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eri_mme_integrate.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 Minimax-Ewald (MME) method for calculating 2-center and 3-center
10!> electron repulsion integrals (ERI) of periodic systems using a
11!> Hermite Gaussian basis.
12!> The method relies on analytical Fourier transforms of Cartesian and
13!> Hermite Gaussian functions and Poisson summation formula to represent
14!> ERIs as a discrete sum over direct lattice vectors or reciprocal
15!> lattice vectors. The reciprocal space potential 1/G^2 is approximated
16!> by a linear combination of Gaussians employing minimax approximation.
17!> Not yet implemented: 3c ERIs for nonorthogonal cells.
18!> \par History
19!> 2015 09 created
20!> \author Patrick Seewald
21! **************************************************************************************************
22
23MODULE eri_mme_integrate
24 USE ao_util, ONLY: exp_radius
25 USE eri_mme_gaussian, ONLY: hermite_gauss_norm
26 USE eri_mme_lattice_summation, ONLY: &
27 ellipsoid_bounds, eri_mme_2c_get_bounds, eri_mme_2c_get_rads, eri_mme_3c_get_bounds, &
28 eri_mme_3c_get_rads, get_l, pgf_sum_2c_gspace_1d, pgf_sum_2c_gspace_3d, &
29 pgf_sum_2c_rspace_1d, pgf_sum_2c_rspace_3d, pgf_sum_3c_1d, pgf_sum_3c_3d
30 USE eri_mme_types, ONLY: eri_mme_param,&
31 get_minimax_from_cutoff
32 USE kinds, ONLY: dp,&
33 int_8
34 USE mathconstants, ONLY: pi
35 USE orbital_pointers, ONLY: coset,&
36 ncoset
37#include "../base/base_uses.f90"
38
39 IMPLICIT NONE
40
41 PRIVATE
42
43 LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .false.
44
45 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'eri_mme_integrate'
46
47 PUBLIC :: eri_mme_2c_integrate, eri_mme_3c_integrate
48
49CONTAINS
50
51! **************************************************************************************************
52!> \brief Low-level integration routine for 2-center ERIs.
53!> \param param ...
54!> \param la_min ...
55!> \param la_max ...
56!> \param lb_min ...
57!> \param lb_max ...
58!> \param zeta ...
59!> \param zetb ...
60!> \param rab ...
61!> \param hab ...
62!> \param o1 ...
63!> \param o2 ...
64!> \param G_count ...
65!> \param R_count ...
66!> \param normalize calculate integrals w.r.t. normalized Hermite-Gaussians
67!> \param potential use exact potential instead of minimax approx. (for testing only)
68!> \param pot_par potential parameter
69! **************************************************************************************************
70 SUBROUTINE eri_mme_2c_integrate(param, la_min, la_max, lb_min, lb_max, zeta, zetb, rab, &
71 hab, o1, o2, G_count, R_count, normalize, potential, pot_par)
72 TYPE(eri_mme_param), INTENT(IN) :: param
73 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max
74 REAL(kind=dp), INTENT(IN) :: zeta, zetb
75 REAL(kind=dp), DIMENSION(3), INTENT(IN) :: rab
76 REAL(kind=dp), DIMENSION(:, :), INTENT(INOUT) :: hab
77 INTEGER, INTENT(IN) :: o1, o2
78 INTEGER, INTENT(INOUT), OPTIONAL :: g_count, r_count
79 LOGICAL, INTENT(IN), OPTIONAL :: normalize
80 INTEGER, INTENT(IN), OPTIONAL :: potential
81 REAL(kind=dp), INTENT(IN), OPTIONAL :: pot_par
82
83 INTEGER :: ax, ay, az, bx, by, bz, grid, i_aw, &
84 i_xyz, ico, jco, l_max, la, lb, n_aw
85 INTEGER(KIND=int_8), DIMENSION(2) :: n_sum_3d
86 INTEGER(KIND=int_8), DIMENSION(2, 3) :: n_sum_1d
87 INTEGER, DIMENSION(3) :: la_xyz, lb_xyz
88 LOGICAL :: do_g_sum, exact, is_ortho, norm
89 REAL(kind=dp) :: alpha_g, alpha_r, cutoff, g_rad, g_res, &
90 imm, inv_lgth, ixyz, lgth, max_error, &
91 prefac, r_rad, r_res, vol
92 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: s_g_1, s_g_2, s_g_no, s_g_no_h
93 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :, :) :: s_g
94 REAL(kind=dp), DIMENSION(3) :: g_bounds, r_bounds
95 REAL(kind=dp), DIMENSION(3, 3) :: h_inv, hmat
96 REAL(kind=dp), DIMENSION(:), POINTER :: aw
97
98 cpassert(param%is_valid)
99
100 grid = 0
101 CALL eri_mme_2c_get_rads(la_max, lb_max, zeta, zetb, 0.0_dp, param%G_min, param%R_min, param%sum_precision, &
102 g_rad=g_rad)
103 cutoff = g_rad**2/2
104 CALL get_minimax_from_cutoff(param%minimax_grid, cutoff, n_aw, aw, grid)
105
106 cpassert(grid .GT. 0)
107
108 ! cell info
109 h_inv = param%h_inv
110 hmat = param%hmat
111 vol = param%vol
112
113 IF (PRESENT(normalize)) THEN
114 norm = normalize
115 ELSE
116 norm = .false.
117 END IF
118
119 l_max = la_max + lb_max
120
121 IF (PRESENT(potential)) THEN
122 exact = .true.
123 ELSE
124 exact = .false.
125 END IF
126
127 IF (exact) THEN
128 is_ortho = .false.
