Calculates the exchange energy for the pbe hole model in a truncated coulomb potential, considering the long range part only. Can be used as longrange correction to a truncated Hartree Fock calculation. More...

Functions
subroutine, public	xpbe_hole_t_c_lr_lda_info (reference, shortform, needs, max_deriv, error)
	returns various information on the functional
subroutine, public	xpbe_hole_t_c_lr_lsd_info (reference, shortform, needs, max_deriv, error)
	returns various information on the functional
subroutine, public	xpbe_hole_t_c_lr_lda_eval (rho_set, deriv_set, order, params, error)
	evaluates the pbe-hole exchange in a truncated coulomb potential
subroutine	xpbe_hole_t_c_lr_lda_calc (npoints, order, rho, norm_drho, e_0, e_rho, e_ndrho, epsilon_rho, epsilon_norm_drho, sx, R, error)
	intermediate level routine in order to decide which branch has to be taken
subroutine, public	xpbe_hole_t_c_lr_lsd_eval (rho_set, deriv_set, order, params, error)
	evaluates the pbe-hole exchange in a truncated coulomb potential
subroutine	xpbe_hole_t_c_lr_lsd_calc (npoints, order, rho, norm_drho, e_0, e_rho, e_ndrho, epsilon_rho, epsilon_norm_drho, sx, R, error)
	intermediate level routine in order to decide which branch has to be taken
subroutine, public	xpbe_hole_t_c_lr_lda_calc_1 (e_0, e_rho, e_ndrho, rho, ndrho, sscale, sx, R, order)
	low level routine that calculates the energy derivatives in one point
subroutine, public	xpbe_hole_t_c_lr_lda_calc_2 (e_0, e_rho, e_ndrho, rho, ndrho, sscale, sx, R, order)
	low level routine that calculates the energy derivatives in one point
REAL(dp)	exei (P, Q)
	These functions evaluate products exp(x)Ei(x) and piexp(x)*erfc(sqrt(x)), as well as their derivatives with respect to various combinations of rho and norm_drho.
REAL(dp)	dexeirho (P, Q, dPrho, dQrho)
REAL(dp)	dexeindrho (P, Q, dPndrho, dQndrho)
REAL(dp)	red (rho, ndrho)
REAL(dp)	dsdrho (rho, ndrho)
REAL(dp)	dsdndrho (rho, ndrho)
Variables
REAL(KIND=dp), parameter	a1 = 0.00979681_dp
REAL(KIND=dp), parameter	a2 = 0.04108340_dp
REAL(KIND=dp), parameter	a3 = 0.18744000_dp
REAL(KIND=dp), parameter	a4 = 0.00120824_dp
REAL(KIND=dp), parameter	a5 = 0.0347188_dp
REAL(KIND=dp), parameter	A = 1.0161144_dp
REAL(KIND=dp), parameter	B = -0.37170836_dp
REAL(KIND=dp), parameter	C = -0.077215461_dp
REAL(KIND=dp), parameter	D = 0.57786348_dp
REAL(KIND=dp), parameter	E = -0.051955731_dp
REAL(KIND=dp), parameter	F2 = 0.47965830_dp
REAL(KIND=dp), parameter	F1 = 6.4753871_dp
REAL(KIND=dp), parameter	clda = -0.73855876638202240588423_dp
REAL(KIND=dp), parameter	expcutoff = 700.0_dp
REAL(KIND=dp), parameter	smax = 8.572844_dp
REAL(KIND=dp), parameter	sconst = 18.79622316_dp
REAL(KIND=dp), parameter	scutoff = 8.3_dp
REAL(KIND=dp), parameter	gcutoff = 0.08_dp
REAL(KIND=dp), parameter	g1 = -0.02628417880_dp/E
REAL(KIND=dp), parameter	g2 = -0.07117647788_dp/E
REAL(KIND=dp), parameter	g3 = 0.08534541323_dp/E
REAL(KIND=dp), parameter	g4 = 0.0_dp
REAL(KIND=dp), parameter	wcutoff = 14.0_dp
REAL(KIND=dp), parameter	EPS_RHO = 0.00000001_dp
CHARACTER(len=*), parameter, private	moduleN = 'xc_xpbe_hole_t_c_lr'

Detailed Description

Calculates the exchange energy for the pbe hole model in a truncated coulomb potential, considering the long range part only. Can be used as longrange correction to a truncated Hartree Fock calculation.

