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xc_lyp.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 lyp correlation functional
10 !> \par History
11 !> 11.2003 created [fawzi]
12 !> \author fawzi
13 ! **************************************************************************************************
14 MODULE xc_lyp
15  USE bibliography, ONLY: lee1988,&
16  cite_reference
17  USE input_section_types, ONLY: section_vals_type,&
18  section_vals_val_get
19  USE kinds, ONLY: dp
20  USE mathconstants, ONLY: pi
21  USE xc_derivative_desc, ONLY: deriv_norm_drho,&
22  deriv_norm_drhoa,&
23  deriv_norm_drhob,&
24  deriv_rho,&
25  deriv_rhoa,&
26  deriv_rhob
27  USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
28  xc_dset_get_derivative
29  USE xc_derivative_types, ONLY: xc_derivative_get,&
30  xc_derivative_type
31  USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
32  USE xc_rho_set_types, ONLY: xc_rho_set_get,&
33  xc_rho_set_type
34 #include "../base/base_uses.f90"
35 
36  IMPLICIT NONE
37  PRIVATE
38 
39  LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .true.
40  CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_lyp'
41  REAL(kind=dp), PARAMETER, PRIVATE :: a = 0.04918_dp, b = 0.132_dp, &
42  c = 0.2533_dp, d = 0.349_dp
43 
44  PUBLIC :: lyp_lda_info, lyp_lsd_info, lyp_lda_eval, lyp_lsd_eval
45 CONTAINS
46 
47 ! **************************************************************************************************
48 !> \brief return various information on the functional
49 !> \param reference string with the reference of the actual functional
50 !> \param shortform string with the shortform of the functional name
51 !> \param needs the components needed by this functional are set to
52 !> true (does not set the unneeded components to false)
53 !> \param max_deriv ...
54 !> \par History
55 !> 11.2003 created [fawzi]
56 !> \author fawzi
57 ! **************************************************************************************************
58  SUBROUTINE lyp_lda_info(reference, shortform, needs, max_deriv)
59  CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
60  TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
61  INTEGER, INTENT(out), OPTIONAL :: max_deriv
62 
63  IF (PRESENT(reference)) THEN
64  reference = "C. Lee, W. Yang, R.G. Parr, Phys. Rev. B, 37, 785 (1988) {LDA version}"
65  END IF
66  IF (PRESENT(shortform)) THEN
67  shortform = "Lee-Yang-Parr correlation energy functional (LDA)"
68  END IF
69  IF (PRESENT(needs)) THEN
70  needs%rho = .true.
71  needs%rho_1_3 = .true.
72  needs%norm_drho = .true.
73  END IF
74  IF (PRESENT(max_deriv)) max_deriv = 3
75 
76  END SUBROUTINE lyp_lda_info
77 
78 ! **************************************************************************************************
79 !> \brief return various information on the functional
80 !> \param reference string with the reference of the actual functional
81 !> \param shortform string with the shortform of the functional name
82 !> \param needs the components needed by this functional are set to
83 !> true (does not set the unneeded components to false)
84 !> \param max_deriv ...
85 !> \par History
86 !> 11.2003 created [fawzi]
87 !> \author fawzi
88 ! **************************************************************************************************
89  SUBROUTINE lyp_lsd_info(reference, shortform, needs, max_deriv)
90  CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
91  TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
92  INTEGER, INTENT(out), OPTIONAL :: max_deriv
93 
94  IF (PRESENT(reference)) THEN
95  reference = "C. Lee, W. Yang, R.G. Parr, Phys. Rev. B, 37, 785 (1988) {LSD version}"
96  END IF
97  IF (PRESENT(shortform)) THEN
98  shortform = "Lee-Yang-Parr correlation energy functional (LSD)"
99  END IF
100  IF (PRESENT(needs)) THEN
101  needs%rho_spin = .true.
102  needs%norm_drho_spin = .true.
103  needs%norm_drho = .true.
104  END IF
105  IF (PRESENT(max_deriv)) max_deriv = 2
106 
107  END SUBROUTINE lyp_lsd_info
108 
109 ! **************************************************************************************************
110 !> \brief evaluates the lyp correlation functional for lda
111 !> \param rho_set the density where you want to evaluate the functional
112 !> \param deriv_set place where to store the functional derivatives (they are
113 !> added to the derivatives)
114 !> \param grad_deriv degree of the derivative that should be evaluated,
115 !> if positive all the derivatives up to the given degree are evaluated,
116 !> if negative only the given degree is calculated
117 !> \param lyp_params input parameters (scaling)
118 !> \par History
119 !> 11.2003 created [fawzi]
120 !> 01.2007 added scaling [Manuel Guidon]
121 !> \author fawzi
122 ! **************************************************************************************************
123  SUBROUTINE lyp_lda_eval(rho_set, deriv_set, grad_deriv, lyp_params)
124  TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
125  TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
126  INTEGER, INTENT(in) :: grad_deriv
127  TYPE(section_vals_type), POINTER :: lyp_params
128 
129  CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lda_eval'
130 
131  INTEGER :: handle, npoints
132  INTEGER, DIMENSION(2, 3) :: bo
133  REAL(kind=dp) :: epsilon_norm_drho, epsilon_rho, sc
134  REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndrho, &
135  e_ndrho_ndrho, e_ndrho_ndrho_rho, e_ndrho_rho, e_ndrho_rho_rho, e_rho, e_rho_rho, &
136  e_rho_rho_rho, norm_drho, rho, rho_1_3
137  TYPE(xc_derivative_type), POINTER :: deriv
138 
139  CALL timeset(routinen, handle)
140 
141  CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
142  CALL cite_reference(lee1988)
143 
144  CALL xc_rho_set_get(rho_set, rho_1_3=rho_1_3, rho=rho, &
145  norm_drho=norm_drho, local_bounds=bo, rho_cutoff=epsilon_rho, &
146  drho_cutoff=epsilon_norm_drho)
147  npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
148 
149  dummy => rho
150 
151  e_0 => dummy
152  e_rho => dummy
153  e_ndrho => dummy
154  e_rho_rho => dummy
155  e_ndrho_rho => dummy
156  e_ndrho_ndrho => dummy
157  e_rho_rho_rho => dummy
158  e_ndrho_rho_rho => dummy
159  e_ndrho_ndrho_rho => dummy
160 
161  IF (grad_deriv >= 0) THEN
162  deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
163  allocate_deriv=.true.)
164  CALL xc_derivative_get(deriv, deriv_data=e_0)
165  END IF
166  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
167  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
168  allocate_deriv=.true.)
169  CALL xc_derivative_get(deriv, deriv_data=e_rho)
170  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
171  allocate_deriv=.true.)
172  CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
173  END IF
174  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
175  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
176  allocate_deriv=.true.)
177  CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
178  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rho], &
179  allocate_deriv=.true.)
180  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho)
181  deriv => xc_dset_get_derivative(deriv_set, &
182  [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
183  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
184  END IF
185  IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
186  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
187  allocate_deriv=.true.)
188  CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
189  deriv => xc_dset_get_derivative(deriv_set, &
190  [deriv_norm_drho, deriv_rho, deriv_rho], allocate_deriv=.true.)
191  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_rho_rho)
192  deriv => xc_dset_get_derivative(deriv_set, &
193  [deriv_norm_drho, deriv_norm_drho, deriv_rho], allocate_deriv=.true.)
194  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_rho)
195 !FM deriv => xc_dset_get_derivative(deriv_set,&
196 !FM [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.TRUE.,&
197 !FM
198 !FM call xc_derivative_get(deriv,deriv_data=e_ndrho_ndrho_ndrho)
199  END IF
200  IF (grad_deriv > 3 .OR. grad_deriv < -3) THEN
201  cpabort("derivatives bigger than 3 not implemented")
202  END IF
203 
204 !$OMP PARALLEL DEFAULT(NONE) &
205 !$OMP SHARED(rho, rho_1_3, norm_drho, e_0, e_rho, e_ndrho) &
206 !$OMP SHARED(e_rho_rho, e_ndrho_rho, e_ndrho_ndrho) &
207 !$OMP SHARED(e_rho_rho_rho, e_ndrho_rho_rho) &
208 !$OMP SHARED(e_ndrho_ndrho_rho, grad_deriv, npoints) &
209 !$OMP SHARED(epsilon_rho, sc)
210 
211  CALL lyp_lda_calc(rho=rho, rho_1_3=rho_1_3, norm_drho=norm_drho, &
212  e_0=e_0, e_rho=e_rho, e_ndrho=e_ndrho, e_rho_rho=e_rho_rho, &
213  e_ndrho_rho=e_ndrho_rho, e_ndrho_ndrho=e_ndrho_ndrho, &
214  e_rho_rho_rho=e_rho_rho_rho, e_ndrho_rho_rho=e_ndrho_rho_rho, &
215  e_ndrho_ndrho_rho=e_ndrho_ndrho_rho, &
216  grad_deriv=grad_deriv, &
217  npoints=npoints, epsilon_rho=epsilon_rho, sc=sc)
218 
219 !$OMP END PARALLEL
220 
221  CALL timestop(handle)
222  END SUBROUTINE lyp_lda_eval
223 
224 ! **************************************************************************************************
225 !> \brief evaluates the lyp correlation functional for lda
226 !> \param rho the density where you want to evaluate the functional
227 !> \param rho_1_3 ...