129 ELSE
130 is_ortho = param%is_ortho
131 END IF
132
133 IF (is_ortho) THEN
134 ALLOCATE (s_g(0:l_max, 3, n_aw))
135 s_g = 0.0_dp
136
137 IF (param%debug) THEN
138 ALLOCATE (s_g_1(0:l_max))
139 ALLOCATE (s_g_2(0:l_max))
140 END IF
141 ELSE
142 ALLOCATE (s_g_no(ncoset(l_max)))
143 s_g_no(:) = 0.0_dp
144 ALLOCATE (s_g_no_h(ncoset(l_max)))
145 END IF
146
147 IF (exact) THEN
148 alpha_g = 0.25_dp/zeta + 0.25_dp/zetb
149 ! resolution for Gaussian width
150 g_res = 0.5_dp*param%G_min
151 r_res = 0.5_dp*param%R_min
152
153 g_rad = exp_radius(l_max, alpha_g, 0.01*param%sum_precision, 1.0_dp, epsabs=g_res)
154 g_bounds(:) = ellipsoid_bounds(g_rad, transpose(hmat)/(2.0_dp*pi))
155 CALL pgf_sum_2c_gspace_3d(s_g_no, l_max, -rab, alpha_g, h_inv, g_bounds, g_rad, vol, potential, pot_par)
156 ELSE
157
158 DO i_aw = 1, n_aw
159
160 CALL eri_mme_2c_get_bounds(hmat, h_inv, vol, is_ortho, param%G_min, param%R_min, la_max, lb_max, &
161 zeta, zetb, aw(i_aw), param%sum_precision, n_sum_1d, n_sum_3d, &
162 g_bounds, g_rad, r_bounds, r_rad)
163 alpha_g = aw(i_aw) + 0.25_dp/zeta + 0.25_dp/zetb
164 alpha_r = 0.25_dp/alpha_g
165 IF (is_ortho) THEN ! orthorhombic cell
166
167 ! 1) precompute Ewald-like sum
168
169 DO i_xyz = 1, 3
170 lgth = abs(hmat(i_xyz, i_xyz))
171 inv_lgth = abs(h_inv(i_xyz, i_xyz))
172
173 ! perform sum in R or G space. Choose the space in which less summands are required for convergence
174 do_g_sum = n_sum_1d(1, i_xyz) < n_sum_1d(2, i_xyz) !G_bounds < R_bounds
175
176 IF (do_g_sum) THEN
177 CALL pgf_sum_2c_gspace_1d(s_g(:, i_xyz, i_aw), -rab(i_xyz), alpha_g, inv_lgth, g_bounds(i_xyz))
178 IF (PRESENT(g_count)) g_count = g_count + 1
179 ELSE
180 CALL pgf_sum_2c_rspace_1d(s_g(:, i_xyz, i_aw), -rab(i_xyz), alpha_r, lgth, r_bounds(i_xyz))
181 IF (PRESENT(r_count)) r_count = r_count + 1
182 END IF
183
184 IF (param%debug) THEN
185 ! check consistency of summation methods
186 CALL pgf_sum_2c_gspace_1d(s_g_1, -rab(i_xyz), alpha_g, inv_lgth, g_bounds(i_xyz))
187 CALL pgf_sum_2c_rspace_1d(s_g_2, -rab(i_xyz), alpha_r, lgth, r_bounds(i_xyz))
188 max_error = maxval(abs(s_g_1 - s_g_2)/(0.5_dp*(abs(s_g_1) + abs(s_g_2)) + 1.0_dp))
189
190 cpassert(max_error .LE. param%debug_delta)
191 END IF
192 END DO
193
194 ELSE ! general cell
195
196 do_g_sum = n_sum_3d(1) < n_sum_3d(2) !PRODUCT(2*R_bounds+1) .GT. PRODUCT(2*G_bounds+1)
197
198 IF (do_g_sum) THEN
199 CALL pgf_sum_2c_gspace_3d(s_g_no_h, l_max, -rab, alpha_g, h_inv, g_bounds, g_rad, vol)
200 IF (PRESENT(g_count)) g_count = g_count + 1
201 ELSE
202 CALL pgf_sum_2c_rspace_3d(s_g_no_h, l_max, -rab, alpha_r, hmat, h_inv, r_bounds, r_rad)
203 IF (PRESENT(r_count)) r_count = r_count + 1
204 END IF
205 s_g_no(:) = s_g_no(:) + aw(n_aw + i_aw)*s_g_no_h
206 END IF
207 END DO
208 END IF
209
210 ! prefactor for integral values (unnormalized Hermite Gaussians)
211 prefac = sqrt(1.0_dp/(zeta*zetb))
212
213 ! 2) Assemble integral values from Ewald sums
214 DO jco = ncoset(lb_min - 1) + 1, ncoset(lb_max)
215 CALL get_l(jco, lb, bx, by, bz)
216 lb_xyz = [bx, by, bz]
217 DO ico = ncoset(la_min - 1) + 1, ncoset(la_max)
218 CALL get_l(ico, la, ax, ay, az)
219 la_xyz = [ax, ay, az]
220 IF (is_ortho) THEN
221 imm = 0.0_dp
222 DO i_aw = 1, n_aw
223 ixyz = 1.0_dp
224 DO i_xyz = 1, 3
225 ixyz = ixyz*s_g(la_xyz(i_xyz) + lb_xyz(i_xyz), i_xyz, i_aw)*prefac
226 END DO
227 imm = imm + aw(n_aw + i_aw)*ixyz
228 END DO
229 ELSE
230 imm = s_g_no(coset(ax + bx, ay + by, az + bz))*prefac**3
231 END IF
232 IF (la + lb .EQ. 0 .AND. .NOT. exact) THEN
233 imm = imm - sum(aw(n_aw + 1:2*n_aw))*prefac**3/vol ! subtracting G = 0 term
234 END IF
235 IF (.NOT. norm) THEN
236 ! rescaling needed due to Hermite Gaussians (such that they can be contracted same way as Cartesian Gaussians)
237 ! and factor of 4 pi**4 (-1)**lb
238 hab(o1 + ico, o2 + jco) = imm*4.0_dp*pi**4/((2.0_dp*zeta)**la*(-2.0_dp*zetb)**lb)
239 ELSE
240 ! same thing for normalized Hermite Gaussians
241 hab(o1 + ico, o2 + jco) = imm*4.0_dp*pi**4*(-1.0_dp)**lb*hermite_gauss_norm(zeta, la_xyz)* &
242 hermite_gauss_norm(zetb, lb_xyz)
243 END IF
244 END DO ! la
245 END DO ! lb
246
247 END SUBROUTINE eri_mme_2c_integrate
248
249! **************************************************************************************************
250!> \brief Low-level integration routine for 3-center ERIs
251!> \param param ...
