Line data Source code
1 : !--------------------------------------------------------------------------------------------------!
2 : ! CP2K: A general program to perform molecular dynamics simulations !
3 : ! Copyright 2000-2026 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: &
27 : cp_fm_create, cp_fm_get_info, cp_fm_get_submatrix, cp_fm_release, cp_fm_set_all, &
28 : cp_fm_to_fm, cp_fm_to_fm_submat, cp_fm_to_fm_submat_general, cp_fm_type
29 : USE cp_log_handling, ONLY: cp_get_default_logger,&
30 : cp_logger_get_default_unit_nr,&
31 : cp_logger_type
32 : USE input_section_types, ONLY: section_vals_get_subs_vals,&
33 : section_vals_type,&
34 : section_vals_val_get
35 : USE kinds, ONLY: dp
36 : USE mathconstants, ONLY: pi
37 : USE mp2_types, ONLY: mp2_type
38 : USE parallel_gemm_api, ONLY: parallel_gemm
39 : USE physcon, ONLY: c_light_au,&
40 : evolt
41 : USE qs_environment_types, ONLY: get_qs_env,&
42 : qs_environment_type
43 : USE qs_mo_types, ONLY: allocate_mo_set,&
44 : deallocate_mo_set,&
45 : init_mo_set,&
46 : mo_set_type
47 : #include "./base/base_uses.f90"
48 :
49 : IMPLICIT NONE
50 :
51 : PRIVATE
52 :
53 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'bse_properties'
54 :
55 : PUBLIC :: exciton_descr_type
56 :
57 : PUBLIC :: get_exciton_descriptors, get_oscillator_strengths, compute_and_print_absorption_spectrum, &
58 : calculate_NTOs
59 :
60 : ! TYPE definitions for exciton wavefunction descriptors
61 :
62 : TYPE exciton_descr_type
63 : REAL(KIND=dp), DIMENSION(3) :: r_e = 0.0_dp, &
64 : r_h = 0.0_dp, &
65 : r_e_sq = 0.0_dp, &
66 : r_h_sq = 0.0_dp, &
67 : r_e_shift = 0.0_dp, &
68 : r_h_shift = 0.0_dp, &
69 : d_eh_dir = 0.0_dp, &
70 : sigma_e_dir = 0.0_dp, &
71 : sigma_h_dir = 0.0_dp, &
72 : d_exc_dir = 0.0_dp
73 : REAL(KIND=dp), DIMENSION(3, 3) :: r_e_h = 0.0_dp, &
74 : cov_e_h = 0.0_dp, &
75 : corr_e_h_matrix = 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 38 : 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, n_exc
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
131 152 : TYPE(cp_fm_type), DIMENSION(3) :: fm_dipole_MO_trunc_reordered, &
132 304 : fm_dipole_per_dir, fm_trans_mom_bse
133 :
134 38 : CALL timeset(routineN, handle)
135 :
136 : ! an iterative solver provides fewer excitations than transitions
137 38 : CALL cp_fm_get_info(fm_eigvec_X, ncol_global=n_exc)
138 :
139 : CALL cp_fm_struct_create(fm_struct_dipole_MO_trunc_reordered, fm_eigvec_X%matrix_struct%para_env, &
140 38 : fm_eigvec_X%matrix_struct%context, 1, homo_red*virtual_red)
141 : CALL cp_fm_struct_create(fm_struct_trans_mom_bse, fm_eigvec_X%matrix_struct%para_env, &
142 38 : fm_eigvec_X%matrix_struct%context, 1, n_exc)
143 :
144 : ! Include excitonic amplitudes in dipoles, i.e. obtain "BSE dipoles":
145 : ! \vec{D}_n = sqrt(2) * sum_{i,a} \vec{D}_ai (X_{ai}^{(n)} + Y_{ai}^{(n)})
146 :
147 : ! Reorder dipoles in order to execute the sum over i and a by parallel gemm
148 152 : DO idir = 1, 3
149 : CALL cp_fm_create(fm_dipole_MO_trunc_reordered(idir), matrix_struct=fm_struct_dipole_MO_trunc_reordered, &
150 114 : name="dipoles_mo_reordered")
151 114 : CALL cp_fm_set_all(fm_dipole_MO_trunc_reordered(idir), 0.0_dp)
152 : CALL fm_general_add_bse(fm_dipole_MO_trunc_reordered(idir), fm_dipole_ai_trunc(idir), 1.0_dp, &
153 : 1, 1, &
154 : 1, virtual_red, &
155 114 : unit_nr, [2, 4, 3, 1], mp2_env)
156 152 : CALL cp_fm_release(fm_dipole_per_dir(idir))
157 : END DO
158 :
159 152 : DO idir = 1, 3
160 : CALL cp_fm_create(fm_trans_mom_bse(idir), matrix_struct=fm_struct_trans_mom_bse, &
161 114 : name="excitonic_dipoles")
162 152 : CALL cp_fm_set_all(fm_trans_mom_bse(idir), 0.0_dp)
163 : END DO
164 :
165 : ! If TDA is invoked, Y is not present as it is simply 0
166 38 : CALL cp_fm_create(fm_eigvec_XYsum, matrix_struct=fm_eigvec_X%matrix_struct, name="excit_amplitude_sum")
167 38 : CALL cp_fm_set_all(fm_eigvec_XYsum, 0.0_dp)
168 38 : CALL cp_fm_to_fm(fm_eigvec_X, fm_eigvec_XYsum)
169 38 : IF (PRESENT(fm_eigvec_Y)) THEN
170 22 : CALL cp_fm_scale_and_add(1.0_dp, fm_eigvec_XYsum, 1.0_dp, fm_eigvec_Y)
171 : END IF
172 152 : DO idir = 1, 3
173 : CALL parallel_gemm('N', 'N', 1, n_exc, homo_red*virtual_red, SQRT(2.0_dp), &
174 152 : fm_dipole_MO_trunc_reordered(idir), fm_eigvec_XYsum, 0.0_dp, fm_trans_mom_bse(idir))
175 : END DO
176 :
177 : ! Get oscillator strengths themselves
178 114 : ALLOCATE (oscill_str(n_exc))
179 : ! trans_mom_bse needs to be a 2D array per direction idir, such that cp_fm_get_submatrix can directly
180 : ! write to it
181 114 : ALLOCATE (trans_mom_bse(3, 1, n_exc))
182 114 : ALLOCATE (polarizability_residues(3, 3, n_exc))
183 38 : trans_mom_bse(:, :, :) = 0.0_dp
184 :
185 : ! Sum over all directions
186 152 : DO idir = 1, 3
187 152 : CALL cp_fm_get_submatrix(fm_trans_mom_bse(idir), trans_mom_bse(idir, :, :))
188 : END DO
189 :
190 1568 : DO n = 1, n_exc
191 6120 : DO idir = 1, 3
192 19890 : DO jdir = 1, 3
193 18360 : polarizability_residues(idir, jdir, n) = 2.0_dp*Exc_ens(n)*trans_mom_bse(idir, 1, n)*trans_mom_bse(jdir, 1, n)
194 : END DO
195 : END DO
196 6158 : oscill_str(n) = 2.0_dp/3.0_dp*Exc_ens(n)*SUM(ABS(trans_mom_bse(:, 1, n))**2)
197 : END DO
198 :
199 38 : CALL cp_fm_struct_release(fm_struct_dipole_MO_trunc_reordered)
200 38 : CALL cp_fm_struct_release(fm_struct_trans_mom_bse)
201 152 : DO idir = 1, 3
202 114 : CALL cp_fm_release(fm_dipole_MO_trunc_reordered(idir))
203 114 : CALL cp_fm_release(fm_trans_mom_bse(idir))
204 152 : CALL cp_fm_release(fm_dipole_ai_trunc(idir))
205 : END DO
206 38 : CALL cp_fm_release(fm_eigvec_XYsum)
207 :
208 38 : CALL timestop(handle)
209 :
210 114 : END SUBROUTINE get_oscillator_strengths
211 :
212 : ! **************************************************************************************************
213 : !> \brief Computes and returns absorption spectrum for the frequency range and broadening
214 : !> provided by the user.
