Line data Source code
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 : ! **************************************************************************************************
17 : MODULE 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 : !***
47 : CONTAINS
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 1692 : 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 :
67 846 : CALL section_vals_val_get(tpss_params, "SCALE_C", r_val=sc)
68 846 : CALL section_vals_val_get(tpss_params, "SCALE_X", r_val=sx)
69 :
70 846 : IF (PRESENT(reference)) THEN
71 12 : IF (sx == 1._dp .AND. sc == 1._dp) THEN
72 12 : 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 0 : "J. Tao, J.P.Perdew, V.N.Staroverov, E.Scuseria PRL, 91, 146401 (2003)", &
76 0 : sx, sc
77 : END IF
78 : END IF
79 846 : IF (PRESENT(shortform)) THEN
80 12 : IF (sx == 1._dp .AND. sc == 1._dp) THEN
81 12 : shortform = "TPSS meta-GGA functional (LDA)"
82 : ELSE
83 : WRITE (shortform, "(a,'sx=',f5.3,'sc=',f5.3,' (LDA)')") &
84 0 : "TPSS meta-GGA functional", &
85 0 : sx, sc
86 : END IF
87 : END IF
88 846 : IF (PRESENT(needs)) THEN
89 834 : needs%rho = .TRUE.
90 834 : needs%tau = .TRUE.
91 834 : needs%norm_drho = .TRUE.
92 : END IF
93 846 : IF (PRESENT(max_deriv)) max_deriv = 1
94 :
95 846 : 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 4248 : 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 1062 : POINTER :: dummy, e_0, e_ndrho, e_rho, e_tau, &
122 1062 : norm_drho, rho, tau
123 : TYPE(cp_logger_type), POINTER :: logger
124 : TYPE(xc_derivative_type), POINTER :: deriv
125 :
126 1062 : CALL timeset(routineN, handle)
127 :
128 1062 : 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 1062 : tau=tau, tau_cutoff=epsilon_tau)
133 1062 : npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
134 :
135 1062 : dummy => rho
136 :
137 1062 : e_0 => dummy
138 1062 : e_rho => dummy
139 1062 : e_ndrho => dummy
140 1062 : e_tau => dummy
141 :
142 1062 : IF (grad_deriv >= 0) THEN
143 : deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
144 1062 : allocate_deriv=.TRUE.)
145 1062 : CALL xc_derivative_get(deriv, deriv_data=e_0)
146 : END IF
147 1062 : IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
148 : deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
149 1062 : allocate_deriv=.TRUE.)
150 1062 : CALL xc_derivative_get(deriv, deriv_data=e_rho)
151 : deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
152 1062 : allocate_deriv=.TRUE.)
153 1062 : CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
154 : deriv => xc_dset_get_derivative(deriv_set, [deriv_tau], &
155 1062 : allocate_deriv=.TRUE.)
156 1062 : CALL xc_derivative_get(deriv, deriv_data=e_tau)
157 : END IF
158 1062 : IF (grad_deriv > 1 .OR. grad_deriv < -1) THEN
159 0 : CPABORT("derivatives bigger than 1 not implemented")
160 : END IF
161 :
162 1062 : non_coer = 0
163 1062 : CALL section_vals_val_get(tpss_params, "SCALE_C", r_val=scale_ec)