228 !> \param norm_drho ...
229 !> \param e_0 ...
230 !> \param e_rho ...
231 !> \param e_ndrho ...
232 !> \param e_rho_rho ...
233 !> \param e_ndrho_rho ...
234 !> \param e_ndrho_ndrho ...
235 !> \param e_rho_rho_rho ...
236 !> \param e_ndrho_rho_rho ...
237 !> \param e_ndrho_ndrho_rho ...
238 !> \param grad_deriv degree of the derivative that should be evaluated,
239 !> if positive all the derivatives up to the given degree are evaluated,
240 !> if negative only the given degree is calculated
241 !> \param npoints ...
242 !> \param epsilon_rho ...
243 !> \param sc scaling-parameter for correlation
244 !> \par History
245 !> 11.2003 created [fawzi]
246 !> 01.2007 added scaling [Manuel Guidon]
247 !> \author fawzi
248 ! **************************************************************************************************
249  SUBROUTINE lyp_lda_calc(rho, rho_1_3, norm_drho, &
250  e_0, e_rho, e_ndrho, e_rho_rho, e_ndrho_rho, &
251  e_ndrho_ndrho, e_rho_rho_rho, e_ndrho_rho_rho, e_ndrho_ndrho_rho, &
252  grad_deriv, npoints, epsilon_rho, sc)
253  INTEGER, INTENT(in) :: npoints, grad_deriv
254  REAL(kind=dp), DIMENSION(1:npoints), INTENT(inout) :: e_ndrho_ndrho_rho, e_ndrho_rho_rho, &
255  e_rho_rho_rho, e_ndrho_ndrho, &
256  e_ndrho_rho, e_rho_rho, e_ndrho, &
257  e_rho, e_0
258  REAL(kind=dp), DIMENSION(1:npoints), INTENT(in) :: norm_drho, rho_1_3, rho
259  REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
260 
261  INTEGER :: ii
262  REAL(kind=dp) :: cf, epsilon_rho13, my_ndrho, my_rho, my_rho_1_3, t1, t102, t103, t105, &
263  t106, t11, t112, t123, t124, t127, t128, t13, t133, t134, t14, t161, t165, t166, t173, &
264  t176, t184, t185, t189, t192, t193, t196, t199, t2, t200, t201, t202, t203, t215, t22, &
265  t227, t228, t231, t245, t246, t248, t26, t265, t278, t279, t3, t332, t37, t38, t39, t4, &
266  t40, t41, t44, t45, t48, t5, t52, t6, t61, t62, t69, t7, t70, t77, t78, t80, t87, t88, &
267  t89, t93, t94, t95, t98, t99
268 
269  epsilon_rho13 = epsilon_rho**(1.0_dp/3.0_dp)
270  cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
271  SELECT CASE (grad_deriv)
272  CASE (1)
273 !$OMP DO
274  DO ii = 1, npoints
275  my_rho = rho(ii)
276  IF (my_rho > epsilon_rho) THEN
277  my_rho_1_3 = rho_1_3(ii)
278  my_ndrho = norm_drho(ii)
279  t1 = my_rho_1_3**2
280  t2 = t1*my_rho
281  t3 = 0.1e1_dp/t2
282  t4 = a*t3
283  t5 = my_rho**2
284  t6 = t5*my_rho
285  t7 = my_rho_1_3*t6
286  t11 = 0.1e1_dp/my_rho_1_3
287  t13 = exp(-c*t11)
288  t14 = b*t13
289  t22 = my_ndrho**2
290  t26 = my_rho_1_3*t22
291  t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
292  t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
293  & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
294  &*t26*c + 0.7e1_dp*t14*t22*c*d
295  t38 = my_rho_1_3 + d
296  t39 = t38**2
297  t40 = 0.1e1_dp/t39
298  t41 = t37*t40
299 
300  e_0(ii) = e_0(ii) &
301  + (t4*t41/0.72e2_dp)*sc
302  t44 = 0.1e1_dp/t1/t5
303  t45 = a*t44
304  t48 = my_rho_1_3*t5
305  t52 = b*c
306  t61 = t13*cf
307  t62 = t61*d
308  t69 = 0.1e1_dp/t1
309  t70 = t69*t13
310  t77 = 0.1e1_dp/my_rho
311  t78 = t52*t77
312  t80 = t13*t22*d
313  t87 = c**2
314  t88 = b*t87
315  t89 = t77*t13
316  t93 = my_rho_1_3*my_rho
317  t94 = 0.1e1_dp/t93
318  t95 = t88*t94
319  t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
320  & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
321  0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
322  &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
323  t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
324  0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
325  0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
326  t80
327  t99 = t98*t40
328  t102 = 0.1e1_dp/t48
329  t103 = a*t102
330  t105 = 0.1e1_dp/t39/t38
331  t106 = t37*t105
332 
333  e_rho(ii) = e_rho(ii) &
334  - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
335  & + t103*t106/0.108e3_dp)*sc
336 
337  t112 = my_rho_1_3*my_ndrho
338  t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
339  &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
340  my_ndrho*c*d
341  t124 = t123*t40
342 
343  e_ndrho(ii) = e_ndrho(ii) &
344  + (t4*t124/0.72e2_dp)*sc
345  END IF
346  END DO
347 !$OMP END DO
348  CASE default
349 !$OMP DO
350  DO ii = 1, npoints
351  my_rho = rho(ii)
352  IF (my_rho > epsilon_rho) THEN
353  my_rho_1_3 = rho_1_3(ii)
354  my_ndrho = norm_drho(ii)
355  t1 = my_rho_1_3**2
356  t2 = t1*my_rho
357  t3 = 0.1e1_dp/t2
358  t4 = a*t3
359  t5 = my_rho**2
360  t6 = t5*my_rho
361  t7 = my_rho_1_3*t6
362  t11 = 0.1e1_dp/my_rho_1_3
363  t13 = exp(-c*t11)
364  t14 = b*t13
365  t22 = my_ndrho**2
366  t26 = my_rho_1_3*t22
367  t37 = -0.72e2_dp*t7 - 0.72e2_dp*t6*d - 0.72e2_dp*t14* &
368  t7*cf - 0.72e2_dp*t14*t6*cf*d + 0.3e1_dp*t14&
369  & *t1*t22 + 0.10e2_dp*t14*t26*d + 0.7e1_dp*t14 &
370  &*t26*c + 0.7e1_dp*t14*t22*c*d
371  t38 = my_rho_1_3 + d
372  t39 = t38**2
373  t40 = 0.1e1_dp/t39
374  t41 = t37*t40
375 
376  IF (grad_deriv >= 0) THEN
377  e_0(ii) = e_0(ii) &
378  + (t4*t41/0.72e2_dp)*sc
379  END IF
380 
381  t44 = 0.1e1_dp/t1/t5
382  t45 = a*t44
383  t48 = my_rho_1_3*t5
384  t52 = b*c
385  t61 = t13*cf
386  t62 = t61*d
387  t69 = 0.1e1_dp/t1
388  t70 = t69*t13
389  t77 = 0.1e1_dp/my_rho
390  t78 = t52*t77
391  t80 = t13*t22*d
392  t87 = c**2
393  t88 = b*t87
394  t89 = t77*t13
395  t93 = my_rho_1_3*my_rho
396  t94 = 0.1e1_dp/t93
397  t95 = t88*t94
398  t98 = -0.240e3_dp*t48 - 0.216e3_dp*t5*d - 0.24e2_dp*t52&
