Exchange and Correlation functional calculations. More...

Functions/Subroutines
logical function, public	xc_uses_kinetic_energy_density (xc_fun_section, lsd)
	...

logical function, public	xc_uses_norm_drho (xc_fun_section, lsd)
	...

subroutine, public	xc_vxc_pw_create1 (vxc_rho, vxc_tau, rho_r, rho_g, tau, exc, xc_section, pw_pool, compute_virial, virial_xc, exc_r)
	Exchange and Correlation functional calculations. depending on the selected functional_routine calls the correct routine.

subroutine, public	smooth_cutoff (pot, rho, rhoa, rhob, rho_cutoff, rho_smooth_cutoff_range, e_0, e_0_scale_factor)
	smooths the cutoff on rho with a function smoothderiv_rho that is 0 for rho<rho_cutoff and 1 for rho>rho_cutoffrho_smooth_cutoff_range: E= integral e_0smoothderiv_rho => dE/d...= de/d... * smooth, dE/drho = de/drho * smooth + e_0 * dsmooth/drho

subroutine, public	calc_xc_density (pot, rho, rho_cutoff)

subroutine, public	xc_vxc_pw_create (vxc_rho, vxc_tau, exc, rho_r, rho_g, tau, xc_section, pw_pool, compute_virial, virial_xc, exc_r)
	Exchange and Correlation functional calculations.

real(kind=dp) function, public	xc_exc_calc (rho_r, rho_g, tau, xc_section, pw_pool)
	calculates just the exchange and correlation energy (no vxc)

subroutine, public	xc_calc_2nd_deriv (v_xc, v_xc_tau, deriv_set, rho_set, rho1_r, rho1_g, tau1_r, pw_pool, xc_section, gapw, vxg, do_excitations, do_sf, do_triplet, compute_virial, virial_xc)
	Caller routine to calculate the second order potential in the direction of rho1_r.

subroutine, public	xc_calc_2nd_deriv_numerical (v_xc, v_tau, rho_set, rho1_r, rho1_g, tau1_r, pw_pool, xc_section, do_triplet, calc_virial, virial_xc, deriv_set)
	calculates 2nd derivative numerically

subroutine, public	xc_calc_2nd_deriv_analytical (v_xc, v_xc_tau, deriv_set, rho_set, rho1_set, pw_pool, xc_section, gapw, vxg, tddfpt_fac, compute_virial, virial_xc, spinflip)
	Calculates the second derivative of E_xc at rho in the direction rho1 (if you see the second derivative as bilinear form) partial_rho\|_(rho=rho) partial_rho\|_(rho=rho) E_xc drho(rho1)drho The other direction is still undetermined, thus it returns a potential (partial integration is performed to reduce it to function of rho, removing the dependence from its partial derivs) Has to be called after the setup by xc_prep_2nd_deriv.

subroutine, public	xc_calc_3rd_deriv_analytical (v_xc, v_xc_tau, deriv_set, rho_set, rho1_set, pw_pool, xc_section, spinflip)
	Calculates the third functional derivative of the exchange-correlation functional, E_xc. Any GGA functional can be written as:

subroutine, public	xc_prep_2nd_deriv (deriv_set, rho_set, rho_r, pw_pool, xc_section, tau_r)
	Prepare objects for the calculation of the 2nd derivatives of the density functional. The calculation must then be performed with xc_calc_2nd_deriv.

subroutine, public	xc_prep_3rd_deriv (deriv_set, rho_set, rho_r, pw_pool, xc_section, tau_r, do_sf)
	Prepare deriv_set for the calculation of the 3rd derivatives of the density functional. The calculation must then be performed with xc_calc_3rd_deriv.

subroutine, public	divide_by_norm_drho (deriv_set, rho_set, lsd)
	divides derivatives from deriv_set by norm_drho

Detailed Description

Exchange and Correlation functional calculations.

History: (13-Feb-2001) JGH, based on earlier version of apsi 02.2003 Many many changes [fawzi] 03.2004 new xc interface [fawzi] 04.2004 kinetic functionals [fawzi]

Author: fawzi

Function/Subroutine Documentation

◆ xc_uses_kinetic_energy_density()

logical function, public xc::xc_uses_kinetic_energy_density	(	type(section_vals_type), intent(in), pointer	xc_fun_section,
		logical, intent(in)	lsd
	)

...

Parameters

xc_fun_section	...
lsd	...

Returns: ...

Definition at line 90 of file xc.F.