164 1062 : 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 1062 : !$OMP REDUCTION(+: non_coer)
171 :
172 : CALL tpss_lda_calc(rho=rho, norm_drho=norm_drho, &
173 : tau=tau, e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_tau=e_tau, &
174 : grad_deriv=grad_deriv, npoints=npoints, epsilon_rho=epsilon_rho, &
175 : epsilon_tau=epsilon_tau, scale_ec=scale_ec, scale_ex=scale_ex, non_coer=non_coer)
176 :
177 : !$OMP END PARALLEL
178 :
179 1062 : 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 1062 : non_coer = 0
183 : END IF
184 :
185 1062 : CALL timestop(handle)
186 1062 : 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 1062 : 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 1062 : abs_grad_deriv = ABS(grad_deriv)
270 :
271 1062 : kappa = 0.804e0_dp
272 1062 : beta = 0.66725e-1_dp
273 1062 : mu = 0.21951e0_dp
274 1062 : gamma_var = (0.1e1_dp - LOG(0.2e1_dp))/pi**2
275 1062 : b = 0.4e0_dp
276 1062 : c = 0.159096e1_dp
277 1062 : e_var = 0.1537e1_dp
278 1062 : d = 0.28e1_dp
279 1062 : p_1 = 0.10e1_dp
280 1062 : A_1 = 0.31091e-1_dp
281 1062 : alpha_1_1 = 0.21370e0_dp
282 1062 : beta_1_1 = 0.75957e1_dp
283 1062 : beta_2_1 = 0.35876e1_dp
284 1062 : beta_3_1 = 0.16382e1_dp
285 1062 : beta_4_1 = 0.49294e0_dp
286 1062 : p_2 = 0.10e1_dp
287 1062 : A_2 = 0.15545e-1_dp
288 1062 : alpha_1_2 = 0.20548e0_dp
289 1062 : beta_1_2 = 0.141189e2_dp
290 1062 : beta_2_2 = 0.61977e1_dp
291 1062 : beta_3_2 = 0.33662e1_dp
292 1062 : beta_4_2 = 0.62517e0_dp
293 1062 : p_3 = 0.10e1_dp
294 :
295 1062 : t1 = 3._dp**(0.1e1_dp/0.3e1_dp)
296 1062 : t2 = 4._dp**(0.1e1_dp/0.3e1_dp)
297 1062 : t3 = t2**2
298 1062 : t4 = t1*t3
299 1062 : t5 = 2._dp**(0.1e1_dp/0.3e1_dp)
300 1062 : t6 = 0.1e1_dp/pi
301 1062 : t12 = t5**2
302 :
303 1062 : !$OMP DO
304 :
305 : DO ii = 1, npoints
306 24682723 : my_tau = tau(ii)
307 24682723 : my_rho = rho(ii)
308 24682723 : IF (my_rho > epsilon_rho .AND. my_tau > epsilon_tau) THEN
309 20673528 : my_ndrho = norm_drho(ii)
310 :
311 20673528 : t7 = 0.1e1_dp/my_rho
312 20673528 : t254 = my_ndrho**2
313 20673528 : tau_w = t254*t7/0.8e1_dp
314 :
315 20673528 : IF (my_tau < tau_w) THEN
316 : ! enforce z=norm_rho**2/(8._dp*rho*tau) <1
317 1012669 : m = 0.5_dp*t254 + 4.0_dp*my_rho*my_tau
318 1012669 : my_tau = m/8._dp/my_rho
319 1012669 : my_ndrho = SQRT(m)
320 1012669 : t254 = m
321 1012669 : non_coer = non_coer + 1
322 : END IF
323 :
324 20673528 : t9 = (t6*t7)**(0.1e1_dp/0.3e1_dp)
325 20673528 : rs_s1 = t4*t5*t9/0.4e1_dp
326 20673528 : phi_s1 = t12/0.2e1_dp
327 20673528 : t13 = t1*t12
328 20673528 : t14 = pi**2
329 20673528 : t16 = (t14*my_rho)**(0.1e1_dp/0.3e1_dp)
330 20673528 : k_f_s1 = t13*t16/0.2e1_dp
331 20673528 : t19 = SQRT(k_f_s1*t6)
332 20673528 : k_s_s1 = 0.2e1_dp*t19
333 20673528 : t20 = 0.1e1_dp/phi_s1
334 20673528 : t21 = my_ndrho*t20
335 20673528 : t22 = 0.1e1_dp/k_s_s1
336 20673528 : t_s1 = t21*t22*t7/0.2e1_dp