252!> \param la_min ...
253!> \param la_max ...
254!> \param lb_min ...
255!> \param lb_max ...
256!> \param lc_min ...
257!> \param lc_max ...
258!> \param zeta ...
259!> \param zetb ...
260!> \param zetc ...
261!> \param RA ...
262!> \param RB ...
263!> \param RC ...
264!> \param habc ...
265!> \param o1 ...
266!> \param o2 ...
267!> \param o3 ...
268!> \param GG_count ...
269!> \param GR_count ...
270!> \param RR_count ...
271! **************************************************************************************************
272 SUBROUTINE eri_mme_3c_integrate(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, RA, RB, RC, &
273 habc, o1, o2, o3, GG_count, GR_count, RR_count)
274 TYPE(eri_mme_param), INTENT(IN) :: param
275 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max, lc_min, &
276 lc_max
277 REAL(kind=dp), INTENT(IN) :: zeta, zetb, zetc
278 REAL(kind=dp), DIMENSION(3), INTENT(IN) :: ra, rb, rc
279 REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT) :: habc
280 INTEGER, INTENT(IN) :: o1, o2, o3
281 INTEGER, INTENT(INOUT), OPTIONAL :: gg_count, gr_count, rr_count
282
283 cpassert(param%is_valid)
284 IF (param%is_ortho) THEN
285 CALL eri_mme_3c_integrate_ortho(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, ra, rb, rc, &
286 habc, o1, o2, o3, rr_count)
287
288 ELSE
289 CALL eri_mme_3c_integrate_nonortho(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, ra, rb, rc, &
290 habc, o1, o2, o3, gg_count, gr_count, rr_count)
291
292 END IF
293 END SUBROUTINE eri_mme_3c_integrate
294
295! **************************************************************************************************
296!> \brief ...
297!> \param param ...
298!> \param la_min ...
299!> \param la_max ...
300!> \param lb_min ...
301!> \param lb_max ...
302!> \param lc_min ...
303!> \param lc_max ...
304!> \param zeta ...
305!> \param zetb ...
306!> \param zetc ...
307!> \param RA ...
308!> \param RB ...
309!> \param RC ...
310!> \param habc ...
311!> \param o1 ...
312!> \param o2 ...
313!> \param o3 ...
314!> \param RR_count ...
315! **************************************************************************************************
316 SUBROUTINE eri_mme_3c_integrate_ortho(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, RA, RB, RC, &
317 habc, o1, o2, o3, RR_count)
318 TYPE(eri_mme_param), INTENT(IN) :: param
319 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max, lc_min, &
320 lc_max
321 REAL(kind=dp), INTENT(IN) :: zeta, zetb, zetc
322 REAL(kind=dp), DIMENSION(3), INTENT(IN) :: ra, rb, rc
323 REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT) :: habc
324 INTEGER, INTENT(IN) :: o1, o2, o3
325 INTEGER, INTENT(INOUT), OPTIONAL :: rr_count
326
327 INTEGER :: grid, i_aw, lmax_0, n_aw
328 INTEGER(KIND=int_8), DIMENSION(3) :: n_sum_3d
329 INTEGER(KIND=int_8), DIMENSION(3, 3) :: n_sum_1d
330 REAL(kind=dp) :: alpha_r_0, cutoff, g_res, lgth, prefac, &
331 r_rad_0, r_res, vol
332 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: s_g_0
333 REAL(kind=dp), ALLOCATABLE, &
334 DIMENSION(:, :, :, :, :) :: s_g
335 REAL(kind=dp), DIMENSION(2) :: r_rads_3
336 REAL(kind=dp), DIMENSION(2, 3) :: r_bounds_3
337 REAL(kind=dp), DIMENSION(3) :: g_rads_1, r_rads_2
338 REAL(kind=dp), DIMENSION(3, 3) :: g_bounds_1, h_inv, hmat, r_bounds_2
339 REAL(kind=dp), DIMENSION(:), POINTER :: aw
340
341 grid = 0
342
343 CALL eri_mme_3c_get_rads(la_max, lb_max, lc_max, zeta, zetb, zetc, 0.0_dp, param%G_min, param%R_min, &
344 param%sum_precision, g_rads_1=g_rads_1)
345
346 cutoff = (min(g_rads_1(1), g_rads_1(2) + g_rads_1(3)))**2/2
347
348 CALL get_minimax_from_cutoff(param%minimax_grid, cutoff, n_aw, aw, grid)
349
350 cpassert(grid .GT. 0)
351
352 ! minimax coeffs
353 n_aw = param%minimax_grid(grid)%n_minimax
354 aw => param%minimax_grid(grid)%minimax_aw
355
356 ! cell info
357 h_inv = param%h_inv
358 hmat = param%hmat
359 vol = param%vol
360
361 ! prefactor for integral values (unnormalized Hermite Gaussians)
362 prefac = (zeta*zetb*zetc)**(-1.5_dp)*pi**(11.0_dp/2.0_dp)*4.0_dp
363
364 ! Preparations for G=0 component
365 g_res = 0.5_dp*param%G_min
366 r_res = 0.5_dp*param%R_min
367
368 ALLOCATE (s_g(n_aw, 3, 0:la_max, 0:lb_max, 0:lc_max))
369
370 ! G= 0 components
371 IF (lc_min == 0) THEN