215 : !> Prelim Ref.: C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications
216 : !> (Oxford University Press, Oxford, 2012), Eq. 7.51
217 : !> \param oscill_str ...
218 : !> \param polarizability_residues ...
219 : !> \param Exc_ens ...
220 : !> \param info_approximation ...
221 : !> \param unit_nr ...
222 : !> \param mp2_env ...
223 : ! **************************************************************************************************
224 2 : SUBROUTINE compute_and_print_absorption_spectrum(oscill_str, polarizability_residues, Exc_ens, &
225 : info_approximation, unit_nr, mp2_env)
226 :
227 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
228 : INTENT(IN) :: oscill_str
229 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
230 : INTENT(IN) :: polarizability_residues
231 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), &
232 : INTENT(IN) :: Exc_ens
233 : CHARACTER(LEN=10) :: info_approximation
234 : INTEGER, INTENT(IN) :: unit_nr
235 : TYPE(mp2_type), INTENT(INOUT) :: mp2_env
236 :
237 : CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_and_print_absorption_spectrum'
238 :
239 : CHARACTER(LEN=10) :: eta_str, width_eta_format_str
240 : CHARACTER(LEN=40) :: file_name_crosssection, &
241 : file_name_spectrum
242 : INTEGER :: handle, i, idir, j, jdir, k, num_steps, &
243 : unit_nr_file, width_eta
244 : REAL(KIND=dp) :: eta, freq_end, freq_start, freq_step, &
245 : omega
246 2 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: abs_cross_section, abs_spectrum
247 2 : REAL(KIND=dp), DIMENSION(:), POINTER :: eta_list
248 : TYPE(cp_logger_type), POINTER :: logger
249 :
250 2 : CALL timeset(routineN, handle)
251 :
252 2 : freq_step = mp2_env%bse%bse_spectrum_freq_step_size
253 2 : freq_start = mp2_env%bse%bse_spectrum_freq_start
254 2 : freq_end = mp2_env%bse%bse_spectrum_freq_end
255 2 : eta_list => mp2_env%bse%bse_eta_spectrum_list
256 :
257 : ! Calculate number of steps to fit given frequency range
258 2 : num_steps = NINT((freq_end - freq_start)/freq_step) + 1
259 :
260 4 : DO k = 1, SIZE(eta_list)
261 2 : eta = eta_list(k)
262 :
263 : ! Some magic to get a nice formatting of the eta value in filenames
264 2 : width_eta = MAX(1, INT(LOG10(eta)) + 1) + 4
265 2 : WRITE (width_eta_format_str, "(A2,I0,A3)") '(F', width_eta, '.3)'
266 2 : WRITE (eta_str, width_eta_format_str) eta*evolt
267 : ! Filename itself
268 2 : file_name_spectrum = 'BSE'//TRIM(ADJUSTL(info_approximation))//'eta='//TRIM(eta_str)//'.spectrum'
269 2 : file_name_crosssection = 'BSE'//TRIM(ADJUSTL(info_approximation))//'eta='//TRIM(eta_str)//'.crosssection'
270 :
271 : ! First column is frequency in eV, second column is imaginary part of the trace of the polarizability
272 : ! The following 9 columns are the entries of the polarizability tensor
273 6 : ALLOCATE (abs_spectrum(num_steps, 11))
274 2 : abs_spectrum(:, :) = 0.0_dp
275 : ! Also calculate and print the photoabsorption cross section tensor
276 : ! σ_{µ µ'}(ω) = 4πω Im{α_{µ µ'}(ω)} / c
277 4 : ALLOCATE (abs_cross_section(num_steps, 11))
278 2 : abs_cross_section(:, :) = 0.0_dp
279 :
280 : ! Calculate the imaginary part of the mean dipole polarizability α_{avg}(ω)
281 : ! which is given by (cf. C. Ullrichs Book on TDDFT, Eq. 7.51)
282 : ! We introduce an additional - due to his convention for charge vs particle density, see also:
283 : ! Computer Physics Communications, 208:149–161, November 2016
284 : ! https://doi.org/10.1016/j.cpc.2016.06.019
285 : ! α_{avg}(ω) = - \sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}
286 : ! and then the imaginary part is (in the limit η -> 0)
287 : ! Im[α_{avg}(ω)] = - \sum_{n=1}^{N_exc} f_n * η / ((ω - Ω^n)² + η²)
288 : ! where f_n are the oscillator strengths and E_exc the excitation energies
289 : ! For the full polarizability tensor, we have
290 : ! α_{µ µ'}(ω) = - \sum_n [2 Ω^n d^n_µ d^n_µ'] / [(ω+iη)^2- (Ω^n)^2]
291 : ! = - \sum_n "polarizability_residues" / [(ω+iη)^2- (Ω^n)^2]
292 2004 : DO i = 1, num_steps
293 2002 : omega = freq_start + (i - 1)*freq_step
294 2002 : abs_spectrum(i, 1) = omega
295 98100 : DO j = 1, SIZE(oscill_str)
296 : abs_spectrum(i, 2) = abs_spectrum(i, 2) - oscill_str(j)* &
297 96096 : AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
298 386386 : DO idir = 1, 3
299 1249248 : DO jdir = 1, 3
300 : ! Factor 2 from formula for tensor is already in the polarizability_residues
301 : ! to follow the same convention as the oscillator strengths
302 : abs_spectrum(i, 2 + (idir - 1)*3 + jdir) = abs_spectrum(i, 2 + (idir - 1)*3 + jdir) &
303 : - polarizability_residues(idir, jdir, j)* &
304 1153152 : AIMAG(1/((omega + CMPLX(0.0, eta, kind=dp))**2 - Exc_ens(j)**2))
305 : END DO
306 : END DO
307 : END DO
308 : END DO
309 :
310 : ! Extract cross section σ from polarizability tensor
311 2004 : DO i = 1, num_steps
312 2002 : omega = abs_spectrum(i, 1)
313 2002 : abs_cross_section(i, 1) = omega
314 22024 : abs_cross_section(i, 2:) = 4.0_dp*pi*abs_spectrum(i, 2:)*omega/c_light_au
315 : END DO
316 :
317 : !For debug runs: Export an entry of the two tensors to allow regtests on spectra
