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xc_perdew86.F
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1 !--------------------------------------------------------------------------------------------------!
2 ! CP2K: A general program to perform molecular dynamics simulations !
3 ! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
4 ! !
5 ! SPDX-License-Identifier: GPL-2.0-or-later !
6 !--------------------------------------------------------------------------------------------------!
7 
8 ! **************************************************************************************************
9 !> \brief Calculate the Perdew Correlation from 1986
10 !> \par History
11 !> JGH (26.02.2003) : OpenMP enabled
12 !> fawzi (04.2004) : adapted to the new xc interface
13 !> \author JGH (03.03.2002)
14 ! **************************************************************************************************
15 MODULE xc_perdew86
16 
17  USE input_section_types, ONLY: section_vals_type
18  USE kinds, ONLY: dp
19  USE xc_derivative_desc, ONLY: deriv_norm_drho,&
20  deriv_rho
21  USE xc_derivative_set_types, ONLY: xc_derivative_set_type,&
22  xc_dset_get_derivative
23  USE xc_derivative_types, ONLY: xc_derivative_get,&
24  xc_derivative_type
25  USE xc_functionals_utilities, ONLY: calc_rs_pw,&
26  set_util
27  USE xc_input_constants, ONLY: pz_orig
28  USE xc_perdew_zunger, ONLY: pz_lda_eval
29  USE xc_rho_cflags_types, ONLY: xc_rho_cflags_type
30  USE xc_rho_set_types, ONLY: xc_rho_set_get,&
31  xc_rho_set_type
32 #include "../base/base_uses.f90"
33 
34  IMPLICIT NONE
35 
36  PRIVATE
37 
38 ! *** Global parameters ***
39 
40  REAL(KIND=dp), PARAMETER :: pi = 3.14159265358979323846264338_dp
41  REAL(KIND=dp), PARAMETER :: f13 = 1.0_dp/3.0_dp, &
42  f23 = 2.0_dp*f13, &
43  f43 = 4.0_dp*f13, &
44  f53 = 5.0_dp*f13, &
45  f76 = 7.0_dp/6.0_dp, &
46  frs = 1.6119919540164696407_dp, &
47  fpe = 0.19199566167376364_dp
48 
49  PUBLIC :: p86_lda_info, p86_lda_eval
50 
51  REAL(KIND=dp) :: eps_rho
52  LOGICAL :: debug_flag
53 
54  REAL(KIND=dp), PARAMETER :: a = 0.023266_dp, &
55  b = 7.389e-6_dp, &
56  c = 8.723_dp, &
57  d = 0.472_dp, &
58  pc1 = 0.001667_dp, &
59  pc2 = 0.002568_dp, &
60  pci = pc1 + pc2
61  CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'xc_perdew86'
62 
63 CONTAINS
64 
65 ! **************************************************************************************************
66 !> \brief ...
67 !> \param cutoff ...
68 !> \param debug ...
69 ! **************************************************************************************************
70  SUBROUTINE p86_init(cutoff, debug)
71 
72  REAL(KIND=dp), INTENT(IN) :: cutoff
73  LOGICAL, INTENT(IN), OPTIONAL :: debug
74 
75  eps_rho = cutoff
76  CALL set_util(cutoff)
77 
78  IF (PRESENT(debug)) THEN
79  debug_flag = debug
80  ELSE
81  debug_flag = .false.
82  END IF
83 
84  END SUBROUTINE p86_init
85 
86 ! **************************************************************************************************
87 !> \brief ...
88 !> \param reference ...
89 !> \param shortform ...
90 !> \param needs ...
91 !> \param max_deriv ...
92 ! **************************************************************************************************
93  SUBROUTINE p86_lda_info(reference, shortform, needs, max_deriv)
94  CHARACTER(LEN=*), INTENT(OUT), OPTIONAL :: reference, shortform
95  TYPE(xc_rho_cflags_type), INTENT(inout), OPTIONAL :: needs
96  INTEGER, INTENT(out), OPTIONAL :: max_deriv
97 
98  IF (PRESENT(reference)) THEN
99  reference = "J. P. Perdew, Phys. Rev. B, 33, 8822 (1986) {LDA version}"
100  END IF
101  IF (PRESENT(shortform)) THEN
102  shortform = "Perdew 1986 correlation energy functional {LDA}"
103  END IF
104  IF (PRESENT(needs)) THEN
105  needs%rho = .true.
106  needs%norm_drho = .true.