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◆ xc_uses_norm_drho()

logical function, public xc::xc_uses_norm_drho	(	type(section_vals_type), intent(in), pointer	xc_fun_section,
		logical, intent(in)	lsd
	)

...

Parameters

xc_fun_section	...
lsd	...

Returns: ...

Definition at line 110 of file xc.F.

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◆ xc_vxc_pw_create1()

subroutine, public xc::xc_vxc_pw_create1	(	type(pw_r3d_rs_type), dimension(:), pointer	vxc_rho,
		type(pw_r3d_rs_type), dimension(:), pointer	vxc_tau,
		type(pw_r3d_rs_type), dimension(:), pointer	rho_r,
		type(pw_c1d_gs_type), dimension(:), pointer	rho_g,
		type(pw_r3d_rs_type), dimension(:), pointer	tau,
		real(kind=dp), intent(out)	exc,
		type(section_vals_type), pointer	xc_section,
		type(pw_pool_type), pointer	pw_pool,
		logical, intent(in)	compute_virial,
		real(kind=dp), dimension(3, 3), intent(out)	virial_xc,
		type(pw_r3d_rs_type), intent(inout), optional	exc_r
	)

Exchange and Correlation functional calculations. depending on the selected functional_routine calls the correct routine.

Parameters

vxc_rho	will contain the v_xc part that depend on rho (if one of the chosen xc functionals has it it is allocated and you are responsible for it)
vxc_tau	will contain the kinetic tau part of v_xcthe functional (if one of the chosen xc functionals has it it is allocated and you are responsible for it)
rho_r	the value of the density in the real space
rho_g	value of the density in the g space (needs to be associated only for gradient corrections)
tau	value of the kinetic density tau on the grid (can be null, used only with meta functionals)
exc	the xc energy
xc_section	parameters selecting the xc and the method used to calculate it
pw_pool	the pool for the grids
compute_virial	should the virial be computed... if so virial_xc must be present
virial_xc	for calculating the GGA part of the stress
exc_r	...

Author: fawzi

Definition at line 148 of file xc.F.

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◆ smooth_cutoff()

subroutine, public xc::smooth_cutoff	(	real(kind=dp), dimension(:, :, :), intent(in), pointer	pot,
		real(kind=dp), dimension(:, :, :), intent(in), pointer	rho,
		real(kind=dp), dimension(:, :, :), intent(in), pointer	rhoa,
		real(kind=dp), dimension(:, :, :), intent(in), pointer	rhob,
		real(kind=dp), intent(in)	rho_cutoff,
		real(kind=dp), intent(in)	rho_smooth_cutoff_range,
		real(kind=dp), dimension(:, :, :), optional, pointer	e_0,
		real(kind=dp), intent(in), optional	e_0_scale_factor
	)

smooths the cutoff on rho with a function smoothderiv_rho that is 0 for rho<rho_cutoff and 1 for rho>rho_cutoff*rho_smooth_cutoff_range: E= integral e_0*smoothderiv_rho => dE/d...= de/d... * smooth, dE/drho = de/drho * smooth + e_0 * dsmooth/drho

Parameters

pot	the potential to smooth
rho,rhoa,rhob	the value of the density (used to apply the cutoff)
rhoa	...
rhob	...
rho_cutoff	the value at whch the cutoff function must go to 0
rho_smooth_cutoff_range	range of the smoothing
e_0	value of e_0, if given it is assumed that pot is the derivative wrt. to rho, and needs the dsmooth*e_0 contribution
e_0_scale_factor	...

Author: Fawzi Mohamed

Definition at line 912 of file xc.F.

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◆ calc_xc_density()

subroutine, public xc::calc_xc_density	(	type(pw_r3d_rs_type), intent(inout)	pot,
		type(pw_r3d_rs_type), dimension(:), intent(inout)	rho,
		real(kind=dp), intent(in)	rho_cutoff
	)

Definition at line 1073 of file xc.F.

◆ xc_vxc_pw_create()

subroutine, public xc::xc_vxc_pw_create	(	type(pw_r3d_rs_type), dimension(:), pointer	vxc_rho,
		type(pw_r3d_rs_type), dimension(:), pointer	vxc_tau,
		real(kind=dp), intent(out)	exc,
		type(pw_r3d_rs_type), dimension(:), pointer	rho_r,
		type(pw_c1d_gs_type), dimension(:), pointer	rho_g,
		type(pw_r3d_rs_type), dimension(:), pointer	tau,
		type(section_vals_type), pointer	xc_section,
		type(pw_pool_type), pointer	pw_pool,
		logical	compute_virial,
		real(kind=dp), dimension(3, 3), intent(out)	virial_xc,
		type(pw_r3d_rs_type), intent(inout), optional	exc_r
	)

Exchange and Correlation functional calculations.