399  & *t5*t13*cf - 0.240e3_dp*t14*t48*cf - &
400  0.24e2_dp*t52*t2*t62 - 0.216e3_dp*t14*t5*cf &
401  &*d + 0.10e2_dp/0.3e1_dp*t52*t70*t22 + 0.2e1_dp* &
402  t14*t11*t22 + 0.10e2_dp/0.3e1_dp*t78*t80 + &
403  0.10e2_dp/0.3e1_dp*t14*t69*t22*d + 0.7e1_dp/ &
404  0.3e1_dp*t88*t89*t22 + 0.7e1_dp/0.3e1_dp*t95* &
405  t80
406  t99 = t98*t40
407  t102 = 0.1e1_dp/t48
408  t103 = a*t102
409  t105 = 0.1e1_dp/t39/t38
410  t106 = t37*t105
411  t112 = my_rho_1_3*my_ndrho
412  t123 = 0.6e1_dp*t14*t1*my_ndrho + 0.20e2_dp*t14*t112 &
413  &*d + 0.14e2_dp*t14*t112*c + 0.14e2_dp*t14* &
414  my_ndrho*c*d
415  t124 = t123*t40
416 
417  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
418  e_rho(ii) = e_rho(ii) &
419  - (0.5e1_dp/0.216e3_dp*t45*t41 - t4*t99/0.72e2_dp&
420  & + t103*t106/0.108e3_dp)*sc
421  e_ndrho(ii) = e_ndrho(ii) &
422  + (t4*t124/0.72e2_dp)*sc
423  END IF
424 
425  t127 = 0.1e1_dp/t1/t6
426  t128 = a*t127
427  t133 = 0.1e1_dp/t7
428  t134 = a*t133
429  t161 = t3*t13
430  t165 = 0.1e1_dp/t5
431  t166 = t165*t13
432  t173 = t52*t165
433  t176 = t88*t102
434  t184 = b*t87*c
435  t185 = t102*t13
436  t189 = t184*t44
437  t192 = -0.560e3_dp*t93 - 0.432e3_dp*my_rho*d - 0.128e3_dp&
438  & *t52*my_rho*t13*cf - 0.8e1_dp*t88*t1*t13* &
439  cf - 0.560e3_dp*t14*t93*cf - 0.112e3_dp*t52*t1&
440  & *t62 - 0.8e1_dp*t88*my_rho_1_3*t62 - 0.432e3_dp* &
441  t14*my_rho*cf*d - 0.14e2_dp/0.9e1_dp*t52* &
442  t161*t22 - 0.11e2_dp/0.9e1_dp*t88*t166*t22 - &
443  0.2e1_dp/0.3e1_dp*t14*t94*t22 - 0.20e2_dp/ &
444  0.9e1_dp*t173*t80 - 0.2e1_dp*t176*t80 - &
445  0.20e2_dp/0.9e1_dp*t14*t3*t22*d + 0.7e1_dp/ &
446  0.9e1_dp*t184*t185*t22 + 0.7e1_dp/0.9e1_dp* &
447  t189*t80
448  t193 = t192*t40
449  t196 = t98*t105
450  t199 = 0.1e1_dp/t6
451  t200 = a*t199
452  t201 = t39**2
453  t202 = 0.1e1_dp/t201
454  t203 = t37*t202
455  t215 = t13*my_ndrho*d
456  t227 = 0.20e2_dp/0.3e1_dp*t52*t70*my_ndrho + 0.4e1_dp* &
457  t14*t11*my_ndrho + 0.20e2_dp/0.3e1_dp*t78*t215&
458  & + 0.20e2_dp/0.3e1_dp*t14*t69*my_ndrho*d + &
459  0.14e2_dp/0.3e1_dp*t88*t89*my_ndrho + 0.14e2_dp &
460  &/0.3e1_dp*t95*t215
461  t228 = t227*t40
462  t231 = t123*t105
463  t245 = 0.6e1_dp*t14*t1 + 0.20e2_dp*t14*my_rho_1_3*d + &
464  0.14e2_dp*t14*my_rho_1_3*c + 0.14e2_dp*t14*c* &
465  d
466  t246 = t245*t40
467 
468  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
469  e_rho_rho(ii) = e_rho_rho(ii) &
470  + (0.5e1_dp/0.81e2_dp*t128*t41 - 0.5e1_dp/0.108e3_dp&
471  & *t45*t99 + t134*t106/0.27e2_dp + t4*t193/ &
472  0.72e2_dp - t103*t196/0.54e2_dp + t200*t203/ &
473  0.108e3_dp)*sc
474  e_ndrho_rho(ii) = e_ndrho_rho(ii) &
475  - (0.5e1_dp/0.216e3_dp*t45*t124 - t4*t228/ &
476  0.72e2_dp + t103*t231/0.108e3_dp)*sc
477  e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii) &
478  + (t4*t246/0.72e2_dp)*sc
479  END IF
480 
481  t248 = t5**2
482  t265 = 0.1e1_dp/t248
483  t278 = t87**2
484  t279 = b*t278
485  t332 = -0.432e3_dp*d - 0.2240e4_dp/0.3e1_dp*my_rho_1_3 - &
486  0.74e2_dp/0.27e2_dp*t184*t127*t80 + 0.100e3_dp/ &
487  0.27e2_dp*t14*t44*t22*d + 0.7e1_dp/0.27e2_dp* &
488  t279*t127*t13*t22 - 0.8e1_dp/0.3e1_dp*t184* &
489  t70*cf - 0.2240e4_dp/0.3e1_dp*t14*my_rho_1_3* &
490  cf - 0.48e2_dp*t88*t11*t13*cf - 0.944e3_dp/ &
491  0.3e1_dp*t52*t61 - 0.40e2_dp*t88*t69*t62 - &
492  0.656e3_dp/0.3e1_dp*t52*t11*t62 + 0.7e1_dp/ &
493  0.27e2_dp*t279*t265*t80 + 0.64e2_dp/0.27e2_dp* &
494  t52*t44*t13*t22 - 0.8e1_dp/0.3e1_dp*t184*t77&
495  & *t62 - 0.432e3_dp*t14*cf*d + 0.52e2_dp/ &
496  0.27e2_dp*t88*t199*t13*t22 - 0.20e2_dp/ &
497  0.9e1_dp*t184*t133*t13*t22 + 0.8e1_dp/0.9e1_dp&
498  & *t14*t102*t22 + 0.100e3_dp/0.27e2_dp*t52*t199&
499  & *t80 + 0.106e3_dp/0.27e2_dp*t88*t133*t80
500 
501  IF (grad_deriv >= 3 .OR. grad_deriv == -3) THEN
502  e_rho_rho_rho(ii) = e_rho_rho_rho(ii) &
503  - (0.55e2_dp/0.243e3_dp*a/t1/t248*t41 - 0.5e1_dp &
504  &/0.27e2_dp*t128*t99 + 0.40e2_dp/0.243e3_dp*a/ &
505  my_rho_1_3/t248*t106 + 0.5e1_dp/0.72e2_dp*t45* &
506  t193 - t134*t196/0.9e1_dp + 0.7e1_dp/0.108e3_dp* &
507  a*t265*t203 - t4*t332*t40/0.72e2_dp + t103* &
508  t192*t105/0.36e2_dp - t200*t98*t202/0.36e2_dp &
509  &+ t128*t37/t201/t38/0.81e2_dp)*sc
510  e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii) &
511  + (0.5e1_dp/0.81e2_dp*t128*t124 - 0.5e1_dp/ &
512  0.108e3_dp*t45*t228 + t134*t231/0.27e2_dp + t4*&
513  & (-0.28e2_dp/0.9e1_dp*t52*t161*my_ndrho - &
514  0.22e2_dp/0.9e1_dp*t88*t166*my_ndrho - 0.4e1_dp &
515  &/0.3e1_dp*t14*t94*my_ndrho - 0.40e2_dp/0.9e1_dp &
516  &*t173*t215 - 0.4e1_dp*t176*t215 - 0.40e2_dp/ &
517  0.9e1_dp*t14*t3*my_ndrho*d + 0.14e2_dp/ &
518  0.9e1_dp*t184*t185*my_ndrho + 0.14e2_dp/0.9e1_dp&
519  & *t189*t215)*t40/0.72e2_dp - t103*t227*t105/ &
520  0.54e2_dp + t200*t123*t202/0.108e3_dp)*sc
521  e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii) &
522  - (0.5e1_dp/0.216e3_dp*t45*t246 - t4*(0.20e2_dp/ &
523  0.3e1_dp*t52*t70 + 0.4e1_dp*t14*t11 + 0.20e2_dp &
524  &/0.3e1_dp*t52*t89*d + 0.20e2_dp/0.3e1_dp*t14* &
525  t69*d + 0.14e2_dp/0.3e1_dp*t88*t89 + 0.14e2_dp/ &
526  0.3e1_dp*t88*t94*t13*d)*t40/0.72e2_dp + t103&
527  & *t245*t105/0.108e3_dp)*sc
528  END IF
529  END IF
530 
531 !FM t1 = my_rho_1_3 ** 2
532 !FM t2 = t1 * my_rho
533 !FM t3 = 0.1e1_dp / t2
534 !FM t4 = a * t3
535 !FM t5 = my_rho ** 2
536 !FM t6 = t5 * my_rho
537 !FM t7 = my_rho_1_3 * t6
538 !FM t11 = 0.1e1_dp / my_rho_1_3
539 !FM t13 = exp(-c * t11)
540 !FM t14 = b * t13
541 !FM t22 = my_ndrho ** 2
542 !FM t26 = my_rho_1_3 * t22
543 !FM t37 = -0.72e2_dp *( t7 - t14 *&