318 2 : IF (mp2_env%bse%bse_debug_print) THEN
319 2 : IF (unit_nr > 0) THEN
320 1 : WRITE (unit_nr, '(T2,A10,T13,A,T65,F16.4)') 'BSE|DEBUG|', &
321 1 : 'Averaged dynamical dipole polarizability at 8.2 eV:', &
322 2 : abs_spectrum(83, 2)
323 1 : WRITE (unit_nr, '(T2,A10,T13,A,T65,F16.4)') 'BSE|DEBUG|', &
324 1 : 'Averaged photoabsorption cross section at 8.2 eV:', &
325 2 : abs_cross_section(83, 2)
326 : END IF
327 : END IF
328 :
329 : ! Print it to file
330 2 : logger => cp_get_default_logger()
331 2 : IF (logger%para_env%is_source()) THEN
332 2 : unit_nr_file = cp_logger_get_default_unit_nr()
333 : ELSE
334 0 : unit_nr_file = -1
335 : END IF
336 :
337 2 : IF (unit_nr_file > 0) THEN
338 : CALL open_file(file_name_crosssection, unit_number=unit_nr_file, &
339 2 : file_status="UNKNOWN", file_action="WRITE")
340 : WRITE (unit_nr_file, '(A,A6)') "# Photoabsorption cross section σ_{µ µ'}(ω) = -4πω/c * Im[ \sum_n "// &
341 2 : "[2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²] ] from Bethe Salpeter equation for method ", &
342 4 : TRIM(ADJUSTL(info_approximation))
343 2 : WRITE (unit_nr_file, '(A20,1X,10(2X,A20,1X))') "# Frequency (eV)", "σ_{avg}(ω)", "σ_xx(ω)", &
344 2 : "σ_xy(ω)", "σ_xz(ω)", "σ_yx(ω)", "σ_yy(ω)", "σ_yz(ω)", "σ_zx(ω)", &
345 4 : "σ_zy(ω)", "σ_zz(ω)"
346 2004 : DO i = 1, num_steps
347 2004 : WRITE (unit_nr_file, '(11(F20.8,1X))') abs_cross_section(i, 1)*evolt, abs_cross_section(i, 2:11)
348 : END DO
349 2 : CALL close_file(unit_nr_file)
350 : END IF
351 2 : DEALLOCATE (abs_cross_section)
352 :
353 2 : IF (unit_nr_file > 0) THEN
354 : CALL open_file(file_name_spectrum, unit_number=unit_nr_file, &
355 2 : file_status="UNKNOWN", file_action="WRITE")
356 : WRITE (unit_nr_file, '(A,A6)') "# Imaginary part of polarizability α_{µ µ'}(ω) = -\sum_n "// &
357 2 : "[2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²] from Bethe Salpeter equation for method ", &
358 4 : TRIM(ADJUSTL(info_approximation))
359 2 : WRITE (unit_nr_file, '(A20,1X,10(2X,A20,1X))') "# Frequency (eV)", "Im{α_{avg}(ω)}", "Im{α_xx(ω)}", &
360 2 : "Im{α_xy(ω)}", "Im{α_xz(ω)}", "Im{α_yx(ω)}", "Im{α_yy(ω)}", "Im{α_yz(ω)}", "Im{α_zx(ω)}", &
361 4 : "Im{α_zy(ω)}", "Im{α_zz(ω)}"
362 2004 : DO i = 1, num_steps
363 2004 : WRITE (unit_nr_file, '(11(F20.8,1X))') abs_spectrum(i, 1)*evolt, abs_spectrum(i, 2:11)
364 : END DO
365 2 : CALL close_file(unit_nr_file)
366 : END IF
367 4 : DEALLOCATE (abs_spectrum)
368 : END DO
369 :
370 2 : IF (unit_nr > 0) THEN
371 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
372 : WRITE (unit_nr, '(T2,A4,T7,A,A)') &
373 1 : 'BSE|', "Printed optical absorption spectrum to local files, e.g. "
374 : WRITE (unit_nr, '(T2,A4,T7,A)') &
375 1 : 'BSE|', file_name_spectrum
376 : WRITE (unit_nr, '(T2,A4,T7,A,A)') &
377 1 : 'BSE|', "as well as photoabsorption cross section to, e.g. "
378 : WRITE (unit_nr, '(T2,A4,T7,A)') &
379 1 : 'BSE|', file_name_crosssection
380 : WRITE (unit_nr, '(T2,A4,T7,A52)') &
381 1 : 'BSE|', "using the Eq. (7.51) from C. Ullrichs Book on TDDFT:"
382 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
383 : WRITE (unit_nr, '(T2,A4,T10,A75)') &
384 1 : 'BSE|', "Im{α_{avg}(ω)} = -Im{\sum_{n=1}^{N_exc} \frac{f_n}{(ω+iη)² - (Ω^n)²}}"
385 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
386 : WRITE (unit_nr, '(T2,A4,T7,A)') &
387 1 : 'BSE|', "or for the full polarizability tensor:"
388 : WRITE (unit_nr, '(T2,A4,T10,A)') &
389 1 : 'BSE|', "α_{µ µ'}(ω) = -\sum_n [2 Ω^n d_µ^n d_µ'^n] / [(ω+iη)²- (Ω^n)²]"
390 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
391 : WRITE (unit_nr, '(T2,A4,T7,A)') &
392 1 : 'BSE|', "as well as Eq. (7.48):"
393 : WRITE (unit_nr, '(T2,A4,T10,A)') &
394 1 : 'BSE|', "σ_{µ µ'}(ω) = 4πω Im{α_{µ µ'}(ω)} / c"
395 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
396 : WRITE (unit_nr, '(T2,A4,T7,A)') &
397 1 : 'BSE|', "with transition moments d_µ^n, oscillator strengths f_n,"
398 : WRITE (unit_nr, '(T2,A4,T7,A)') &
399 1 : 'BSE|', "excitation energies Ω^n and the speed of light c."
400 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
401 : WRITE (unit_nr, '(T2,A4,T7,A)') &
402 1 : 'BSE|', "Please note that we adopt an additional minus sign for both quantities,"
403 : WRITE (unit_nr, '(T2,A4,T7,A)') &
404 1 : 'BSE|', "due to the convention for charge vs particle density as done in MolGW:"
405 : WRITE (unit_nr, '(T2,A4,T7,A)') &
406 1 : 'BSE|', "https://doi.org/10.1016/j.cpc.2016.06.019."
407 1 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
408 : END IF
409 :
410 2 : CALL timestop(handle)
411 :
412 4 : END SUBROUTINE compute_and_print_absorption_spectrum
413 :
414 : ! **************************************************************************************************
415 : !> \brief ...
416 : !> \param fm_X ...
417 : !> \param fm_Y ...
418 : !> \param mo_coeff ...
419 : !> \param homo ...
420 : !> \param virtual ...
421 : !> \param info_approximation ...
422 : !> \param oscill_str ...
423 : !> \param qs_env ...
424 : !> \param unit_nr ...
425 : !> \param mp2_env ...