372 ALLOCATE (s_g_0(0:la_max + lb_max, 3))
373
374 alpha_r_0 = zeta*zetb/(zeta + zetb)
375 lmax_0 = la_max + lb_max
376 r_rad_0 = exp_radius(lmax_0, alpha_r_0, param%sum_precision, 1.0_dp, epsabs=r_res)
377
378 lgth = abs(hmat(1, 1))
379 CALL pgf_sum_2c_rspace_1d(s_g_0(:, 1), rb(1) - ra(1), alpha_r_0, lgth, r_rad_0/lgth)
380 lgth = abs(hmat(2, 2))
381 CALL pgf_sum_2c_rspace_1d(s_g_0(:, 2), rb(2) - ra(2), alpha_r_0, lgth, r_rad_0/lgth)
382 lgth = abs(hmat(3, 3))
383 CALL pgf_sum_2c_rspace_1d(s_g_0(:, 3), rb(3) - ra(3), alpha_r_0, lgth, r_rad_0/lgth)
384 END IF
385
386 DO i_aw = 1, n_aw
387 CALL eri_mme_3c_get_bounds(hmat, h_inv, vol, .true., param%G_min, param%R_min, la_max, lb_max, lc_max, &
388 zeta, zetb, zetc, aw(i_aw), param%sum_precision, n_sum_1d, n_sum_3d, &
389 g_bounds_1, g_rads_1, r_bounds_2, r_rads_2, r_bounds_3, r_rads_3)
390 CALL pgf_sum_3c_1d(s_g(i_aw, 1, :, :, :), ra(1), rb(1), rc(1), &
391 zeta, zetb, zetc, aw(i_aw), abs(hmat(1, 1)), &
392 r_bounds_3(:, 1))
393
394 CALL pgf_sum_3c_1d(s_g(i_aw, 2, :, :, :), ra(2), rb(2), rc(2), &
395 zeta, zetb, zetc, aw(i_aw), abs(hmat(2, 2)), &
396 r_bounds_3(:, 2))
397
398 CALL pgf_sum_3c_1d(s_g(i_aw, 3, :, :, :), ra(3), rb(3), rc(3), &
399 zeta, zetb, zetc, aw(i_aw), abs(hmat(3, 3)), &
400 r_bounds_3(:, 3))
401
402 IF (PRESENT(rr_count)) rr_count = rr_count + 3
403 END DO
404
405 CALL eri_mme_3c_collect_ortho(vol, la_min, la_max, lb_min, lb_max, lc_min, lc_max, &
406 zeta, zetb, zetc, n_aw, aw, s_g, s_g_0, prefac, habc, o1, o2, o3)
407
408 END SUBROUTINE
409
410! **************************************************************************************************
411!> \brief ...
412!> \param param ...
413!> \param la_min ...
414!> \param la_max ...
415!> \param lb_min ...
416!> \param lb_max ...
417!> \param lc_min ...
418!> \param lc_max ...
419!> \param zeta ...
420!> \param zetb ...
421!> \param zetc ...
422!> \param RA ...
423!> \param RB ...
424!> \param RC ...
425!> \param habc ...
426!> \param o1 ...
427!> \param o2 ...
428!> \param o3 ...
429!> \param GG_count ...
430!> \param GR_count ...
431!> \param RR_count ...
432! **************************************************************************************************
433 SUBROUTINE eri_mme_3c_integrate_nonortho(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, RA, RB, RC, &
434 habc, o1, o2, o3, GG_count, GR_count, RR_count)
435
436 TYPE(eri_mme_param), INTENT(IN) :: param
437 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max, lc_min, &
438 lc_max
439 REAL(kind=dp), INTENT(IN) :: zeta, zetb, zetc
440 REAL(kind=dp), DIMENSION(3), INTENT(IN) :: ra, rb, rc
441 REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT) :: habc
442 INTEGER, INTENT(IN) :: o1, o2, o3
443 INTEGER, INTENT(INOUT), OPTIONAL :: gg_count, gr_count, rr_count
444
445 INTEGER :: ax, ay, az, bx, by, bz, cx, cy, cz, &
446 grid, i_aw, ico, ir, jco, kco, la, lb, &
447 lc, lmax_0, method, n_aw, nresults, &
448 sum_method
449 INTEGER(KIND=int_8), DIMENSION(3) :: n_sum_3d
450 INTEGER(KIND=int_8), DIMENSION(3, 3) :: n_sum_1d
451 LOGICAL :: db_sum1, db_sum2, db_sum3, do_g_sum_0
452 REAL(kind=dp) :: alpha_g_0, alpha_r_0, cutoff, g_rad_0, &
453 g_res, max_error, max_result, &
454 min_result, prefac, r_rad_0, r_res, vol
455 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: results_no, s_g_0_no
456 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :, :) :: s_g_no, s_g_no_1, s_g_no_2, s_g_no_3, &
457 s_g_no_h
458 REAL(kind=dp), DIMENSION(2) :: r_rads_3
459 REAL(kind=dp), DIMENSION(2, 3) :: r_bounds_3
460 REAL(kind=dp), DIMENSION(3) :: g_bound_0, g_rads_1, r_0, r_bound_0, &
461 r_rads_2
462 REAL(kind=dp), DIMENSION(3, 3) :: g_bounds_1, h_inv, hmat, r_bounds_2
463 REAL(kind=dp), DIMENSION(:), POINTER :: aw
464
465 cpassert(param%is_valid)
466
467 grid = 0
468
469 CALL eri_mme_3c_get_rads(la_max, lb_max, lc_max, zeta, zetb, zetc, 0.0_dp, param%G_min, param%R_min, &
470 param%sum_precision, g_rads_1=g_rads_1)
471
472 cutoff = (min(g_rads_1(1), g_rads_1(2) + g_rads_1(3)))**2/2
473
474 CALL get_minimax_from_cutoff(param%minimax_grid, cutoff, n_aw, aw, grid)
475
476 cpassert(grid .GT. 0)
477
478 ! minimax coeffs
479 n_aw = param%minimax_grid(grid)%n_minimax
480 aw => param%minimax_grid(grid)%minimax_aw