337 20673528 : rs_s2 = rs_s1
338 20673528 : phi_s2 = phi_s1
339 20673528 : t26 = SQRT(k_f_s1*t6)
340 20673528 : k_s_s2 = 0.2e1_dp*t26
341 20673528 : t27 = 0.1e1_dp/phi_s2
342 20673528 : t28 = my_ndrho*t27
343 20673528 : t29 = 0.1e1_dp/k_s_s2
344 20673528 : t_s2 = t28*t29*t7/0.2e1_dp
345 20673528 : t35 = 0.1e1_dp/A_1
346 20673528 : t36 = SQRT(rs_s2)
347 20673528 : t39 = t36*rs_s2
348 20673528 : t41 = p_1 + 0.1e1_dp
349 20673528 : 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 20673528 : t55 = SQRT(rs_s1)
353 20673528 : t58 = t55*rs_s1
354 20673528 : 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 20673528 : t71 = 0.1e1_dp + alpha_1_2*rs_s2
358 20673528 : t73 = 0.1e1_dp/A_2
359 20673528 : t77 = p_2 + 0.1e1_dp
360 20673528 : t78 = rs_s2**t77
361 20673528 : t79 = beta_4_2*t78
362 20673528 : t80 = beta_1_2*t36 + beta_2_2*rs_s2 + beta_3_2*t39 + t79
363 20673528 : t84 = 0.1e1_dp + t73/t80/0.2e1_dp
364 20673528 : t85 = LOG(t84)
365 20673528 : e_c_u_1_s2 = -0.2e1_dp*A_2*t71*t85
366 20673528 : t89 = 0.1e1_dp + alpha_1_2*rs_s1
367 20673528 : t94 = rs_s1**t77
368 20673528 : t95 = beta_4_2*t94
369 20673528 : t96 = beta_1_2*t55 + beta_2_2*rs_s1 + beta_3_2*t58 + t95
370 20673528 : t100 = 0.1e1_dp + t73/t96/0.2e1_dp
371 20673528 : t101 = LOG(t100)
372 20673528 : e_c_u_1_s1 = -0.2e1_dp*A_2*t89*t101
373 20673528 : t111 = p_3 + 1._dp
374 20673528 : rs = t4*t9/0.4e1_dp
375 20673528 : t138 = 0.1e1_dp + alpha_1_1*rs
376 20673528 : t140 = SQRT(rs)
377 20673528 : t143 = t140*rs
378 20673528 : t145 = rs**t41
379 20673528 : t146 = beta_4_1*t145
380 20673528 : t147 = beta_1_1*t140 + beta_2_1*rs + beta_3_1*t143 + t146
381 20673528 : t151 = 0.1e1_dp + t35/t147/0.2e1_dp
382 20673528 : t152 = LOG(t151)
383 20673528 : e_c_u_0 = -0.2e1_dp*A_1*t138*t152
384 20673528 : 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 20673528 : t177 = rs**t111
388 20673528 : t186 = 0.1e1_dp/gamma_var
389 20673528 : t187 = beta*t186
390 20673528 : t189 = phi_s1**2
391 20673528 : t190 = t189*phi_s1
392 20673528 : t191 = 0.1e1_dp/t190
393 20673528 : t193 = EXP(-e_c_u_1_s1*t186*t191)
394 20673528 : t194 = t193 - 0.1e1_dp
395 20673528 : A_s1 = t187/t194
396 20673528 : t196 = gamma_var*t190
397 20673528 : t197 = t_s1**2
398 20673528 : t198 = A_s1*t197
399 20673528 : t199 = 0.1e1_dp + t198
400 20673528 : t201 = A_s1**2
401 20673528 : t202 = t197**2
402 20673528 : t204 = 0.1e1_dp + t198 + t201*t202
403 20673528 : t205 = 0.1e1_dp/t204
404 20673528 : t208 = 0.1e1_dp + t187*t197*t199*t205
405 20673528 : t209 = LOG(t208)
406 20673528 : epsilon_cGGA_1_0 = e_c_u_1_s1 + t196*t209
407 20673528 : t211 = phi_s2**2
408 20673528 : t212 = t211*phi_s2
409 20673528 : t213 = 0.1e1_dp/t212
410 20673528 : t215 = EXP(-e_c_u_1_s2*t186*t213)
411 20673528 : t216 = t215 - 0.1e1_dp
412 20673528 : A_s2 = t187/t216
413 20673528 : t218 = gamma_var*t212
414 20673528 : t219 = t_s2**2
415 20673528 : t220 = A_s2*t219
416 20673528 : t221 = t220 + 0.1e1_dp