426 : ! **************************************************************************************************
427 4 : SUBROUTINE calculate_NTOs(fm_X, fm_Y, &
428 4 : mo_coeff, homo, virtual, &
429 : info_approximation, &
430 : oscill_str, &
431 : qs_env, unit_nr, mp2_env)
432 :
433 : TYPE(cp_fm_type), INTENT(IN) :: fm_X
434 : TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_Y
435 : TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: mo_coeff
436 : INTEGER, INTENT(IN) :: homo, virtual
437 : CHARACTER(LEN=10) :: info_approximation
438 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: oscill_str
439 : TYPE(qs_environment_type), POINTER :: qs_env
440 : INTEGER, INTENT(IN) :: unit_nr
441 : TYPE(mp2_type), INTENT(INOUT) :: mp2_env
442 :
443 : CHARACTER(LEN=*), PARAMETER :: routineN = 'calculate_NTOs'
444 : REAL(KIND=dp), PARAMETER :: coeff_err = 1.0E-5_dp
445 :
446 : CHARACTER(LEN=20), DIMENSION(2) :: nto_name
447 : INTEGER :: handle, homo_irred, i, i_nto, info_svd, &
448 : j, n_exc, n_nto, nao_full, nao_trunc
449 4 : INTEGER, DIMENSION(:), POINTER :: stride
450 : LOGICAL :: append_cube, cube_file
451 4 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: eigval_svd_squ
452 4 : REAL(KIND=dp), DIMENSION(:), POINTER :: eigval_svd
453 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_m, fm_struct_mo_coeff, &
454 : fm_struct_nto_holes, &
455 : fm_struct_nto_particles, &
456 : fm_struct_nto_set
457 : TYPE(cp_fm_type) :: fm_eigvl, fm_eigvr_t, fm_m, fm_mo_coeff, fm_nto_coeff_holes, &
458 : fm_nto_coeff_particles, fm_nto_set, fm_X_ia, fm_Y_ai
459 4 : TYPE(mo_set_type), ALLOCATABLE, DIMENSION(:) :: nto_set
460 : TYPE(section_vals_type), POINTER :: bse_section, input, nto_section
461 :
462 4 : CALL timeset(routineN, handle)
463 : CALL get_qs_env(qs_env=qs_env, &
464 4 : input=input)
465 4 : bse_section => section_vals_get_subs_vals(input, "DFT%XC%WF_CORRELATION%RI_RPA%GW%BSE")
466 :
467 4 : nao_full = qs_env%mos(1)%nao
468 4 : nao_trunc = homo + virtual
469 : ! This is not influenced by the BSE cutoff
470 4 : homo_irred = qs_env%mos(1)%homo
471 : ! M will have a block structure and is quadratic in homo+virtual, i.e.
472 : ! occ virt
473 : ! | 0 X_i,a | occ = homo
474 : ! M = | Y_a,i 0 | virt = virtual
475 : !
476 : ! X and Y are here not the eigenvectors X_ia,n - instead we fix n and reshape the combined ia index
477 : ! Notice the index structure of the lower block, i.e. X is transposed
478 : CALL cp_fm_struct_create(fm_struct_m, &
479 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
480 4 : nao_trunc, nao_trunc)
481 : CALL cp_fm_struct_create(fm_struct_mo_coeff, &
482 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
483 4 : nao_full, nao_trunc)
484 : CALL cp_fm_struct_create(fm_struct_nto_holes, &
485 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
486 4 : nao_full, nao_trunc)
487 : CALL cp_fm_struct_create(fm_struct_nto_particles, &
488 : fm_X%matrix_struct%para_env, fm_X%matrix_struct%context, &
489 4 : nao_full, nao_trunc)
490 :
491 : CALL cp_fm_create(fm_mo_coeff, matrix_struct=fm_struct_mo_coeff, &
492 4 : name="mo_coeff")
493 : ! Here, we take care of possible cutoffs
494 : ! Simply truncating the matrix causes problems with the print function
495 : ! Therefore, we keep the dimension, but set the coefficients of truncated indices to 0
496 : CALL cp_fm_to_fm_submat_general(mo_coeff(1), fm_mo_coeff, &
497 : nao_full, nao_trunc, &
498 : 1, homo_irred - homo + 1, &
499 : 1, 1, &
500 4 : mo_coeff(1)%matrix_struct%context)
501 :
502 : ! Print some information about the NTOs
503 4 : IF (unit_nr > 0) THEN
504 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
505 4 : 'The Natural Transition Orbital (NTO) pairs φ_I(r_e) and χ_I(r_h) for a fixed'
506 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
507 4 : 'excitation index n are obtained by singular value decomposition of T'
508 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
509 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
510 4 : ' = (0 X)'
511 2 : IF (PRESENT(fm_Y)) THEN
512 1 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
513 2 : 'T = (Y^T 0)'
514 : ELSE
515 1 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
516 2 : 'T = (0 0)'
517 : END IF
518 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
519 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
520 4 : 'T = U Λ V^T'
521 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
522 4 : 'φ_I(r_e) = \sum_p V_pI ψ_p(r_e)'
523 2 : WRITE (unit_nr, '(T2,A4,T15,A)') 'BSE|', &
524 4 : 'χ_I(r_h) = \sum_p U_pI ψ_p(r_e)'
525 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
526 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
527 4 : 'where we have introduced'
528 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
529 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
530 2 : 'BSE|', "ψ_p:", "occupied and virtual molecular orbitals,"
531 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
532 2 : 'BSE|', "φ_I(r_e):", "NTO state for the electron,"
533 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
534 2 : 'BSE|', "χ_I(r_h):", "NTO state for the hole,"
535 : WRITE (unit_nr, '(T2,A4,T7,A,T20,A)') &
536 2 : 'BSE|', "Λ:", "diagonal matrix of NTO weights λ_I,"