107  END IF
108  IF (PRESENT(max_deriv)) max_deriv = 3
109 
110  END SUBROUTINE p86_lda_info
111 
112 ! **************************************************************************************************
113 !> \brief ...
114 !> \param rho_set ...
115 !> \param deriv_set ...
116 !> \param order ...
117 !> \param p86_params ...
118 ! **************************************************************************************************
119  SUBROUTINE p86_lda_eval(rho_set, deriv_set, order, p86_params)
120 
121  TYPE(xc_rho_set_type), INTENT(IN) :: rho_set
122  TYPE(xc_derivative_set_type), INTENT(IN) :: deriv_set
123  INTEGER, INTENT(IN) :: order
124  TYPE(section_vals_type), POINTER :: p86_params
125 
126  CHARACTER(len=*), PARAMETER :: routinen = 'p86_lda_eval'
127 
128  INTEGER :: handle, m, npoints
129  INTEGER, DIMENSION(2, 3) :: bo
130  REAL(kind=dp) :: drho_cutoff, rho_cutoff
131  REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: rs
132  REAL(kind=dp), CONTIGUOUS, DIMENSION(:, :, :), POINTER :: e_0, e_ndrho, e_ndrho_ndrho, &
133  e_ndrho_ndrho_ndrho, e_rho, e_rho_ndrho, e_rho_ndrho_ndrho, e_rho_rho, e_rho_rho_ndrho, &
134  e_rho_rho_rho, grho, rho
135  TYPE(xc_derivative_type), POINTER :: deriv
136 
137  CALL timeset(routinen, handle)
138  NULLIFY (rho, e_0, e_rho, e_ndrho, &
139  e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
140  e_rho_rho_rho, e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho)
141 
142  ! calculate the perdew_zunger correlation
143  CALL pz_lda_eval(pz_orig, rho_set, deriv_set, order, p86_params)
144 
145  CALL xc_rho_set_get(rho_set, rho=rho, &
146  norm_drho=grho, local_bounds=bo, rho_cutoff=rho_cutoff, &
147  drho_cutoff=drho_cutoff)
148  npoints = (bo(2, 1) - bo(1, 1) + 1)*(bo(2, 2) - bo(1, 2) + 1)*(bo(2, 3) - bo(1, 3) + 1)
149  CALL p86_init(rho_cutoff)
150  m = abs(order)
151 
152  ALLOCATE (rs(npoints))
153 
154  CALL calc_rs_pw(rho, rs, npoints)
155  IF (order >= 0) THEN
156  deriv => xc_dset_get_derivative(deriv_set, [INTEGER::], &
157  allocate_deriv=.true.)
158  CALL xc_derivative_get(deriv, deriv_data=e_0)
159 
160  CALL p86_u_0(rho, rs, grho, e_0, npoints)
161  END IF
162  IF (order >= 1 .OR. order == -1) THEN
163  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho], &
164  allocate_deriv=.true.)
165  CALL xc_derivative_get(deriv, deriv_data=e_rho)
166  deriv => xc_dset_get_derivative(deriv_set, [deriv_norm_drho], &
167  allocate_deriv=.true.)
168  CALL xc_derivative_get(deriv, deriv_data=e_ndrho)
169 
170  CALL p86_u_1(rho, grho, rs, e_rho, &
171  e_ndrho, npoints)
172  END IF
173  IF (order >= 2 .OR. order == -2) THEN
174  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho], &
175  allocate_deriv=.true.)
176  CALL xc_derivative_get(deriv, deriv_data=e_rho_rho)
177  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_norm_drho], &
178  allocate_deriv=.true.)
179  CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho)
180  deriv => xc_dset_get_derivative(deriv_set, &
181  [deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
182  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho)
183 
184  CALL p86_u_2(rho, grho, rs, e_rho_rho, &
185  e_rho_ndrho, e_ndrho_ndrho, npoints)
186  END IF
187  IF (order >= 3 .OR. order == -3) THEN
188  deriv => xc_dset_get_derivative(deriv_set, [deriv_rho, deriv_rho, deriv_rho], &
189  allocate_deriv=.true.)
190  CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_rho)
191  deriv => xc_dset_get_derivative(deriv_set, &
192  [deriv_rho, deriv_rho, deriv_norm_drho], allocate_deriv=.true.)
