atom_utils Module Reference

Some basic routines for atomic calculations. More...

Data Types
interface	integrate_grid

Functions/Subroutines
subroutine, public	atom_set_occupation (ostring, occupation, wfnocc, multiplicity)
	Set occupation of atomic orbitals.
pure integer function, public	get_maxl_occ (occupation)
	Return the maximum orbital quantum number of occupied orbitals.
pure integer function, dimension(0:lmat), public	get_maxn_occ (occupation)
	Return the maximum principal quantum number of occupied orbitals.
pure subroutine, public	atom_denmat (pmat, wfn, nbas, occ, maxl, maxn)
	Calculate a density matrix using atomic orbitals.
subroutine, public	atom_density (density, pmat, basis, maxl, typ, rr)
	Map the electron density on an atomic radial grid.
subroutine, public	atom_write_zmp_restart (atom)
	ZMP subroutine to write external restart file.
subroutine, public	atom_read_zmp_restart (atom, doguess, iw)
	ZMP subroutine to read external restart file.
subroutine, public	atom_read_external_density (density, atom, iw)
	ZMP subroutine to read external density from linear grid of density matrix.
subroutine, public	atom_read_external_vxc (vxc, atom, iw)
	ZMP subroutine to read external v_xc in the atomic code.
pure subroutine, public	atom_orbital_charge (charge, wfn, rcov, l, basis)
	...
subroutine, public	atom_core_density (corden, potential, typ, rr)
	...
pure subroutine, public	atom_local_potential (locpot, gthpot, rr)
	...
pure subroutine, public	atom_orbital_max (rmax, wfn, rcov, l, basis)
	...
pure subroutine, public	atom_orbital_nodes (node, wfn, rcov, l, basis)
	...
pure subroutine, public	atom_wfnr0 (value, wfn, basis)
	...
subroutine, public	atom_solve (hmat, umat, orb, ener, nb, nv, maxl)
	Solve the generalised eigenproblem for every angular momentum.
subroutine, public	coulomb_potential_numeric (cpot, density, grid)
	Numerically compute the Coulomb potential on an atomic radial grid.
subroutine, public	coulomb_potential_analytic (cpot, pmat, basis, grid, maxl)
	Analytically compute the Coulomb potential on an atomic radial grid.
subroutine, public	exchange_numeric (kmat, state, occ, wfn, basis, hfx_pot)
	Calculate the exchange potential numerically.
subroutine, public	exchange_semi_analytic (kmat, state, occ, wfn, basis, hfx_pot)
	Calculate the exchange potential semi-analytically.
pure real(kind=dp) function, public	atom_trace (opmat, pmat)
	Compute Trace[opmat * pmat] == Trace[opmat * pmat^T] .
subroutine, public	numpot_matrix (imat, cpot, basis, derivatives)
	Calculate a potential matrix by integrating the potential on an atomic radial grid.
pure subroutine, public	ceri_contract (jmat, erint, pmat, nsize, all_nu)
	Contract Coulomb Electron Repulsion Integrals.
pure subroutine, public	eeri_contract (kmat, erint, pmat, nsize)
	Contract exchange Electron Repulsion Integrals.
pure subroutine, public	err_matrix (emat, demax, kmat, pmat, umat, upmat, nval, nbs)
	Calculate the error matrix for each angular momentum.
subroutine, public	slater_density (density1, density2, zcore, state, grid)
	Calculate Slater density on a radial grid.
pure subroutine, public	wigner_slater_functional (rho, vxc)
	Calculate the functional derivative of the Wigner (correlation) - Slater (exchange) density functional.
pure logical function, public	atom_consistent_method (method, multiplicity)
	Check that the atomic multiplicity is consistent with the electronic structure method.
subroutine, public	get_rho0 (atom, rho0)
	Calculate the total electron density at R=0.
subroutine, public	atom_condnumber (basis, crad, iw)
	Print condition numbers of the given atomic basis set.
subroutine, public	atom_completeness (basis, zv, iw)
	Estimate completeness of the given atomic basis set.
subroutine, public	atom_basis_condnum (basis, rad, cnum)
	Calculate the condition number of the given atomic basis set.
subroutine, public	contract2 (int, omat, cm)
	Transform a matrix expressed in terms of a uncontracted basis set to a contracted one.
subroutine, public	contract2add (int, omat, cm)
	Same as contract2(), but add the new contracted matrix to the old one instead of overwriting it.
subroutine, public	contract4 (eri, omat, cm1, cm2)
	Contract a matrix of Electron Repulsion Integrals (ERI-s).