History: Manuel Guidon (01.2009) : initial version

Author:: Manuel Guidon (01.2009)

Function Documentation

REAL(dp) xc_xpbe_hole_t_c_lr::dexeindrho	(	REAL(dp),intent(in)	P,
		REAL(dp),intent(in)	Q,
		REAL(dp),intent(in)	dPndrho,
		REAL(dp),intent(in)	dQndrho
	)		`[private]`

Definition at line 1248 of file xc_xpbe_hole_t_c_lr.f90.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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REAL(dp) xc_xpbe_hole_t_c_lr::dexeirho	(	REAL(dp),intent(in)	P,
		REAL(dp),intent(in)	Q,
		REAL(dp),intent(in)	dPrho,
		REAL(dp),intent(in)	dQrho
	)		`[private]`

Definition at line 1241 of file xc_xpbe_hole_t_c_lr.f90.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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REAL(dp) xc_xpbe_hole_t_c_lr::dsdndrho	(	REAL(dp),intent(in)	rho,
		REAL(dp),intent(in)	ndrho
	)		`[private]`

Definition at line 1273 of file xc_xpbe_hole_t_c_lr.f90.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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REAL(dp) xc_xpbe_hole_t_c_lr::dsdrho	(	REAL(dp),intent(in)	rho,
		REAL(dp),intent(in)	ndrho
	)		`[private]`

Definition at line 1264 of file xc_xpbe_hole_t_c_lr.f90.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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REAL(dp) xc_xpbe_hole_t_c_lr::exei	(	REAL(dp),intent(in)	P,
		REAL(dp),intent(in)	Q
	)		`[private]`

These functions evaluate products exp(x)*Ei(x) and pi*exp(x)*erfc(sqrt(x)), as well as their derivatives with respect to various combinations of rho and norm_drho.

Parameters:

Q,dQrho,dQndrho,P,dPrho,dPndrho where Q = s^2*H*R^2*kf^2, P = 9/4*s^2*H/A and dX = dP(Q)/drho(ndrho)

Note:

In order to avoid numerical instabilities, these routines use Taylor- expansions for the above core-products for large arguments.
red calculates the reduced gradient in a save way (i.e. using a fixed cutoff EPS_RHO)

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 1198 of file xc_xpbe_hole_t_c_lr.f90.

References EPS_RHO.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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REAL(dp) xc_xpbe_hole_t_c_lr::red	(	REAL(dp),intent(in)	rho,
		REAL(dp),intent(in)	ndrho
	)		`[private]`

Definition at line 1255 of file xc_xpbe_hole_t_c_lr.f90.

Referenced by xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

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subroutine xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_calc	(	INTEGER,intent(in)	npoints,
		INTEGER,intent(in)	order,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	rho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	norm_drho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_0,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_rho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_ndrho,
		REAL(kind=dp),intent(in)	epsilon_rho,
		REAL(kind=dp),intent(in)	epsilon_norm_drho,
		REAL(kind=dp),intent(in)	sx,
		REAL(kind=dp),intent(in)	R,
		TYPE(cp_error_type),intent(inout)	error
	)		`[private]`

intermediate level routine in order to decide which branch has to be taken

Parameters:

npoints	number of points on the grid
order	order of the derivatives
rho,norm_drho	values of density and gradient on the grid
e_0,e_rho,e_ndrho	derivatives of the energy on the grid
epsilon_rho,epsilon_norm_drho	cutoffs
sx,R	functional parameters
error	variable to control error logging, stopping,... see module cp_error_handling

Note:: For numerical reasons there are two different branches

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 280 of file xc_xpbe_hole_t_c_lr.f90.