481
482 ! cell info
483 h_inv = param%h_inv
484 hmat = param%hmat
485 vol = param%vol
486
487 ! prefactor for integral values (unnormalized Hermite Gaussians)
488 prefac = (zeta*zetb*zetc)**(-1.5_dp)*pi**(11.0_dp/2.0_dp)*4.0_dp
489
490 IF (param%debug) THEN
491 ALLOCATE (s_g_no_1(ncoset(la_max), ncoset(lb_max), ncoset(lc_max)))
492 ALLOCATE (s_g_no_2(ncoset(la_max), ncoset(lb_max), ncoset(lc_max)))
493 ALLOCATE (s_g_no_3(ncoset(la_max), ncoset(lb_max), ncoset(lc_max)))
494 END IF
495
496 ! Preparations for G=0 component
497 g_res = 0.5_dp*param%G_min
498 r_res = 0.5_dp*param%R_min
499
500 ALLOCATE (s_g_no(ncoset(la_max), ncoset(lb_max), ncoset(lc_max)))
501
502 s_g_no(:, :, :) = 0.0_dp
503 IF (param%debug) THEN
504 s_g_no_1(:, :, :) = -1.0_dp
505 s_g_no_2(:, :, :) = -1.0_dp
506 s_g_no_3(:, :, :) = -1.0_dp
507 END IF
508 ALLOCATE (s_g_no_h(ncoset(la_max), ncoset(lb_max), ncoset(lc_max)))
509
510 ! G= 0 components
511 IF (lc_min == 0) THEN
512 ALLOCATE (s_g_0_no(ncoset(la_max + lb_max)))
513 alpha_g_0 = 0.25_dp/zetb + 0.25_dp/zeta
514 alpha_r_0 = 0.25_dp/alpha_g_0
515 lmax_0 = la_max + lb_max
516 r_0 = rb - ra
517 g_rad_0 = exp_radius(lmax_0, alpha_g_0, param%sum_precision, 1.0_dp, epsabs=g_res)
518 r_rad_0 = exp_radius(lmax_0, alpha_r_0, param%sum_precision, 1.0_dp, epsabs=r_res)
519 g_bound_0 = ellipsoid_bounds(g_rad_0, transpose(hmat)/(2.0_dp*pi))
520 r_bound_0 = ellipsoid_bounds(r_rad_0, h_inv)
521 do_g_sum_0 = product(2*r_bound_0 + 1) .GT. product(2*g_bound_0 + 1)
522 IF (do_g_sum_0) THEN
523 CALL pgf_sum_2c_gspace_3d(s_g_0_no, lmax_0, r_0, alpha_g_0, h_inv, g_bound_0, g_rad_0, vol)
524 ELSE
525 CALL pgf_sum_2c_rspace_3d(s_g_0_no, lmax_0, r_0, alpha_r_0, hmat, h_inv, r_bound_0, r_rad_0)
526 END IF
527 END IF
528
529 DO i_aw = 1, n_aw
530 CALL eri_mme_3c_get_bounds(hmat, h_inv, vol, .false., param%G_min, param%R_min, la_max, lb_max, lc_max, &
531 zeta, zetb, zetc, aw(i_aw), param%sum_precision, n_sum_1d, n_sum_3d, &
532 g_bounds_1, g_rads_1, r_bounds_2, r_rads_2, r_bounds_3, r_rads_3)
533 sum_method = minloc(n_sum_3d, dim=1)
534
535 CALL pgf_sum_3c_3d(s_g_no_h, la_max, lb_max, lc_max, ra, rb, rc, &
536 zeta, zetb, zetc, aw(i_aw), hmat, h_inv, vol, &
537 g_bounds_1, r_bounds_2, r_bounds_3, &
538 g_rads_1, r_rads_2, r_rads_3, &
539 method=sum_method, method_out=method)
540 s_g_no(:, :, :) = s_g_no(:, :, :) + aw(n_aw + i_aw)*s_g_no_h(:, :, :)
541
542 SELECT CASE (method)
543 CASE (1)
544 IF (PRESENT(gg_count)) gg_count = gg_count + 1
545 CASE (2)
546 IF (PRESENT(gr_count)) gr_count = gr_count + 1
547 CASE (3)
548 IF (PRESENT(rr_count)) rr_count = rr_count + 1
549 CASE DEFAULT
550 cpabort("")
551 END SELECT
552
553 IF (param%debug) THEN
554 nresults = 0
555 ! check consistency of summation methods
556
557 db_sum1 = (n_sum_3d(1)) .LT. int(param%debug_nsum, kind=int_8)
558 db_sum2 = (n_sum_3d(2)) .LT. int(param%debug_nsum, kind=int_8)
559 db_sum3 = (n_sum_3d(3)) .LT. int(param%debug_nsum, kind=int_8)
560
561 IF (param%unit_nr > 0) THEN
562 WRITE (param%unit_nr, *) "ERI_MME DEBUG | number of summands (GG / GR / RR)", n_sum_3d
563 WRITE (param%unit_nr, *) "ERI_MME DEBUG | sum methods to be compared (GG / GR / RR)", db_sum1, db_sum2, db_sum3
564 END IF
565
566 s_g_no_1(:, :, :) = 0.0_dp
567 s_g_no_2(:, :, :) = 0.0_dp
568 s_g_no_3(:, :, :) = 0.0_dp
569
570 IF (db_sum1) THEN
571 CALL pgf_sum_3c_3d(s_g_no_1, la_max, lb_max, lc_max, ra, rb, rc, &
572 zeta, zetb, zetc, aw(i_aw), hmat, h_inv, vol, &
573 g_bounds_1, r_bounds_2, r_bounds_3, &
574 g_rads_1, r_rads_2, r_rads_3, &
575 method=1)
576 nresults = nresults + 1
577 END IF
578
579 IF (db_sum2) THEN
580 CALL pgf_sum_3c_3d(s_g_no_2, la_max, lb_max, lc_max, ra, rb, rc, &
581 zeta, zetb, zetc, aw(i_aw), hmat, h_inv, vol, &
582 g_bounds_1, r_bounds_2, r_bounds_3, &
583 g_rads_1, r_rads_2, r_rads_3, &
584 method=2)
585 nresults = nresults + 1
586 END IF
587
588 IF (db_sum3) THEN
589 CALL pgf_sum_3c_3d(s_g_no_3, la_max, lb_max, lc_max, ra, rb, rc, &
590 zeta, zetb, zetc, aw(i_aw), hmat, h_inv, vol, &
591 g_bounds_1, r_bounds_2, r_bounds_3, &
592 g_rads_1, r_rads_2, r_rads_3, &
593 method=3)
594 nresults = nresults + 1
595 END IF
596
597 max_error = 0.0_dp
598 ALLOCATE (results_no(nresults))
599