544 !FM & t7 * cf - t6 * d * (1.0_dp+ t14 * cf)) + t14 *(t22*(0.3e1_dp &
545 !FM & * t1 + 0.7e1_dp * c * d)&
546 !FM + 0.10e2_dp * t26 * d + 0.7e1_dp &
547 !FM &* t26 * c )
548 !FM t38 = my_rho_1_3 + d
549 !FM t39 = t38 ** 2
550 !FM t40 = 0.1e1_dp / t39
551 !FM t41 = t37 * t40
552 !FM
553 !FM IF (grad_deriv>=0.AND.my_rho>epsilon_rho) THEN
554 !FM e_0(ii) = e_0(ii)&
555 !FM + t4 * t41 / 0.72e2_dp
556 !FM END IF
557 !FM
558 !FM t44 = 0.1e1_dp / (t1 * t5)
559 !FM t45 = a * t44
560 !FM t48 = my_rho_1_3 * t5
561 !FM t52 = b * c
562 !FM t61 = t13 * cf
563 !FM t62 = t61 * d
564 !FM t69 = 0.1e1_dp / t1
565 !FM t70 = t69 * t13
566 !FM t77 = 0.1e1_dp / my_rho
567 !FM t78 = t52 * t77
568 !FM t80 = t13 * t22 * d
569 !FM t87 = c ** 2
570 !FM t88 = b * t87
571 !FM t89 = t77 * t13
572 !FM t93 = my_rho_1_3 * my_rho
573 !FM t94 = 0.1e1_dp / t93
574 !FM t95 = t88 * t94
575 !FM t98 = -0.216e3_dp * t5 *d -0.240e3_dp * t48(1.0_dp+ t14 * cf) -&
576 !FM & 0.24e2_dp * t52 * (t2 * t62 +t13*t5*cf) &
577 !FM - 0.216e3_dp * t14 * t5 * cf &
578 !FM &* d + t22 *(0.10e2_dp / 0.3e1_dp * t52 * t70 + 0.2e1_dp *&
579 !FM & t14 * t11 + 0.10e2_dp / 0.3e1_dp * t14 * t69 * d + 0.7e1_dp /&
580 !FM & 0.3e1_dp * t88 * t89 ) +(0.10e2_dp / 0.3e1_dp * t78 +&
581 !FM & 0.7e1_dp / 0.3e1_dp * t95 ) *&
582 !FM & t80
583 !FM t99 = t98 * t40
584 !FM t102 = 0.1e1_dp / t48
585 !FM t103 = a * t102
586 !FM t105 = 0.1e1_dp / (t39 * t38)
587 !FM t106 = t37 * t105
588 !FM t112 = my_rho_1_3 * my_ndrho
589 !FM t123 = t14 *(0.6e1_dp t1 * my_ndrho + t112 * 0.20e2_dp &
590 !FM &* d + 0.14e2_dp * c *(t112 + t14 *&
591 !FM & my_ndrho * d))
592 !FM t124 = t123 * t40
593 !FM
594 !FM IF (grad_deriv>=1.OR.grad_deriv==-1) THEN
595 !FM e_rho(ii) = e_rho(ii) &
596 !FM -0.5e1_dp / 0.216e3_dp * t45 * t41 + t4 * t99 / 0.72e2_dp&
597 !FM & - t103 * t106 / 0.108e3_dp
598 !FM e_ndrho(ii) = e_ndrho(ii)&
599 !FM +t4 * t124 / 0.72e2_dp
600 !FM END IF
601 !FM
602 !FM t127 = 0.1e1_dp / (t1 * t6)
603 !FM t128 = a * t127
604 !FM t133 = 0.1e1_dp / t7
605 !FM t134 = a * t133
606 !FM t161 = t3 * t13
607 !FM t165 = 0.1e1_dp / t5
608 !FM t166 = t165 * t13
609 !FM t173 = t52 * t165
610 !FM t176 = t88 * t102
611 !FM t184 = b * t87 * c
612 !FM t185 = t102 * t13
613 !FM t189 = t184 * t44
614 !FM t192 = -0.560e3_dp * t93 - 0.432e3_dp * my_rho * d +cf*(&
615 !FM -t13*(0.128e3_dp&
616 !FM & * t52 * my_rho + 0.8e1_dp * t88 * t1 )&
617 !FM & - 0.560e3_dp * t14 * t93 ) - 0.112e3_dp * t52 * t1&
618 !FM & * t62 - 0.8e1_dp * t88 * my_rho_1_3 * t62 - 0.432e3_dp *&
619 !FM & t14 * my_rho * cf * d - 0.14e2_dp / 0.9e1_dp * t52 *&
620 !FM & t161 * t22 - 0.11e2_dp / 0.9e1_dp * t88 * t166 * t22 -&
621 !FM & 0.2e1_dp / 0.3e1_dp * t14 * t94 * t22 - 0.20e2_dp /&
622 !FM & 0.9e1_dp * t173 * t80 - 0.2e1_dp * t176 * t80 -&
623 !FM & 0.20e2_dp / 0.9e1_dp * t14 * t3 * t22 * d + 0.7e1_dp /&
624 !FM & 0.9e1_dp * t184 * t185 * t22 + 0.7e1_dp / 0.9e1_dp *&
625 !FM & t189 * t80
626 !FM t193 = t192 * t40
627 !FM t196 = t98 * t105
628 !FM t199 = 0.1e1_dp / t6
629 !FM t200 = a * t199
630 !FM t201 = t39 ** 2
631 !FM t202 = 0.1e1_dp / t201
632 !FM t203 = t37 * t202
633 !FM t215 = t13 * my_ndrho * d
634 !FM t227 = 0.20e2_dp / 0.3e1_dp * t52 * t70 * my_ndrho + 0.4e1_dp *&
635 !FM & t14 * t11 * my_ndrho + 0.20e2_dp / 0.3e1_dp * t78 * t215&
636 !FM & + 0.20e2_dp / 0.3e1_dp * t14 * t69 * my_ndrho * d +&
637 !FM & 0.14e2_dp / 0.3e1_dp * t88 * t89 * my_ndrho + 0.14e2_dp &
638 !FM &/ 0.3e1_dp * t95 * t215
639 !FM t228 = t227 * t40
640 !FM t231 = t123 * t105
641 !FM t245 = 0.6e1_dp * t14 * t1 + 0.20e2_dp * t14 * my_rho_1_3 * d +&
642 !FM & 0.14e2_dp * t14 * my_rho_1_3 * c + 0.14e2_dp * t14 * c *&
643 !FM & d
644 !FM t246 = t245 * t40
645 !FM
646 !FM IF (grad_deriv>=2 .OR.grad_deriv==-2) THEN
647 !FM e_rho_rho(ii) = e_rho_rho(ii)&
648 !FM +0.5e1_dp / 0.81e2_dp * t128 * t41 - 0.5e1_dp / 0.108e3_dp&
649 !FM & * t45 * t99 + t134 * t106 / 0.27e2_dp + t4 * t193 /&
650 !FM & 0.72e2_dp - t103 * t196 / 0.54e2_dp + t200 * t203 /&
651 !FM & 0.108e3_dp
652 !FM e_ndrho_rho(ii) = e_ndrho_rho(ii)&
653 !FM -0.5e1_dp / 0.216e3_dp * t45 * t124 + t4 * t228 /&
654 !FM & 0.72e2_dp - t103 * t231 / 0.108e3_dp
655 !FM e_ndrho_ndrho(ii) = e_ndrho_ndrho(ii)&
656 !FM +t4 * t246 / 0.72e2_dp
657 !FM END IF
658 !FM
659 !FM t248 = t5 ** 2
660 !FM t265 = 0.1e1_dp / t248
661 !FM t278 = t87 ** 2
662 !FM t279 = b * t278
663 !FM t332 = -0.432e3_dp * d - 0.2240e4_dp / 0.3e1_dp * my_rho_1_3 -&
664 !FM & 0.74e2_dp / 0.27e2_dp * t184 * t127 * t80 + 0.100e3_dp /&
665 !FM & 0.27e2_dp * t14 * t44 * t22 * d + 0.7e1_dp / 0.27e2_dp *&
666 !FM & t279 * t127 * t13 * t22 - 0.8e1_dp / 0.3e1_dp * t184 *&
667 !FM & t70 * cf - 0.2240e4_dp / 0.3e1_dp * t14 * my_rho_1_3 *&
668 !FM & cf - 0.48e2_dp * t88 * t11 * t13 * cf - 0.944e3_dp /&
669 !FM & 0.3e1_dp * t52 * t61 - 0.40e2_dp * t88 * t69 * t62 -&
670 !FM & 0.656e3_dp / 0.3e1_dp * t52 * t11 * t62 + 0.7e1_dp /&
671 !FM & 0.27e2_dp * t279 * t265 * t80 + 0.64e2_dp / 0.27e2_dp *&
672 !FM & t52 * t44 * t13 * t22 - 0.8e1_dp / 0.3e1_dp * t184 * t77&
673 !FM & * t62 - 0.432e3_dp * t14 * cf * d + 0.52e2_dp /&
674 !FM & 0.27e2_dp * t88 * t199 * t13 * t22 - 0.20e2_dp /&
675 !FM & 0.9e1_dp * t184 * t133 * t13 * t22 + 0.8e1_dp / 0.9e1_dp&
676 !FM & * t14 * t102 * t22 + 0.100e3_dp / 0.27e2_dp * t52 * t199&
677 !FM & * t80 + 0.106e3_dp / 0.27e2_dp * t88 * t133 * t80
678 !FM
679 !FM IF (grad_deriv>=3 .OR. grad_deriv==-3) THEN
680 !FM e_rho_rho_rho(ii) = e_rho_rho_rho(ii)&
681 !FM -0.55e2_dp / 0.243e3_dp * a / t1 / t248 * t41 + 0.5e1_dp &
