Routines for the full diagonalization of GW + Bethe-Salpeter for computing electronic excitations. More...

Functions/Subroutines
subroutine, public	create_a (fm_mat_s_ia_bse, fm_mat_s_bar_ij_bse, fm_mat_s_ab_bse, fm_a, eigenval, unit_nr, homo, virtual, dimen_ri, mp2_env, para_env)
	Matrix A constructed from GW energies and 3c-B-matrices (cf. subroutine mult_B_with_W) A_ia,jb = (ε_a-ε_i) δ_ij δ_ab + α * v_ia,jb - W_ij,ab ε_a, ε_i are GW singleparticle energies from Eigenval_reduced α is a spin-dependent factor v_ia,jb = \sum_P B^P_ia B^P_jb (unscreened Coulomb interaction) W_ij,ab = \sum_P \bar{B}^P_ij B^P_ab (screened Coulomb interaction)

subroutine, public	create_b (fm_mat_s_ia_bse, fm_mat_s_bar_ia_bse, fm_b, homo, virtual, dimen_ri, unit_nr, mp2_env)
	Matrix B constructed from 3c-B-matrices (cf. subroutine mult_B_with_W) B_ia,jb = α * v_ia,jb - W_ib,aj α is a spin-dependent factor v_ia,jb = \sum_P B^P_ia B^P_jb (unscreened Coulomb interaction) W_ib,aj = \sum_P \bar{B}^P_ib B^P_aj (screened Coulomb interaction)

subroutine, public	create_hermitian_form_of_abba (fm_a, fm_b, fm_c, fm_sqrt_a_minus_b, fm_inv_sqrt_a_minus_b, homo, virtual, unit_nr, mp2_env, diag_est)
	Construct Matrix C=(A-B)^0.5 (A+B) (A-B)^0.5 to solve full BSE matrix as a hermitian problem (cf. Eq. (A7) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001)). We keep fm_sqrt_A_minus_B and fm_inv_sqrt_A_minus_B for print of singleparticle transitions of ABBA as described in Eq. (A10) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001).

subroutine, public	diagonalize_c (fm_c, homo, virtual, homo_irred, fm_sqrt_a_minus_b, fm_inv_sqrt_a_minus_b, unit_nr, diag_est, mp2_env)
	Solving eigenvalue equation C Z^n = (Ω^n)^2 Z^n . Here, the eigenvectors Z^n relate to X^n via Eq. (A10) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001).

subroutine, public	diagonalize_a (fm_a, homo, virtual, homo_irred, unit_nr, diag_est, mp2_env)
	Solving hermitian eigenvalue equation A X^n = Ω^n X^n.

Detailed Description

Routines for the full diagonalization of GW + Bethe-Salpeter for computing electronic excitations.

History: 10.2023 created [Maximilian Graml]

Function/Subroutine Documentation

◆ create_a()

subroutine, public bse_full_diag::create_a	(	type(cp_fm_type), intent(in)	fm_mat_s_ia_bse,
		type(cp_fm_type), intent(in)	fm_mat_s_bar_ij_bse,
		type(cp_fm_type), intent(in)	fm_mat_s_ab_bse,
		type(cp_fm_type), intent(inout)	fm_a,
		real(kind=dp), dimension(:)	eigenval,
		integer, intent(in)	unit_nr,
		integer, intent(in)	homo,
		integer, intent(in)	virtual,
		integer, intent(in)	dimen_ri,
		type(mp2_type), intent(inout)	mp2_env,
		type(mp_para_env_type), intent(inout)	para_env
	)

Matrix A constructed from GW energies and 3c-B-matrices (cf. subroutine mult_B_with_W) A_ia,jb = (ε_a-ε_i) δ_ij δ_ab + α * v_ia,jb - W_ij,ab ε_a, ε_i are GW singleparticle energies from Eigenval_reduced α is a spin-dependent factor v_ia,jb = \sum_P B^P_ia B^P_jb (unscreened Coulomb interaction) W_ij,ab = \sum_P \bar{B}^P_ij B^P_ab (screened Coulomb interaction)

Parameters

fm_mat_S_ia_bse	...
fm_mat_S_bar_ij_bse	...
fm_mat_S_ab_bse	...
fm_A	...
Eigenval	...
unit_nr	...
homo	...
virtual	...
dimen_RI	...
mp2_env	...
para_env	...

Definition at line 73 of file bse_full_diag.F.