537 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
538 2 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
539 4 : "The NTOs are calculated with the following settings:"
540 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
541 2 : WRITE (unit_nr, '(T2,A4,T7,A,T71,I10)') 'BSE|', 'Number of excitations, for which NTOs are computed', &
542 4 : mp2_env%bse%num_print_exc_ntos
543 2 : IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
544 0 : WRITE (unit_nr, '(T2,A4,T7,A,T71,F10.3)') 'BSE|', 'Threshold for oscillator strength f^n', &
545 0 : mp2_env%bse%eps_nto_osc_str
546 : ELSE
547 2 : WRITE (unit_nr, '(T2,A4,T7,A,T71,A10)') 'BSE|', 'Threshold for oscillator strength f^n', &
548 4 : ADJUSTL("---")
549 : END IF
550 2 : WRITE (unit_nr, '(T2,A4,T7,A,T72,F10.3)') 'BSE|', 'Threshold for NTO weights (λ_I)^2', &
551 4 : mp2_env%bse%eps_nto_eigval
552 : END IF
553 :
554 : ! Write the header of NTO info table
555 4 : IF (unit_nr > 0) THEN
556 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
557 2 : IF (.NOT. PRESENT(fm_Y)) THEN
558 1 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
559 2 : 'NTOs from solving the BSE within the TDA:'
560 : ELSE
561 1 : WRITE (unit_nr, '(T2,A4,T7,A)') 'BSE|', &
562 2 : 'NTOs from solving the BSE without the TDA:'
563 : END IF
564 2 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
565 2 : WRITE (unit_nr, '(T2,A4,T8,A12,T22,A8,T33,A14,T62,A)') 'BSE|', &
566 4 : 'Excitation n', "TDA/ABBA", "Index of NTO I", 'NTO weights (λ_I)^2'
567 : END IF
568 :
569 104 : DO j = 1, mp2_env%bse%num_print_exc_ntos
570 100 : n_exc = mp2_env%bse%bse_nto_state_list_final(j)
571 : ! Takes care of unallocated oscill_str array in case of Triplet
572 100 : IF (mp2_env%bse%eps_nto_osc_str > 0.0_dp) THEN
573 : ! Check actual values
574 0 : IF (oscill_str(n_exc) < mp2_env%bse%eps_nto_osc_str) THEN
575 : ! Print skipped levels to table
576 0 : IF (unit_nr > 0) THEN
577 0 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
578 0 : WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T42,A39)') 'BSE|', &
579 0 : n_exc, info_approximation, "Skipped (Oscillator strength too small)"
580 : END IF
581 : CYCLE
582 : END IF
583 : END IF
584 :
585 : CALL cp_fm_create(fm_m, matrix_struct=fm_struct_m, &
586 100 : name="single_part_trans_dm")
587 100 : CALL cp_fm_set_all(fm_m, 0.0_dp)
588 :
589 : CALL cp_fm_create(fm_nto_coeff_holes, matrix_struct=fm_struct_nto_holes, &
590 100 : name="nto_coeffs_holes")
591 100 : CALL cp_fm_set_all(fm_nto_coeff_holes, 0.0_dp)
592 :
593 : CALL cp_fm_create(fm_nto_coeff_particles, matrix_struct=fm_struct_nto_particles, &
594 100 : name="nto_coeffs_particles")
595 100 : CALL cp_fm_set_all(fm_nto_coeff_particles, 0.0_dp)
596 :
597 : ! Reshuffle from X_ia,n_exc to X_i,a
598 : CALL reshuffle_eigvec(fm_X, fm_X_ia, homo, virtual, n_exc, &
599 100 : .FALSE., unit_nr, mp2_env)
600 :
601 : ! Copy X to upper block in M, i.e. starting from column homo+1
602 : CALL cp_fm_to_fm_submat(fm_X_ia, fm_m, &
603 : homo, virtual, &
604 : 1, 1, &
605 100 : 1, homo + 1)
606 100 : CALL cp_fm_release(fm_X_ia)
607 : ! Copy Y if present
608 100 : IF (PRESENT(fm_Y)) THEN
609 : ! Reshuffle from Y_ia,n_exc to Y_a,i
610 : CALL reshuffle_eigvec(fm_Y, fm_Y_ai, homo, virtual, n_exc, &
611 50 : .TRUE., unit_nr, mp2_env)
612 :
613 : ! Copy Y^T to lower block in M, i.e. starting from row homo+1
614 : CALL cp_fm_to_fm_submat(fm_Y_ai, fm_m, &
615 : virtual, homo, &
616 : 1, 1, &
617 50 : homo + 1, 1)
618 :
619 50 : CALL cp_fm_release(fm_Y_ai)
620 :
621 : END IF
622 :
623 : ! Now we compute the SVD of M_{occ+virt,occ+virt}, which yields
624 : ! M = U * Lambda * V^T
625 : ! Initialize matrices and arrays to store left/right eigenvectors and singular values
626 : CALL cp_fm_create(matrix=fm_eigvl, &
627 : matrix_struct=fm_m%matrix_struct, &
628 100 : name="LEFT_SINGULAR_MATRIX")
629 100 : CALL cp_fm_set_all(fm_eigvl, alpha=0.0_dp)
630 : CALL cp_fm_create(matrix=fm_eigvr_t, &
631 : matrix_struct=fm_m%matrix_struct, &
632 100 : name="RIGHT_SINGULAR_MATRIX")
633 100 : CALL cp_fm_set_all(fm_eigvr_t, alpha=0.0_dp)
634 :
635 300 : ALLOCATE (eigval_svd(nao_trunc))
636 1700 : eigval_svd(:) = 0.0_dp
637 : info_svd = 0
638 100 : CALL cp_fm_svd(fm_m, fm_eigvl, fm_eigvr_t, eigval_svd, info_svd)
639 604 : IF (info_svd /= 0) THEN
640 0 : IF (unit_nr > 0) THEN
641 : CALL cp_warn(__LOCATION__, &
642 : "SVD for computation of NTOs not successful. "// &
643 0 : "Skipping print of NTOs.")
644 0 : IF (info_svd > 0) THEN
645 : CALL cp_warn(__LOCATION__, &
646 : "PDGESVD detected heterogeneity. "// &
647 0 : "Decreasing number of MPI ranks might solve this issue.")
648 : END IF
649 : END IF
650 : ! Release matrices to avoid memory leaks
651 0 : CALL cp_fm_release(fm_m)
652 0 : CALL cp_fm_release(fm_nto_coeff_holes)
653 0 : CALL cp_fm_release(fm_nto_coeff_particles)
654 : ELSE
655 : ! Rescale singular values as done in Martin2003 (10.1063/1.1558471)
656 200 : ALLOCATE (eigval_svd_squ(nao_trunc))
657 1700 : eigval_svd_squ(:) = eigval_svd(:)**2
658 : ! Sanity check for TDA: In case of TDA, the sum should be \sum_ia |X_ia|^2 = 1
659 100 : IF (.NOT. PRESENT(fm_Y)) THEN
660 850 : IF (ABS(SUM(eigval_svd_squ) - 1) >= coeff_err) THEN
661 0 : CPWARN("Sum of NTO coefficients deviates from 1!")