682 !FM &/ 0.27e2_dp * t128 * t99 - 0.40e2_dp / 0.243e3_dp * a /&
683 !FM & my_rho_1_3 / t248 * t106 - 0.5e1_dp / 0.72e2_dp * t45 *&
684 !FM & t193 + t134 * t196 / 0.9e1_dp - 0.7e1_dp / 0.108e3_dp *&
685 !FM & a * t265 * t203 + t4 * t332 * t40 / 0.72e2_dp - t103 *&
686 !FM & t192 * t105 / 0.36e2_dp + t200 * t98 * t202 / 0.36e2_dp &
687 !FM &- t128 * t37 / t201 / t38 / 0.81e2_dp
688 !FM e_ndrho_rho_rho(ii) = e_ndrho_rho_rho(ii)&
689 !FM +0.5e1_dp / 0.81e2_dp * t128 * t124 - 0.5e1_dp /&
690 !FM & 0.108e3_dp * t45 * t228 + t134 * t231 / 0.27e2_dp + t4 *&
691 !FM & (-0.28e2_dp / 0.9e1_dp * t52 * t161 * my_ndrho -&
692 !FM & 0.22e2_dp / 0.9e1_dp * t88 * t166 * my_ndrho - 0.4e1_dp &
693 !FM &/ 0.3e1_dp * t14 * t94 * my_ndrho - 0.40e2_dp / 0.9e1_dp &
694 !FM &* t173 * t215 - 0.4e1_dp * t176 * t215 - 0.40e2_dp /&
695 !FM & 0.9e1_dp * t14 * t3 * my_ndrho * d + 0.14e2_dp /&
696 !FM & 0.9e1_dp * t184 * t185 * my_ndrho + 0.14e2_dp / 0.9e1_dp&
697 !FM & * t189 * t215) * t40 / 0.72e2_dp - t103 * t227 * t105 /&
698 !FM & 0.54e2_dp + t200 * t123 * t202 / 0.108e3_dp
699 !FM e_ndrho_ndrho_rho(ii) = e_ndrho_ndrho_rho(ii)&
700 !FM -0.5e1_dp / 0.216e3_dp * t45 * t246 + t4 * (0.20e2_dp /&
701 !FM & 0.3e1_dp * t52 * t70 + 0.4e1_dp * t14 * t11 + 0.20e2_dp &
702 !FM &/ 0.3e1_dp * t52 * t89 * d + 0.20e2_dp / 0.3e1_dp * t14 *&
703 !FM & t69 * d + 0.14e2_dp / 0.3e1_dp * t88 * t89 + 0.14e2_dp /&
704 !FM & 0.3e1_dp * t88 * t94 * t13 * d) * t40 / 0.72e2_dp - t103&
705 !FM & * t245 * t105 / 0.108e3_dp
706 !FM END IF
707 
708  END DO
709 
710 !$OMP END DO
711 
712  END SELECT
713  END SUBROUTINE lyp_lda_calc
714 
715 ! **************************************************************************************************
716 !> \brief evaluates the becke 88 exchange functional for lsd
717 !> \param rho_set ...
718 !> \param deriv_set ...
719 !> \param grad_deriv ...
720 !> \param lyp_params input parameter (scaling)
721 !> \par History
722 !> 11.2003 created [fawzi]
723 !> 01.2007 added scaling [Manuel Guidon]
724 !> \author fawzi
725 ! **************************************************************************************************
726  SUBROUTINE lyp_lsd_eval(rho_set, deriv_set, grad_deriv, lyp_params)
727  TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
728  TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
729  INTEGER, INTENT(in) :: grad_deriv
730  TYPE(section_vals_type), POINTER :: lyp_params
731 
732  CHARACTER(len=*), PARAMETER :: routinen = 'lyp_lsd_eval'
733 
734  INTEGER :: handle, npoints
735  INTEGER, DIMENSION(2, 3) :: bo
736  REAL(kind=dp) :: epsilon_drho, epsilon_rho, sc
737  REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: dummy, e_0, e_ndr, e_ndr_ndr, &
738  e_ndr_ra, e_ndr_rb, e_ndra, e_ndra_ndra, e_ndra_ra, e_ndra_rb, e_ndrb, e_ndrb_ndrb, &
739  e_ndrb_ra, e_ndrb_rb, e_ra, e_ra_ra, e_ra_rb, e_rb, e_rb_rb, norm_drho, norm_drhoa, &
740  norm_drhob, rhoa, rhob
741  TYPE(xc_derivative_type), POINTER :: deriv
742 
743  CALL timeset(routinen, handle)
744  NULLIFY (deriv)
745 
746  CALL section_vals_val_get(lyp_params, "scale_c", r_val=sc)
747  CALL cite_reference(lee1988)
748 
749  CALL xc_rho_set_get(rho_set, &
750  rhoa=rhoa, rhob=rhob, norm_drhoa=norm_drhoa, &
751  norm_drhob=norm_drhob, norm_drho=norm_drho, &
752  rho_cutoff=epsilon_rho, &
753  drho_cutoff=epsilon_drho, local_bounds=bo)
754  npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
755 
756  dummy => rhoa
757  e_0 => dummy
758  e_ra => dummy
759  e_rb => dummy
760  e_ndra_ra => dummy
761  e_ndra_rb => dummy
762  e_ndrb_ra => dummy
763  e_ndrb_rb => dummy
764  e_ndr_ndr => dummy
765  e_ndra_ndra => dummy
766  e_ndrb_ndrb => dummy
767  e_ndr => dummy
768  e_ndra => dummy
769  e_ndrb => dummy
770  e_ra_ra => dummy
771  e_ra_rb => dummy
772  e_rb_rb => dummy
773  e_ndr_ra => dummy
774  e_ndr_rb => dummy
775 
776  IF (grad_deriv >= 0) THEN
777  deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
778  allocate_deriv=.true.)
779  CALL xc_derivative_get(deriv, deriv_data=e_0)
780  END IF
781  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
782  deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa], &
783  allocate_deriv=.true.)
784  CALL xc_derivative_get(deriv, deriv_data=e_ra)
785  deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob], &
786  allocate_deriv=.true.)
787  CALL xc_derivative_get(deriv, deriv_data=e_rb)
788  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
789  allocate_deriv=.true.)
790  CALL xc_derivative_get(deriv, deriv_data=e_ndr)
791  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa], &
792  allocate_deriv=.true.)
793  CALL xc_derivative_get(deriv, deriv_data=e_ndra)
794  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob], &
795  allocate_deriv=.true.)
796  CALL xc_derivative_get(deriv, deriv_data=e_ndrb)
797  END IF
798  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
799  deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhoa], &
800  allocate_deriv=.true.)
801  CALL xc_derivative_get(deriv, deriv_data=e_ra_ra)
802  deriv => xc_dset_get_derivative(deriv_set, [deriv_rhoa, deriv_rhob], &
803  allocate_deriv=.true.)
804  CALL xc_derivative_get(deriv, deriv_data=e_ra_rb)
805  deriv => xc_dset_get_derivative(deriv_set, [deriv_rhob, deriv_rhob], &
806  allocate_deriv=.true.)
807  CALL xc_derivative_get(deriv, deriv_data=e_rb_rb)
808  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhoa], &
809  allocate_deriv=.true.)