References error, gcutoff, sconst, scutoff, smax, xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

Referenced by xpbe_hole_t_c_lr_lda_eval().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_calc_1	(	REAL(KIND=dp),intent(inout)	e_0,
		REAL(KIND=dp),intent(inout)	e_rho,
		REAL(KIND=dp),intent(inout)	e_ndrho,
		REAL(KIND=dp),intent(in)	rho,
		REAL(KIND=dp),intent(in)	ndrho,
		REAL(KIND=dp),intent(in)	sscale,
		REAL(KIND=dp),intent(in)	sx,
		REAL(KIND=dp),intent(in)	R,
		INTEGER,intent(in)	order
	)

low level routine that calculates the energy derivatives in one point

Parameters:

e_0,e_rho,e_ndrho	derivatives of the energy on the grid
rho,ndrho	values of density and gradient on the grid
sscale,sx,R	functional parameters
order	order of the derivatives
error	variable to control error logging, stopping,... see module cp_error_handling

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 558 of file xc_xpbe_hole_t_c_lr.f90.

References A, a1, a2, a3, a4, a5, B, C, D, dexeindrho(), dexeirho(), dsdndrho(), dsdrho(), E, exei(), mathlib::expint(), F1, F2, and red().

Referenced by xc_xbr_pbe_lda_hole_t_c_lr::xbr_pbe_lda_hole_tc_lr_lda_calc(), xc_xbr_pbe_lda_hole_t_c_lr::xbr_pbe_lda_hole_tc_lr_lsd_calc(), xpbe_hole_t_c_lr_lda_calc(), and xpbe_hole_t_c_lr_lsd_calc().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_calc_2	(	REAL(KIND=dp),intent(inout)	e_0,
		REAL(KIND=dp),intent(inout)	e_rho,
		REAL(KIND=dp),intent(inout)	e_ndrho,
		REAL(KIND=dp),intent(in)	rho,
		REAL(KIND=dp),intent(in)	ndrho,
		REAL(KIND=dp),intent(in)	sscale,
		REAL(KIND=dp),intent(in)	sx,
		REAL(KIND=dp),intent(in)	R,
		INTEGER,intent(in)	order
	)

low level routine that calculates the energy derivatives in one point

Parameters:

e_0,e_rho,e_ndrho	derivatives of the energy on the grid
rho,ndrho	values of density and gradient on the grid
sscale,sx,R	functional parameters
order	order of the derivatives
error	variable to control error logging, stopping,... see module cp_error_handling

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 927 of file xc_xpbe_hole_t_c_lr.f90.

References A, a1, a2, a3, a4, a5, B, C, D, dexeindrho(), dexeirho(), dsdndrho(), dsdrho(), E, mathconstants::euler, exei(), expcutoff, mathlib::expint(), F1, F2, g1, g2, g3, g4, and red().

Referenced by xpbe_hole_t_c_lr_lda_calc(), and xpbe_hole_t_c_lr_lsd_calc().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_eval	(	TYPE(xc_rho_set_type),pointer	rho_set,
		TYPE(xc_derivative_set_type),pointer	deriv_set,
		INTEGER,intent(in)	order,
		TYPE(section_vals_type),pointer	params,
		TYPE(cp_error_type),intent(inout)	error
	)

evaluates the pbe-hole exchange in a truncated coulomb potential

Parameters:

rho_set	the density where you want to evaluate the functional
deriv_set	place where to store the functional derivatives (they are added to the derivatives)
order	degree of the derivative that should be evalated, if positive all the derivatives up to the given degree are evaluated, if negative only the given degree is calculated
params	input parameters (scaling,cutoff)
error	variable to control error logging, stopping,... see module cp_error_handling

Note:

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 160 of file xc_xpbe_hole_t_c_lr.f90.

References CPPostcondition, CPPostconditionNoFail, timings::timeset(), xc_derivative_types::xc_derivative_get(), xc_rho_set_types::xc_rho_set_get(), and xpbe_hole_t_c_lr_lda_calc().