662 : END IF
663 : END IF
664 :
665 : ! Create NTO coefficients for later print to grid via TDDFT routine
666 : ! Apply U = fm_eigvl to MO coeffs, which yields hole states
667 : CALL parallel_gemm("N", "N", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvl, 0.0_dp, &
668 100 : fm_nto_coeff_holes)
669 :
670 : ! Apply V^T = fm_eigvr_t to MO coeffs, which yields particle states
671 : CALL parallel_gemm("N", "T", nao_full, nao_trunc, nao_trunc, 1.0_dp, fm_mo_coeff, fm_eigvr_t, 0.0_dp, &
672 100 : fm_nto_coeff_particles)
673 :
674 : !Release intermediary work matrices
675 100 : CALL cp_fm_release(fm_m)
676 100 : CALL cp_fm_release(fm_eigvl)
677 100 : CALL cp_fm_release(fm_eigvr_t)
678 :
679 : ! Transfer NTO coefficients to sets
680 100 : nto_name(1) = 'Hole_coord'
681 100 : nto_name(2) = 'Particle_coord'
682 300 : ALLOCATE (nto_set(2))
683 : ! Extract number of significant NTOs
684 100 : n_nto = 0
685 320 : DO i_nto = 1, nao_trunc
686 320 : IF (eigval_svd_squ(i_nto) > mp2_env%bse%eps_nto_eigval) THEN
687 220 : n_nto = n_nto + 1
688 : ELSE
689 : ! Since svd orders in descending order, we can exit the loop if smaller
690 : EXIT
691 : END IF
692 : END DO
693 :
694 100 : IF (unit_nr > 0) THEN
695 50 : WRITE (unit_nr, '(T2,A4)') 'BSE|'
696 160 : DO i_nto = 1, n_nto
697 110 : WRITE (unit_nr, '(T2,A4,T8,I12,T24,A6,T41,I6,T71,F10.5)') 'BSE|', &
698 270 : n_exc, info_approximation, i_nto, eigval_svd_squ(i_nto)
699 : END DO
700 : END IF
701 :
702 : CALL cp_fm_struct_create(fm_struct_nto_set, template_fmstruct=fm_struct_nto_holes, &
703 100 : ncol_global=n_nto)
704 100 : CALL cp_fm_create(fm_nto_set, fm_struct_nto_set)
705 300 : DO i = 1, 2
706 200 : CALL allocate_mo_set(nto_set(i), nao_trunc, n_nto, 0, 0.0_dp, 2.0_dp, 0.0_dp)
707 300 : CALL init_mo_set(nto_set(i), fm_ref=fm_nto_set, name=nto_name(i))
708 : END DO
709 100 : CALL cp_fm_release(fm_nto_set)
710 100 : CALL cp_fm_struct_release(fm_struct_nto_set)
711 :
712 : ! Fill NTO sets
713 100 : CALL cp_fm_to_fm(fm_nto_coeff_holes, nto_set(1)%mo_coeff, ncol=n_nto)
714 100 : CALL cp_fm_to_fm(fm_nto_coeff_particles, nto_set(2)%mo_coeff, ncol=n_nto)
715 :
716 : ! Cube files
717 100 : nto_section => section_vals_get_subs_vals(bse_section, "NTO_ANALYSIS")
718 100 : CALL section_vals_val_get(nto_section, "CUBE_FILES", l_val=cube_file)
719 100 : CALL section_vals_val_get(nto_section, "STRIDE", i_vals=stride)
720 100 : CALL section_vals_val_get(nto_section, "APPEND", l_val=append_cube)
721 100 : IF (cube_file) THEN
722 : CALL print_bse_nto_cubes(qs_env, nto_set, n_exc, info_approximation, &
723 0 : stride, append_cube, nto_section)
724 : END IF
725 :
726 100 : CALL cp_fm_release(fm_nto_coeff_holes)
727 100 : CALL cp_fm_release(fm_nto_coeff_particles)
728 100 : DEALLOCATE (eigval_svd)
729 100 : DEALLOCATE (eigval_svd_squ)
730 300 : DO i = 1, 2
731 300 : CALL deallocate_mo_set(nto_set(i))
732 : END DO
733 400 : DEALLOCATE (nto_set)
734 : END IF
735 : END DO
736 :
737 4 : CALL cp_fm_release(fm_mo_coeff)
738 4 : CALL cp_fm_struct_release(fm_struct_m)
739 4 : CALL cp_fm_struct_release(fm_struct_nto_holes)
740 4 : CALL cp_fm_struct_release(fm_struct_nto_particles)
741 4 : CALL cp_fm_struct_release(fm_struct_mo_coeff)
742 :
743 4 : CALL timestop(handle)
744 :
745 8 : END SUBROUTINE calculate_NTOs
746 :
747 : ! **************************************************************************************************
748 : !> \brief ...
749 : !> \param exc_descr Allocated and initialized on exit
750 : !> \param fm_X_ia ...
751 : !> \param fm_multipole_ij_trunc ...
752 : !> \param fm_multipole_ab_trunc ...
753 : !> \param fm_multipole_ai_trunc ...
754 : !> \param i_exc ...
755 : !> \param homo ...
756 : !> \param virtual ...
757 : !> \param fm_Y_ia ...
758 : ! **************************************************************************************************
759 110 : SUBROUTINE get_exciton_descriptors(exc_descr, fm_X_ia, &
760 : fm_multipole_ij_trunc, fm_multipole_ab_trunc, &
761 : fm_multipole_ai_trunc, &
762 : i_exc, homo, virtual, &
763 : fm_Y_ia)
764 :
765 : TYPE(exciton_descr_type), ALLOCATABLE, &
766 : DIMENSION(:) :: exc_descr
767 : TYPE(cp_fm_type), INTENT(IN) :: fm_X_ia
768 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:), &
769 : INTENT(IN) :: fm_multipole_ij_trunc, &
770 : fm_multipole_ab_trunc, &
771 : fm_multipole_ai_trunc
772 : INTEGER, INTENT(IN) :: i_exc, homo, virtual
773 : TYPE(cp_fm_type), INTENT(IN), OPTIONAL :: fm_Y_ia
774 :
775 : CHARACTER(LEN=*), PARAMETER :: routineN = 'get_exciton_descriptors'
776 :
777 : INTEGER :: handle, i_dir, j_dir
778 : INTEGER, DIMENSION(3) :: mask_quadrupole
779 : LOGICAL :: flag_TDA
780 : REAL(KIND=dp) :: norm_X, norm_XpY, norm_Y
781 : REAL(KIND=dp), DIMENSION(3) :: r_e_sq_X, r_e_sq_Y, r_e_X, r_e_Y, &
782 : r_h_sq_X, r_h_sq_Y, r_h_X, r_h_Y
783 : REAL(KIND=dp), DIMENSION(3, 3) :: r_e_h_XX, r_e_h_XY, r_e_h_YY
784 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_ab, fm_struct_ia
785 : TYPE(cp_fm_type) :: fm_work_ba, fm_work_ia, fm_work_ia_2
786 :
787 110 : CALL timeset(routineN, handle)
788 110 : IF (PRESENT(fm_Y_ia)) THEN
789 : flag_TDA = .FALSE.
790 : ELSE
791 60 : flag_TDA = .TRUE.
792 : END IF
793 :
794 : ! translates 1,2,3 to diagonal entries of quadrupoles xx, yy, zz
795 : ! Ordering in quadrupole moments is x, y, z, xx, xy, xz, yy, yz, zz
796 110 : mask_quadrupole = [4, 7, 9]
797 :
798 : CALL cp_fm_struct_create(fm_struct_ia, &
799 110 : context=fm_X_ia%matrix_struct%context, nrow_global=homo, ncol_global=virtual)
800 : CALL cp_fm_struct_create(fm_struct_ab, &
801 110 : context=fm_X_ia%matrix_struct%context, nrow_global=virtual, ncol_global=virtual)
802 :
803 110 : r_e_X(:) = 0.0_dp
804 110 : r_e_Y(:) = 0.0_dp
805 110 : r_h_X(:) = 0.0_dp
806 110 : r_h_Y(:) = 0.0_dp
807 110 : r_e_sq_X(:) = 0.0_dp
808 110 : r_h_sq_X(:) = 0.0_dp
809 110 : r_e_sq_Y(:) = 0.0_dp
810 110 : r_h_sq_Y(:) = 0.0_dp
811 110 : r_e_h_XX(:, :) = 0.0_dp
812 110 : r_e_h_XY(:, :) = 0.0_dp
813 110 : r_e_h_YY(:, :) = 0.0_dp
814 :
815 : norm_X = 0.0_dp
816 : norm_Y = 0.0_dp
817 110 : norm_XpY = 0.0_dp
818 :
819 : ! Initialize values of exciton descriptors
820 440 : exc_descr(i_exc)%r_e(:) = 0.0_dp
821 440 : exc_descr(i_exc)%r_h(:) = 0.0_dp
822 440 : exc_descr(i_exc)%r_e_sq(:) = 0.0_dp
823 440 : exc_descr(i_exc)%r_h_sq(:) = 0.0_dp
824 1430 : exc_descr(i_exc)%r_e_h(:, :) = 0.0_dp
825 :
826 110 : exc_descr(i_exc)%flag_TDA = flag_TDA
827 110 : exc_descr(i_exc)%norm_XpY = 0.0_dp
828 :
829 : ! Norm of X
830 110 : CALL cp_fm_trace(fm_X_ia, fm_X_ia, norm_X)
831 110 : norm_XpY = norm_X
832 : ! Norm of Y
833 110 : IF (.NOT. flag_TDA) THEN
834 50 : CALL cp_fm_trace(fm_Y_ia, fm_Y_ia, norm_Y)
835 50 : norm_XpY = norm_XpY + norm_Y
836 : END IF
837 :
838 110 : exc_descr(i_exc)%norm_XpY = norm_XpY
839 :
840 : ! <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
841 440 : DO i_dir = 1, 3
842 : ! <r_h>_X = X_ai µ_ij X_ja + ...
