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xc_tpss.F
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1!--------------------------------------------------------------------------------------------------!
2! CP2K: A general program to perform molecular dynamics simulations !
3! Copyright 2000-2026 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 maximum degree of the derivative that should be evaluated
103!> \param tpss_params ...
104!> \author fawzi
105! **************************************************************************************************
106 SUBROUTINE tpss_lda_eval(rho_set, deriv_set, grad_deriv, tpss_params)
107 TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
108 TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
109 INTEGER, INTENT(in) :: grad_deriv
110 TYPE(section_vals_type), POINTER :: tpss_params
111
112 CHARACTER(len=*), PARAMETER :: routinen = 'tpss_lda_eval'
113
114 INTEGER :: handle, non_coer, npoints
115 INTEGER, DIMENSION(2, 3) :: bo
116 REAL(kind=dp) :: epsilon_rho, epsilon_tau, scale_ec, &
117 scale_ex
118 REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), &
119 POINTER :: dummy, e_0, e_ndrho, e_rho, e_tau, &
120 norm_drho, rho, tau
121 TYPE(cp_logger_type), POINTER :: logger
122 TYPE(xc_derivative_type), POINTER :: deriv
123
124 CALL timeset(routinen, handle)
125
126 CALL cite_reference(tao2003)
127
128 CALL xc_rho_set_get(rho_set, rho=rho, &
129 norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho, &
130 tau=tau, tau_cutoff=epsilon_tau)
131 npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
132
133 dummy => rho
134
135 e_0 => dummy
136 e_rho => dummy
137 e_ndrho => dummy
138 e_tau => dummy
139
140 IF (grad_deriv >= 0) THEN
141 deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
142 allocate_deriv=.true.)
143 CALL xc_derivative_get(deriv, deriv_data=e_0)
144 END IF
145 IF (grad_deriv >= 1) THEN
146 deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
147 allocate_deriv=.true.)
148 CALL xc_derivative_get(deriv, deriv_data=e_rho)
149 deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
150 allocate_deriv=.true.)
151 CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
152 deriv => xc_dset_get_derivative(deriv_set, [deriv_tau], &
153 allocate_deriv=.true.)
154 CALL xc_derivative_get(deriv, deriv_data=e_tau)
155 END IF
156 IF (grad_deriv > 1) THEN
157 cpabort("derivatives bigger than 1 not implemented")
158 END IF
159
160 non_coer = 0
161 CALL section_vals_val_get(tpss_params, "SCALE_C", r_val=scale_ec)
162 CALL section_vals_val_get(tpss_params, "SCALE_X", r_val=scale_ex)
163
164!$OMP PARALLEL DEFAULT(NONE) &
165!$OMP SHARED(rho, tau, norm_drho, e_0, e_rho, e_ndrho, e_tau) &
166!$OMP SHARED(epsilon_rho, epsilon_tau, npoints, grad_deriv) &
167!$OMP SHARED(scale_ec, scale_ex) &
168!$OMP REDUCTION(+: non_coer)
169
170 CALL tpss_lda_calc(rho=rho, norm_drho=norm_drho, &
171 tau=tau, e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_tau=e_tau, &
172 grad_deriv=grad_deriv, npoints=npoints, epsilon_rho=epsilon_rho, &
173 epsilon_tau=epsilon_tau, scale_ec=scale_ec, scale_ex=scale_ex, non_coer=non_coer)
174
175!$OMP END PARALLEL
176
177 logger => cp_get_default_logger()
178 ! we could check if tau/grad were consistent, but don't do anything here
179 IF (non_coer > 0) THEN
180 non_coer = 0
181 END IF
182
183 CALL timestop(handle)
184 END SUBROUTINE tpss_lda_eval
185
186! **************************************************************************************************
187!> \brief low level calculation routine for the unpolarized (lda) tpss
188!> \param rho ...
189!> \param norm_drho ...
190!> \param tau ...
191!> \param e_0 ...
192!> \param e_rho ...
193!> \param e_ndrho ...
194!> \param e_tau ...
195!> \param npoints ...
196!> \param grad_deriv ...
197!> \param epsilon_rho ...
198!> \param epsilon_tau ...
199!> \param scale_ec ...
200!> \param scale_ex ...
201!> \param non_coer ...