600 DO kco = ncoset(lc_min - 1) + 1, ncoset(lc_max)
601 CALL get_l(kco, lc, cx, cy, cz)
602 DO jco = ncoset(lb_min - 1) + 1, ncoset(lb_max)
603 CALL get_l(jco, lb, bx, by, bz)
604 DO ico = ncoset(la_min - 1) + 1, ncoset(la_max)
605 CALL get_l(ico, la, ax, ay, az)
606
607 max_error = 0.0_dp
608 ir = 0
609 IF (db_sum1) THEN
610 ir = ir + 1
611 results_no(ir) = s_g_no_1(ico, jco, kco)
612 END IF
613
614 IF (db_sum2) THEN
615 ir = ir + 1
616 results_no(ir) = s_g_no_2(ico, jco, kco)
617 END IF
618
619 IF (db_sum3) THEN
620 ir = ir + 1
621 results_no(ir) = s_g_no_3(ico, jco, kco)
622 END IF
623
624 max_result = maxval(results_no)
625 min_result = minval(results_no)
626 IF (nresults > 0) max_error = max(max_error, &
627 (max_result - min_result)/(0.5_dp*(abs(max_result) + abs(min_result)) + 1.0_dp))
628 END DO
629 END DO
630 END DO
631
632 cpassert(max_error .LE. param%debug_delta)
633 DEALLOCATE (results_no)
634 END IF
635 END DO
636
637 ! assemble integral values
638
639 CALL eri_mme_3c_collect_nonortho(vol, la_min, la_max, lb_min, lb_max, lc_min, lc_max, &
640 zeta, zetb, zetc, n_aw, aw, s_g_no, s_g_0_no, prefac, habc, o1, o2, o3)
641
642 END SUBROUTINE
643
644! **************************************************************************************************
645!> \brief ...
646!> \param vol ...
647!> \param la_min ...
648!> \param la_max ...
649!> \param lb_min ...
650!> \param lb_max ...
651!> \param lc_min ...
652!> \param lc_max ...
653!> \param zeta ...
654!> \param zetb ...
655!> \param zetc ...
656!> \param n_aw ...
657!> \param aw ...
658!> \param S_G ...
659!> \param S_G_0 ...
660!> \param prefac ...
661!> \param habc ...
662!> \param o1 ...
663!> \param o2 ...
664!> \param o3 ...
665! **************************************************************************************************
666 SUBROUTINE eri_mme_3c_collect_ortho(vol, la_min, la_max, lb_min, lb_max, lc_min, lc_max, &
667 zeta, zetb, zetc, n_aw, aw, S_G, S_G_0, prefac, habc, o1, o2, o3)
668 REAL(kind=dp), INTENT(IN) :: vol
669 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max, lc_min, &
670 lc_max
671 REAL(kind=dp), INTENT(IN) :: zeta, zetb, zetc
672 INTEGER, INTENT(IN) :: n_aw
673 REAL(kind=dp), DIMENSION(2*n_aw), INTENT(IN) :: aw
674 REAL(kind=dp), DIMENSION(:, :, 0:, 0:, 0:), &
675 INTENT(IN) :: s_g
676 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :), &
677 INTENT(IN) :: s_g_0
678 REAL(kind=dp), INTENT(IN) :: prefac
679 REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT) :: habc
680 INTEGER, INTENT(IN) :: o1, o2, o3
681
682 INTEGER :: ax, ay, az, bx, by, bz, cx, cy, cz, ico, &
683 jco, kco, la, la_prev, lb, lb_prev, &
684 lc, lc_prev
685 REAL(kind=dp) :: imm, ixyz_0, mone_lb, resc_a, &
686 resc_a_init, resc_b, resc_b_init, &
687 resc_c, resc_c_init
688
689 ! Initialization of rescaling factors due to Hermite Gaussians
690 resc_a_init = (2.0_dp*zeta)**la_min
691 resc_b_init = (2.0_dp*zetb)**lb_min
692 resc_c_init = (2.0_dp*zetc)**lc_min
693
694 resc_c = resc_c_init
695 lc_prev = lc_min
696 DO kco = ncoset(lc_min - 1) + 1, ncoset(lc_max)
697 CALL get_l(kco, lc, cx, cy, cz)
698 IF (lc_prev < lc) resc_c = resc_c*(2.0_dp*zetc)
699
700 resc_b = resc_b_init
701 lb_prev = lb_min
702 DO jco = ncoset(lb_min - 1) + 1, ncoset(lb_max)
703 CALL get_l(jco, lb, bx, by, bz)
704 mone_lb = (-1.0_dp)**lb
705 IF (lb_prev < lb) resc_b = resc_b*(2.0_dp*zetb)
706
707 resc_a = resc_a_init
708 la_prev = la_min
709 DO ico = ncoset(la_min - 1) + 1, ncoset(la_max)
710 CALL get_l(ico, la, ax, ay, az)
711
712 IF (la_prev < la) resc_a = resc_a*(2.0_dp*zeta)
713 ixyz_0 = 0.0_dp
714 IF (lc == 0) THEN
715 ixyz_0 = s_g_0(ax + bx, 1)* &
716 s_g_0(ay + by, 2)* &
717 s_g_0(az + bz, 3) &
718 /vol*mone_lb
719 END IF
720 imm = sum(aw(n_aw + 1:2*n_aw)*( &
721 s_g(1:n_aw, 1, ax, bx, cx)* &
722 s_g(1:n_aw, 2, ay, by, cy)* &
723 s_g(1:n_aw, 3, az, bz, cz)) - ixyz_0)
724
725 ! rescaling needed due to Hermite Gaussians
726 habc(o1 + ico, o2 + jco, o3 + kco) = imm*prefac/(resc_a*resc_b*resc_c)
727 la_prev = la
728 END DO ! la
729 lb_prev = lb
730 END DO ! lb
731 lc_prev = lc
732 END DO ! lc
733
734 END SUBROUTINE
735
736! **************************************************************************************************
737!> \brief ...