843 330 : CALL trace_exciton_descr(fm_X_ia, fm_multipole_ij_trunc(i_dir), fm_X_ia, r_h_X(i_dir))
844 330 : r_h_X(i_dir) = r_h_X(i_dir)/norm_XpY
845 440 : IF (.NOT. flag_TDA) THEN
846 : ! <r_h>_X = ... + Y_ia µ_ab Y_bi
847 150 : CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, fm_multipole_ab_trunc(i_dir), r_h_Y(i_dir))
848 150 : r_h_Y(i_dir) = r_h_Y(i_dir)/norm_XpY
849 : END IF
850 : END DO
851 440 : exc_descr(i_exc)%r_h(:) = r_h_X(:) + r_h_Y(:)
852 :
853 : ! <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
854 440 : DO i_dir = 1, 3
855 : ! <r_e>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
856 330 : CALL trace_exciton_descr(fm_X_ia, fm_X_ia, fm_multipole_ab_trunc(i_dir), r_e_X(i_dir))
857 330 : r_e_X(i_dir) = r_e_X(i_dir)/norm_XpY
858 440 : IF (.NOT. flag_TDA) THEN
859 : ! <r_e>_X = ... + Y_ai µ_ij Y_ja
860 150 : CALL trace_exciton_descr(fm_Y_ia, fm_multipole_ij_trunc(i_dir), fm_Y_ia, r_e_Y(i_dir))
861 150 : r_e_Y(i_dir) = r_e_Y(i_dir)/norm_XpY
862 : END IF
863 : END DO
864 440 : exc_descr(i_exc)%r_e(:) = r_e_X(:) + r_e_Y(:)
865 :
866 : ! <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
867 440 : DO i_dir = 1, 3
868 : ! <r_h^2>_X = X_ai M_ij X_ja + ...
869 : CALL trace_exciton_descr(fm_X_ia, fm_multipole_ij_trunc(mask_quadrupole(i_dir)), &
870 330 : fm_X_ia, r_h_sq_X(i_dir))
871 330 : r_h_sq_X(i_dir) = r_h_sq_X(i_dir)/norm_XpY
872 440 : IF (.NOT. flag_TDA) THEN
873 : ! <r_h^2>_X = ... + Y_ia M_ab Y_bi
874 : CALL trace_exciton_descr(fm_Y_ia, fm_Y_ia, &
875 150 : fm_multipole_ab_trunc(mask_quadrupole(i_dir)), r_h_sq_Y(i_dir))
876 150 : r_h_sq_Y(i_dir) = r_h_sq_Y(i_dir)/norm_XpY
877 : END IF
878 : END DO
879 440 : exc_descr(i_exc)%r_h_sq(:) = r_h_sq_X(:) + r_h_sq_Y(:)
880 :
881 : ! <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
882 440 : DO i_dir = 1, 3
883 : ! <r_e^2>_X = work_ib X_bi + ... = X_ib^T work_ib + ...
884 : CALL trace_exciton_descr(fm_X_ia, fm_X_ia, &
885 330 : fm_multipole_ab_trunc(mask_quadrupole(i_dir)), r_e_sq_X(i_dir))
886 330 : r_e_sq_X(i_dir) = r_e_sq_X(i_dir)/norm_XpY
887 440 : IF (.NOT. flag_TDA) THEN
888 : ! <r_e^2>_X = ... + Y_ai M_ij Y_ja
889 : CALL trace_exciton_descr(fm_Y_ia, fm_multipole_ij_trunc(mask_quadrupole(i_dir)), &
890 150 : fm_Y_ia, r_e_sq_Y(i_dir))
891 150 : r_e_sq_Y(i_dir) = r_e_sq_Y(i_dir)/norm_XpY
892 : END IF
893 : END DO
894 440 : exc_descr(i_exc)%r_e_sq(:) = r_e_sq_X(:) + r_e_sq_Y(:)
895 :
896 : ! <r_e^\mu r_h^\mu'>_X
897 : ! = Tr[ X^T µ'_ij X µ_ab + Y^T µ_ij Y µ'_ab + 2 X µ_ai Y µ'_ai ]
898 : ! = X_bj µ'_ji X_ia µ_ab + Y_bj µ_ji Y_ia µ'_ab + 2 X_ia µ_aj Y_jb µ'_bi
899 : ! The i_dir and j_dir convert to mu and mu'. µ (electron) sits between a (from X) and j (from Y),
900 : ! µ' (hole) between i (from X) and b (from Y); Tr[ Y µ'_ai X µ_ai ] = Tr[ X µ_ai Y µ'_ai ] by cyclicity, hence the 2.
901 110 : CALL cp_fm_create(fm_work_ia, fm_struct_ia)
902 110 : CALL cp_fm_create(fm_work_ia_2, fm_struct_ia)
903 110 : CALL cp_fm_create(fm_work_ba, fm_struct_ab)
904 440 : DO i_dir = 1, 3
905 1430 : DO j_dir = 1, 3
906 : ! First term - X^T µ'_ij X µ_ab
907 990 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
908 990 : CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
909 : ! work_ib = X_ia µ_ab
910 : CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
911 990 : fm_X_ia, fm_multipole_ab_trunc(i_dir), 0.0_dp, fm_work_ia)
912 : ! work_ja_2 = µ'_ji work_ia
913 : CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
914 990 : fm_multipole_ij_trunc(j_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
915 : ! <r_e^\mu r_h^\mu'>_X = work_ia_2 X_bj + ... = X^T work_ia_2 + ...
916 990 : CALL cp_fm_trace(fm_X_ia, fm_work_ia_2, r_e_h_XX(i_dir, j_dir))
917 990 : r_e_h_XX(i_dir, j_dir) = r_e_h_XX(i_dir, j_dir)/norm_XpY
918 1320 : IF (.NOT. flag_TDA) THEN
919 : ! Second term - Y^T µ_ij Y µ'_ab
920 450 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
921 450 : CALL cp_fm_set_all(fm_work_ia_2, 0.0_dp)
922 : ! work_ib = Y_ia µ'_ab
923 : CALL parallel_gemm("N", "N", homo, virtual, virtual, 1.0_dp, &
924 450 : fm_Y_ia, fm_multipole_ab_trunc(j_dir), 0.0_dp, fm_work_ia)
925 : ! work_ja_2 = µ_ji work_ia
926 : CALL parallel_gemm("N", "N", homo, virtual, homo, 1.0_dp, &
927 450 : fm_multipole_ij_trunc(i_dir), fm_work_ia, 0.0_dp, fm_work_ia_2)
928 : ! <r_h r_e>_X = work_ia_2 Y_bj + ... = Y^T work_ia_2 + ...