193  CALL xc_derivative_get(deriv, deriv_data=e_rho_rho_ndrho)
194  deriv => xc_dset_get_derivative(deriv_set, &
195  [deriv_rho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
196  CALL xc_derivative_get(deriv, deriv_data=e_rho_ndrho_ndrho)
197  deriv => xc_dset_get_derivative(deriv_set, &
198  [deriv_norm_drho, deriv_norm_drho, deriv_norm_drho], allocate_deriv=.true.)
199  CALL xc_derivative_get(deriv, deriv_data=e_ndrho_ndrho_ndrho)
200 
201  CALL p86_u_3(rho, grho, rs, e_rho_rho_rho, &
202  e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, &
203  npoints)
204  END IF
205  IF (order > 3 .OR. order < -3) THEN
206  cpabort("derivatives bigger than 3 not implemented")
207  END IF
208  DEALLOCATE (rs)
209  CALL timestop(handle)
210 
211  END SUBROUTINE p86_lda_eval
212 
213 ! **************************************************************************************************
214 !> \brief ...
215 !> \param rho ...
216 !> \param rs ...
217 !> \param grho ...
218 !> \param e_0 ...
219 !> \param npoints ...
220 ! **************************************************************************************************
221  SUBROUTINE p86_u_0(rho, rs, grho, e_0, npoints)
222 
223  REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, rs, grho
224  REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_0
225  INTEGER, INTENT(in) :: npoints
226 
227  INTEGER :: ip
228  REAL(kind=dp) :: cr, ep, g, or, phi, r, x
229 
230 !$OMP PARALLEL DO PRIVATE(ip,g,r,x,or,cr,phi,ep) DEFAULT(NONE)&
231 !$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_0)
232  DO ip = 1, npoints
233 
234  IF (rho(ip) > eps_rho) THEN
235  g = grho(ip)
236  r = rs(ip)
237  x = r*frs
238  or = 1.0_dp/rho(ip)
239  cr = pc1 + (pc2 + a*r + b*r*r)/(1.0_dp + c*r + d*r*r + 1.e4_dp*b*r*r*r)
240  phi = fpe*pci/cr*g*sqrt(x)*or
241  ep = exp(-phi)
242  e_0(ip) = e_0(ip) + x*or*g*g*cr*ep
243  END IF
244 
245  END DO
246 
247  END SUBROUTINE p86_u_0
248 
249 ! **************************************************************************************************
250 !> \brief ...
251 !> \param rho ...
252 !> \param grho ...
253 !> \param rs ...
254 !> \param e_rho ...
255 !> \param e_ndrho ...
256 !> \param npoints ...
257 ! **************************************************************************************************
258  SUBROUTINE p86_u_1(rho, grho, rs, e_rho, e_ndrho, npoints)
259 
260  REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, rs
261  REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho, e_ndrho
262  INTEGER, INTENT(in) :: npoints
263 
264  INTEGER :: ip
265  REAL(kind=dp) :: cr, dcr, dphig, dphir, dpv, dq, ep, ff, &
266  g, or, p, phi, q, r, x
267 
268 !$OMP PARALLEL DO PRIVATE(ip,g,r,x,or,p,dpv,q,dq,cr,dcr,dphig,phi,dphir,ep,ff) DEFAULT(NONE)&
269 !$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_rho,e_ndrho)
270  DO ip = 1, npoints
271 
272  IF (rho(ip) > eps_rho) THEN
273  g = grho(ip)
274  r = rs(ip)
275  x = r*frs
276  or = 1.0_dp/rho(ip)
277  p = pc2 + a*r + b*r*r
278  dpv = a + 2.0_dp*b*r
279  q = 1.0_dp + c*r + d*r*r + 1.e4_dp*b*r*r*r
280  dq = c + 2.0_dp*d*r + 3.e4_dp*b*r*r
281  cr = pc1 + p/q
282  dcr = (dpv*q - p*dq)/(q*q)*(-f13*r*or)
283  dphig = fpe*pci/cr*sqrt(x)*or
284  phi = dphig*g
285  dphir = -phi*(dcr/cr + f76*or)
286  ep = exp(-phi)
287  ff = x*or*g*ep
288  e_rho(ip) = e_rho(ip) + ff*g*dcr - ff*g*cr*dphir - ff*g*cr*f43*or
289  e_ndrho(ip) = e_ndrho(ip) + ff*cr*(2.0_dp - g*dphig)
290  END IF
291 
292  END DO
293 
294  END SUBROUTINE p86_u_1
295 
296 ! **************************************************************************************************
297 !> \brief ...
