Line data Source code
1 : !--------------------------------------------------------------------------------------------------!
2 : ! CP2K: A general program to perform molecular dynamics simulations !
3 : ! Copyright 2000-2025 CP2K developers group <https://cp2k.org> !
4 : ! !
5 : ! SPDX-License-Identifier: GPL-2.0-or-later !
6 : !--------------------------------------------------------------------------------------------------!
7 :
8 : ! **************************************************************************************************
9 : !> \brief Routines for computing excitonic properties, e.g. exciton diameter, from the BSE
10 : !> \par History
11 : !> 10.2024 created [Maximilian Graml]
12 : ! **************************************************************************************************
13 : MODULE bse_properties
14 : USE bse_util, ONLY: fm_general_add_bse,&
15 : print_bse_nto_cubes,&
16 : reshuffle_eigvec,&
17 : trace_exciton_descr
18 : USE cp_files, ONLY: close_file,&
19 : open_file
20 : USE cp_fm_basic_linalg, ONLY: cp_fm_scale_and_add,&
21 : cp_fm_trace
22 : USE cp_fm_diag, ONLY: cp_fm_svd
23 : USE cp_fm_struct, ONLY: cp_fm_struct_create,&
24 : cp_fm_struct_release,&
25 : cp_fm_struct_type
26 : USE cp_fm_types, ONLY: cp_fm_create,&
27 : cp_fm_get_submatrix,&
28 : cp_fm_release,&
29 : cp_fm_set_all,&
30 : cp_fm_to_fm,&
31 : cp_fm_to_fm_submat,&
32 : cp_fm_to_fm_submat_general,&
33 : cp_fm_type
34 : USE cp_log_handling, ONLY: cp_get_default_logger,&
35 : cp_logger_get_default_unit_nr,&
36 : cp_logger_type
37 : USE input_section_types, ONLY: section_vals_get_subs_vals,&
38 : section_vals_type,&
39 : section_vals_val_get
40 : USE kinds, ONLY: dp
41 : USE mathconstants, ONLY: pi
42 : USE mp2_types, ONLY: mp2_type
43 : USE parallel_gemm_api, ONLY: parallel_gemm
44 : USE physcon, ONLY: c_light_au,&
45 : evolt
46 : USE qs_environment_types, ONLY: get_qs_env,&
47 : qs_environment_type
48 : USE qs_mo_types, ONLY: allocate_mo_set,&
49 : deallocate_mo_set,&
50 : init_mo_set,&
51 : mo_set_type
52 : #include "./base/base_uses.f90"
53 :
54 : IMPLICIT NONE
55 :
56 : PRIVATE
57 :
58 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'bse_properties'
59 :
60 : PUBLIC :: exciton_descr_type
61 :
62 : PUBLIC :: get_exciton_descriptors, get_oscillator_strengths, compute_absorption_spectrum, &
63 : calculate_NTOs
64 :
65 : ! TYPE definitions for exciton wavefunction descriptors
66 :
67 : TYPE exciton_descr_type
68 : REAL(KIND=dp), DIMENSION(3) :: r_e = 0.0_dp, &
69 : r_h = 0.0_dp, &
70 : r_e_sq = 0.0_dp, &
71 : r_h_sq = 0.0_dp, &
72 : r_e_h = 0.0_dp, &
73 : r_e_shift = 0.0_dp, &
74 : r_h_shift = 0.0_dp, &
75 : cov_e_h = 0.0_dp
76 : REAL(KIND=dp) :: sigma_e = 0.0_dp, &
77 : sigma_h = 0.0_dp, &
78 : cov_e_h_sum = 0.0_dp, &
79 : corr_e_h = 0.0_dp, &
80 : diff_r_abs = 0.0_dp, &
81 : diff_r_sqr = 0.0_dp, &
82 : norm_XpY = 0.0_dp
83 : LOGICAL :: flag_TDA = .FALSE.
84 : END TYPE exciton_descr_type
85 :
86 : CONTAINS
87 :
88 : ! **************************************************************************************************
89 : !> \brief Compute and return BSE dipoles d_r^n = sqrt(2) sum_ia < ψ_i | r | ψ_a > ( X_ia^n + Y_ia^n )
90 : !> and oscillator strengths f^n = 2/3 * Ω^n sum_r∈(x,y,z) ( d_r^n )^2
91 : !> Prelim Ref.: Eqs. (23), (24)
92 : !> in J. Chem. Phys. 152, 044105 (2020); https://doi.org/10.1063/1.5123290
93 : !> \param fm_eigvec_X ...
94 : !> \param Exc_ens ...
95 : !> \param fm_dipole_ai_trunc ...
96 : !> \param trans_mom_bse BSE dipole vectors in real space per excitation level
97 : !> \param oscill_str Oscillator strength per excitation level
98 : !> \param polarizability_residues Residues of polarizability ("tensorial oscillator strength")
99 : !> per excitation level
100 : !> \param mp2_env ...
101 : !> \param homo_red ...
102 : !> \param virtual_red ...
103 : !> \param unit_nr ...
104 : !> \param fm_eigvec_Y ...
105 : ! **************************************************************************************************
106 42 : SUBROUTINE get_oscillator_strengths(fm_eigvec_X, Exc_ens, fm_dipole_ai_trunc, &
107 : trans_mom_bse, oscill_str, polarizability_residues, &
108 : mp2_env, homo_red, virtual_red, unit_nr, &
109 : fm_eigvec_Y)
110 :
111 : TYPE(cp_fm_type), INTENT(IN) :: fm_eigvec_X
112 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
113 : INTENT(IN) :: Exc_ens
114 : TYPE(cp_fm_type), DIMENSION(3) :: fm_dipole_ai_trunc
115 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
116 : INTENT(OUT) :: trans_mom_bse
117 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
118 : INTENT(OUT) :: oscill_str
119 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
120 : INTENT(OUT) :: polarizability_residues
121 : TYPE(mp2_type), INTENT(IN) :: mp2_env
122 : INTEGER, INTENT(IN) :: homo_red, virtual_red, unit_nr
123 : TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_eigvec_Y
124 :
125 : CHARACTER(LEN=*), PARAMETER :: routineN = 'get_oscillator_strengths'
126 :
127 : INTEGER :: handle, idir, jdir, n
128 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_dipole_MO_trunc_reordered, &
129 : fm_struct_trans_mom_bse
130 : TYPE(cp_fm_type) :: fm_eigvec_XYsum
131 168 : TYPE(cp_fm_type), DIMENSION(3) :: fm_dipole_MO_trunc_reordered, &
132 336 : fm_dipole_per_dir, fm_trans_mom_bse
133 :
134 42 : CALL timeset(routineN, handle)
135 :
136 : CALL cp_fm_struct_create(fm_struct_dipole_MO_trunc_reordered, fm_eigvec_X%matrix_struct%para_env, &
137 42 : fm_eigvec_X%matrix_struct%context, 1, homo_red*virtual_red)
138 : CALL cp_fm_struct_create(fm_struct_trans_mom_bse, fm_eigvec_X%matrix_struct%para_env, &
139 42 : fm_eigvec_X%matrix_struct%context, 1, homo_red*virtual_red)
140 :
141 : ! Include excitonic amplitudes in dipoles, i.e. obtain "BSE dipoles":
142 : ! \vec{D}_n = sqrt(2) * sum_{i,a} \vec{D}_ai (X_{ai}^{(n)} + Y_{ai}^{(n)})
143 :
144 : ! Reorder dipoles in order to execute the sum over i and a by parallel gemm
145 168 : DO idir = 1, 3