417 20673528 : t223 = A_s2**2
418 20673528 : t224 = t219**2
419 20673528 : t226 = 0.1e1_dp + t220 + t223*t224
420 20673528 : t227 = 0.1e1_dp/t226
421 20673528 : t230 = 0.1e1_dp + t187*t219*t221*t227
422 20673528 : t231 = LOG(t230)
423 20673528 : epsilon_cGGA_0_1 = e_c_u_1_s2 + t218*t231
424 20673528 : t233 = SQRT(t1*t16*t6)
425 20673528 : k_s = 0.2e1_dp*t233
426 20673528 : t234 = 0.1e1_dp/k_s
427 20673528 : t235 = my_ndrho*t234
428 20673528 : t = t235*t7/0.2e1_dp
429 20673528 : t238 = EXP(-e_c_u_0*t186)
430 20673528 : t239 = -0.1e1_dp + t238
431 20673528 : A = t187/t239
432 20673528 : t241 = t**2
433 20673528 : t242 = A*t241
434 20673528 : t243 = 0.1e1_dp + t242
435 20673528 : t245 = A**2
436 20673528 : t246 = t241**2
437 20673528 : t248 = 0.1e1_dp + t242 + t245*t246
438 20673528 : t249 = 0.1e1_dp/t248
439 20673528 : t252 = 0.1e1_dp + t187*t241*t243*t249
440 20673528 : t253 = LOG(t252)
441 20673528 : epsilon_cGGA = e_c_u_0 + gamma_var*t253
442 20673528 : ma = MAX(epsilon_cGGA_1_0, epsilon_cGGA)
443 20673528 : mb = MAX(epsilon_cGGA_0_1, epsilon_cGGA)
444 20673528 : t256 = tau_w**2
445 20673528 : t260 = ma/0.2e1_dp + mb/0.2e1_dp
446 20673528 : t263 = 0.53e0_dp*epsilon_cGGA*t256 - 0.153e1_dp*t256*t260
447 20673528 : t264 = my_tau**2
448 20673528 : t265 = 0.1e1_dp/t264
449 20673528 : epsilon_cRevPKZB = epsilon_cGGA + t263*t265
450 20673528 : t267 = my_rho*epsilon_cRevPKZB
451 20673528 : t268 = d*epsilon_cRevPKZB
452 20673528 : t269 = t256*tau_w
453 20673528 : t271 = 0.1e1_dp/t264/my_tau
454 20673528 : t272 = t269*t271
455 20673528 : t274 = 0.1e1_dp + t268*t272
456 20673528 : t275 = t254*t1
457 20673528 : t276 = t14**(0.1e1_dp/0.3e1_dp)
458 20673528 : t277 = t276**2
459 20673528 : t278 = 0.1e1_dp/t277
460 20673528 : t279 = my_rho**2
461 20673528 : t280 = my_rho**(0.1e1_dp/0.3e1_dp)
462 20673528 : t281 = t280**2
463 20673528 : t284 = t278/t281/t279
464 20673528 : p = t275*t284/0.12e2_dp
465 20673528 : t286 = 0.1e1_dp/my_tau
466 20673528 : z = tau_w*t286
467 20673528 : t288 = 0.1e1_dp/z - 0.1e1_dp
468 20673528 : alpha = 0.5e1_dp/0.3e1_dp*p*t288
469 20673528 : t290 = alpha - 0.1e1_dp
470 20673528 : t291 = b*alpha
471 20673528 : t293 = 0.1e1_dp + t291*t290
472 20673528 : t294 = SQRT(t293)
473 20673528 : t295 = 0.1e1_dp/t294
474 20673528 : tildeq_b = 0.9e1_dp/0.20e2_dp*t290*t295 + 0.2e1_dp/0.3e1_dp*p
475 20673528 : t299 = z**2
476 20673528 : t301 = 0.1e1_dp + t299
477 20673528 : t302 = t301**2
478 20673528 : t303 = 0.1e1_dp/t302
479 20673528 : t305 = 0.10e2_dp/0.81e2_dp + c*t299*t303
480 20673528 : t307 = tildeq_b**2
481 20673528 : t310 = p**2
482 20673528 : t313 = SQRT(0.18e2_dp*t299 + 0.50e2_dp*t310)
483 20673528 : t316 = 0.1e1_dp/kappa
484 20673528 : t319 = SQRT(e_var)
485 20673528 : 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 20673528 : t310 + 0.4e1_dp/0.45e2_dp*t319*t299 + t322*t310*p
489 20673528 : t327 = 0.1e1_dp + t319*p
490 20673528 : t328 = t327**2