298 !> \param rho ...
299 !> \param grho ...
300 !> \param rs ...
301 !> \param e_rho_rho ...
302 !> \param e_rho_ndrho ...
303 !> \param e_ndrho_ndrho ...
304 !> \param npoints ...
305 ! **************************************************************************************************
306  SUBROUTINE p86_u_2(rho, grho, rs, e_rho_rho, e_rho_ndrho, e_ndrho_ndrho, &
307  npoints)
308 
309  REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, rs
310  REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho_rho, e_rho_ndrho, e_ndrho_ndrho
311  INTEGER, INTENT(in) :: npoints
312 
313  INTEGER :: ip
314  REAL(kind=dp) :: cr, d2cr, d2p, d2phir, d2q, dcr, dphig, &
315  dphigr, dphir, dpv, dq, ep, g, or, p, &
316  phi, q, r, x
317 
318 !$OMP PARALLEL DO PRIVATE(ip,x,r,cr,phi,ep,g,or,p,q,dpv,dq,dphir,dcr) &
319 !$OMP PRIVATE(dphig,dphigr,d2phir,d2cr,d2p,d2q) DEFAULT(NONE) &
320 !$OMP SHARED(npoints,rho,eps_rho,grho,rs,e_rho_rho,e_rho_ndrho,e_ndrho_ndrho)
321  DO ip = 1, npoints
322 
323  IF (rho(ip) > eps_rho) THEN
324  g = grho(ip)
325  r = rs(ip)
326  x = r*frs
327  or = 1.0_dp/rho(ip)
328  p = pc2 + a*r + b*r*r
329  dpv = a + 2.0_dp*b*r
330  d2p = 2.0_dp*b
331  q = 1.0_dp + c*r + d*r*r + 1.e4_dp*b*r*r*r
332  dq = c + 2.0_dp*d*r + 3.e4_dp*b*r*r
333  d2q = 2.0_dp*d + 6.e4_dp*b*r
334  cr = pc1 + p/q
335  dcr = (dpv*q - p*dq)/(q*q)*(-f13*r*or)
336  d2cr = (d2p*q*q - p*q*d2q - 2*dpv*dq*q + 2*p*dq*dq)/(q*q*q)*(f13*r*or)**2 + &
337  (dpv*q - p*dq)/(q*q)*f13*f43*r*or*or
338  dphig = fpe*pci/cr*sqrt(x)*or
339  phi = dphig*g
340  dphir = -phi*(dcr/cr + f76*or)
341  d2phir = -dphir*(dcr/cr + f76*or) - &
342  phi*((d2cr*cr - dcr*dcr)/(cr*cr) - f76*or*or)
343  dphigr = -dphig*(dcr/cr + f76*or)
344  ep = exp(-phi)
345  e_rho_rho(ip) = e_rho_rho(ip) + x*or*ep*g*g* &
346  (-f43*or*dcr + d2cr - dcr*dphir + &
347  f43*or*cr*dphir - dcr*dphir - cr*d2phir + cr*dphir*dphir + &
348  f43*or*(7.*f13*or*cr - dcr + cr*dphir))
349  e_rho_ndrho(ip) = e_rho_ndrho(ip) + x*or*ep*g* &
350  (-2*f43*cr*or + 2*dcr - 2*cr*dphir + f43*or*g*cr*dphig - &
351  g*dcr*dphig + g*cr*dphir*dphig - g*cr*dphigr)
352  e_ndrho_ndrho(ip) = e_ndrho_ndrho(ip) + x*or*ep*cr* &
353  (2.0_dp - 4.0_dp*g*dphig + g*g*dphig*dphig)
354  END IF
355 
356  END DO
357 
358  END SUBROUTINE p86_u_2
359 
360 ! **************************************************************************************************
361 !> \brief ...
362 !> \param rho ...
363 !> \param grho ...
364 !> \param rs ...
365 !> \param e_rho_rho_rho ...
366 !> \param e_rho_rho_ndrho ...
367 !> \param e_rho_ndrho_ndrho ...
368 !> \param e_ndrho_ndrho_ndrho ...
369 !> \param npoints ...