202!> \author fawzi
203!> \note
204!> maple is nice, but if you want the uman readable version of the code
205!> look in doc/tpss.mw
206! **************************************************************************************************
207 SUBROUTINE tpss_lda_calc(rho, norm_drho, tau, e_0, e_rho, e_ndrho, e_tau, &
208 npoints, grad_deriv, epsilon_rho, epsilon_tau, &
209 scale_ec, scale_ex, non_coer)
210 REAL(kind=dp), DIMENSION(*), INTENT(in) :: rho, norm_drho, tau
211 REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_rho, e_ndrho, e_tau
212 INTEGER, INTENT(in) :: npoints, grad_deriv
213 REAL(kind=dp), INTENT(in) :: epsilon_rho, epsilon_tau, scale_ec, &
214 scale_ex
215 INTEGER, INTENT(inout) :: non_coer
216
217 INTEGER :: ii
218 LOGICAL :: clipped_tau, floored_tau, t571, t639
219 REAL(dp) :: incoming_gradient, incoming_rho, incoming_tau, partial_gradient, partial_rho, &
220 partial_tau, tau_floor, tau_unif_inverse
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, regular_tau, rs, rs_s1, rs_s1rho, rs_s2, rs_s2rho, rsrho, t, t1, t100, t101, t111, &
230 t12, t13, t138, t14, t140, t143, t145, t146, t147, t151, t152, t16, t161, t168, t177, &
231 t186, t187, t189, t19, t190, t191, t193, t194, t196, t197, t198, t199, t2, t20, t201, &
232 t202, t204, t205, t208, t209, t21, t211, t212, t213, t215, t216, t218, t219, t22, t220, &
233 t221, t223, t224, t226, t227, t230, t231, t233, t234, t235, t238, t239, t241, t242, t243, &
234 t245, t246, t248, t249, t252, t253, t254, t256, t26, t260, t263
235 REAL(kind=dp) :: t264, t265, t267, t268, t269, t27, t271, t272, t274, t275, t276, t277, &
236 t278, t279, t28, t280, t281, t284, t286, t29, t290, t291, t293, t294, t295, t299, t3, &
237 t301, t302, t303, t305, t307, t310, t313, t316, t319, t322, t325, t327, t328, t329, t331, &
238 t337, t340, t343, t344, t35, t351, t36, t370, t371, t376, t383, t385, t386, t39, t390, &
239 t391, t395, t396, t398, t4, t403, t404, t406, t41, t410, t411, t419, t42, t437, t445, &
240 t450, t452, t464, t472, t475, t485, t489, t49, t490, t5, t505, t513, t517, t536, t541, &
241 t542, 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 kappa = 0.804e0_dp
249 beta = 0.66725e-1_dp
250 mu = 0.21951e0_dp
251 gamma_var = (0.1e1_dp - log(0.2e1_dp))/pi**2
252 b = 0.4e0_dp
253 c = 0.159096e1_dp
254 e_var = 0.1537e1_dp
255 d = 0.28e1_dp
256 p_1 = 0.10e1_dp
257 a_1 = 0.31091e-1_dp
258 alpha_1_1 = 0.21370e0_dp
259 beta_1_1 = 0.75957e1_dp
260 beta_2_1 = 0.35876e1_dp
261 beta_3_1 = 0.16382e1_dp
262 beta_4_1 = 0.49294e0_dp
263 p_2 = 0.10e1_dp
264 a_2 = 0.15545e-1_dp
265 alpha_1_2 = 0.20548e0_dp
266 beta_1_2 = 0.141189e2_dp
267 beta_2_2 = 0.61977e1_dp
268 beta_3_2 = 0.33662e1_dp
269 beta_4_2 = 0.62517e0_dp
270 p_3 = 0.10e1_dp
271
272 tau_floor = max(epsilon_tau, epsilon(0.0_dp))
273 t1 = 3._dp**(0.1e1_dp/0.3e1_dp)
274 t2 = 4._dp**(0.1e1_dp/0.3e1_dp)
275 t3 = t2**2
276 t4 = t1*t3
277 t5 = 2._dp**(0.1e1_dp/0.3e1_dp)
278 t6 = 0.1e1_dp/pi
279 t12 = t5**2
280
281!$OMP DO
282
283 DO ii = 1, npoints
284 ! Fourier interpolation can give negative tau even at finite density.
285 ! Continue the energy through tau=0; discarding these points makes it
286 ! discontinuous and invalidates the potential and geometry derivatives.