Referenced by xc_derivatives::xc_functional_eval().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lda_info	(	CHARACTER(LEN=*),intent(out),optional	reference,
		CHARACTER(LEN=*),intent(out),optional	shortform,
		TYPE(xc_rho_cflags_type),intent(inout),optional	needs,
		INTEGER,intent(out),optional	max_deriv,
		TYPE(cp_error_type),intent(inout)	error
	)

returns various information on the functional

Parameters:

reference	string with the reference of the actual functional
shortform	string with the shortform of the functional name
needs	the components needed by this functional are set to true (does not set the unneeded components to false)
max_deriv	controls the number of derivatives
error	variable to control error logging, stopping,... see module cp_error_handling

History: 01.2009 created [mguidon]

Author:: mguidon

Definition at line 89 of file xc_xpbe_hole_t_c_lr.f90.

subroutine xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lsd_calc	(	INTEGER,intent(in)	npoints,
		INTEGER,intent(in)	order,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	rho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	norm_drho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_0,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_rho,
		REAL(kind=dp),dimension(1:npoints),intent(inout)	e_ndrho,
		REAL(kind=dp),intent(in)	epsilon_rho,
		REAL(kind=dp),intent(in)	epsilon_norm_drho,
		REAL(kind=dp),intent(in)	sx,
		REAL(kind=dp),intent(in)	R,
		TYPE(cp_error_type),intent(inout)	error
	)		`[private]`

intermediate level routine in order to decide which branch has to be taken

Parameters:

npoints	number of points on the grid
order	order of the derivatives
rho,norm_drho	values of density and gradient on the grid
e_0,e_rho,e_ndrho	derivatives of the energy on the grid
epsilon_rho,epsilon_norm_drho	cutoffs
sx,R	functional parameters
error	variable to control error logging, stopping,... see module cp_error_handling

Note:: For numerical reasons there are two different branches. This code calls the lda version applying spin scaling relations

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 486 of file xc_xpbe_hole_t_c_lr.f90.

References error, gcutoff, sconst, scutoff, smax, xpbe_hole_t_c_lr_lda_calc_1(), and xpbe_hole_t_c_lr_lda_calc_2().

Referenced by xpbe_hole_t_c_lr_lsd_eval().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lsd_eval	(	TYPE(xc_rho_set_type),pointer	rho_set,
		TYPE(xc_derivative_set_type),pointer	deriv_set,
		INTEGER,intent(in)	order,
		TYPE(section_vals_type),pointer	params,
		TYPE(cp_error_type),intent(inout)	error
	)

evaluates the pbe-hole exchange in a truncated coulomb potential

Parameters:

rho_set	the density where you want to evaluate the functional
deriv_set	place where to store the functional derivatives (they are added to the derivatives)
order	degree of the derivative that should be evalated, if positive all the derivatives up to the given degree are evaluated, if negative only the given degree is calculated
params	input parameters (scaling,cutoff)
error	variable to control error logging, stopping,... see module cp_error_handling

Note:

History: 01.2009 created [Manuel Guidon]

Author:: Manuel Guidon

Definition at line 352 of file xc_xpbe_hole_t_c_lr.f90.

References CPPostcondition, CPPostconditionNoFail, timings::timeset(), xc_derivative_types::xc_derivative_get(), xc_rho_set_types::xc_rho_set_get(), and xpbe_hole_t_c_lr_lsd_calc().

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subroutine,public xc_xpbe_hole_t_c_lr::xpbe_hole_t_c_lr_lsd_info	(	CHARACTER(LEN=*),intent(out),optional	reference,
		CHARACTER(LEN=*),intent(out),optional	shortform,
		TYPE(xc_rho_cflags_type),intent(inout),optional	needs,
		INTEGER,intent(out),optional	max_deriv,
		TYPE(cp_error_type),intent(inout)	error
	)

returns various information on the functional

Parameters:

reference	string with the reference of the actual functional
shortform	string with the shortform of the functional name
needs	the components needed by this functional are set to true (does not set the unneeded components to false)
max_deriv	controls the number of derivatives
error	variable to control error logging, stopping,... see module cp_error_handling