146 : CALL cp_fm_create(fm_dipole_MO_trunc_reordered(idir), matrix_struct=fm_struct_dipole_MO_trunc_reordered, &
147 126 : name="dipoles_mo_reordered")
148 126 : CALL cp_fm_set_all(fm_dipole_MO_trunc_reordered(idir), 0.0_dp)
149 : CALL fm_general_add_bse(fm_dipole_MO_trunc_reordered(idir), fm_dipole_ai_trunc(idir), 1.0_dp, &
150 : 1, 1, &
151 : 1, virtual_red, &
152 126 : unit_nr, (/2, 4, 3, 1/), mp2_env)
153 168 : CALL cp_fm_release(fm_dipole_per_dir(idir))
154 : END DO
155 :
156 168 : DO idir = 1, 3
157 : CALL cp_fm_create(fm_trans_mom_bse(idir), matrix_struct=fm_struct_trans_mom_bse, &
158 126 : name="excitonic_dipoles")
159 168 : CALL cp_fm_set_all(fm_trans_mom_bse(idir), 0.0_dp)
160 : END DO
161 :
162 : ! If TDA is invoked, Y is not present as it is simply 0
163 42 : CALL cp_fm_create(fm_eigvec_XYsum, matrix_struct=fm_eigvec_X%matrix_struct, name="excit_amplitude_sum")
164 42 : CALL cp_fm_set_all(fm_eigvec_XYsum, 0.0_dp)
165 42 : CALL cp_fm_to_fm(fm_eigvec_X, fm_eigvec_XYsum)
166 42 : IF (PRESENT(fm_eigvec_Y)) THEN
167 26 : CALL cp_fm_scale_and_add(1.0_dp, fm_eigvec_XYsum, 1.0_dp, fm_eigvec_Y)
168 : END IF
169 168 : DO idir = 1, 3
170 : CALL parallel_gemm('N', 'N', 1, homo_red*virtual_red, homo_red*virtual_red, SQRT(2.0_dp), &
171 168 : fm_dipole_MO_trunc_reordered(idir), fm_eigvec_XYsum, 0.0_dp, fm_trans_mom_bse(idir))
172 : END DO
173 :
174 : ! Get oscillator strengths themselves
175 126 : ALLOCATE (oscill_str(homo_red*virtual_red))
176 126 : ALLOCATE (trans_mom_bse(3, 1, homo_red*virtual_red))
177 126 : ALLOCATE (polarizability_residues(3, 3, homo_red*virtual_red))
178 10122 : trans_mom_bse(:, :, :) = 0.0_dp
179 :
180 : ! Sum over all directions
181 168 : DO idir = 1, 3
182 168 : CALL cp_fm_get_submatrix(fm_trans_mom_bse(idir), trans_mom_bse(idir, :, :))
183 : END DO
184 :
185 2058 : DO n = 1, homo_red*virtual_red
186 8064 : DO idir = 1, 3
187 26208 : DO jdir = 1, 3
188 24192 : polarizability_residues(idir, jdir, n) = 2.0_dp*Exc_ens(n)*trans_mom_bse(idir, 1, n)*trans_mom_bse(jdir, 1, n)
189 : END DO
190 : END DO
191 10122 : oscill_str(n) = 2.0_dp/3.0_dp*Exc_ens(n)*SUM(ABS(trans_mom_bse(:, :, n))**2)
192 : END DO
193 :
194 42 : CALL cp_fm_struct_release(fm_struct_dipole_MO_trunc_reordered)
195 42 : CALL cp_fm_struct_release(fm_struct_trans_mom_bse)
196 168 : DO idir = 1, 3
197 126 : CALL cp_fm_release(fm_dipole_MO_trunc_reordered(idir))
198 126 : CALL cp_fm_release(fm_trans_mom_bse(idir))
199 168 : CALL cp_fm_release(fm_dipole_ai_trunc(idir))
200 : END DO
201 42 : CALL cp_fm_release(fm_eigvec_XYsum)
202 :
203 42 : CALL timestop(handle)
204 :
205 126 : END SUBROUTINE get_oscillator_strengths
206 :
207 : ! **************************************************************************************************
208 : !> \brief Computes and returns absorption spectrum for the frequency range and broadening
209 : !> provided by the user.
210 : !> Prelim Ref.: C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications
211 : !> (Oxford University Press, Oxford, 2012), Eq. 7.51
212 : !> \param oscill_str ...
213 : !> \param polarizability_residues ...
214 : !> \param Exc_ens ...
215 : !> \param info_approximation ...
216 : !> \param unit_nr ...
217 : !> \param mp2_env ...
218 : ! **************************************************************************************************
219 4 : SUBROUTINE compute_absorption_spectrum(oscill_str, polarizability_residues, Exc_ens, &
220 : info_approximation, unit_nr, mp2_env)
221 :
222 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
223 : INTENT(IN) :: oscill_str
224 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
225 : INTENT(IN) :: polarizability_residues
226 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
227 : INTENT(IN) :: Exc_ens
228 : CHARACTER(LEN=10) :: info_approximation
229 : INTEGER, INTENT(IN) :: unit_nr
230 : TYPE(mp2_type), INTENT(INOUT) :: mp2_env
231 :
232 : CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_absorption_spectrum'
233 :
234 : CHARACTER(LEN=10) :: eta_str, width_eta_format_str
235 : CHARACTER(LEN=40) :: file_name_crosssection, &
236 : file_name_spectrum
237 : INTEGER :: handle, i, idir, j, jdir, k, num_steps, &
238 : unit_nr_file, width_eta
239 : REAL(KIND=dp) :: eta, freq_end, freq_start, freq_step, &
240 : omega
241 4 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: abs_cross_section, abs_spectrum
242 4 : REAL(KIND=dp), DIMENSION(:), POINTER :: eta_list
243 : TYPE(cp_logger_type), POINTER :: logger
244 :
245 4 : CALL timeset(routineN, handle)
246 :
247 4 : freq_step = mp2_env%bse%bse_spectrum_freq_step_size
248 4 : freq_start = mp2_env%bse%bse_spectrum_freq_start
249 4 : freq_end = mp2_env%bse%bse_spectrum_freq_end
250 4 : eta_list => mp2_env%bse%bse_eta_spectrum_list
251 :
252 : ! Calculate number of steps to fit given frequency range
253 4 : num_steps = NINT((freq_end - freq_start)/freq_step) + 1
254 :
255 8 : DO k = 1, SIZE(eta_list)
256 4 : eta = eta_list(k)
257 :
258 : ! Some magic to get a nice formatting of the eta value in filenames
259 4 : width_eta = MAX(1, INT(LOG10(eta)) + 1) + 4
260 4 : WRITE (width_eta_format_str, "(A2,I0,A3)") '(F', width_eta, '.3)'
261 4 : WRITE (eta_str, width_eta_format_str) eta*evolt
262 : ! Filename itself
263 4 : file_name_spectrum = 'BSE'//TRIM(ADJUSTL(info_approximation))//'eta='//TRIM(eta_str)//'.spectrum'
264 4 : file_name_crosssection = 'BSE'//TRIM(ADJUSTL(info_approximation))//'eta='//TRIM(eta_str)//'.crosssection'
265 :
266 : ! First column is frequency in eV, second column is imaginary part of the trace of the polarizability
267 : ! The following 9 columns are the entries of the polarizability tensor
268 12 : ALLOCATE (abs_spectrum(num_steps, 11))
269 44092 : abs_spectrum(:, :) = 0.0_dp
270 : ! Also calculate and print the photoabsorption cross section tensor
271 : ! σ_{µ µ'}(ω) = 4πω Im{α_{µ µ'}(ω)} / c
272 8 : ALLOCATE (abs_cross_section(num_steps, 11))
273 44092 : abs_cross_section(:, :) = 0.0_dp