Detailed Description

Some basic routines for atomic calculations.

Author

jgh

Date

01.04.2008

Version

1.0

Function/Subroutine Documentation

atom_set_occupation()

subroutine, public atom_utils::atom_set_occupation	(	character(len=default_string_length), dimension(:), pointer	ostring,
		real(kind=dp), dimension(0:lmat, 10)	occupation,
		real(kind=dp), dimension(0:lmat, 10)	wfnocc,
		integer, intent(out), optional	multiplicity
	)

Set occupation of atomic orbitals.

Parameters

ostring	list of electronic states
occupation	...
wfnocc	...
multiplicity	...

History

• 11.2009 unrestricted KS and HF methods [Juerg Hutter]
• 08.2008 created [Juerg Hutter]

Definition at line 102 of file atom_utils.F.

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get_maxl_occ()

pure integer function, public atom_utils::get_maxl_occ

(

real(kind=dp), dimension(0:lmat, 10), intent(in)

occupation

)

Return the maximum orbital quantum number of occupied orbitals.

Parameters

occupation

...

Returns

...

History

• 08.2008 created [Juerg Hutter]

Definition at line 280 of file atom_utils.F.

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get_maxn_occ()

pure integer function, dimension(0:lmat), public atom_utils::get_maxn_occ

(

real(kind=dp), dimension(0:lmat, 10), intent(in)

occupation

)

Return the maximum principal quantum number of occupied orbitals.

Parameters

occupation

...

Returns

...

History

• 08.2008 created [Juerg Hutter]

Definition at line 300 of file atom_utils.F.

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atom_denmat()

pure subroutine, public atom_utils::atom_denmat	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	pmat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	wfn,
		integer, dimension(0:lmat), intent(in)	nbas,
		real(kind=dp), dimension(0:, :), intent(in)	occ,
		integer, intent(in)	maxl,
		integer, dimension(0:lmat), intent(in)	maxn
	)

Calculate a density matrix using atomic orbitals.

Parameters

pmat	electron density matrix
wfn	atomic wavefunctions
nbas	number of basis functions
occ	occupation numbers
maxl	maximum angular momentum to consider
maxn	maximum principal quantum number for each angular momentum

History

• 08.2008 created [Juerg Hutter]

Definition at line 326 of file atom_utils.F.

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atom_density()

subroutine, public atom_utils::atom_density	(	real(kind=dp), dimension(:), intent(out)	density,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat,
		type(atom_basis_type), intent(in)	basis,
		integer, intent(in)	maxl,
		character(len=*), optional	typ,
		real(kind=dp), dimension(:), intent(in), optional	rr
	)

Map the electron density on an atomic radial grid.

Parameters

density	computed electron density
pmat	electron density matrix
basis	atomic basis set
maxl	maximum angular momentum to consider
typ	type of the matrix to map: RHO – density matrix; DER – first derivatives of the electron density; KIN – kinetic energy density; LAP – second derivatives of the electron density.
rr	abscissa on the radial grid (required for typ == 'KIN')

History

• 08.2008 created [Juerg Hutter]

Definition at line 365 of file atom_utils.F.

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atom_write_zmp_restart()

subroutine, public atom_utils::atom_write_zmp_restart

(

type(atom_type), intent(in)

atom

)

ZMP subroutine to write external restart file.

Parameters

atom	information about the atomic kind

Date

07.10.2013

Author

D. Varsano [danie.nosp@m.le.v.nosp@m.arsan.nosp@m.o@na.nosp@m.no.cn.nosp@m.r.it]

Version

1.0

Definition at line 422 of file atom_utils.F.