929 450 : CALL cp_fm_trace(fm_Y_ia, fm_work_ia_2, r_e_h_YY(i_dir, j_dir))
930 450 : r_e_h_YY(i_dir, j_dir) = r_e_h_YY(i_dir, j_dir)/norm_XpY
931 :
932 : ! Third term (counted twice) - X µ_ai Y µ'_ai = X_ia µ_aj Y_jb µ'_bi
933 : ! Reshuffle for usage of trace (where first argument is transposed)
934 : ! = µ_aj Y_jb µ'_bi X_ia =
935 : ! \___________/
936 : ! fm_work_ai
937 : ! fm_work_ai = µ_aj Y_jb µ'_bi
938 : ! fm_work_ia = µ'_ib Y_bj µ_ja
939 : ! \_____/
940 : ! fm_work_ba
941 450 : CALL cp_fm_set_all(fm_work_ba, 0.0_dp)
942 450 : CALL cp_fm_set_all(fm_work_ia, 0.0_dp)
943 : ! fm_work_ba = Y_bj µ_ja
944 : CALL parallel_gemm("T", "T", virtual, virtual, homo, 1.0_dp, &
945 450 : fm_Y_ia, fm_multipole_ai_trunc(i_dir), 0.0_dp, fm_work_ba)
946 : ! fm_work_ia = µ'_ib fm_work_ba
947 : CALL parallel_gemm("T", "N", homo, virtual, virtual, 1.0_dp, &
948 450 : fm_multipole_ai_trunc(j_dir), fm_work_ba, 0.0_dp, fm_work_ia)
949 : ! <r_e r_h>_X = ... + 2 X_ia µ_aj Y_jb µ'_bi
950 450 : CALL cp_fm_trace(fm_work_ia, fm_X_ia, r_e_h_XY(i_dir, j_dir))
951 450 : r_e_h_XY(i_dir, j_dir) = 2.0_dp*r_e_h_XY(i_dir, j_dir)/norm_XpY
952 : END IF
953 : END DO
954 : END DO
955 1430 : exc_descr(i_exc)%r_e_h(:, :) = r_e_h_XX(:, :) + r_e_h_XY(:, :) + r_e_h_YY(:, :)
956 :
957 110 : CALL cp_fm_release(fm_work_ia)
958 110 : CALL cp_fm_release(fm_work_ia_2)
959 110 : CALL cp_fm_release(fm_work_ba)
960 :
961 : ! Now we compute all the descriptors and correlation coefficients
962 : ! Order is: Directional ones, then covariances and correlation coefficients and
963 :
964 : ! diff_r_abs = |<r_h>_X - <r_e>_X|
965 440 : exc_descr(i_exc)%diff_r_abs = SQRT(SUM((exc_descr(i_exc)%r_h(:) - exc_descr(i_exc)%r_e(:))**2))
966 :
967 : ! σ_e = sqrt( <r_e^2>_X - <r_e>_X^2 )
968 770 : exc_descr(i_exc)%sigma_e = SQRT(SUM(exc_descr(i_exc)%r_e_sq(:)) - SUM(exc_descr(i_exc)%r_e(:)**2))
969 :
970 : ! σ_h = sqrt( <r_h^2>_X - <r_h>_X^2 )
971 770 : exc_descr(i_exc)%sigma_h = SQRT(SUM(exc_descr(i_exc)%r_h_sq(:)) - SUM(exc_descr(i_exc)%r_h(:)**2))
972 :
973 : ! Now directed ones
974 440 : DO i_dir = 1, 3
975 330 : exc_descr(i_exc)%d_eh_dir(i_dir) = ABS(exc_descr(i_exc)%r_h(i_dir) - exc_descr(i_exc)%r_e(i_dir))
976 330 : exc_descr(i_exc)%sigma_e_dir(i_dir) = SQRT(exc_descr(i_exc)%r_e_sq(i_dir) - exc_descr(i_exc)%r_e(i_dir)**2)
977 440 : exc_descr(i_exc)%sigma_h_dir(i_dir) = SQRT(exc_descr(i_exc)%r_h_sq(i_dir) - exc_descr(i_exc)%r_h(i_dir)**2)
978 : END DO
979 :
980 : ! Covariance and correlation coefficient (as well as crosscorrelation matrices)
981 : ! COV(r_e, r_h) = < r_e r_h >_X - < r_e >_X < r_h >_X
982 110 : exc_descr(i_exc)%cov_e_h_sum = 0.0_dp
983 1430 : exc_descr(i_exc)%cov_e_h(:, :) = 0.0_dp
984 1430 : exc_descr(i_exc)%corr_e_h_matrix(:, :) = 0.0_dp
985 440 : DO i_dir = 1, 3
986 1320 : DO j_dir = 1, 3
987 : exc_descr(i_exc)%cov_e_h(i_dir, j_dir) = exc_descr(i_exc)%r_e_h(i_dir, j_dir) &
988 990 : - exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(j_dir)
989 : exc_descr(i_exc)%corr_e_h_matrix(i_dir, j_dir) = &
990 : exc_descr(i_exc)%cov_e_h(i_dir, j_dir)/ &
991 1320 : (exc_descr(i_exc)%sigma_e_dir(i_dir)*exc_descr(i_exc)%sigma_h_dir(j_dir))
992 : END DO
993 : exc_descr(i_exc)%cov_e_h_sum = exc_descr(i_exc)%cov_e_h_sum + &
994 : exc_descr(i_exc)%r_e_h(i_dir, i_dir) - &
995 440 : exc_descr(i_exc)%r_e(i_dir)*exc_descr(i_exc)%r_h(i_dir)
996 : END DO
997 :
998 : ! e-h-correlation coefficient R_eh = COV(r_e, r_h) / ( σ_e σ_h )
999 110 : 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)
1000 :
1001 : ! root-mean-square e-h separation
1002 : exc_descr(i_exc)%diff_r_sqr = SQRT(exc_descr(i_exc)%diff_r_abs**2 + &
1003 : exc_descr(i_exc)%sigma_e**2 + exc_descr(i_exc)%sigma_h**2 &
1004 110 : - 2*exc_descr(i_exc)%cov_e_h_sum)
1005 :
1006 440 : DO i_dir = 1, 3
1007 : exc_descr(i_exc)%d_exc_dir(i_dir) = SQRT(exc_descr(i_exc)%d_eh_dir(i_dir)**2 + &
1008 : exc_descr(i_exc)%sigma_e_dir(i_dir)**2 + &
1009 : exc_descr(i_exc)%sigma_h_dir(i_dir)**2 - &
1010 440 : 2*exc_descr(i_exc)%cov_e_h(i_dir, i_dir))
1011 : END DO
1012 :
1013 : ! Expectation values of r_e and r_h
1014 440 : exc_descr(i_exc)%r_e_shift(:) = exc_descr(i_exc)%r_e(:)
1015 440 : exc_descr(i_exc)%r_h_shift(:) = exc_descr(i_exc)%r_h(:)
1016 :
1017 110 : CALL cp_fm_struct_release(fm_struct_ia)
1018 110 : CALL cp_fm_struct_release(fm_struct_ab)
1019 :
1020 110 : CALL timestop(handle)
1021 :
1022 330 : END SUBROUTINE get_exciton_descriptors
1023 :
1024 0 : END MODULE bse_properties
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