287 floored_tau = tau(ii) <= tau_floor
288 regular_tau = max(tau(ii), tau_floor)
289 my_tau = regular_tau
290 my_rho = rho(ii)
291 IF (my_rho > epsilon_rho) THEN
292 my_ndrho = norm_drho(ii)
293 IF (grad_deriv > 0) THEN
294 incoming_rho = e_rho(ii)
295 incoming_gradient = e_ndrho(ii)
296 incoming_tau = e_tau(ii)
297 END IF
298
299 t7 = 0.1e1_dp/my_rho
300 t254 = my_ndrho**2
301 tau_w = t254*t7/0.8e1_dp
302
303 clipped_tau = my_tau < tau_w
304 IF (clipped_tau) THEN
305 ! Project the gradient and kinetic density onto z=1.
306 m = 0.5_dp*t254 + 4.0_dp*my_rho*my_tau
307 my_tau = m/8._dp/my_rho
308 my_ndrho = sqrt(m)
309 t254 = m
310 tau_w = my_tau
311 non_coer = non_coer + 1
312 END IF
313
314 t9 = (t6*t7)**(0.1e1_dp/0.3e1_dp)
315 rs_s1 = t4*t5*t9/0.4e1_dp
316 phi_s1 = t12/0.2e1_dp
317 t13 = t1*t12
318 t14 = pi**2
319 t16 = (t14*my_rho)**(0.1e1_dp/0.3e1_dp)
320 k_f_s1 = t13*t16/0.2e1_dp
321 t19 = sqrt(k_f_s1*t6)
322 k_s_s1 = 0.2e1_dp*t19
323 t20 = 0.1e1_dp/phi_s1
324 t21 = my_ndrho*t20
325 t22 = 0.1e1_dp/k_s_s1
326 t_s1 = t21*t22*t7/0.2e1_dp
327 rs_s2 = rs_s1
328 phi_s2 = phi_s1
329 t26 = sqrt(k_f_s1*t6)
330 k_s_s2 = 0.2e1_dp*t26
331 t27 = 0.1e1_dp/phi_s2
332 t28 = my_ndrho*t27
333 t29 = 0.1e1_dp/k_s_s2
334 t_s2 = t28*t29*t7/0.2e1_dp
335 t35 = 0.1e1_dp/a_1
336 t36 = sqrt(rs_s2)
337 t39 = t36*rs_s2
338 t41 = p_1 + 0.1e1_dp
339 t42 = rs_s2**t41
340 t49 = log(0.1e1_dp + t35/(beta_1_1*t36 + beta_2_1*rs_s2 + &
341 beta_3_1*t39 + beta_4_1*t42)/0.2e1_dp)
342 t55 = sqrt(rs_s1)
343 t58 = t55*rs_s1
344 t60 = rs_s1**t41
345 t67 = log(0.1e1_dp + t35/(beta_1_1*t55 + beta_2_1*rs_s1 + &
346 beta_3_1*t58 + beta_4_1*t60)/0.2e1_dp)
347 t71 = 0.1e1_dp + alpha_1_2*rs_s2
348 t73 = 0.1e1_dp/a_2
349 t77 = p_2 + 0.1e1_dp
350 t78 = rs_s2**t77
351 t79 = beta_4_2*t78
352 t80 = beta_1_2*t36 + beta_2_2*rs_s2 + beta_3_2*t39 + t79
353 t84 = 0.1e1_dp + t73/t80/0.2e1_dp
354 t85 = log(t84)
355 e_c_u_1_s2 = -0.2e1_dp*a_2*t71*t85
356 t89 = 0.1e1_dp + alpha_1_2*rs_s1
357 t94 = rs_s1**t77
358 t95 = beta_4_2*t94
359 t96 = beta_1_2*t55 + beta_2_2*rs_s1 + beta_3_2*t58 + t95
360 t100 = 0.1e1_dp + t73/t96/0.2e1_dp
361 t101 = log(t100)
362 e_c_u_1_s1 = -0.2e1_dp*a_2*t89*t101
363 t111 = p_3 + 1._dp
364 rs = t4*t9/0.4e1_dp
365 t138 = 0.1e1_dp + alpha_1_1*rs
366 t140 = sqrt(rs)
367 t143 = t140*rs
368 t145 = rs**t41
369 t146 = beta_4_1*t145
370 t147 = beta_1_1*t140 + beta_2_1*rs + beta_3_1*t143 + t146
371 t151 = 0.1e1_dp + t35/t147/0.2e1_dp
372 t152 = log(t151)