810  CALL xc_derivative_get(deriv, deriv_data=e_ndr_ra)
811  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho, deriv_rhob], &
812  allocate_deriv=.true.)
813  CALL xc_derivative_get(deriv, deriv_data=e_ndr_rb)
814  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhoa], &
815  allocate_deriv=.true.)
816  CALL xc_derivative_get(deriv, deriv_data=e_ndra_ra)
817  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhoa, deriv_rhob], &
818  allocate_deriv=.true.)
819  CALL xc_derivative_get(deriv, deriv_data=e_ndra_rb)
820  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drhob, deriv_rhob], &
821  allocate_deriv=.true.)
822  CALL xc_derivative_get(deriv, deriv_data=e_ndrb_rb)
823  deriv => xc_dset_get_derivative(deriv_set, &
824  [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
825  CALL xc_derivative_get(deriv, deriv_data=e_ndr_ndr)
826  deriv => xc_dset_get_derivative(deriv_set, &
827  [deriv_norm_drhoa, deriv_norm_drhoa], allocate_deriv=.true.)
828  CALL xc_derivative_get(deriv, deriv_data=e_ndra_ndra)
829  deriv => xc_dset_get_derivative(deriv_set, &
830  [deriv_norm_drhob, deriv_norm_drhob], allocate_deriv=.true.)
831  CALL xc_derivative_get(deriv, deriv_data=e_ndrb_ndrb)
832  END IF
833 
834 !$OMP PARALLEL DEFAULT(NONE) &
835 !$OMP SHARED(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob) &
836 !$OMP SHARED(e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra) &
837 !$OMP SHARED(e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb) &
838 !$OMP SHARED(e_ndr, e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb) &
839 !$OMP SHARED(e_ndr_ra, e_ndr_rb, grad_deriv) &
840 !$OMP SHARED(npoints, epsilon_rho, sc)
841 
842  CALL lyp_lsd_calc( &
843  rhoa=rhoa, rhob=rhob, norm_drho=norm_drho, norm_drhoa=norm_drhoa, &
844  norm_drhob=norm_drhob, e_0=e_0, e_ra=e_ra, e_rb=e_rb, &
845  e_ndra_ra=e_ndra_ra, e_ndra_rb=e_ndra_rb, e_ndrb_ra&
846  &=e_ndrb_ra, e_ndrb_rb=e_ndrb_rb, e_ndr_ndr=e_ndr_ndr, &
847  e_ndra_ndra=e_ndra_ndra, e_ndrb_ndrb=e_ndrb_ndrb, e_ndr=e_ndr, &
848  e_ndra=e_ndra, e_ndrb=e_ndrb, e_ra_ra=e_ra_ra, &
849  e_ra_rb=e_ra_rb, e_rb_rb=e_rb_rb, e_ndr_ra=e_ndr_ra, &
850  e_ndr_rb=e_ndr_rb, &
851  grad_deriv=grad_deriv, npoints=npoints, &
852  epsilon_rho=epsilon_rho, sc=sc)
853 
854 !$OMP END PARALLEL
855 
856  CALL timestop(handle)
857  END SUBROUTINE lyp_lsd_eval
858 
859 ! **************************************************************************************************
860 !> \brief low level calculation of the becke 88 exchange functional for lsd
861 !> \param rhoa alpha spin density
862 !> \param rhob beta spin density
863 !> \param norm_drho || grad rhoa + grad rhob ||
864 !> \param norm_drhoa || grad rhoa ||
865 !> \param norm_drhob || grad rhob ||
866 !> \param e_0 adds to it the local value of the functional
867 !> \param e_ra e_*: derivative of the functional wrt. to the variables
868 !> named where the * is.
869 !> \param e_rb ...
870 !> \param e_ndra_ra ...
871 !> \param e_ndra_rb ...
872 !> \param e_ndrb_ra ...
873 !> \param e_ndrb_rb ...
874 !> \param e_ndr_ndr ...
875 !> \param e_ndra_ndra ...
876 !> \param e_ndrb_ndrb ...
877 !> \param e_ndr ...
878 !> \param e_ndra ...
879 !> \param e_ndrb ...
880 !> \param e_ra_ra ...
881 !> \param e_ra_rb ...
882 !> \param e_rb_rb ...
883 !> \param e_ndr_ra ...
884 !> \param e_ndr_rb ...
885 !> \param grad_deriv ...
886 !> \param npoints ...
887 !> \param epsilon_rho ...
888 !> \param sc scaling parameter for correlation
889 !> \par History
890 !> 01.2004 created [fawzi]
891 !> \author fawzi
892 ! **************************************************************************************************
893  SUBROUTINE lyp_lsd_calc(rhoa, rhob, norm_drho, norm_drhoa, norm_drhob, &
894  e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, &
895  e_ndra_ndra, e_ndrb_ndrb, e_ndr, &
896  e_ndra, e_ndrb, e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb, &
897  grad_deriv, npoints, epsilon_rho, sc)
898  REAL(kind=dp), DIMENSION(*), INTENT(in) :: rhoa, rhob, norm_drho, norm_drhoa, &
899  norm_drhob
900  REAL(kind=dp), DIMENSION(*), INTENT(inout) :: e_0, e_ra, e_rb, e_ndra_ra, e_ndra_rb, &
901  e_ndrb_ra, e_ndrb_rb, e_ndr_ndr, e_ndra_ndra, e_ndrb_ndrb, e_ndr, e_ndra, e_ndrb, &
902  e_ra_ra, e_ra_rb, e_rb_rb, e_ndr_ra, e_ndr_rb
903  INTEGER, INTENT(in) :: grad_deriv, npoints
904  REAL(kind=dp), INTENT(in) :: epsilon_rho, sc
905 
906  INTEGER :: ii
907  REAL(kind=dp) :: cf, my_ndrho, my_ndrhoa, my_ndrhob, my_rho, my_rhoa, my_rhob, t1, t100, &
908  t101, t102, t103, t104, t107, t108, t109, t112, t115, t118, t12, t120, t124, t129, t13, &
909  t130, t132, t135, t138, t14, t140, t142, t145, t15, t153, t155, t159, t16, t164, t168, &
910  t17, t171, t176, t18, t181, t182, t185, t189, t194, t195, t198, t2, t20, t202, t205, &
911  t206, t21, t210, t214, t215, t218, t22, t222, t228, t23, t232, t236, t238, t24, t243, &
912  t249, t25, t252, t253, t255, t257, t26, t260, t265, t268, t27, t270, t29, t3, t30, t304, &
913  t31, t310, t313, t316, t319, t322, t326, t329, t332, t334, t341, t35
914  REAL(kind=dp) :: t354, t356, t360, t363, t37, t373, t376, t381, t39, t391, t4, t40, t408, &
915  t41, t415, t419, t422, t430, t44, t445, t449, t45, t452, t46, t467, t47, t48, t483, t487, &
916  t49, t490, t5, t50, t505, t515, t519, t52, t520, t54, t56, t57, t6, t61, t62, t64, t66, &
917  t7, t72, t75, t78, t8, t82, t85, t86, t87, t88, t90, t92, t94, t95, t98, t99
918 
919  cf = 0.3_dp*(3._dp*pi*pi)**(2._dp/3._dp)
920 
921 !$OMP DO
922 
923  DO ii = 1, npoints
924  my_rhoa = max(rhoa(ii), 0.0_dp)
925  my_rhob = max(rhob(ii), 0.0_dp)
926  my_rho = my_rhoa + my_rhob
927  IF (my_rho > epsilon_rho) THEN
928  my_ndrho = norm_drho(ii)
929  my_ndrhoa = norm_drhoa(ii)