Parameters

vxc_rho	will contain the v_xc part that depend on rho (if one of the chosen xc functionals has it it is allocated and you are responsible for it)
vxc_tau	will contain the kinetic tau part of v_xc (if one of the chosen xc functionals has it it is allocated and you are responsible for it)
exc	the xc energy
rho_r	the value of the density in the real space
rho_g	value of the density in the g space (needs to be associated only for gradient corrections)
tau	value of the kinetic density tau on the grid (can be null, used only with meta functionals)
xc_section	which functional to calculate, and how to do it
pw_pool	the pool for the grids
compute_virial	...
virial_xc	...
exc_r	the value of the xc functional in the real space

History: JGH (13-Jun-2002): adaptation to new functionals Fawzi (11.2002): drho_g(1:3)->drho_g Fawzi (1.2003). lsd version Fawzi (11.2003): version using the new xc interface Fawzi (03.2004): fft free for smoothed density and derivs, gga lsd Fawzi (04.2004): metafunctionals mguidon (12.2008) : laplace functionals

Author: fawzi; based LDA version of JGH, based on earlier version of apsi

Note: Beware: some really dirty pointer handling! energy should be kept consistent with xc_exc_calc

Definition at line 1143 of file xc.F.

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◆ xc_exc_calc()

real(kind=dp) function, public xc::xc_exc_calc	(	type(pw_r3d_rs_type), dimension(:), pointer	rho_r,
		type(pw_c1d_gs_type), dimension(:), pointer	rho_g,
		type(pw_r3d_rs_type), dimension(:), pointer	tau,
		type(section_vals_type), pointer	xc_section,
		type(pw_pool_type), pointer	pw_pool
	)

calculates just the exchange and correlation energy (no vxc)

Parameters

rho_r	realspace density on the grid
rho_g	g-space density on the grid
tau	kinetic energy density on the grid
xc_section	XC parameters
pw_pool	pool of plain-wave grids

Returns: the XC energy

History: 11.2003 created [fawzi]

Author: fawzi

Note: has to be kept consistent with xc_vxc_pw_create

Definition at line 1458 of file xc.F.

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◆ xc_calc_2nd_deriv()

subroutine, public xc::xc_calc_2nd_deriv	(	type(pw_r3d_rs_type), dimension(:), pointer	v_xc,
		type(pw_r3d_rs_type), dimension(:), pointer	v_xc_tau,
		type(xc_derivative_set_type)	deriv_set,
		type(xc_rho_set_type)	rho_set,
		type(pw_r3d_rs_type), dimension(:), pointer	rho1_r,
		type(pw_c1d_gs_type), dimension(:), pointer	rho1_g,
		type(pw_r3d_rs_type), dimension(:), pointer	tau1_r,
		type(pw_pool_type), intent(in), pointer	pw_pool,
		type(section_vals_type), intent(in), pointer	xc_section,
		logical, intent(in)	gapw,
		real(kind=dp), dimension(:, :, :, :), optional, pointer	vxg,
		logical, intent(in), optional	do_excitations,
		logical, intent(in), optional	do_sf,
		logical, intent(in), optional	do_triplet,
		logical, intent(in), optional	compute_virial,
		real(kind=dp), dimension(3, 3), intent(inout), optional	virial_xc
	)

Caller routine to calculate the second order potential in the direction of rho1_r.

Parameters

v_xc	XC potential, will be allocated, to be integrated with the KS density
v_xc_tau	...
deriv_set	XC derivatives from xc_prep_2nd_deriv
rho_set	XC rho set from KS rho from xc_prep_2nd_deriv
rho1_r	first-order density in r space
rho1_g	first-order density in g space
tau1_r	...
pw_pool	pw pool to create new grids
xc_section	XC section to calculate the derivatives from
gapw	whether to carry out GAPW (not possible with numerical derivatives)
vxg	GAPW potential
do_excitations	...
do_triplet	...
compute_virial	...
virial_xc	virial terms will be collected here

Definition at line 1528 of file xc.F.