373 e_c_u_0 = -0.2e1_dp*a_1*t138*t152
374 t161 = rs**t77
375 t168 = log(0.1e1_dp + t73/(beta_1_2*t140 + beta_2_2*rs + &
376 beta_3_2*t143 + beta_4_2*t161)/0.2e1_dp)
377 t177 = rs**t111
378 t186 = 0.1e1_dp/gamma_var
379 t187 = beta*t186
380 t189 = phi_s1**2
381 t190 = t189*phi_s1
382 t191 = 0.1e1_dp/t190
383 t193 = exp(-e_c_u_1_s1*t186*t191)
384 t194 = t193 - 0.1e1_dp
385 a_s1 = t187/t194
386 t196 = gamma_var*t190
387 t197 = t_s1**2
388 t198 = a_s1*t197
389 t199 = 0.1e1_dp + t198
390 t201 = a_s1**2
391 t202 = t197**2
392 t204 = 0.1e1_dp + t198 + t201*t202
393 t205 = 0.1e1_dp/t204
394 t208 = 0.1e1_dp + t187*t197*t199*t205
395 t209 = log(t208)
396 epsilon_cgga_1_0 = e_c_u_1_s1 + t196*t209
397 t211 = phi_s2**2
398 t212 = t211*phi_s2
399 t213 = 0.1e1_dp/t212
400 t215 = exp(-e_c_u_1_s2*t186*t213)
401 t216 = t215 - 0.1e1_dp
402 a_s2 = t187/t216
403 t218 = gamma_var*t212
404 t219 = t_s2**2
405 t220 = a_s2*t219
406 t221 = t220 + 0.1e1_dp
407 t223 = a_s2**2
408 t224 = t219**2
409 t226 = 0.1e1_dp + t220 + t223*t224
410 t227 = 0.1e1_dp/t226
411 t230 = 0.1e1_dp + t187*t219*t221*t227
412 t231 = log(t230)
413 epsilon_cgga_0_1 = e_c_u_1_s2 + t218*t231
414 t233 = sqrt(t1*t16*t6)
415 k_s = 0.2e1_dp*t233
416 t234 = 0.1e1_dp/k_s
417 t235 = my_ndrho*t234
418 t = t235*t7/0.2e1_dp
419 t238 = exp(-e_c_u_0*t186)
420 t239 = -0.1e1_dp + t238
421 a = t187/t239
422 t241 = t**2
423 t242 = a*t241
424 t243 = 0.1e1_dp + t242
425 t245 = a**2
426 t246 = t241**2
427 t248 = 0.1e1_dp + t242 + t245*t246
428 t249 = 0.1e1_dp/t248
429 t252 = 0.1e1_dp + t187*t241*t243*t249
430 t253 = log(t252)
431 epsilon_cgga = e_c_u_0 + gamma_var*t253
432 ma = max(epsilon_cgga_1_0, epsilon_cgga)
433 mb = max(epsilon_cgga_0_1, epsilon_cgga)
434 t256 = tau_w**2
435 t260 = ma/0.2e1_dp + mb/0.2e1_dp
436 t263 = 0.53e0_dp*epsilon_cgga*t256 - 0.153e1_dp*t256*t260
437 t264 = my_tau**2
438 t265 = 0.1e1_dp/t264
439 epsilon_crevpkzb = epsilon_cgga + t263*t265
440 t267 = my_rho*epsilon_crevpkzb
441 t268 = d*epsilon_crevpkzb
442 t269 = t256*tau_w
443 t271 = 0.1e1_dp/t264/my_tau
444 t272 = t269*t271
445 t274 = 0.1e1_dp + t268*t272
446 t275 = t254*t1
447 t276 = t14**(0.1e1_dp/0.3e1_dp)
448 t277 = t276**2
449 t278 = 0.1e1_dp/t277
450 t279 = my_rho**2
451 t280 = my_rho**(0.1e1_dp/0.3e1_dp)
452 t281 = t280**2
453 t284 = t278/t281/t279
454 p = t275*t284/0.12e2_dp
455 t286 = 0.1e1_dp/my_tau
456 z = tau_w*t286
457 ! Use the finite stationary-density limit of (5/3)*p*(1/z-1).