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atom_read_zmp_restart()

subroutine, public atom_utils::atom_read_zmp_restart	(	type(atom_type), intent(inout)	atom,
		logical, intent(inout)	doguess,
		integer, intent(in)	iw
	)

ZMP subroutine to read external restart file.

Parameters

atom	information about the atomic kind
doguess	flag that indicates that the restart file has not been read, so the initial guess is required
iw	output file unit

Date

07.10.2013

Author

D. Varsano [danie.nosp@m.le.v.nosp@m.arsan.nosp@m.o@na.nosp@m.no.cn.nosp@m.r.it]

Version

1.0

Definition at line 456 of file atom_utils.F.

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atom_read_external_density()

subroutine, public atom_utils::atom_read_external_density	(	real(kind=dp), dimension(:), intent(out)	density,
		type(atom_type), intent(inout)	atom,
		integer, intent(in)	iw
	)

ZMP subroutine to read external density from linear grid of density matrix.

Parameters

density	external density
atom	information about the atomic kind
iw	output file unit

Date

07.10.2013

Author

D. Varsano [danie.nosp@m.le.v.nosp@m.arsan.nosp@m.o@na.nosp@m.no.cn.nosp@m.r.it]

Version

1.0

Definition at line 515 of file atom_utils.F.

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atom_read_external_vxc()

subroutine, public atom_utils::atom_read_external_vxc	(	real(kind=dp), dimension(:), intent(out)	vxc,
		type(atom_type), intent(inout)	atom,
		integer, intent(in)	iw
	)

ZMP subroutine to read external v_xc in the atomic code.

Parameters

vxc	external exchange-correlation potential
atom	information about the atomic kind
iw	output file unit

Author

D. Varsano [danie.nosp@m.le.v.nosp@m.arsan.nosp@m.o@na.nosp@m.no.cn.nosp@m.r.it]

Definition at line 606 of file atom_utils.F.

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atom_orbital_charge()

pure subroutine, public atom_utils::atom_orbital_charge	(	real(kind=dp), intent(out)	charge,
		real(kind=dp), dimension(:), intent(in)	wfn,
		real(kind=dp), intent(in)	rcov,
		integer, intent(in)	l,
		type(atom_basis_type), intent(in)	basis
	)

...

Parameters

charge	...
wfn	...
rcov	...
l	...
basis	...

Definition at line 652 of file atom_utils.F.

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atom_core_density()

subroutine, public atom_utils::atom_core_density	(	real(kind=dp), dimension(:), intent(inout)	corden,
		type(atom_potential_type), intent(in)	potential,
		character(len=*), optional	typ,
		real(kind=dp), dimension(:), intent(in)	rr
	)

...

Parameters

corden	...
potential	...
typ	...
rr	...

History

• 01.2017 rewritten [Juerg Hutter]
• 03.2010 extension of GTH pseudo-potential definition [Juerg Hutter]

Definition at line 692 of file atom_utils.F.

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atom_local_potential()

pure subroutine, public atom_utils::atom_local_potential	(	real(kind=dp), dimension(:), intent(inout)	locpot,
		type(atom_gthpot_type), intent(in)	gthpot,
		real(kind=dp), dimension(:), intent(in)	rr
	)

...

Parameters

locpot	...
gthpot	...
rr	...

Definition at line 798 of file atom_utils.F.

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atom_orbital_max()

pure subroutine, public atom_utils::atom_orbital_max	(	real(kind=dp), intent(out)	rmax,
		real(kind=dp), dimension(:), intent(in)	wfn,
		real(kind=dp), intent(in)	rcov,
		integer, intent(in)	l,
		type(atom_basis_type), intent(in)	basis
	)

...

Parameters

rmax	...
wfn	...
rcov	...
l	...
basis	...

Definition at line 841 of file atom_utils.F.