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◆ xc_calc_2nd_deriv_numerical()

subroutine, public xc::xc_calc_2nd_deriv_numerical	(	type(pw_r3d_rs_type), dimension(:), intent(in), pointer	v_xc,
		type(pw_r3d_rs_type), dimension(:), intent(in), pointer	v_tau,
		type(xc_rho_set_type), intent(in)	rho_set,
		type(pw_r3d_rs_type), dimension(:), intent(in), pointer	rho1_r,
		type(pw_c1d_gs_type), dimension(:), intent(in), pointer	rho1_g,
		type(pw_r3d_rs_type), dimension(:), intent(in), pointer	tau1_r,
		type(pw_pool_type), intent(in), pointer	pw_pool,
		type(section_vals_type), intent(in), pointer	xc_section,
		logical, intent(in)	do_triplet,
		logical, intent(in), optional	calc_virial,
		real(kind=dp), dimension(3, 3), intent(inout), optional	virial_xc,
		type(xc_derivative_set_type), optional	deriv_set
	)

calculates 2nd derivative numerically

Parameters

v_xc	potential to be calculated (has to be allocated already)
v_tau	tau-part of the potential to be calculated (has to be allocated already)
rho_set	KS density from xc_prep_2nd_deriv
rho1_r	first-order density in r-space
rho1_g	first-order density in g-space
tau1_r	first-order kinetic-energy density in r-space
pw_pool	pw pool for new grids
xc_section	XC section to calculate the derivatives from
do_triplet	...
calc_virial	whether to calculate virial terms
virial_xc	collects stress tensor components (no metaGGAs!)
deriv_set	deriv set from xc_prep_2nd_deriv (only for virials)

Definition at line 1660 of file xc.F.

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◆ xc_calc_2nd_deriv_analytical()

subroutine, public xc::xc_calc_2nd_deriv_analytical	(	type(pw_r3d_rs_type), dimension(:), pointer	v_xc,
		type(pw_r3d_rs_type), dimension(:), pointer	v_xc_tau,
		type(xc_derivative_set_type)	deriv_set,
		type(xc_rho_set_type), intent(in)	rho_set,
		type(xc_rho_set_type), intent(in)	rho1_set,
		type(pw_pool_type), pointer	pw_pool,
		type(section_vals_type), pointer	xc_section,
		logical, intent(in), optional	gapw,
		real(kind=dp), dimension(:, :, :, :), optional, pointer	vxg,
		real(kind=dp), intent(in), optional	tddfpt_fac,
		logical, intent(in), optional	compute_virial,
		real(kind=dp), dimension(3, 3), intent(inout), optional	virial_xc,
		logical, intent(in), optional	spinflip
	)

Calculates the second derivative of E_xc at rho in the direction rho1 (if you see the second derivative as bilinear form) partial_rho|_(rho=rho) partial_rho|_(rho=rho) E_xc drho(rho1)drho The other direction is still undetermined, thus it returns a potential (partial integration is performed to reduce it to function of rho, removing the dependence from its partial derivs) Has to be called after the setup by xc_prep_2nd_deriv.

Parameters

v_xc	exchange-correlation potential
v_xc_tau	...
deriv_set	derivatives of the exchange-correlation potential
rho_set	object containing the density at which the derivatives were calculated
rho1_set	object containing the density with which to fold
pw_pool	the pool for the grids
xc_section	XC parameters
gapw	Gaussian and augmented plane waves calculation
vxg	...
tddfpt_fac	factor that multiplies the crossterms (tddfpt triplets on a closed shell system it should be -1, defaults to 1)
compute_virial	...
virial_xc	...

Note: The old version of this routine was smarter: it handled split_desc(1) and split_desc(2) separately, thus the code automatically handled all possible cross terms (you only had to check if it was diagonal to avoid double counting). I think that is the way to go if you want to add more terms (tau,rho in LSD,...). The problem with the old code was that it because of the old functional structure it sometime guessed wrongly which derivative was where. There were probably still bugs with gradient corrected functionals (never tested), and it didn't contain first derivatives with respect to drho (that contribute also to the second derivative wrt. rho). The code was a little complex because it really tried to handle any functional derivative in the most efficient way with the given contents of rho_set. Anyway I strongly encourage whoever wants to modify this code to give a look to the old version. [fawzi]

Definition at line 2647 of file xc.F.