458 tau_unif_inverse = 10.0_dp/9.0_dp*t1*t278/(t281*my_rho)
459 alpha = (my_tau - tau_w)*tau_unif_inverse
460 t290 = alpha - 0.1e1_dp
461 t291 = b*alpha
462 t293 = 0.1e1_dp + t291*t290
463 t294 = sqrt(t293)
464 t295 = 0.1e1_dp/t294
465 tildeq_b = 0.9e1_dp/0.20e2_dp*t290*t295 + 0.2e1_dp/0.3e1_dp*p
466 t299 = z**2
467 t301 = 0.1e1_dp + t299
468 t302 = t301**2
469 t303 = 0.1e1_dp/t302
470 t305 = 0.10e2_dp/0.81e2_dp + c*t299*t303
471 t307 = tildeq_b**2
472 t310 = p**2
473 t313 = sqrt(0.18e2_dp*t299 + 0.50e2_dp*t310)
474 t316 = 0.1e1_dp/kappa
475 t319 = sqrt(e_var)
476 t322 = e_var*mu
477 t325 = t305*p + 0.146e3_dp/0.2025e4_dp*t307 - 0.73e2_dp/ &
478 0.4050e4_dp*tildeq_b*t313 + 0.100e3_dp/0.6561e4_dp*t316* &
479 t310 + 0.4e1_dp/0.45e2_dp*t319*t299 + t322*t310*p
480 t327 = 0.1e1_dp + t319*p
481 t328 = t327**2
482 t329 = 0.1e1_dp/t328
483 t331 = 0.1e1_dp + t325*t329*t316
484 fx = 0.1e1_dp + kappa - kappa/t331
485 ex_unif = -0.3e1_dp/0.4e1_dp*t1*t16*t6
486 t337 = my_rho*ex_unif
487
488 e_0(ii) = e_0(ii) + &
489 scale_ec*t267*t274 + scale_ex*t337*fx
490
491 IF (grad_deriv > 0) THEN
492 t340 = t9**2
493 t343 = 0.1e1_dp/t279
494 t344 = 0.1e1_dp/t340*t6*t343
495 rsrho = -t4*t344/0.12e2_dp
496 t351 = t147**2
497 e_c_u_0rho = -0.2e1_dp*a_1*alpha_1_1*rsrho*t152 + t138/ &
498 t351*(beta_1_1/t140*rsrho/0.2e1_dp + beta_2_1*rsrho + &
499 0.3e1_dp/0.2e1_dp*beta_3_1*t140*rsrho + t146*t41*rsrho/ &
500 rs)/t151
501 t370 = t16**2
502 t371 = 0.1e1_dp/t370
503 t376 = k_s**2
504 trho = -my_ndrho/t376*t7/t233*t1*t371*t14*t6 &
505 /0.6e1_dp - t235*t343/0.2e1_dp
506 t383 = gamma_var**2
507 t385 = beta/t383
508 t386 = t239**2
509 arho = t385/t386*e_c_u_0rho*t238
510 t390 = t187*t
511 t391 = t243*t249
512 t395 = arho*t241
513 t396 = a*t
514 t398 = 0.2e1_dp*t396*trho
515 t403 = t187*t241
516 t404 = t248**2
517 t406 = t243/t404
518 t410 = t241*t
519 t411 = t245*t410
520 t419 = 0.1e1_dp/t252
521 epsilon_cggarho = e_c_u_0rho + gamma_var*(0.2e1_dp*t390*t391 &
522 *trho + t187*t241*(t395 + t398)*t249 - t403*t406*(t395 + &
523 t398 + 0.2e1_dp*a*t246*arho + 0.4e1_dp*t411*trho))*t419
524 tau_wrho = -t254*t343/0.8e1_dp
525 prho = -0.2e1_dp/0.9e1_dp*t275*t278/t281/t279/my_rho
526 zrho = tau_wrho*t286
527 alpharho = 5.0_dp/3.0_dp*(p - alpha)*t7
528 t437 = t290/t294/t293
529 tildeq_brho = 0.9e1_dp/0.20e2_dp*alpharho*t295 - 0.9e1_dp/ &
530 0.40e2_dp*t437*(b*alpharho*t290 + t291*alpharho) + &
531 0.2e1_dp/0.3e1_dp*prho
532 t445 = c*z
533 t450 = c*t299*z
534 t452 = 0.1e1_dp/t302/t301
535 ! The associated first-gradient factors vanish at t313=0.