370 ! **************************************************************************************************
371  SUBROUTINE p86_u_3(rho, grho, rs, e_rho_rho_rho, &
372  e_rho_rho_ndrho, e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho, &
373  npoints)
374 
375  REAL(kind=dp), DIMENSION(*), INTENT(IN) :: rho, grho, rs
376  REAL(kind=dp), DIMENSION(*), INTENT(INOUT) :: e_rho_rho_rho, e_rho_rho_ndrho, &
377  e_rho_ndrho_ndrho, e_ndrho_ndrho_ndrho
378  INTEGER, INTENT(in) :: npoints
379 
380  INTEGER :: ip
381  REAL(kind=dp) :: cr, d2cr, d2p, d2phir, d2phirg, d2pq, d2q, d2z, d3cr, d3phir, d3pq, d3q, &
382  d3z, dcr, dphig, dphigr, dphir, dpq, dpv, dq, dz, ep, g, or, oz, p, phi, pq, q, r, x
383 
384 !$OMP PARALLEL DO PRIVATE(ip,x, r, cr, phi, ep, g, or, p, q, dpv, dq, dphir, dcr, dphig) &
385 !$OMP PRIVATE(dphigr, d2phir, d3phir, d2cr, d3cr, d2p, d2q, d2phirg, d3q) &
386 !$OMP PRIVATE(pq, dpq, d2pq, d3pq, oz, dz, d2z, d3z) DEFAULT(NONE) &
387 !$OMP SHARED(npoints,rho,eps_rho,grho,e_rho_rho_rho,e_rho_rho_ndrho,e_rho_ndrho_ndrho,e_ndrho_ndrho_ndrho)
388  DO ip = 1, npoints
389 
390  IF (rho(ip) > eps_rho) THEN
391  g = grho(ip)
392  r = rs(ip)
393  x = r*frs
394  or = 1.0_dp/rho(ip)
395  p = pc2 + a*r + b*r*r
396  dpv = a + 2.0_dp*b*r
397  d2p = 2.0_dp*b
398  q = 1.0_dp + c*r + d*r*r + 1.e4_dp*b*r*r*r
399  dq = c + 2.0_dp*d*r + 3.e4_dp*b*r*r
400  d2q = 2.0_dp*d + 6.e4*b*r
401  d3q = 6.e4*b
402  pq = p/q
403  dpq = (dpv*q - p*dq)/(q*q)
404  d2pq = (d2p*q*q - 2*dpv*dq*q + 2*p*dq*dq - p*d2q*q)/(q*q*q)
405  d3pq = -(3*d2p*dq*q*q - 6*dpv*dq*dq*q + 3*dpv*d2q*q*q + 6*p*dq*dq*dq - 6*p*dq*d2q*q &
406  + p*d3q*q*q)/(q*q*q*q)
407  cr = pc1 + pq
408  dcr = dpq*(-f13*r*or)
409  d2cr = d2pq*f13*f13*r*r*or*or + dpq*f13*f43*r*or*or
410  d3cr = d3pq*(-f13*r*or)**3 + 3*d2pq*(-f13*f13*f43*r*r*or*or*or) + &
411  dpq*(-f13*f43*f13*7*r*or*or*or)
412  oz = sqrt(x)*or/cr
413  dz = dcr/cr + f76*or
414  d2z = d2cr/cr + 2*f76*dcr/cr*or + f76/6.*or*or
415  d3z = d3cr/cr + 3*f76*d2cr/cr*or + 3*f76/6.*dcr/cr*or*or - 5*f76/36.*or*or*or
416  dphig = fpe*pci*oz
417  phi = dphig*g
418  dphir = -phi*dz
419  dphigr = -dphig*dz
420  d2phir = -phi*(d2z - 2*dz*dz)
421  d3phir = -phi*(d3z - 6*d2z*dz + 6*dz*dz*dz)
422  d2phirg = -dphigr*dz - &
423  dphig*((d2cr*cr - dcr*dcr)/(cr*cr) - f76*or*or)
424  ep = exp(-phi)
425  e_rho_rho_rho(ip) = e_rho_rho_rho(ip) &
426  + g*g*x*or*ep*(-280./27.*or*or*or*cr + 3*28./9.*or*or*dcr + &
427  3*28./9.*or*or*cr*(-dphir) - 4*or*d2cr - 8*or*dcr*(-dphir) - &
428  4*or*cr*(-d2phir + dphir*dphir) + d3cr + 3*d2cr*(-dphir) + &
429  3*dcr*(-d2phir + dphir*dphir) + cr*(-d3phir + 3*dphir*d2phir - &
430  dphir**3))
431  e_rho_rho_ndrho(ip) = e_rho_rho_ndrho(ip) &
432  + 2.*x*or*ep*g*(-f43*or*dcr + d2cr - dcr*dphir + &
433  f43*or*cr*dphir - dcr*dphir - cr*d2phir + cr*dphir*dphir + &
434  f43*or*(7.*f13*or*cr - dcr + cr*dphir)) - &
435  dphig*x*or*ep*g*g*(-f43*or*dcr + d2cr - dcr*dphir + &
436  f43*or*cr*dphir - dcr*dphir - cr*d2phir + cr*dphir*dphir + &
437  f43*or*(7.*f13*or*cr - dcr + cr*dphir)) + &
438  x*or*ep*g*g*(-dcr*dphigr + f43*or*cr*dphigr - dcr*dphigr - cr*d2phirg + &