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◆ xc_calc_3rd_deriv_analytical()

subroutine, public xc::xc_calc_3rd_deriv_analytical	(	type(pw_r3d_rs_type), dimension(:), pointer	v_xc,
		type(pw_r3d_rs_type), dimension(:), pointer	v_xc_tau,
		type(xc_derivative_set_type)	deriv_set,
		type(xc_rho_set_type), intent(in)	rho_set,
		type(xc_rho_set_type), intent(in)	rho1_set,
		type(pw_pool_type), pointer	pw_pool,
		type(section_vals_type), pointer	xc_section,
		logical, intent(in), optional	spinflip
	)

Calculates the third functional derivative of the exchange-correlation functional, E_xc. Any GGA functional can be written as:

E_xc[\rho] = \int e_xc(\rho,\nabla\rho)dr

This routine gives you back the contraction of the derivatives of e_xc with respect to the alpha or beta density or with respect to the norm of their gradients contracted with rho1. For example, the alpha component would be (d stands for total derivative):

                                d^3 e_xc

v_xc(1) = \sum_{s,s'}^{a,b} ------------------—\rhos1\rho1s' d\rhoa d\rhos d\rhos'

Parameters

v_xc	Third derivative of the exchange-correlation functional
v_xc_tau	...
deriv_set	derivatives of the exchange-correlation potential, e_xc
rho_set	object containing the density at which the derivatives were calculated, \rho
rho1_set	object containing the density with which to fold, \rho1s
pw_pool	the pool for the grids
xc_section	XC parameters

History

07.2024 Created [LHS]

Definition at line 5326 of file xc.F.

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◆ xc_prep_2nd_deriv()

subroutine, public xc::xc_prep_2nd_deriv	(	type(xc_derivative_set_type)	deriv_set,
		type(xc_rho_set_type)	rho_set,
		type(pw_r3d_rs_type), dimension(:), pointer	rho_r,
		type(pw_pool_type), pointer	pw_pool,
		type(section_vals_type), pointer	xc_section,
		type(pw_r3d_rs_type), dimension(:), optional, pointer	tau_r
	)

Prepare objects for the calculation of the 2nd derivatives of the density functional. The calculation must then be performed with xc_calc_2nd_deriv.

Parameters

deriv_set	object containing the XC derivatives (out)
rho_set	object that will contain the density at which the derivatives were calculated
rho_r	the place where you evaluate the derivative
pw_pool	the pool for the grids
xc_section	which functional should be used and how to calculate it
tau_r	kinetic energy density in real space

Definition at line 6129 of file xc.F.

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◆ xc_prep_3rd_deriv()

subroutine, public xc::xc_prep_3rd_deriv	(	type(xc_derivative_set_type)	deriv_set,
		type(xc_rho_set_type)	rho_set,
		type(pw_r3d_rs_type), dimension(:), pointer	rho_r,
		type(pw_pool_type), pointer	pw_pool,
		type(section_vals_type), pointer	xc_section,
		type(pw_r3d_rs_type), dimension(:), optional, pointer	tau_r,
		logical, optional	do_sf
	)

Prepare deriv_set for the calculation of the 3rd derivatives of the density functional. The calculation must then be performed with xc_calc_3rd_deriv.

Parameters

deriv_set	object containing the XC derivatives (out)
rho_set	object that will contain the density at which the derivatives were calculated
rho_r	the place where you evaluate the derivative
pw_pool	the pool for the grids
xc_section	which functional should be used and how to calculate it
tau_r	kinetic energy density in real space
do_sf	Flag to activate the noncollinear kernel for spin flip calculations

History

07.2024 Created [LHS]

Definition at line 6186 of file xc.F.

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◆ divide_by_norm_drho()

subroutine, public xc::divide_by_norm_drho	(	type(xc_derivative_set_type), intent(inout)	deriv_set,
		type(xc_rho_set_type), intent(in)	rho_set,
		logical, intent(in)	lsd
	)

divides derivatives from deriv_set by norm_drho

Parameters

deriv_set	...
rho_set	...
lsd	...

Definition at line 6238 of file xc.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ xc_uses_kinetic_energy_density()

◆ xc_uses_norm_drho()

◆ xc_vxc_pw_create1()

◆ smooth_cutoff()

◆ calc_xc_density()

◆ xc_vxc_pw_create()

◆ xc_exc_calc()

◆ xc_calc_2nd_deriv()

◆ xc_calc_2nd_deriv_numerical()

◆ xc_calc_2nd_deriv_analytical()

◆ xc_calc_3rd_deriv_analytical()

◆ xc_prep_2nd_deriv()

◆ xc_prep_3rd_deriv()

◆ divide_by_norm_drho()