536 t464 = 0.0_dp
537 IF (t313 > 0.0_dp) t464 = tildeq_b/t313
538 t472 = t316*p
539 t475 = t319*z
540 t485 = t325/t328/t327
541 t489 = t331**2
542 t490 = 0.1e1_dp/t489
543 rs_s1rho = -t4*t5*t344/0.12e2_dp
544 k_f_s1rho = t13*t371*t14/0.6e1_dp
545 t505 = k_s_s1**2
546 t_s1rho = -t21/t505*t7/t19*k_f_s1rho*t6/0.2e1_dp - t21 &
547 *t22*t343/0.2e1_dp
548 t513 = a_2*alpha_1_2
549 t517 = t96**2
550 e_c_u_1_s1rho = -0.2e1_dp*t513*rs_s1rho*t101 + t89/t517* &
551 (beta_1_2/t55*rs_s1rho/0.2e1_dp + beta_2_2*rs_s1rho + &
552 0.3e1_dp/0.2e1_dp*beta_3_2*t55*rs_s1rho + t95*t77* &
553 rs_s1rho/rs_s1)/t100
554 t536 = t194**2
555 a_s1rho = t385/t536*e_c_u_1_s1rho*t191*t193
556 t541 = t187*t_s1
557 t542 = t199*t205
558 t546 = a_s1rho*t197
559 t547 = a_s1*t_s1
560 t549 = 0.2e1_dp*t547*t_s1rho
561 t554 = t187*t197
562 t555 = t204**2
563 t557 = t199/t555
564 t561 = t197*t_s1
565 t562 = t201*t561
566 t569 = 0.1e1_dp/t208
567 t571 = epsilon_cgga < epsilon_cgga_1_0
568 IF (t571) THEN
569 marho = e_c_u_1_s1rho + t196*(0.2e1_dp*t541*t542 &
570 *t_s1rho + t187*t197*(t546 + t549)*t205 - t554*t557*(t546 &
571 + t549 + 0.2e1_dp*a_s1*t202*a_s1rho + 0.4e1_dp*t562* &
572 t_s1rho))*t569
573 ELSE
574 marho = epsilon_cggarho
575 END IF
576 rs_s2rho = rs_s1rho
577 t574 = k_s_s2**2
578 t_s2rho = -t28/t574*t7/t26*k_f_s1rho*t6/0.2e1_dp - t28 &
579 *t29*t343/0.2e1_dp
580 t585 = t80**2
581 e_c_u_1_s2rho = -0.2e1_dp*t513*rs_s2rho*t85 + t71/t585*( &
582 beta_1_2/t36*rs_s2rho/0.2e1_dp + beta_2_2*rs_s2rho + &
583 0.3e1_dp/0.2e1_dp*beta_3_2*t36*rs_s2rho + t79*t77* &
584 rs_s2rho/rs_s2)/t84
585 t604 = t216**2
586 a_s2rho = t385/t604*e_c_u_1_s2rho*t213*t215
587 t609 = t187*t_s2
588 t610 = t221*t227
589 t614 = a_s2rho*t219
590 t615 = a_s2*t_s2
591 t617 = 0.2e1_dp*t615*t_s2rho
592 t622 = t187*t219
593 t623 = t226**2
594 t625 = t221/t623
595 t629 = t219*t_s2
596 t630 = t223*t629
597 t637 = 0.1e1_dp/t230
598 t639 = epsilon_cgga < epsilon_cgga_0_1
599 IF (t639) THEN
600 mbrho = e_c_u_1_s2rho + t218*(0.2e1_dp*t609*t610 &
601 *t_s2rho + t187*t219*(t614 + t617)*t227 - t622*t625*(t614 &
602 + t617 + 0.2e1_dp*a_s2*t224*a_s2rho + 0.4e1_dp*t630* &
603 t_s2rho))*t637
604 ELSE
605 mbrho = epsilon_cggarho
606 END IF
607 t642 = epsilon_cgga*tau_w
608 t645 = tau_w*t260
609 epsilon_crevpkzbrho = epsilon_cggarho + (0.53e0_dp* &
610 epsilon_cggarho*t256 + 0.106e1_dp*t642*tau_wrho - 0.306e1_dp* &
611 t645*tau_wrho - 0.153e1_dp*t256*(marho/0.2e1_dp + mbrho/ &
612 0.2e1_dp))*t265
613 t659 = t256*t271
614
615 e_rho(ii) = e_rho(ii) + &
616 scale_ec*(epsilon_crevpkzb*t274 + my_rho* &
617 epsilon_crevpkzbrho*t274 + t267*(d*epsilon_crevpkzbrho*t272 &
618 + 0.3e1_dp*t268*t659*tau_wrho)) + scale_ex*(ex_unif*fx - &
619 my_rho*pi*t1*t371*fx/0.4e1_dp + t337* &
620 t490*(((0.2e1_dp*t445*t303*zrho - 0.4e1_dp*t450*t452* &
621 zrho)*p + t305*prho + 0.292e3_dp/0.2025e4_dp*tildeq_b* &