491 20673528 : t329 = 0.1e1_dp/t328
492 20673528 : t331 = 0.1e1_dp + t325*t329*t316
493 20673528 : Fx = 0.1e1_dp + kappa - kappa/t331
494 20673528 : ex_unif = -0.3e1_dp/0.4e1_dp*t1*t16*t6
495 20673528 : t337 = my_rho*ex_unif
496 :
497 20673528 : IF (grad_deriv >= 0) THEN
498 : e_0(ii) = e_0(ii) + &
499 20673528 : scale_ec*t267*t274 + scale_ex*t337*Fx
500 : END IF
501 :
502 20673528 : IF (abs_grad_deriv > 0) THEN
503 20673528 : t340 = t9**2
504 20673528 : t343 = 0.1e1_dp/t279
505 20673528 : t344 = 0.1e1_dp/t340*t6*t343
506 20673528 : rsrho = -t4*t344/0.12e2_dp
507 20673528 : 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 20673528 : rs)/t151
512 20673528 : t370 = t16**2
513 20673528 : t371 = 0.1e1_dp/t370
514 20673528 : t376 = k_s**2
515 : trho = -my_ndrho/t376*t7/t233*t1*t371*t14*t6 &
516 20673528 : /0.6e1_dp - t235*t343/0.2e1_dp
517 20673528 : t383 = gamma_var**2
518 20673528 : t385 = beta/t383
519 20673528 : t386 = t239**2
520 20673528 : Arho = t385/t386*e_c_u_0rho*t238
521 20673528 : t390 = t187*t
522 20673528 : t391 = t243*t249
523 20673528 : t395 = Arho*t241
524 20673528 : t396 = A*t
525 20673528 : t398 = 0.2e1_dp*t396*trho
526 20673528 : t403 = t187*t241
527 20673528 : t404 = t248**2
528 20673528 : t406 = t243/t404
529 20673528 : t410 = t241*t
530 20673528 : t411 = t245*t410
531 20673528 : 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 20673528 : t398 + 0.2e1_dp*A*t246*Arho + 0.4e1_dp*t411*trho))*t419
535 20673528 : tau_wrho = -t254*t343/0.8e1_dp
536 20673528 : prho = -0.2e1_dp/0.9e1_dp*t275*t278/t281/t279/my_rho
537 20673528 : zrho = tau_wrho*t286
538 20673528 : t430 = p/t299
539 : alpharho = 0.5e1_dp/0.3e1_dp*prho*t288 - 0.5e1_dp/0.3e1_dp &
540 20673528 : *t430*zrho
541 20673528 : 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 20673528 : 0.2e1_dp/0.3e1_dp*prho
545 20673528 : t445 = c*z
546 20673528 : t450 = c*t299*z
547 20673528 : t452 = 0.1e1_dp/t302/t301
548 20673528 : t464 = tildeq_b/t313
549 20673528 : t472 = t316*p
550 20673528 : t475 = t319*z
551 20673528 : t485 = t325/t328/t327
552 20673528 : t489 = t331**2
553 20673528 : t490 = 0.1e1_dp/t489
554 20673528 : rs_s1rho = -t4*t5*t344/0.12e2_dp
555 20673528 : k_f_s1rho = t13*t371*t14/0.6e1_dp
556 20673528 : t505 = k_s_s1**2
557 : t_s1rho = -t21/t505*t7/t19*k_f_s1rho*t6/0.2e1_dp - t21 &
558 20673528 : *t22*t343/0.2e1_dp
559 20673528 : t513 = A_2*alpha_1_2
560 20673528 : 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 20673528 : rs_s1rho/rs_s1)/t100
565 20673528 : t536 = t194**2
566 20673528 : A_s1rho = t385/t536*e_c_u_1_s1rho*t191*t193
567 20673528 : t541 = t187*t_s1
568 20673528 : t542 = t199*t205
569 20673528 : t546 = A_s1rho*t197
570 20673528 : t547 = A_s1*t_s1
571 20673528 : t549 = 0.2e1_dp*t547*t_s1rho
572 20673528 : t554 = t187*t197
573 20673528 : t555 = t204**2
574 20673528 : t557 = t199/t555
575 20673528 : t561 = t197*t_s1
576 20673528 : t562 = t201*t561
577 20673528 : t569 = 0.1e1_dp/t208