274 :
275 : ! Calculate the imaginary part of the mean dipole polarizability α_{avg}(ω)
276 : ! which is given by (cf. C. Ullrichs Book on TDDFT, Eq. 7.51)
277 : ! We introduce an additional - due to his convention for charge vs particle density, see also:
278 : ! Computer Physics Communications, 208:149–161, November 2016
279 : ! https://doi.org/10.1016/j.cpc.2016.06.019
280 : ! α_{avg}(ω) = - \sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}
281 : ! and then the imaginary part is (in the limit η -> 0)
282 : ! Im[α_{avg}(ω)] = - \sum_{n=1}^{N_exc} f_n * η / ((ω - Ω^n)² + η²)
283 : ! where f_n are the oscillator strengths and E_exc the excitation energies
284 : ! For the full polarizability tensor, we have
285 : ! α_{µ µ'}(ω) = - \sum_n [2 Ω^n d^n_µ d^n_µ'] / [(ω+iη)^2- (Ω^n)^2]
286 : ! = - \sum_n "polarizability_residues" / [(ω+iη)^2- (Ω^n)^2]
287 4008 : DO i = 1, num_steps
288 4004 : omega = freq_start + (i - 1)*freq_step
289 4004 : abs_spectrum(i, 1) = omega
290 196200 : DO j = 1, SIZE(oscill_str)
291 : abs_spectrum(i, 2) = abs_spectrum(i, 2) - oscill_str(j)* &
292 192192 : AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
293 772772 : DO idir = 1, 3
294 2498496 : DO jdir = 1, 3
295 : ! Factor 2 from formula for tensor is already in the polarizability_residues
296 : ! to follow the same convention as the oscillator strengths
297 : abs_spectrum(i, 2 + (idir - 1)*3 + jdir) = abs_spectrum(i, 2 + (idir - 1)*3 + jdir) &
298 : - polarizability_residues(idir, jdir, j)* &
299 2306304 : AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
300 : END DO
301 : END DO
302 : END DO
303 : END DO
304 :
305 : ! Extract cross section σ from polarizability tensor
306 4008 : DO i = 1, num_steps
307 4004 : omega = abs_spectrum(i, 1)
308 4004 : abs_cross_section(i, 1) = omega
309 44048 : abs_cross_section(i, 2:) = 4.0_dp*pi*abs_spectrum(i, 2:)*omega/c_light_au
310 : END DO
311 :
312 : !For debug runs: Export an entry of the two tensors to allow regtests on spectra
313 4 : IF (mp2_env%bse%bse_debug_print) THEN
314 4 : IF (unit_nr > 0) THEN
315 2 : WRITE (unit_nr, '(T2,A10,T13,A,T65,F16.4)') 'BSE|DEBUG|', &
316 2 : 'Averaged dynamical dipole polarizability at 8.2 eV:', &
317 4 : abs_spectrum(83, 2)
318 2 : WRITE (unit_nr, '(T2,A10,T13,A,T65,F16.4)') 'BSE|DEBUG|', &
319 2 : 'Averaged photoabsorption cross section at 8.2 eV:', &
320 4 : abs_cross_section(83, 2)
321 : END IF
322 : END IF
323 :
324 : ! Print it to file
325 4 : logger => cp_get_default_logger()
326 4 : IF (logger%para_env%is_source()) THEN
327 4 : unit_nr_file = cp_logger_get_default_unit_nr()
328 : ELSE
329 0 : unit_nr_file = -1
330 : END IF
331 :
332 4 : IF (unit_nr_file > 0) THEN
333 : CALL open_file(file_name_crosssection, unit_number=unit_nr_file, &
334 4 : file_status="UNKNOWN", file_action="WRITE")
335 : WRITE (unit_nr_file, '(A,A6)') "# Photoabsorption cross section σ_{µ µ'}(ω) = -4πω/c * Im[ \sum_n "// &
336 4 : "[2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²] ] from Bethe Salpeter equation for method ", &
337 8 : TRIM(ADJUSTL(info_approximation))
338 4 : WRITE (unit_nr_file, '(A20,1X,10(2X,A20,1X))') "# Frequency (eV)", "σ_{avg}(ω)", "σ_xx(ω)", &
339 4 : "σ_xy(ω)", "σ_xz(ω)", "σ_yx(ω)", "σ_yy(ω)", "σ_yz(ω)", "σ_zx(ω)", &
340 8 : "σ_zy(ω)", "σ_zz(ω)"
341 4008 : DO i = 1, num_steps
342 4008 : WRITE (unit_nr_file, '(11(F20.8,1X))') abs_cross_section(i, 1)*evolt, abs_cross_section(i, 2:11)
343 : END DO
344 4 : CALL close_file(unit_nr_file)
345 : END IF
346 4 : DEALLOCATE (abs_cross_section)
347 :
348 4 : IF (unit_nr_file > 0) THEN
349 : CALL open_file(file_name_spectrum, unit_number=unit_nr_file, &
350 4 : file_status="UNKNOWN", file_action="WRITE")
351 : WRITE (unit_nr_file, '(A,A6)') "# Imaginary part of polarizability α_{µ µ'}(ω) = -\sum_n "// &
352 4 : "[2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²] from Bethe Salpeter equation for method ", &
353 8 : TRIM(ADJUSTL(info_approximation))
354 4 : WRITE (unit_nr_file, '(A20,1X,10(2X,A20,1X))') "# Frequency (eV)", "Im{α_{avg}(ω)}", "Im{α_xx(ω)}", &
355 4 : "Im{α_xy(ω)}", "Im{α_xz(ω)}", "Im{α_yx(ω)}", "Im{α_yy(ω)}", "Im{α_yz(ω)}", "Im{α_zx(ω)}", &
356 8 : "Im{α_zy(ω)}", "Im{α_zz(ω)}"
357 4008 : DO i = 1, num_steps
358 4008 : WRITE (unit_nr_file, '(11(F20.8,1X))') abs_spectrum(i, 1)*evolt, abs_spectrum(i, 2:11)
359 : END DO
360 4 : CALL close_file(unit_nr_file)
361 : END IF
362 8 : DEALLOCATE (abs_spectrum)
363 : END DO
364 :
365 4 : IF (unit_nr > 0) THEN
366 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
367 : WRITE (unit_nr, '(T2,A4,T7,A,A)') &
368 2 : 'BSE|', "Printed optical absorption spectrum to local files, e.g. ", file_name_spectrum
369 : WRITE (unit_nr, '(T2,A4,T7,A,A)') &
370 2 : 'BSE|', "as well as photoabsorption cross section to, e.g. ", file_name_crosssection
371 : WRITE (unit_nr, '(T2,A4,T7,A52)') &
372 2 : 'BSE|', "using the Eq. (7.51) from C. Ullrichs Book on TDDFT:"
373 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
374 : WRITE (unit_nr, '(T2,A4,T10,A73)') &
375 2 : 'BSE|', "Im{α_{avg}(ω)} = -Im{\sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}}"
376 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
377 : WRITE (unit_nr, '(T2,A4,T7,A)') &
378 2 : 'BSE|', "or for the full polarizability tensor:"
379 : WRITE (unit_nr, '(T2,A4,T10,A)') &
380 2 : 'BSE|', "α_{µ µ'}(ω) = -\sum_n [2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²]"
381 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
382 : WRITE (unit_nr, '(T2,A4,T7,A)') &
383 2 : 'BSE|', "as well as Eq. (7.48):"
384 : WRITE (unit_nr, '(T2,A4,T10,A)') &
385 2 : 'BSE|', "σ_{µ µ'}(ω) = 4πω Im{α_{µ µ'}(ω)} / c"
386 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
387 : WRITE (unit_nr, '(T2,A4,T7,A)') &
388 2 : 'BSE|', "with transition moments d_µ^n, oscillator strengths f_n,"
389 : WRITE (unit_nr, '(T2,A4,T7,A)') &
390 2 : 'BSE|', "excitation energies Ω^n and the speed of light c."