930  my_ndrhob = norm_drhob(ii)
931 
932  t1 = my_rho**(0.1e1_dp/0.3e1_dp)
933  t2 = 0.1e1_dp/t1
934  t3 = d*t2
935  t4 = 0.1e1_dp + t3
936  t5 = 0.1e1_dp/t4
937  t6 = a*t5
938  t7 = my_rhoa*my_rhob
939  t8 = 0.1e1_dp/my_rho
940  t12 = a*b
941  t13 = c*t2
942  t14 = exp(-t13)
943  t15 = t12*t14
944  t16 = my_rho**2
945  t17 = t16*my_rho
946  t18 = t1**2
947  t20 = 0.1e1_dp/t18/t17
948  t21 = t5*t20
949  t22 = 2**(0.1e1_dp/0.3e1_dp)
950  t23 = t22**2
951  t24 = t23*cf
952  t25 = my_rhoa**2
953  t26 = my_rhoa**(0.1e1_dp/0.3e1_dp)
954  t27 = t26**2
955  t29 = my_rhob**2
956  t30 = my_rhob**(0.1e1_dp/0.3e1_dp)
957  t31 = t30**2
958  t35 = 0.8e1_dp*t24*(t27*t25 + t31*t29)
959  t37 = t3*t5
960  t39 = 0.47e2_dp/0.18e2_dp - 0.7e1_dp/0.18e2_dp*t13 - &
961  0.7e1_dp/0.18e2_dp*t37
962  t40 = my_ndrho**2
963  t41 = t39*t40
964  t44 = 0.5e1_dp/0.2e1_dp - t13/0.18e2_dp - t37/0.18e2_dp
965  t45 = my_ndrhoa**2
966  t46 = my_ndrhob**2
967  t47 = t45 + t46
968  t48 = t44*t47
969  t49 = t13 + t37 - 0.11e2_dp
970  t50 = my_rhoa*t8
971  t52 = my_rhob*t8
972  t54 = t50*t45 + t52*t46
973  t56 = t49*t54/0.9e1_dp
974  t57 = t35 + t41 - t48 - t56
975  t61 = 0.2e1_dp/0.3e1_dp*t16
976  t62 = t61 - t25
977  t64 = t61 - t29
978  t66 = t7*t57 - 0.2e1_dp/0.3e1_dp*t16*t40 + t62*t46 + &
979  t64*t45
980 
981  IF (grad_deriv >= 0 .AND. my_rho > epsilon_rho) THEN
982  e_0(ii) = e_0(ii) &
983  - (0.4e1_dp*t6*t7*t8 + t15*t21*t66)*sc
984  END IF
985  !--------
986 
987  t72 = t27*my_rhoa
988  t75 = t49*t8
989  t78 = 0.64e2_dp/0.3e1_dp*t24*t72 - t75*t45/0.9e1_dp
990  t82 = my_rhob*t57 + t7*t78 - 0.2e1_dp*my_rhoa*t46
991  t85 = t4**2
992  t86 = 0.1e1_dp/t85
993  t87 = a*t86
994  t88 = t87*my_rhoa
995  t90 = 0.1e1_dp/t1/t16
996  t92 = my_rhob*t90*d
997  t94 = 0.4e1_dp/0.3e1_dp*t88*t92
998  t95 = 0.1e1_dp/t16
999  t98 = 0.4e1_dp*t6*t7*t95
1000  t99 = t12*c
1001  t100 = t16**2
1002  t101 = t100*my_rho
1003  t102 = 0.1e1_dp/t101
1004  t103 = t102*t14
1005  t104 = t5*t66
1006  t107 = t99*t103*t104/0.3e1_dp
1007  t108 = t86*t102
1008  t109 = t66*d
1009  t112 = t15*t108*t109/0.3e1_dp
1010  t115 = t5/t18/t100
1011  t118 = 0.11e2_dp/0.3e1_dp*t15*t115*t66
1012  t120 = 0.1e1_dp/t1/my_rho
1013  t124 = d**2
1014  t129 = c*t120 + d*t120*t5 - t124/t18/my_rho*t86
1015  t130 = 0.7e1_dp/0.54e2_dp*t129
1016  t132 = t129/0.54e2_dp
1017  t135 = -t129/0.3e1_dp
1018  t138 = my_rhoa*t95
1019  t140 = my_rhob*t95
1020  t142 = -t138*t45 - t140*t46
1021  t145 = t130*t40 - t132*t47 - t135*t54/0.9e1_dp - t49* &
1022  t142/0.9e1_dp
1023  t153 = t7*t145 - 0.4e1_dp/0.3e1_dp*my_rho*t40 + &
1024  0.4e1_dp/0.3e1_dp*my_rho*t46 + 0.4e1_dp/0.3e1_dp&
1025  & *my_rho*t45
1026  t155 = t15*t21*t153
1027 
1028  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1029  e_ra(ii) = e_ra(ii) &
1030  - (0.4e1_dp*t6*t52 + t15*t21*t82 + t94 - t98 + &
1031  t107 + t112 - t118 + t155)*sc
1032  END IF
1033 
1034  t159 = t31*my_rhob
1035  t164 = 0.64e2_dp/0.3e1_dp*t24*t159 - t75*t46/0.9e1_dp
1036  t168 = my_rhoa*t57 + t7*t164 - 0.2e1_dp*my_rhob*t45
1037 
1038  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1039  e_rb(ii) = e_rb(ii) &
1040  - (0.4e1_dp*t6*t50 + t15*t21*t168 + t94 - t98 + &
1041  t107 + t112 - t118 + t155)*sc
1042  END IF
1043 
1044  t171 = t39*my_ndrho
1045  t176 = 0.2e1_dp*t7*t171 - 0.4e1_dp/0.3e1_dp*t16*my_ndrho
1046 
1047  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1048  e_ndr(ii) = e_ndr(ii) &
1049  - (t15*t21*t176)*sc
1050  END IF
1051 
1052  t181 = t49*my_rhoa
1053  t182 = t8*my_ndrhoa
1054  t185 = -0.2e1_dp*t44*my_ndrhoa - 0.2e1_dp/0.9e1_dp*t181*t182
1055  t189 = t7*t185 + 0.2e1_dp*t64*my_ndrhoa
1056 
1057  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1058  e_ndra(ii) = e_ndra(ii) &
1059  - (t15*t21*t189)*sc
1060  END IF
1061 
1062  t194 = t49*my_rhob
1063  t195 = t8*my_ndrhob
1064  t198 = -0.2e1_dp*t44*my_ndrhob - 0.2e1_dp/0.9e1_dp*t194*t195
1065  t202 = t7*t198 + 0.2e1_dp*t62*my_ndrhob
1066 
1067  IF (grad_deriv >= 1 .OR. grad_deriv == -1) THEN
1068  e_ndrb(ii) = e_ndrb(ii) &
1069  - (t15*t21*t202)*sc
1070  END IF
1071  !-------
1072 
1073  t205 = t100*t16
1074  t206 = 0.1e1_dp/t205
1075  t210 = 0.26e2_dp/0.9e1_dp*t99*t206*t14*t104
1076  t214 = 0.2e1_dp/0.3e1_dp*t99*t103*t5*t153
1077  t215 = c**2
1078  t218 = 0.1e1_dp/t1/t205
1079  t222 = t12*t215*t218*t14*t104/0.9e1_dp
1080  t228 = 0.2e1_dp/0.9e1_dp*t12*c*t218*t14*t86*t109
1081  t232 = 0.26e2_dp/0.9e1_dp*t15*t86*t206*t109
1082  t236 = 0.2e1_dp/0.3e1_dp*t15*t108*t153*d
1083  t238 = 0.1e1_dp/t85/t4
1084  t243 = 0.2e1_dp/0.9e1_dp*t15*t238*t218*t66*t124
1085  t249 = 0.154e3_dp/0.9e1_dp*t15*t5/t18/t101*t66
1086  t252 = 0.22e2_dp/0.3e1_dp*t15*t115*t153
1087  t253 = t6*t140
1088  t255 = t87*t92
1089  t257 = c*t90
1090  t260 = d*t90*t5
1091  t265 = t124/t18/t16*t86
1092  t268 = 0.1e1_dp/t17
1093  t270 = t124*d*t268*t238
1094  t304 = t15*t21*(t7*((-0.14e2_dp/0.81e2_dp*t257 - &
1095  0.14e2_dp/0.81e2_dp*t260 + 0.7e1_dp/0.27e2_dp* &
1096  t265 - 0.7e1_dp/0.81e2_dp*t270)*t40 - (-0.2e1_dp/ &
1097  0.81e2_dp*t257 - 0.2e1_dp/0.81e2_dp*t260 + t265/ &
1098  0.27e2_dp - t270/0.81e2_dp)*t47 - (0.4e1_dp/ &
1099  0.9e1_dp*t257 + 0.4e1_dp/0.9e1_dp*t260 - 0.2e1_dp &
1100  &/0.3e1_dp*t265 + 0.2e1_dp/0.9e1_dp*t270)*t54/ &
1101  0.9e1_dp - 0.2e1_dp/0.9e1_dp*t135*t142 - t49*&
1102  & (0.2e1_dp*my_rhoa*t268*t45 + 0.2e1_dp*my_rhob* &
1103  t268*t46)/0.9e1_dp) - 0.4e1_dp/0.3e1_dp*t40 + &
1104  0.4e1_dp/0.3e1_dp*t46 + 0.4e1_dp/0.3e1_dp*t45)
1105  t310 = 0.40e2_dp/0.9e1_dp*t88*my_rhob/t1/t17*d
1106  t313 = my_rhob*t20
1107  t316 = 0.8e1_dp/0.9e1_dp*a*t238*my_rhoa*t313*t124
1108  t319 = 0.8e1_dp*t6*t7*t268
1109  t322 = t99*t103*t5*t82
1110  t326 = t15*t108*t82*d
1111  t329 = t15*t115*t82
1112  t332 = t135*t8