738!> \param vol ...
739!> \param la_min ...
740!> \param la_max ...
741!> \param lb_min ...
742!> \param lb_max ...
743!> \param lc_min ...
744!> \param lc_max ...
745!> \param zeta ...
746!> \param zetb ...
747!> \param zetc ...
748!> \param n_aw ...
749!> \param aw ...
750!> \param S_G ...
751!> \param S_G_0 ...
752!> \param prefac ...
753!> \param habc ...
754!> \param o1 ...
755!> \param o2 ...
756!> \param o3 ...
757! **************************************************************************************************
758 PURE SUBROUTINE eri_mme_3c_collect_nonortho(vol, la_min, la_max, lb_min, lb_max, lc_min, lc_max, &
759 zeta, zetb, zetc, n_aw, aw, S_G, S_G_0, prefac, habc, o1, o2, o3)
760 REAL(kind=dp), INTENT(IN) :: vol
761 INTEGER, INTENT(IN) :: la_min, la_max, lb_min, lb_max, lc_min, &
762 lc_max
763 REAL(kind=dp), INTENT(IN) :: zeta, zetb, zetc
764 INTEGER, INTENT(IN) :: n_aw
765 REAL(kind=dp), DIMENSION(2*n_aw), INTENT(IN) :: aw
766 REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN) :: s_g
767 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
768 INTENT(IN) :: s_g_0
769 REAL(kind=dp), INTENT(IN) :: prefac
770 REAL(kind=dp), DIMENSION(:, :, :), INTENT(INOUT) :: habc
771 INTEGER, INTENT(IN) :: o1, o2, o3
772
773 INTEGER :: ax, ay, az, bx, by, bz, cx, cy, cz, ico, &
774 ijco, jco, kco, la, la_prev, lb, &
775 lb_prev, lc, lc_prev
776 REAL(kind=dp) :: imm, mone_lb, resc_a, resc_a_init, &
777 resc_b, resc_b_init, resc_c, &
778 resc_c_init
779
780 ! Initialization of rescaling factors due to Hermite Gaussians
781 resc_a_init = (2.0_dp*zeta)**la_min
782 resc_b_init = (2.0_dp*zetb)**lb_min
783 resc_c_init = (2.0_dp*zetc)**lc_min
784
785 resc_c = resc_c_init
786 lc_prev = lc_min
787 DO kco = ncoset(lc_min - 1) + 1, ncoset(lc_max)
788 CALL get_l(kco, lc, cx, cy, cz)
789 IF (lc_prev < lc) resc_c = resc_c*(2.0_dp*zetc)
790
791 resc_b = resc_b_init
792 lb_prev = lb_min
793 DO jco = ncoset(lb_min - 1) + 1, ncoset(lb_max)
794 CALL get_l(jco, lb, bx, by, bz)
795 mone_lb = (-1.0_dp)**lb
796 IF (lb_prev < lb) resc_b = resc_b*(2.0_dp*zetb)
797
798 resc_a = resc_a_init
799 la_prev = la_min
800 DO ico = ncoset(la_min - 1) + 1, ncoset(la_max)
801 CALL get_l(ico, la, ax, ay, az)
802
803 IF (la_prev < la) resc_a = resc_a*(2.0_dp*zeta)
804 IF (lc .GT. 0) THEN
805 imm = s_g(ico, jco, kco)
806 ELSE
807 ijco = coset(ax + bx, ay + by, az + bz)
808 imm = s_g(ico, jco, kco) - sum(aw(n_aw + 1:2*n_aw))*s_g_0(ijco)/vol*mone_lb
809 END IF
810
811 ! rescaling needed due to Hermite Gaussians
812 habc(o1 + ico, o2 + jco, o3 + kco) = imm*prefac/(resc_a*resc_b*resc_c)
813 la_prev = la
814 END DO ! la
815 lb_prev = lb
816 END DO ! lb
817 lc_prev = lc
818 END DO ! lc
819
820 END SUBROUTINE
821
822END MODULE eri_mme_integrate
ao_util
All kind of helpful little routines.
Definition ao_util.F:14
ao_util::exp_radius
real(kind=dp) function, public exp_radius(l, alpha, threshold, prefactor, epsabs, epsrel, rlow)
The radius of a primitive Gaussian function for a given threshold is calculated. g(r) = prefactor*r**...
Definition ao_util.F:96
eri_mme_gaussian
Methods related to properties of Hermite and Cartesian Gaussian functions.
Definition eri_mme_gaussian.F:15
eri_mme_gaussian::hermite_gauss_norm
pure real(kind=dp) function, public hermite_gauss_norm(zet, l)
Norm of 1d Hermite-Gauss functions.
Definition eri_mme_gaussian.F:76
eri_mme_integrate
Minimax-Ewald (MME) method for calculating 2-center and 3-center electron repulsion integrals (ERI) o...
Definition eri_mme_integrate.F:23
eri_mme_integrate::eri_mme_3c_integrate
subroutine, public eri_mme_3c_integrate(param, la_min, la_max, lb_min, lb_max, lc_min, lc_max, zeta, zetb, zetc, ra, rb, rc, habc, o1, o2, o3, gg_count, gr_count, rr_count)
Low-level integration routine for 3-center ERIs.
