp/0.2025e4_dp*tildeq_b* &
704 tildeq_btau - 0.73e2_dp/0.4050e4_dp*tildeq_btau*t313 - &
705 0.73e2_dp/0.225e3_dp*t464*z*ztau + 0.8e1_dp/0.45e2_dp* &
706 t475*ztau)*t329
707 END IF
708 END IF
709 END IF
710 END DO
711
712!$OMP END DO
713
714 END SUBROUTINE tpss_lda_calc
715
716END MODULE xc_tpss
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition bibliography.F:28
bibliography::tao2003
integer, save, public tao2003
Definition bibliography.F:43
cp_log_handling
various routines to log and control the output. The idea is that decisions about where to log should ...
Definition cp_log_handling.F:41
cp_log_handling::cp_get_default_logger
type(cp_logger_type) function, pointer, public cp_get_default_logger()
returns the default logger
Definition cp_log_handling.F:234
input_section_types
objects that represent the structure of input sections and the data contained in an input section
Definition input_section_types.F:15
input_section_types::section_vals_val_get
subroutine, public section_vals_val_get(section_vals, keyword_name, i_rep_section, i_rep_val, n_rep_val, val, l_val, i_val, r_val, c_val, l_vals, i_vals, r_vals, c_vals, explicit)
returns the requested value
Definition input_section_types.F:1040
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
xc_derivative_desc
Module with functions to handle derivative descriptors. derivative description are strings have the f...
Definition xc_derivative_desc.F:26
xc_derivative_desc::deriv_norm_drho
integer, parameter, public deriv_norm_drho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_tau
integer, parameter, public deriv_tau
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_rho
integer, parameter, public deriv_rho
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_tpss
Calculates the tpss functional.
Definition xc_tpss.F:17
xc_tpss::tpss_lda_eval
subroutine, public tpss_lda_eval(rho_set, deriv_set, grad_deriv, tpss_params)
evaluates the tpss functional in the spin unpolarized (lda) case
Definition xc_tpss.F:109
xc_tpss::tpss_lda_info
subroutine, public tpss_lda_info(tpss_params, reference, shortform, needs, max_deriv)
return various information on the functional
Definition xc_tpss.F:60
cp_log_handling::cp_logger_type
type of a logger, at the moment it contains just a print level starting at which level it should be l...
Definition cp_log_handling.F:140
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