391 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
392 : WRITE (unit_nr, '(T2,A4,T7,A)') &
393 2 : 'BSE|', "Please note that we adopt an additional minus sign for both quantities,"
394 : WRITE (unit_nr, '(T2,A4,T7,A)') &
395 2 : 'BSE|', "due to the convention for charge vs particle density as done in MolGW:"
396 : WRITE (unit_nr, '(T2,A4,T7,A)') &
397 2 : 'BSE|', "https://doi.org/10.1016/j.cpc.2016.06.019."
398 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
399 : END IF
400 :
401 4 : CALL timestop(handle)
402 :
403 8 : END SUBROUTINE
404 :
405 : ! **************************************************************************************************
406 : !> \brief ...
407 : !> \param fm_X ...
408 : !> \param fm_Y ...
409 : !> \param mo_coeff ...
410 : !> \param homo ...
411 : !> \param virtual ...
412 : !> \param info_approximation ...
413 : !> \param oscill_str ...
414 : !> \param qs_env ...
415 : !> \param unit_nr ...
416 : !> \param mp2_env ...
417 : ! **************************************************************************************************
418 4 : SUBROUTINE calculate_NTOs(fm_X, fm_Y, &
419 4 : mo_coeff, homo, virtual, &
420 : info_approximation, &
421 : oscill_str, &
422 : qs_env, unit_nr, mp2_env)
423 :
424 : TYPE(cp_fm_type), INTENT(IN) :: fm_X
425 : TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_Y
426 : TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: mo_coeff
427 : INTEGER, INTENT(IN) :: homo, virtual
428 : CHARACTER(LEN=10) :: info_approximation
429 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: oscill_str
430 : TYPE(qs_environment_type), POINTER :: qs_env
431 : INTEGER, INTENT(IN) :: unit_nr
432 : TYPE(mp2_type), INTENT(INOUT) :: mp2_env
433 :
434 : CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_NTOs'
435 :
436 : CHARACTER(LEN=20), DIMENSION(2) :: nto_name
437 : INTEGER :: handle, homo_irred, i, i_nto, info_svd, &
438 : j, n_exc, n_nto, nao_full, nao_trunc
439 4 : INTEGER, DIMENSION(:), POINTER :: stride
440 : LOGICAL :: append_cube, cube_file
441 4 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: eigval_svd_squ
442 4 : REAL(KIND=dp), DIMENSION(:), POINTER :: eigval_svd
443 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_m, fm_struct_mo_coeff, &
444 : fm_struct_nto_holes, &
445 : fm_struct_nto_particles, &
446 : fm_struct_nto_set
447 : TYPE(cp_fm_type) :: fm_eigvl, fm_eigvr_t, fm_m, fm_mo_coeff, fm_nto_coeff_holes, &
448 : fm_nto_coeff_particles, fm_nto_set, fm_X_ia, fm_Y_ai
449 4 : TYPE(mo_set_type), ALLOCATABLE, DIMENSION(:) :: nto_set
450 : TYPE(section_vals_type), POINTER :: bse_section, input, nto_section
451 :
452 4 : CALL timeset(routineN, handle)
453 : CALL get_qs_env(qs_env=qs_env, &
454 4 : input=input)
455 4 : bse_section => section_vals_get_subs_vals(input, "DFT%XC%WF_CORRELATION%RI_RPA%GW%BSE")
456 :
457 4 : nao_full = qs_env%mos(1)%nao
458 4 : nao_trunc = homo + virtual
459 : ! This is not influenced by the BSE cutoff
460 4 : homo_irred = qs_env%mos(1)%homo
461 : ! M will have a block structure and is quadratic in homo+virtual, i.e.
462 : ! occ virt
463 : ! | 0 X_i,a | occ = homo
464 : ! M = | Y_a,i 0 | virt = virtual
465 : !
466 : ! X and Y are here not the eigenvectors X_ia,n - instead we fix n and reshape the combined ia index
467 : ! Notice the index structure of the lower block, i.e. X is transposed
468 : CALL cp_fm_struct_create(fm_struct_m, &
469 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
470 4 : nao_trunc, nao_trunc)
471 : CALL cp_fm_struct_create(fm_struct_mo_coeff, &
472 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
473 4 : nao_full, nao_trunc)
474 : CALL cp_fm_struct_create(fm_struct_nto_holes, &
475 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
476 4 : nao_full, nao_trunc)
477 : CALL cp_fm_struct_create(fm_struct_nto_particles, &
478 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
479 4 : nao_full, nao_trunc)
480 :
481 : CALL cp_fm_create(fm_mo_coeff, matrix_struct=fm_struct_mo_coeff, &
482 4 : name="mo_coeff")
483 : ! Here, we take care of possible cutoffs
484 : ! Simply truncating the matrix causes problems with the print function
485 : ! Therefore, we keep the dimension, but set the coefficients of truncated indices to 0
486 : CALL cp_fm_to_fm_submat_general(mo_coeff(1), fm_mo_coeff, &
487 : nao_full, nao_trunc, &
488 : 1, homo_irred - homo + 1, &
489 : 1, 1, &
490 4 : mo_coeff(1)%matrix_struct%context)
491 :
492 : ! Print some information about the NTOs
493 4 : IF (unit_nr > 0) THEN
494 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
495 4 : 'The Natural Transition Orbital (NTO) pairs φ_I(r_e) and χ_I(r_h) for a fixed'
496 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
497 4 : 'excitation index n are obtained by singular value decomposition of T'
498 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
499 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
500 4 : ' = (0 X)'
501 2 : IF (PRESENT(fm_Y)) THEN
502 1 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
503 2 : 'T = (Y^T 0)'
504 : ELSE
505 1 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
506 2 : 'T = (0 0)'
507 : END IF
508 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
509 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
510 4 : 'T = U Λ V^T'
511 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
512 4 : 'φ_I(r_e) = \sum_p V_pI ψ_p(r_e)'
513 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
514 4 : 'χ_I(r_h) = \sum_p U_pI ψ_p(r_e)'
515 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
516 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
517 4 : 'where we have introduced'
518 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
519 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