Definition eri_mme_integrate.F:274
eri_mme_integrate::eri_mme_2c_integrate
subroutine, public eri_mme_2c_integrate(param, la_min, la_max, lb_min, lb_max, zeta, zetb, rab, hab, o1, o2, g_count, r_count, normalize, potential, pot_par)
Low-level integration routine for 2-center ERIs.
Definition eri_mme_integrate.F:72
eri_mme_lattice_summation
Ewald sums to represent integrals in direct and reciprocal lattice.
Definition eri_mme_lattice_summation.F:15
eri_mme_lattice_summation::pgf_sum_2c_gspace_1d
pure subroutine, public pgf_sum_2c_gspace_1d(s_g, r, alpha, inv_lgth, g_c)
Compute Ewald-like sum for 2-center ERIs in G space in 1 dimension S_G(l, alpha) = (-i)^l*inv_lgth*su...
Definition eri_mme_lattice_summation.F:359
eri_mme_lattice_summation::eri_mme_2c_get_bounds
subroutine, public eri_mme_2c_get_bounds(hmat, h_inv, vol, is_ortho, g_min, r_min, la_max, lb_max, zeta, zetb, a_mm, sum_precision, n_sum_1d, n_sum_3d, g_bounds, g_rad, r_bounds, r_rad)
Get summation bounds for 2c integrals.
Definition eri_mme_lattice_summation.F:177
eri_mme_lattice_summation::get_l
pure elemental subroutine, public get_l(lco, l, lx, ly, lz)
...
Definition eri_mme_lattice_summation.F:121093
eri_mme_lattice_summation::pgf_sum_3c_3d
subroutine, public pgf_sum_3c_3d(s_g, la_max, lb_max, lc_max, ra, rb, rc, zeta, zetb, zetc, a_mm, hmat, h_inv, vol, g_bounds_1, r_bounds_2, r_bounds_3, g_rads_1, r_rads_2, r_rads_3, method, method_out, order)
As pgf_sum_3c_1d but 3d sum required for non-orthorhombic cells.
Definition eri_mme_lattice_summation.F:120272
eri_mme_lattice_summation::pgf_sum_2c_rspace_3d
pure subroutine, public pgf_sum_2c_rspace_3d(s_r, l_max, r, alpha, hmat, h_inv, r_c, r_rad)
As pgf_sum_2c_rspace_1d but 3d sum required for non-orthorhombic cells.
Definition eri_mme_lattice_summation.F:570
eri_mme_lattice_summation::pgf_sum_2c_gspace_3d
pure subroutine, public pgf_sum_2c_gspace_3d(s_g, l_max, r, alpha, h_inv, g_c, g_rad, vol, potential, pot_par)
As pgf_sum_2c_gspace_1d but 3d sum required for non-orthorhombic cells.
Definition eri_mme_lattice_summation.F:414
eri_mme_lattice_summation::eri_mme_3c_get_rads
subroutine, public eri_mme_3c_get_rads(la_max, lb_max, lc_max, zeta, zetb, zetc, a_mm, g_min, r_min, sum_precision, g_rads_1, r_rads_2, r_rads_3)
Get summation radii for 3c integrals.
Definition eri_mme_lattice_summation.F:111
eri_mme_lattice_summation::pgf_sum_3c_1d
subroutine, public pgf_sum_3c_1d(s_g, ra, rb, rc, zeta, zetb, zetc, a_mm, lgth, r_bounds_3)
Compute Ewald-like sum for 3-center integrals in 1 dimension S_G(l, m, n, alpha, beta,...
Definition eri_mme_lattice_summation.F:736
eri_mme_lattice_summation::eri_mme_2c_get_rads
subroutine, public eri_mme_2c_get_rads(la_max, lb_max, zeta, zetb, a_mm, g_min, r_min, sum_precision, g_rad, r_rad)
Get summation radii for 2c integrals.
Definition eri_mme_lattice_summation.F:73
eri_mme_lattice_summation::ellipsoid_bounds
pure real(kind=dp) function, dimension(3), public ellipsoid_bounds(s_rad, s_to_e)
Compute bounding box for ellipsoid. This is needed in order to find summation bounds for sphere for s...
Definition eri_mme_lattice_summation.F:121050
eri_mme_lattice_summation::eri_mme_3c_get_bounds
subroutine, public eri_mme_3c_get_bounds(hmat, h_inv, vol, is_ortho, g_min, r_min, la_max, lb_max, lc_max, zeta, zetb, zetc, a_mm, sum_precision, n_sum_1d, n_sum_3d, g_bounds_1, g_rads_1, r_bounds_2, r_rads_2, r_bounds_3, r_rads_3)
Get summation bounds for 3c integrals.
Definition eri_mme_lattice_summation.F:244
eri_mme_lattice_summation::pgf_sum_2c_rspace_1d
pure subroutine, public pgf_sum_2c_rspace_1d(s_r, r, alpha, lgth, r_c)
Compute Ewald-like sum for 2-center ERIs in R space in 1 dimension S_R(l, alpha) = SQRT(alpha/pi) sum...
Definition eri_mme_lattice_summation.F:514
eri_mme_types
Types and initialization / release routines for Minimax-Ewald method for electron repulsion integrals...
Definition eri_mme_types.F:16
eri_mme_types::get_minimax_from_cutoff
subroutine, public get_minimax_from_cutoff(grids, cutoff, n_minimax, minimax_aw, grid_no)
...
Definition eri_mme_types.F:421
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::int_8
integer, parameter, public int_8
Definition kinds.F:54
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
orbital_pointers
Provides Cartesian and spherical orbital pointers and indices.
Definition orbital_pointers.F:15
orbital_pointers::ncoset
integer, dimension(:), allocatable, public ncoset
Definition orbital_pointers.F:42
orbital_pointers::coset
integer, dimension(:, :, :), allocatable, public coset
Definition orbital_pointers.F:45
eri_mme_types::eri_mme_param
Definition eri_mme_types.F:63