439  2.*cr*dphigr*dphir + f43*or*cr*dphigr)
440  e_rho_ndrho_ndrho(ip) = e_rho_ndrho_ndrho(ip) &
441  + x*or*ep*(-2*f43*cr*or + 2*dcr - 2*cr*dphir + f43*or*g*cr*dphig - &
442  g*dcr*dphig + g*cr*dphir*dphig - g*cr*dphigr) + &
443  x*or*ep*g*(-2*cr*dphigr + f43*or*cr*dphig - &
444  dcr*dphig + cr*dphir*dphig + g*cr*dphigr*dphig - cr*dphigr) - &
445  x*or*ep*g*dphig*(-2*f43*cr*or + 2*dcr - 2*cr*dphir + f43*or*g*cr*dphig - &
446  g*dcr*dphig + g*cr*dphir*dphig - g*cr*dphigr)
447  e_ndrho_ndrho_ndrho(ip) = e_ndrho_ndrho_ndrho(ip) &
448  + x*or*ep*cr*dphig*(-6.0_dp + 6.0_dp*g*dphig - g*g*dphig*dphig)
449  END IF
450 
451  END DO
452 
453  END SUBROUTINE p86_u_3
454 
455 END MODULE xc_perdew86
456 
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
kinds
Defines the basic variable types.
Definition: kinds.F:23
kinds::dp
integer, parameter, public dp
Definition: kinds.F:34
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_rho
integer, parameter, public deriv_rho
Definition: xc_derivative_desc.F:35
xc_derivative_set_types
represent a group ofunctional derivatives
Definition: xc_derivative_set_types.F:14
xc_derivative_set_types::xc_dset_get_derivative
type(xc_derivative_type) function, pointer, public xc_dset_get_derivative(derivative_set, description, allocate_deriv)
returns the requested xc_derivative
Definition: xc_derivative_set_types.F:66
xc_derivative_types
Provides types for the management of the xc-functionals and their derivatives.
Definition: xc_derivative_types.F:12
xc_derivative_types::xc_derivative_get
subroutine, public xc_derivative_get(deriv, split_desc, order, deriv_data, accept_null_data)
returns various information on the given derivative
Definition: xc_derivative_types.F:103
xc_functionals_utilities
Utility routines for the functional calculations.
Definition: xc_functionals_utilities.F:15
xc_functionals_utilities::calc_rs_pw
subroutine, public calc_rs_pw(rho, rs, n)
...
Definition: xc_functionals_utilities.F:117
xc_functionals_utilities::set_util
subroutine, public set_util(cutoff)
...
Definition: xc_functionals_utilities.F:54
xc_input_constants
input constants for xc
Definition: xc_input_constants.F:10
xc_input_constants::pz_orig
integer, parameter, public pz_orig
Definition: xc_input_constants.F:88
xc_perdew86
Calculate the Perdew Correlation from 1986.
Definition: xc_perdew86.F:15
xc_perdew86::p86_lda_info
subroutine, public p86_lda_info(reference, shortform, needs, max_deriv)
...
Definition: xc_perdew86.F:94
xc_perdew86::p86_lda_eval
subroutine, public p86_lda_eval(rho_set, deriv_set, order, p86_params)
...
Definition: xc_perdew86.F:120
xc_perdew_zunger
Calculate the Perdew-Zunger correlation potential and energy density and ist derivatives with respect...
Definition: xc_perdew_zunger.F:17
xc_perdew_zunger::pz_lda_eval
subroutine, public pz_lda_eval(method, rho_set, deriv_set, order, pz_params)
Calculate the correlation energy and its derivatives wrt to rho (the electron density) up to 3rd orde...
Definition: xc_perdew_zunger.F:137
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