622 tildeq_brho - 0.73e2_dp/0.4050e4_dp*tildeq_brho*t313 - &
623 0.73e2_dp/0.8100e4_dp*t464*(0.36e2_dp*z*zrho + 0.100e3_dp &
624 *p*prho) + 0.200e3_dp/0.6561e4_dp*t472*prho + 0.8e1_dp/ &
625 0.45e2_dp*t475*zrho + 0.3e1_dp*t322*t310*prho)*t329 - &
626 0.2e1_dp*t485*t319*prho))
627
628 tnorm_drho = t234*t7/0.2e1_dp
629 hnorm_drho = gamma_var*(0.2e1_dp*t390*t391*tnorm_drho + &
630 0.2e1_dp*t187*t410*a*tnorm_drho*t249 - t403*t406*( &
631 0.2e1_dp*t396*tnorm_drho + 0.4e1_dp*t411*tnorm_drho))*t419
632 tau_wnorm_drho = my_ndrho*t7/0.4e1_dp
633 pnorm_drho = my_ndrho*t1*t284/0.6e1_dp
634 znorm_drho = tau_wnorm_drho*t286
635 alphanorm_drho = -5.0_dp/3.0_dp*pnorm_drho
636 tildeq_bnorm_drho = 0.9e1_dp/0.20e2_dp*alphanorm_drho*t295 - &
637 0.9e1_dp/0.40e2_dp*t437*(b*alphanorm_drho*t290 + t291* &
638 alphanorm_drho) + 0.2e1_dp/0.3e1_dp*pnorm_drho
639 t_s1norm_drho = t20*t22*t7/0.2e1_dp
640 IF (t571) THEN
641 manorm_drho = t196*(0.2e1_dp*t541*t542* &
642 t_s1norm_drho + 0.2e1_dp*t187*t561*a_s1*t_s1norm_drho*t205 &
643 - t554*t557*(0.2e1_dp*t547*t_s1norm_drho + 0.4e1_dp*t562 &
644 *t_s1norm_drho))*t569
645 ELSE
646 manorm_drho = hnorm_drho
647 END IF
648 t_s2norm_drho = t27*t29*t7/0.2e1_dp
649 IF (t639) THEN
650 mbnorm_drho = t218*(0.2e1_dp*t609*t610* &
651 t_s2norm_drho + 0.2e1_dp*t187*t629*a_s2*t_s2norm_drho*t227 &
652 - t622*t625*(0.2e1_dp*t615*t_s2norm_drho + 0.4e1_dp*t630 &
653 *t_s2norm_drho))*t637
654 ELSE
655 mbnorm_drho = hnorm_drho
656 END IF
657 epsilon_crevpkzbnorm_drho = hnorm_drho + (0.53e0_dp*hnorm_drho* &
658 t256 + 0.106e1_dp*t642*tau_wnorm_drho - 0.306e1_dp*t645* &
659 tau_wnorm_drho - 0.153e1_dp*t256*(manorm_drho/0.2e1_dp + &
660 mbnorm_drho/0.2e1_dp))*t265
661
662 e_ndrho(ii) = e_ndrho(ii) + &
663 scale_ec*(my_rho*epsilon_crevpkzbnorm_drho* &
664 t274 + t267*(d*epsilon_crevpkzbnorm_drho*t272 + 0.3e1_dp* &
665 t268*t659*tau_wnorm_drho)) + scale_ex*t337*t490*((( &
666 0.2e1_dp*t445*t303*znorm_drho - 0.4e1_dp*t450*t452* &
667 znorm_drho)*p + t305*pnorm_drho + 0.292e3_dp/0.2025e4_dp* &
668 tildeq_b*tildeq_bnorm_drho - 0.73e2_dp/0.4050e4_dp* &
669 tildeq_bnorm_drho*t313 - 0.73e2_dp/0.8100e4_dp*t464*( &
670 0.36e2_dp*z*znorm_drho + 0.100e3_dp*p*pnorm_drho) + &
671 0.200e3_dp/0.6561e4_dp*t472*pnorm_drho + 0.8e1_dp/0.45e2_dp &
672 *t475*znorm_drho + 0.3e1_dp*t322*t310*pnorm_drho)*t329 - &
673 0.2e1_dp*t485*t319*pnorm_drho)
674
675 epsilon_crevpkzbtau = -0.2e1_dp*t263*t271
676 t799 = t264**2
677 ztau = -tau_w*t265
678 alphatau = tau_unif_inverse
679 tildeq_btau = 0.9e1_dp/0.20e2_dp*alphatau*t295 - 0.9e1_dp/ &
680 0.40e2_dp*t437*(b*alphatau*t290 + t291*alphatau)
681
682 e_tau(ii) = e_tau(ii) + &
683 scale_ec*(my_rho*epsilon_crevpkzbtau*t274 + t267* &
684 (d*epsilon_crevpkzbtau*t272 - 0.3e1_dp*t268*t269/t799)) + &
685 scale_ex*t337*t490*((0.2e1_dp*t445*t303*ztau - 0.4e1_dp &