1113  t334 = t49*t95
1114  t341 = t15*t21*(my_rhob*t145 + t7*(-t332*t45/ &
1115  0.9e1_dp + t334*t45/0.9e1_dp))
1116 
1117  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1118  e_ra_ra(ii) = e_ra_ra(ii) &
1119  + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
1120  t252 + 0.8e1_dp*t253 - 0.8e1_dp/0.3e1_dp*t255 - &
1121  t304 + t310 - t316 - t319 - 0.2e1_dp/0.3e1_dp*t322 - &
1122  0.2e1_dp/0.3e1_dp*t326 + 0.22e2_dp/0.3e1_dp*t329&
1123  & - 0.2e1_dp*t341 - t15*t21*(0.2e1_dp*my_rhob* &
1124  t78 + 0.320e3_dp/0.9e1_dp*t72*my_rhob*t24 - &
1125  0.2e1_dp*t46))*sc
1126  END IF
1127 
1128  t354 = t99*t103*t5*t168
1129  t356 = t6*t138
1130  t360 = t87*my_rhoa*t90*d
1131  t363 = t15*t115*t168
1132  t373 = t15*t21*(my_rhoa*t145 + t7*(-t332*t46/ &
1133  0.9e1_dp + t334*t46/0.9e1_dp))
1134  t376 = t15*t108*t168*d
1135 
1136  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1137  e_rb_rb(ii) = e_rb_rb(ii) &
1138  + (t210 - t214 - t222 - t228 + t232 - t236 - t243 - t249 + &
1139  t252 - t304 + t310 - t316 - t319 + 0.8e1_dp*t356 - &
1140  0.8e1_dp/0.3e1_dp*t360 + 0.22e2_dp/0.3e1_dp* &
1141  t363 - 0.2e1_dp*t373 - 0.2e1_dp/0.3e1_dp*t354 - &
1142  0.2e1_dp/0.3e1_dp*t376 - t15*t21*(0.2e1_dp* &
1143  my_rhoa*t164 + 0.320e3_dp/0.9e1_dp*my_rhoa* &
1144  t159*t24 - 0.2e1_dp*t45))*sc
1145  END IF
1146 
1147  t381 = -t354/0.3e1_dp + 0.4e1_dp*t356 - 0.4e1_dp/0.3e1_dp&
1148  & *t360 + 0.11e2_dp/0.3e1_dp*t363 - t373 - t341 - &
1149  t376/0.3e1_dp + t310 - 0.4e1_dp*t6*t8 + 0.4e1_dp* &
1150  t253 + t210 - t214 - t222
1151  t391 = -t228 + t232 - t236 - t243 - t249 + t252 - 0.4e1_dp/ &
1152  0.3e1_dp*t255 - t304 - t316 - t319 - t322/0.3e1_dp - &
1153  t326/0.3e1_dp + 0.11e2_dp/0.3e1_dp*t329 - t15* &
1154  t21*(t35 + t41 - t48 - t56 + my_rhob*t164 + my_rhoa &
1155  &*t78)
1156 
1157  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1158  e_ra_rb(ii) = e_ra_rb(ii) &
1159  + (t381 + t391)*sc
1160  END IF
1161 
1162  t408 = t12*t14*t5
1163  t415 = t99*t103*t5*t176/0.3e1_dp
1164  t419 = t15*t108*t176*d/0.3e1_dp
1165  t422 = 0.11e2_dp/0.3e1_dp*t15*t115*t176
1166  t430 = t15*t21*(0.2e1_dp*t7*t130*my_ndrho - 0.8e1_dp &
1167  &/0.3e1_dp*my_rho*my_ndrho)
1168 
1169  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1170  e_ndr_ra(ii) = e_ndr_ra(ii) &
1171  - (0.2e1_dp*t408*t313*t171 + t415 + t419 - t422 + &
1172  t430)*sc
1173  e_ndr_rb(ii) = e_ndr_rb(ii) &
1174  - (0.2e1_dp*t408*t20*my_rhoa*t171 + t415 + t419 - &
1175  t422 + t430)*sc
1176  END IF
1177 
1178  t445 = t99*t103*t5*t189/0.3e1_dp
1179  t449 = t15*t108*t189*d/0.3e1_dp
1180  t452 = 0.11e2_dp/0.3e1_dp*t15*t115*t189
1181  t467 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhoa - &
1182  0.2e1_dp/0.9e1_dp*t135*my_rhoa*t182 + 0.2e1_dp/ &
1183  0.9e1_dp*t181*t95*my_ndrhoa) + 0.8e1_dp/0.3e1_dp&
1184  & *my_rho*my_ndrhoa)
1185 
1186  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1187  e_ndra_ra(ii) = e_ndra_ra(ii) &
1188  - (t15*t21*(my_rhob*t185 - 0.2e1_dp/0.9e1_dp*t7&
1189  & *t75*my_ndrhoa) + t445 + t449 - t452 + t467)*sc
1190  e_ndra_rb(ii) = e_ndra_rb(ii) &
1191  - (t15*t21*(my_rhoa*t185 - 0.4e1_dp*my_rhob* &
1192  my_ndrhoa) + t445 + t449 - t452 + t467)*sc
1193  END IF
1194 
1195  t483 = t99*t103*t5*t202/0.3e1_dp
1196  t487 = t15*t108*t202*d/0.3e1_dp
1197  t490 = 0.11e2_dp/0.3e1_dp*t15*t115*t202
1198  t505 = t15*t21*(t7*(-0.2e1_dp*t132*my_ndrhob - &
1199  0.2e1_dp/0.9e1_dp*t135*my_rhob*t195 + 0.2e1_dp/ &
1200  0.9e1_dp*t194*t95*my_ndrhob) + 0.8e1_dp/0.3e1_dp&
1201  & *my_rho*my_ndrhob)
1202 
1203  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1204  e_ndrb_ra(ii) = e_ndrb_ra(ii) &
1205  - (t15*t21*(my_rhob*t198 - 0.4e1_dp*my_rhoa* &
1206  my_ndrhob) + t483 + t487 - t490 + t505)*sc
1207  e_ndrb_rb(ii) = e_ndrb_rb(ii) &
1208  - (t15*t21*(my_rhoa*t198 - 0.2e1_dp/0.9e1_dp*t7&
1209  & *t75*my_ndrhob) + t483 + t487 - t490 + t505)*sc
1210  END IF
1211 
1212  t515 = 0.4e1_dp/0.3e1_dp*t16
1213 
1214  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1215  e_ndr_ndr(ii) = e_ndr_ndr(ii) &
1216  - (t15*t21*(0.2e1_dp*t7*t39 - t515))*sc
1217  END IF
1218 
1219  t519 = t13/0.9e1_dp
1220  t520 = t37/0.9e1_dp
1221 
1222  IF (grad_deriv >= 2 .OR. grad_deriv == -2) THEN
1223  e_ndra_ndra(ii) = e_ndra_ndra(ii) &
1224  - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1225  &/0.9e1_dp*t181*t8) + t515 - 0.2e1_dp*t29))*sc
1226 
1227  e_ndrb_ndrb(ii) = e_ndrb_ndrb(ii) &
1228  - (t15*t21*(t7*(-0.5e1_dp + t519 + t520 - 0.2e1_dp &
1229  &/0.9e1_dp*t194*t8) + t515 - 0.2e1_dp*t25))*sc
1230  END IF
1231  END IF
1232  END DO
1233 !$OMP END DO
1234 
1235  END SUBROUTINE lyp_lsd_calc
1236 
1237 END MODULE xc_lyp
bibliography
collects all references to literature in CP2K as new algorithms / method are included from literature...
Definition: bibliography.F:28
bibliography::lee1988
integer, save, public lee1988
Definition: bibliography.F:43
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_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_lyp
calculates the lyp correlation functional
Definition: xc_lyp.F:14
xc_lyp::lyp_lda_info
subroutine, public lyp_lda_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition: xc_lyp.F:59
xc_lyp::lyp_lsd_eval
subroutine, public lyp_lsd_eval(rho_set, deriv_set, grad_deriv, lyp_params)
evaluates the becke 88 exchange functional for lsd
Definition: xc_lyp.F:727
xc_lyp::lyp_lsd_info
subroutine, public lyp_lsd_info(reference, shortform, needs, max_deriv)
return various information on the functional
Definition: xc_lyp.F:90
xc_lyp::lyp_lda_eval
subroutine, public lyp_lda_eval(rho_set, deriv_set, grad_deriv, lyp_params)
evaluates the lyp correlation functional for lda
Definition: xc_lyp.F:124
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