520 2 : 'BSE|', "ψ_p:", "occupied and virtual molecular orbitals,"
521 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
522 2 : 'BSE|', "φ_I(r_e):", "NTO state for the electron,"
523 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
524 2 : 'BSE|', "χ_I(r_h):", "NTO state for the hole,"
525 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
526 2 : 'BSE|', "Λ:", "diagonal matrix of NTO weights λ_I,"
527 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
528 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
529 4 : "The NTOs are calculated with the following settings:"
530 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
531 2 : WRITE (unit_nr, '(T2,A4,T7,A,T71,I10)') 'BSE|', 'Number of excitations, for which NTOs are computed', &
532 4 : mp2_env%bse%num_print_exc_ntos
533 2 : IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
534 0 : WRITE (unit_nr, '(T2,A4,T7,A,T71,F10.3)') 'BSE|', 'Threshold for oscillator strength f^n', &
535 0 : mp2_env%bse%eps_nto_osc_str
536 : ELSE
537 2 : WRITE (unit_nr, '(T2,A4,T7,A,T71,A10)') 'BSE|', 'Threshold for oscillator strength f^n', &
538 4 : ADJUSTL("---")
539 : END IF
540 2 : WRITE (unit_nr, '(T2,A4,T7,A,T72,F10.3)') 'BSE|', 'Threshold for NTO weights (λ_I)^2', &
541 4 : mp2_env%bse%eps_nto_eigval
542 : END IF
543 :
544 : ! Write the header of NTO info table
545 4 : IF (unit_nr > 0) THEN
546 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
547 2 : IF (.NOT. PRESENT(fm_Y)) THEN
548 1 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
549 2 : 'NTOs from solving the BSE within the TDA:'
550 : ELSE
551 1 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
552 2 : 'NTOs from solving the BSE without the TDA:'
553 : END IF
554 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
555 2 : WRITE (unit_nr, '(T2,A4,T8,A12,T22,A8,T33,A14,T62,A)') 'BSE|', &
556 4 : 'Excitation n', "TDA/ABBA", "Index of NTO I", 'NTO weights (λ_I)^2'
557 : END IF
558 :
559 104 : DO j = 1, mp2_env%bse%num_print_exc_ntos
560 100 : n_exc = mp2_env%bse%bse_nto_state_list_final(j)
561 : ! Takes care of unallocated oscill_str array in case of Triplet
562 100 : IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
563 : ! Check actual values
564 0 : IF (oscill_str(n_exc) < mp2_env%bse%eps_nto_osc_str) THEN
565 : ! Print skipped levels to table
566 0 : IF (unit_nr > 0) THEN
567 0 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
568 0 : WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T42,A39)') 'BSE|', &
569 0 : n_exc, info_approximation, "Skipped (Oscillator strength too small)"
570 : END IF
571 : CYCLE
572 : END IF
573 : END IF
574 :
575 : CALL cp_fm_create(fm_m, matrix_struct=fm_struct_m, &
576 100 : name="single_part_trans_dm")
577 100 : CALL cp_fm_set_all(fm_m, 0.0_dp)
578 :
579 : CALL cp_fm_create(fm_nto_coeff_holes, matrix_struct=fm_struct_nto_holes, &
580 100 : name="nto_coeffs_holes")
581 100 : CALL cp_fm_set_all(fm_nto_coeff_holes, 0.0_dp)
582 :
583 : CALL cp_fm_create(fm_nto_coeff_particles, matrix_struct=fm_struct_nto_particles, &
584 100 : name="nto_coeffs_particles")
585 100 : CALL cp_fm_set_all(fm_nto_coeff_particles, 0.0_dp)
586 :
587 : ! Reshuffle from X_ia,n_exc to X_i,a
588 : CALL reshuffle_eigvec(fm_X, fm_X_ia, homo, virtual, n_exc, &
589 100 : .FALSE., unit_nr, mp2_env)
590 :
591 : ! Copy X to upper block in M, i.e. starting from column homo+1
592 : CALL cp_fm_to_fm_submat(fm_X_ia, fm_m, &
593 : homo, virtual, &
594 : 1, 1, &
595 100 : 1, homo + 1)
596 100 : CALL cp_fm_release(fm_X_ia)
597 : ! Copy Y if present
598 100 : IF (PRESENT(fm_Y)) THEN
599 : ! Reshuffle from Y_ia,n_exc to Y_a,i
600 : CALL reshuffle_eigvec(fm_Y, fm_Y_ai, homo, virtual, n_exc, &
601 50 : .TRUE., unit_nr, mp2_env)
602 :
603 : ! Copy Y^T to lower block in M, i.e. starting from row homo+1
604 : CALL cp_fm_to_fm_submat(fm_Y_ai, fm_m, &
605 : virtual, homo, &
606 : 1, 1, &
607 50 : homo + 1, 1)
608 :
609 50 : CALL cp_fm_release(fm_Y_ai)
610 :
611 : END IF
612 :
613 : ! Now we compute the SVD of M_{occ+virt,occ+virt}, which yields
614 : ! M = U * Lambda * V^T
615 : ! Initialize matrices and arrays to store left/right eigenvectors and singular values
616 : CALL cp_fm_create(matrix=fm_eigvl, &
617 : matrix_struct=fm_m%matrix_struct, &
618 100 : name="LEFT_SINGULAR_MATRIX")
619 100 : CALL cp_fm_set_all(fm_eigvl, alpha=0.0_dp)
620 : CALL cp_fm_create(matrix=fm_eigvr_t, &
621 : matrix_struct=fm_m%matrix_struct, &
622 100 : name="RIGHT_SINGULAR_MATRIX")
623 100 : CALL cp_fm_set_all(fm_eigvr_t, alpha=0.0_dp)
624 :
625 300 : ALLOCATE (eigval_svd(nao_trunc))
626 1700 : eigval_svd(:) = 0.0_dp
627 : info_svd = 0
628 100 : CALL cp_fm_svd(fm_m, fm_eigvl, fm_eigvr_t, eigval_svd, info_svd)
629 604 : IF (info_svd /= 0) THEN
630 0 : IF (unit_nr > 0) THEN
631 : CALL cp_warn(__LOCATION__, &
632 : "SVD for computation of NTOs not successful. "// &
633 0 : "Skipping print of NTOs.")
634 0 : IF (info_svd > 0) THEN
635 : CALL cp_warn(__LOCATION__, &
636 : "PDGESVD detected heterogeneity. "// &
637 0 : "Decreasing number of MPI ranks might solve this issue.")
638 : END IF
639 : END IF
640 : ! Release matrices to avoid memory leaks
641 0 : CALL cp_fm_release(fm_m)
642 0 : CALL cp_fm_release(fm_nto_coeff_holes)
643 0 : CALL cp_fm_release(fm_nto_coeff_particles)
644 : ELSE
645 : ! Rescale singular values as done in Martin2003 (10.1063/1.1558471)
646 200 : ALLOCATE (eigval_svd_squ(nao_trunc))
647 1700 : eigval_svd_squ(:) = eigval_svd(:)**2
648 : ! Sanity check for TDA: In case of TDA, the sum should be \sum_ia |X_ia|^2 = 1
649 100 : IF (.NOT. PRESENT(fm_Y)) THEN
650 850 : IF (ABS(SUM(eigval_svd_squ) - 1) >= 1e-5) THEN
651 0 : CPWARN("Sum of NTO coefficients deviates from 1!")