686 *t450*t452*ztau)*p + 0.292e3_dp/0.2025e4_dp*tildeq_b* &
687 tildeq_btau - 0.73e2_dp/0.4050e4_dp*tildeq_btau*t313 - &
688 0.73e2_dp/0.225e3_dp*t464*z*ztau + 0.8e1_dp/0.45e2_dp* &
689 t475*ztau)*t329
690 IF (clipped_tau) THEN
691 ! Differentiate the same projected gradient and kinetic density
692 ! used by the energy, preserving other functional contributions.
693 partial_rho = e_rho(ii) - incoming_rho
694 partial_gradient = e_ndrho(ii) - incoming_gradient
695 partial_tau = e_tau(ii) - incoming_tau
696 e_rho(ii) = incoming_rho + partial_rho + &
697 2.0_dp*regular_tau/my_ndrho*partial_gradient - &
698 norm_drho(ii)**2/(16.0_dp*my_rho**2)*partial_tau
699 e_ndrho(ii) = incoming_gradient + &
700 0.5_dp*norm_drho(ii)/my_ndrho*partial_gradient + &
701 norm_drho(ii)/(8.0_dp*my_rho)*partial_tau
702 e_tau(ii) = incoming_tau + 2.0_dp*my_rho/my_ndrho*partial_gradient + 0.5_dp*partial_tau
703 END IF
704 IF (floored_tau) e_tau(ii) = incoming_tau
705 END IF
706 END IF
707 END DO
708
709!$OMP END DO
710
711 END SUBROUTINE tpss_lda_calc
712
713END MODULE xc_tpss
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition bibliography.F:21
bibliography::tao2003
integer, save, public tao2003
Definition bibliography.F:36
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:1052
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
xc_derivative_desc
Module with functions to handle derivative descriptors. derivative description are strings have the f...
Definition xc_derivative_desc.F:26
xc_derivative_desc::deriv_norm_drho
integer, parameter, public deriv_norm_drho
Definition xc_derivative_desc.F:35
xc_derivative_desc::deriv_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:65
xc_derivative_types
Provides types for the management of the xc-functionals and their derivatives.
Definition xc_derivative_types.F:12
xc_derivative_types::xc_derivative_get
subroutine, public xc_derivative_get(deriv, split_desc, order, deriv_data, accept_null_data)
returns various information on the given derivative
Definition xc_derivative_types.F:103
xc_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:107
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:127
xc_derivative_set_types::xc_derivative_set_type
A derivative set contains the different derivatives of a xc-functional in form of a linked list.
Definition xc_derivative_set_types.F:48
xc_derivative_types::xc_derivative_type
represent a derivative of a functional
Definition xc_derivative_types.F:32
xc_rho_cflags_types::xc_rho_cflags_type
contains a flag for each component of xc_rho_set, so that you can use it to tell which components you...
Definition xc_rho_cflags_types.F:48
xc_rho_set_types::xc_rho_set_type
represent a density, with all the representation and data needed to perform a functional evaluation
Definition xc_rho_set_types.F:78