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◆ create_b()

subroutine, public bse_full_diag::create_b	(	type(cp_fm_type), intent(in)	fm_mat_s_ia_bse,
		type(cp_fm_type), intent(in)	fm_mat_s_bar_ia_bse,
		type(cp_fm_type), intent(inout)	fm_b,
		integer, intent(in)	homo,
		integer, intent(in)	virtual,
		integer, intent(in)	dimen_ri,
		integer, intent(in)	unit_nr,
		type(mp2_type), intent(inout)	mp2_env
	)

Matrix B constructed from 3c-B-matrices (cf. subroutine mult_B_with_W) B_ia,jb = α * v_ia,jb - W_ib,aj α is a spin-dependent factor v_ia,jb = \sum_P B^P_ia B^P_jb (unscreened Coulomb interaction) W_ib,aj = \sum_P \bar{B}^P_ib B^P_aj (screened Coulomb interaction)

Parameters

fm_mat_S_ia_bse	...
fm_mat_S_bar_ia_bse	...
fm_B	...
homo	...
virtual	...
dimen_RI	...
unit_nr	...
mp2_env	...

Definition at line 211 of file bse_full_diag.F.

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◆ create_hermitian_form_of_abba()

subroutine, public bse_full_diag::create_hermitian_form_of_abba	(	type(cp_fm_type), intent(in)	fm_a,
		type(cp_fm_type), intent(in)	fm_b,
		type(cp_fm_type), intent(inout)	fm_c,
		type(cp_fm_type), intent(inout)	fm_sqrt_a_minus_b,
		type(cp_fm_type), intent(inout)	fm_inv_sqrt_a_minus_b,
		integer, intent(in)	homo,
		integer, intent(in)	virtual,
		integer, intent(in)	unit_nr,
		type(mp2_type), intent(inout)	mp2_env,
		real(kind=dp), intent(in)	diag_est
	)

Construct Matrix C=(A-B)^0.5 (A+B) (A-B)^0.5 to solve full BSE matrix as a hermitian problem (cf. Eq. (A7) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001)). We keep fm_sqrt_A_minus_B and fm_inv_sqrt_A_minus_B for print of singleparticle transitions of ABBA as described in Eq. (A10) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001).

Parameters

fm_A	...
fm_B	...
fm_C	...
fm_sqrt_A_minus_B	...
fm_inv_sqrt_A_minus_B	...
homo	...
virtual	...
unit_nr	...
mp2_env	...
diag_est	...

Definition at line 291 of file bse_full_diag.F.

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◆ diagonalize_c()

subroutine, public bse_full_diag::diagonalize_c	(	type(cp_fm_type), intent(inout)	fm_c,
		integer, intent(in)	homo,
		integer, intent(in)	virtual,
		integer, intent(in)	homo_irred,
		type(cp_fm_type), intent(inout)	fm_sqrt_a_minus_b,
		type(cp_fm_type), intent(inout)	fm_inv_sqrt_a_minus_b,
		integer, intent(in)	unit_nr,
		real(kind=dp), intent(in)	diag_est,
		type(mp2_type), intent(inout)	mp2_env
	)

Solving eigenvalue equation C Z^n = (Ω^n)^2 Z^n . Here, the eigenvectors Z^n relate to X^n via Eq. (A10) in F. Furche J. Chem. Phys., Vol. 114, No. 14, (2001).

Parameters

fm_C	...
homo	...
virtual	...
homo_irred	...
fm_sqrt_A_minus_B	...
fm_inv_sqrt_A_minus_B	...
unit_nr	...
diag_est	...
mp2_env	...

Definition at line 408 of file bse_full_diag.F.

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◆ diagonalize_a()

subroutine, public bse_full_diag::diagonalize_a	(	type(cp_fm_type), intent(inout)	fm_a,
		integer, intent(in)	homo,
		integer, intent(in)	virtual,
		integer, intent(in)	homo_irred,
		integer, intent(in)	unit_nr,
		real(kind=dp), intent(in)	diag_est,
		type(mp2_type), intent(inout)	mp2_env
	)

Solving hermitian eigenvalue equation A X^n = Ω^n X^n.

Parameters

fm_A	...
homo	...
virtual	...
homo_irred	...
unit_nr	...
diag_est	...
mp2_env	...

Definition at line 496 of file bse_full_diag.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ create_a()

◆ create_b()

◆ create_hermitian_form_of_abba()

◆ diagonalize_c()

◆ diagonalize_a()