652 : END IF
653 : END IF
654 :
655 : ! Create NTO coefficients for later print to grid via TDDFT routine
656 : ! Apply U = fm_eigvl to MO coeffs, which yields hole states
657 : CALL parallel_gemm("N", "N", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvl, 0.0_dp, &
658 100 : fm_nto_coeff_holes)
659 :
660 : ! Apply V^T = fm_eigvr_t to MO coeffs, which yields particle states
661 : CALL parallel_gemm("N", "T", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvr_t, 0.0_dp, &
662 100 : fm_nto_coeff_particles)
663 :
664 : !Release intermediary work matrices
665 100 : CALL cp_fm_release(fm_m)
666 100 : CALL cp_fm_release(fm_eigvl)
667 100 : CALL cp_fm_release(fm_eigvr_t)
668 :
669 : ! Transfer NTO coefficients to sets
670 100 : nto_name(1) = 'Hole_coord'
671 100 : nto_name(2) = 'Particle_coord'
672 300 : ALLOCATE (nto_set(2))
673 : ! Extract number of significant NTOs
674 100 : n_nto = 0
675 320 : DO i_nto = 1, nao_trunc
676 320 : IF (eigval_svd_squ(i_nto) > mp2_env%bse%eps_nto_eigval) THEN
677 220 : n_nto = n_nto + 1
678 : ELSE
679 : ! Since svd orders in descending order, we can exit the loop if smaller
680 : EXIT
681 : END IF
682 : END DO
683 :
684 100 : IF (unit_nr > 0) THEN
685 50 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
686 160 : DO i_nto = 1, n_nto
687 110 : WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T41,I6,T71,F10.5)') 'BSE|', &
688 270 : n_exc, info_approximation, i_nto, eigval_svd_squ(i_nto)
689 : END DO
690 : END IF
691 :
692 : CALL cp_fm_struct_create(fm_struct_nto_set, template_fmstruct=fm_struct_nto_holes, &
693 100 : ncol_global=n_nto)
694 100 : CALL cp_fm_create(fm_nto_set, fm_struct_nto_set)
695 300 : DO i = 1, 2
696 200 : CALL allocate_mo_set(nto_set(i), nao_trunc, n_nto, 0, 0.0_dp, 2.0_dp, 0.0_dp)
697 300 : CALL init_mo_set(nto_set(i), fm_ref=fm_nto_set, name=nto_name(i))
698 : END DO
699 100 : CALL cp_fm_release(fm_nto_set)
700 100 : CALL cp_fm_struct_release(fm_struct_nto_set)
701 :
702 : ! Fill NTO sets
703 100 : CALL cp_fm_to_fm(fm_nto_coeff_holes, nto_set(1)%mo_coeff, ncol=n_nto)
704 100 : CALL cp_fm_to_fm(fm_nto_coeff_particles, nto_set(2)%mo_coeff, ncol=n_nto)
705 :
706 : ! Cube files
707 100 : nto_section => section_vals_get_subs_vals(bse_section, "NTO_ANALYSIS")
708 100 : CALL section_vals_val_get(nto_section, "CUBE_FILES", l_val=cube_file)
709 100 : CALL section_vals_val_get(nto_section, "STRIDE", i_vals=stride)
710 100 : CALL section_vals_val_get(nto_section, "APPEND", l_val=append_cube)
711 100 : IF (cube_file) THEN
712 : CALL print_bse_nto_cubes(qs_env, nto_set, n_exc, info_approximation, &
713 0 : stride, append_cube, nto_section)
714 : END IF
715 :
716 100 : CALL cp_fm_release(fm_nto_coeff_holes)
717 100 : CALL cp_fm_release(fm_nto_coeff_particles)
718 100 : DEALLOCATE (eigval_svd)
719 100 : DEALLOCATE (eigval_svd_squ)
720 300 : DO i = 1, 2
721 300 : CALL deallocate_mo_set(nto_set(i))
722 : END DO
723 400 : DEALLOCATE (nto_set)
724 : END IF
725 : END DO
726 :
727 4 : CALL cp_fm_release(fm_mo_coeff)
728 4 : CALL cp_fm_struct_release(fm_struct_m)
729 4 : CALL cp_fm_struct_release(fm_struct_nto_holes)
730 4 : CALL cp_fm_struct_release(fm_struct_nto_particles)
731 4 : CALL cp_fm_struct_release(fm_struct_mo_coeff)
732 :
733 4 : CALL timestop(handle)
734 :
735 8 : END SUBROUTINE calculate_NTOs
736 :
737 : ! **************************************************************************************************
738 : !> \brief ...
739 : !> \param exc_descr Allocated and initialized on exit
740 : !> \param fm_X_ia ...
741 : !> \param fm_multipole_ij_trunc ...
742 : !> \param fm_multipole_ab_trunc ...
743 : !> \param fm_multipole_ai_trunc ...
744 : !> \param i_exc ...
745 : !> \param homo ...
746 : !> \param virtual ...
747 : !> \param fm_Y_ia ...
748 : ! **************************************************************************************************
749 110 : SUBROUTINE get_exciton_descriptors(exc_descr, fm_X_ia, &
750 : fm_multipole_ij_trunc, fm_multipole_ab_trunc, &
751 : fm_multipole_ai_trunc, &
752 : i_exc, homo, virtual, &
753 : fm_Y_ia)
754 :
755 : TYPE(exciton_descr_type), ALLOCATABLE, &
756 : DIMENSION(:) :: exc_descr
757 : TYPE(cp_fm_type), INTENT(IN) :: fm_X_ia
758 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:), &
759 : INTENT(IN) :: fm_multipole_ij_trunc, &
760 : fm_multipole_ab_trunc, &
761 : fm_multipole_ai_trunc
762 : INTEGER, INTENT(IN) :: i_exc, homo, virtual
763 : TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_Y_ia
764 :
765 : CHARACTER(LEN=*), PARAMETER :: routineN = 'get_exciton_descriptors'
766 :
767 : INTEGER :: handle, i_dir
768 : INTEGER, DIMENSION(3) :: mask_quadrupole
769 : LOGICAL :: flag_TDA
770 : REAL(KIND=dp) :: norm_X, norm_XpY, norm_Y
771 : REAL(KIND=dp), DIMENSION(3) :: r_e_h_XX, r_e_h_XY, r_e_h_YX, r_e_h_YY, &
772 : r_e_sq_X, r_e_sq_Y, r_e_X, r_e_Y, &
773 : r_h_sq_X, r_h_sq_Y, r_h_X, r_h_Y
774 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_ab, fm_struct_ia
775 : TYPE(cp_fm_type) :: fm_work_ba, fm_work_ia, fm_work_ia_2
776 :
777 110 : CALL timeset(routineN, handle)
778 110 : IF (PRESENT(fm_Y_ia)) THEN
779 : flag_TDA = .FALSE.
780 : ELSE
781 60 : flag_TDA = .TRUE.