578 20673528 : t571 = epsilon_cGGA .LT. epsilon_cGGA_1_0
579 20673528 : 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 20620060 : t_s1rho))*t569
584 : ELSE
585 : marho = epsilon_cGGArho
586 : END IF
587 20673528 : rs_s2rho = rs_s1rho
588 20673528 : t574 = k_s_s2**2
589 : t_s2rho = -t28/t574*t7/t26*k_f_s1rho*t6/0.2e1_dp - t28 &
590 20673528 : *t29*t343/0.2e1_dp
591 20673528 : 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 20673528 : rs_s2rho/rs_s2)/t84
596 20673528 : t604 = t216**2
597 20673528 : A_s2rho = t385/t604*e_c_u_1_s2rho*t213*t215
598 20673528 : t609 = t187*t_s2
599 20673528 : t610 = t221*t227
600 20673528 : t614 = A_s2rho*t219
601 20673528 : t615 = A_s2*t_s2
602 20673528 : t617 = 0.2e1_dp*t615*t_s2rho
603 20673528 : t622 = t187*t219
604 20673528 : t623 = t226**2
605 20673528 : t625 = t221/t623
606 20673528 : t629 = t219*t_s2
607 20673528 : t630 = t223*t629
608 20673528 : t637 = 0.1e1_dp/t230
609 20673528 : 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 20673528 : t_s2rho))*t637
615 : ELSE
616 : mbrho = epsilon_cGGArho
617 : END IF
618 20673528 : t642 = epsilon_cGGA*tau_w
619 20673528 : 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 20673528 : 0.2e1_dp))*t265
624 20673528 : t659 = t256*t271
625 :
626 20673528 : 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 20673528 : 0.2e1_dp*t485*t319*prho))
639 : END IF
640 :
641 20673528 : 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 20673528 : 0.2e1_dp*t396*tnorm_drho + 0.4e1_dp*t411*tnorm_drho))*t419
645 20673528 : tau_wnorm_drho = my_ndrho*t7/0.4e1_dp
646 20673528 : pnorm_drho = my_ndrho*t1*t284/0.6e1_dp
647 20673528 : znorm_drho = tau_wnorm_drho*t286
648 : alphanorm_drho = 0.5e1_dp/0.3e1_dp*pnorm_drho*t288 - &
649 20673528 : 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 20673528 : alphanorm_drho) + 0.2e1_dp/0.3e1_dp*pnorm_drho
653 20673528 : t_s1norm_drho = t20*t22*t7/0.2e1_dp
654 20673528 : 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 20620060 : *t_s1norm_drho))*t569
659 : ELSE
660 : manorm_drho = Hnorm_drho
661 : END IF
662 20673528 : 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 20673528 : *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 20673528 : mbnorm_drho/0.2e1_dp))*t265
675 :
676 20673528 : 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 20673528 : 0.2e1_dp*t485*t319*pnorm_drho)
689 : END IF
690 :
691 20673528 : epsilon_cRevPKZBtau = -0.2e1_dp*t263*t271
692 20673528 : t799 = t264**2
693 20673528 : ztau = -tau_w*t265
694 20673528 : alphatau = -0.5e1_dp/0.3e1_dp*t430*ztau
695 : tildeq_btau = 0.9e1_dp/0.20e2_dp*alphatau*t295 - 0.9e1_dp/ &
696 20673528 : 0.40e2_dp*t437*(b*alphatau*t290 + t291*alphatau)
697 :
698 20673528 : 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 20673528 : 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 :
716 : END MODULE xc_tpss
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