782 : END IF
783 :
784 : ! translates 1,2,3 to diagonal entries of quadrupoles xx, yy, zz
785 : ! Ordering in quadrupole moments is x, y, z, xx, xy, xz, yy, yz, zz
786 110 : mask_quadrupole = (/4, 7, 9/)
787 :
788 : CALL cp_fm_struct_create(fm_struct_ia, &
789 110 : context=fm_X_ia%matrix_struct%context, nrow_global=homo, ncol_global=virtual)
790 : CALL cp_fm_struct_create(fm_struct_ab, &
791 110 : context=fm_X_ia%matrix_struct%context, nrow_global=virtual, ncol_global=virtual)
792 :
793 110 : r_e_X(:) = 0.0_dp
794 110 : r_e_Y(:) = 0.0_dp
795 110 : r_h_X(:) = 0.0_dp
796 110 : r_h_Y(:) = 0.0_dp
797 110 : r_e_sq_X(:) = 0.0_dp
798 110 : r_h_sq_X(:) = 0.0_dp
799 110 : r_e_sq_Y(:) = 0.0_dp
800 110 : r_h_sq_Y(:) = 0.0_dp
801 110 : r_e_h_XX(:) = 0.0_dp
802 110 : r_e_h_XY(:) = 0.0_dp
803 110 : r_e_h_YX(:) = 0.0_dp
804 110 : r_e_h_YY(:) = 0.0_dp
805 :
806 : norm_X = 0.0_dp
807 110 : norm_Y = 0.0_dp
808 110 : norm_XpY = 0.0_dp
809 :
810 : ! Initialize values of exciton descriptors
811 440 : exc_descr(i_exc)%r_e(:) = 0.0_dp
812 440 : exc_descr(i_exc)%r_h(:) = 0.0_dp
813 440 : exc_descr(i_exc)%r_e_sq(:) = 0.0_dp
814 440 : exc_descr(i_exc)%r_h_sq(:) = 0.0_dp
815 440 : exc_descr(i_exc)%r_e_h(:) = 0.0_dp
816 :
817 110 : exc_descr(i_exc)%flag_TDA = flag_TDA
818 110 : exc_descr(i_exc)%norm_XpY = 0.0_dp
819 :
820 : ! Norm of X
821 110 : CALL cp_fm_trace(fm_X_ia, fm_X_ia, norm_X)
822 110 : norm_XpY = norm_X
823 : ! Norm of Y
824 110 : IF (.NOT. flag_TDA) THEN
825 50 : CALL cp_fm_trace(fm_Y_ia, fm_Y_ia, norm_Y)
826 50 : norm_XpY = norm_XpY + norm_Y
827 : END IF
828 :
829 110 : exc_descr(i_exc)%norm_XpY = norm_XpY
830 :
831 : ! <r_h>_X = Tr[ X^T µ_ij X + Y µ_ab Y^T ] = X_ai µ_ij X_ja + Y_ia µ_ab Y_bi
832 440 : DO i_dir = 1, 3
833 : ! <r_h>_X = X_ai µ_ij X_ja + ...
834 330 : CALL trace_exciton_descr(fm_X_ia, fm_multipole_ij_trunc(i_dir), fm_X_ia, r_h_X(i_dir))
835 330 : r_h_X(i_dir) = r_h_X(i_dir)/norm_XpY
836 440 : IF (.NOT. flag_TDA) THEN
837 : ! <r_h>_X = ... + Y_ia µ_ab Y_bi
838 150 : CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, fm_multipole_ab_trunc(i_dir), r_h_Y(i_dir))
839 150 : r_h_Y(i_dir) = r_h_Y(i_dir)/norm_XpY
840 : END IF
841 : END DO
842 440 : exc_descr(i_exc)%r_h(:) = r_h_X(:) + r_h_Y(:)
843 :
844 : ! <r_e>_X = Tr[ X µ_ab X^T + Y^T µ_ij Y ] = X_ia µ_ab X_bi + Y_ai µ_ij Y_ja
845 440 : DO i_dir = 1, 3
846 : ! <r_e>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
847 330 : CALL trace_exciton_descr(fm_X_ia, fm_X_ia, fm_multipole_ab_trunc(i_dir), r_e_X(i_dir))
848 330 : r_e_X(i_dir) = r_e_X(i_dir)/norm_XpY
849 440 : IF (.NOT. flag_TDA) THEN
850 : ! <r_e>_X = ... + Y_ai µ_ij Y_ja
851 150 : CALL trace_exciton_descr(fm_Y_ia, fm_multipole_ij_trunc(i_dir), fm_Y_ia, r_e_Y(i_dir))
852 150 : r_e_Y(i_dir) = r_e_Y(i_dir)/norm_XpY
853 : END IF
854 : END DO
855 440 : exc_descr(i_exc)%r_e(:) = r_e_X(:) + r_e_Y(:)
856 :
857 : ! <r_h^2>_X = Tr[ X^T M_ij X + Y M_ab Y^T ] = X_ai M_ij X_ja + Y_ia M_ab Y_bi
858 440 : DO i_dir = 1, 3
859 : ! <r_h^2>_X = X_ai M_ij X_ja + ...
860 : CALL trace_exciton_descr(fm_X_ia, fm_multipole_ij_trunc(mask_quadrupole(i_dir)), &
861 330 : fm_X_ia, r_h_sq_X(i_dir))
862 330 : r_h_sq_X(i_dir) = r_h_sq_X(i_dir)/norm_XpY
863 440 : IF (.NOT. flag_TDA) THEN
864 : ! <r_h^2>_X = ... + Y_ia M_ab Y_bi
865 : CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, &
866 150 : fm_multipole_ab_trunc(mask_quadrupole(i_dir)), r_h_sq_Y(i_dir))
867 150 : r_h_sq_Y(i_dir) = r_h_sq_Y(i_dir)/norm_XpY
868 : END IF
869 : END DO
870 440 : exc_descr(i_exc)%r_h_sq(:) = r_h_sq_X(:) + r_h_sq_Y(:)
871 :
872 : ! <r_e^2>_X = Tr[ X M_ab X^T + Y^T M_ij Y ] = X_ia M_ab X_bi + Y_ai M_ij Y_ja
873 440 : DO i_dir = 1, 3
874 : ! <r_e^2>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
875 : CALL trace_exciton_descr(fm_X_ia, fm_X_ia, &
876 330 : fm_multipole_ab_trunc(mask_quadrupole(i_dir)), r_e_sq_X(i_dir))
877 330 : r_e_sq_X(i_dir) = r_e_sq_X(i_dir)/norm_XpY
878 440 : IF (.NOT. flag_TDA) THEN
879 : ! <r_e^2>_X = ... + Y_ai M_ij Y_ja
880 : CALL trace_exciton_descr(fm_Y_ia, fm_multipole_ij_trunc(mask_quadrupole(i_dir)), &
881 150 : fm_Y_ia, r_e_sq_Y(i_dir))
882 150 : r_e_sq_Y(i_dir) = r_e_sq_Y(i_dir)/norm_XpY
883 : END IF
884 : END DO
885 440 : exc_descr(i_exc)%r_e_sq(:) = r_e_sq_X(:) + r_e_sq_Y(:)
886 :
887 : ! <r_h r_e>_X
888 : ! = Tr[ X^T µ_ij X µ_ab + Y^T µ_ij Y µ_ab + X µ_ai Y µ_ai + Y µ_ai X µ_ai]
889 : ! = X_bj µ_ji X_ia µ_ab + Y_bj µ_ji Y_ia µ_ab + X_ia µ_aj Y_jb µ_bi + Y_ia µ_aj X_jb µ_bi
890 110 : CALL cp_fm_create(fm_work_ia, fm_struct_ia)
891 110 : CALL cp_fm_create(fm_work_ia_2, fm_struct_ia)
892 110 : CALL cp_fm_create(fm_work_ba, fm_struct_ab)
893 440 : DO i_dir = 1, 3
894 : ! First term - X^T µ_ij X µ_ab
895 330 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
896 330 : CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
897 : ! work_ib = X_ia µ_ab
898 : CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
899 330 : fm_X_ia, fm_multipole_ab_trunc(i_dir), 0.0_dp, fm_work_ia)
900 : ! work_ja_2 = µ_ji work_ia
901 : CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
902 330 : fm_multipole_ij_trunc(i_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
903 : ! <r_h r_e>_X = work_ia_2 X_bj + ... = X^T work_ia_2 + ...
904 330 : CALL cp_fm_trace(fm_X_ia, fm_work_ia_2, r_e_h_XX(i_dir))
905 330 : r_e_h_XX(i_dir) = r_e_h_XX(i_dir)/norm_XpY
906 440 : IF (.NOT. flag_TDA) THEN
907 : ! Second term - Y^T µ_ij Y µ_ab
908 150 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
909 150 : CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
910 : ! work_ib = Y_ia µ_ab
911 : CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
912 150 : fm_Y_ia, fm_multipole_ab_trunc(i_dir), 0.0_dp, fm_work_ia)
913 : ! work_ja_2 = µ_ji work_ia
914 : CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
915 150 : fm_multipole_ij_trunc(i_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
916 : ! <r_h r_e>_X = work_ia_2 Y_bj + ... = Y^T work_ia_2 + ...
917 150 : CALL cp_fm_trace(fm_Y_ia, fm_work_ia_2, r_e_h_YY(i_dir))
918 150 : r_e_h_YY(i_dir) = r_e_h_YY(i_dir)/norm_XpY
919 :
920 : ! Third term - X µ_ai Y µ_ai = X_ia µ_aj Y_jb µ_bi
921 : ! Reshuffle for usage of trace (where first argument is transposed)
922 : ! = µ_aj Y_jb µ_bi X_ia =
923 : ! \__________/
924 : ! fm_work_ai
925 : ! fm_work_ai = µ_aj Y_jb µ_bi
926 : ! fm_work_ia = µ_ib Y_bj µ_ja
927 : ! \_____/
928 : ! fm_work_ba
929 150 : CALL cp_fm_set_all(fm_work_ba, 0.0_dp)
930 150 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
931 : ! fm_work_ba = Y_bj µ_ja
932 : CALL parallel_gemm("T", "T", virtual, virtual, homo, 1.0_dp, &
933 150 : fm_Y_ia, fm_multipole_ai_trunc(i_dir), 0.0_dp, fm_work_ba)
934 : ! fm_work_ia = µ_ib fm_work_ba
935 : CALL parallel_gemm("T", "N", homo, virtual, virtual, 1.0_dp, &
936 150 : fm_multipole_ai_trunc(i_dir), fm_work_ba, 0.0_dp, fm_work_ia)
937 : ! <r_h r_e>_X = ... + X_ia µ_aj Y_jb µ_bi
938 150 : CALL cp_fm_trace(fm_work_ia, fm_X_ia, r_e_h_XY(i_dir))
939 150 : r_e_h_XY(i_dir) = r_e_h_XY(i_dir)/norm_XpY
940 :
941 : ! Fourth term - Y µ_ai X µ_ai = Y_ia µ_aj X_jb µ_bi
942 : ! Reshuffle for usage of trace (where first argument is transposed)
943 : ! = µ_aj X_jb µ_bi Y_ia =
944 : ! \__________/
945 : ! fm_work_ai
946 : ! fm_work_ai = µ_aj X_jb µ_bi
947 : ! fm_work_ia = µ_ib X_bj µ_ja
948 : ! \_____/
949 : ! fm_work_ba
950 150 : CALL cp_fm_set_all(fm_work_ba, 0.0_dp)
951 150 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
952 : ! fm_work_ba = Y_bj µ_ja
953 : CALL parallel_gemm("T", "T", virtual, virtual, homo, 1.0_dp, &
954 150 : fm_X_ia, fm_multipole_ai_trunc(i_dir), 0.0_dp, fm_work_ba)
955 : ! fm_work_ia = µ_ib fm_work_ba
956 : CALL parallel_gemm("T", "N", homo, virtual, virtual, 1.0_dp, &
957 150 : fm_multipole_ai_trunc(i_dir), fm_work_ba, 0.0_dp, fm_work_ia)
958 : ! <r_h r_e>_X = ... + X_ia µ_aj Y_jb µ_bi
959 150 : CALL cp_fm_trace(fm_work_ia, fm_Y_ia, r_e_h_YX(i_dir))
960 150 : r_e_h_YX(i_dir) = r_e_h_YX(i_dir)/norm_XpY
961 : END IF
962 : END DO
963 440 : exc_descr(i_exc)%r_e_h(:) = r_e_h_XX(:) + r_e_h_XY(:) + r_e_h_YX(:) + r_e_h_YY(:)
964 :
965 110 : CALL cp_fm_release(fm_work_ia)
966 110 : CALL cp_fm_release(fm_work_ia_2)
967 110 : CALL cp_fm_release(fm_work_ba)
968 :
969 : ! diff_r_abs = |<r_h>_X - <r_e>_X|
970 440 : exc_descr(i_exc)%diff_r_abs = SQRT(SUM((exc_descr(i_exc)%r_h(:) - exc_descr(i_exc)%r_e(:))**2))
971 :
972 : ! σ_e = sqrt( <r_e^2>_X - <r_e>_X^2 )
973 770 : exc_descr(i_exc)%sigma_e = SQRT(SUM(exc_descr(i_exc)%r_e_sq(:)) - SUM(exc_descr(i_exc)%r_e(:)**2))
974 :
975 : ! σ_h = sqrt( <r_h^2>_X - <r_h>_X^2 )
976 770 : exc_descr(i_exc)%sigma_h = SQRT(SUM(exc_descr(i_exc)%r_h_sq(:)) - SUM(exc_descr(i_exc)%r_h(:)**2))
977 :
978 : ! COV(r_e, r_h) = < r_e r_h >_X - < r_e >_X < r_h >_X
979 110 : exc_descr(i_exc)%cov_e_h_sum = 0.0_dp
980 440 : exc_descr(i_exc)%cov_e_h(:) = 0.0_dp
981 440 : DO i_dir = 1, 3
982 : exc_descr(i_exc)%cov_e_h(i_dir) = exc_descr(i_exc)%r_e_h(i_dir) &
983 330 : - exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(i_dir)
984 : exc_descr(i_exc)%cov_e_h_sum = exc_descr(i_exc)%cov_e_h_sum + &
985 440 : exc_descr(i_exc)%r_e_h(i_dir) - exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(i_dir)
986 : END DO
987 :
988 : ! root-mean-square e-h separation
989 : exc_descr(i_exc)%diff_r_sqr = SQRT(exc_descr(i_exc)%diff_r_abs**2 + &
990 : exc_descr(i_exc)%sigma_e**2 + exc_descr(i_exc)%sigma_h**2 &
991 110 : - 2*exc_descr(i_exc)%cov_e_h_sum)
992 :
993 : ! e-h-correlation coefficient R_eh = COV(r_e, r_h) / ( σ_e σ_h )
994 110 : exc_descr(i_exc)%corr_e_h = exc_descr(i_exc)%cov_e_h_sum/(exc_descr(i_exc)%sigma_e*exc_descr(i_exc)%sigma_h)
995 :
996 : ! Expectation values of r_e and r_h
997 440 : exc_descr(i_exc)%r_e_shift(:) = exc_descr(i_exc)%r_e(:)
998 440 : exc_descr(i_exc)%r_h_shift(:) = exc_descr(i_exc)%r_h(:)
999 :
1000 110 : CALL cp_fm_struct_release(fm_struct_ia)
1001 110 : CALL cp_fm_struct_release(fm_struct_ab)
1002 :
1003 110 : CALL timestop(handle)
1004 :
1005 330 : END SUBROUTINE get_exciton_descriptors
1006 :
1007 0 : END MODULE bse_properties
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