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atom_orbital_nodes()

pure subroutine, public atom_utils::atom_orbital_nodes	(	integer, intent(out)	node,
		real(kind=dp), dimension(:), intent(in)	wfn,
		real(kind=dp), intent(in)	rcov,
		integer, intent(in)	l,
		type(atom_basis_type), intent(in)	basis
	)

...

Parameters

node	...
wfn	...
rcov	...
l	...
basis	...

Definition at line 880 of file atom_utils.F.

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atom_wfnr0()

pure subroutine, public atom_utils::atom_wfnr0	(	real(kind=dp), intent(out)	value,
		real(kind=dp), dimension(:), intent(in)	wfn,
		type(atom_basis_type), intent(in)	basis
	)

...

Parameters

value	...
wfn	...
basis	...

Definition at line 915 of file atom_utils.F.

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atom_solve()

subroutine, public atom_utils::atom_solve	(	real(kind=dp), dimension(:, :, 0:), intent(in)	hmat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	umat,
		real(kind=dp), dimension(:, :, 0:), intent(inout)	orb,
		real(kind=dp), dimension(:, 0:), intent(inout)	ener,
		integer, dimension(0:), intent(in)	nb,
		integer, dimension(0:), intent(in)	nv,
		integer, intent(in)	maxl
	)

Solve the generalised eigenproblem for every angular momentum.

Parameters

hmat	Hamiltonian matrix
umat	transformation matrix which reduces the overlap matrix to its unitary form
orb	atomic wavefunctions
ener	atomic orbital energies
nb	number of contracted basis functions
nv	number of linear-independent contracted basis functions
maxl	maximum angular momentum to consider

History

• 08.2008 created [Juerg Hutter]

Definition at line 942 of file atom_utils.F.

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coulomb_potential_numeric()

subroutine, public atom_utils::coulomb_potential_numeric	(	real(kind=dp), dimension(:), intent(inout)	cpot,
		real(kind=dp), dimension(:), intent(in)	density,
		type(grid_atom_type), intent(in)	grid
	)

Numerically compute the Coulomb potential on an atomic radial grid.

Parameters

cpot	Coulomb potential on the radial grid
density	electron density on the radial grid
grid	atomic radial grid

History

• 08.2008 created [Juerg Hutter]

Definition at line 1075 of file atom_utils.F.

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coulomb_potential_analytic()

subroutine, public atom_utils::coulomb_potential_analytic	(	real(kind=dp), dimension(:), intent(inout)	cpot,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat,
		type(atom_basis_type), intent(in)	basis,
		type(grid_atom_type)	grid,
		integer, intent(in)	maxl
	)

Analytically compute the Coulomb potential on an atomic radial grid.

Parameters

cpot	Coulomb potential on the radial grid
pmat	density matrix
basis	atomic basis set
grid	atomic radial grid
maxl	maximum angular momentum to consider

History

• 08.2008 created [Juerg Hutter]

Definition at line 1113 of file atom_utils.F.

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exchange_numeric()

subroutine, public atom_utils::exchange_numeric	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	kmat,
		type(atom_state), intent(in)	state,
		real(kind=dp), dimension(0:, :), intent(in)	occ,
		real(kind=dp), dimension(:, :, :), pointer	wfn,
		type(atom_basis_type), intent(in)	basis,
		type(atom_hfx_type), intent(in)	hfx_pot
	)

Calculate the exchange potential numerically.

Parameters

kmat	Kohn-Sham matrix
state	electronic state
occ	occupation numbers
wfn	wavefunctions
basis	atomic basis set
hfx_pot	potential parameters from Hartree-Fock section

History

• 01.2009 created [Juerg Hutter]

Definition at line 1218 of file atom_utils.F.

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exchange_semi_analytic()

subroutine, public atom_utils::exchange_semi_analytic	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	kmat,
		type(atom_state), intent(in)	state,
		real(kind=dp), dimension(0:, :), intent(in)	occ,
		real(kind=dp), dimension(:, :, :), pointer	wfn,
		type(atom_basis_type), intent(in)	basis,
		type(atom_hfx_type), intent(in)	hfx_pot
	)

Calculate the exchange potential semi-analytically.

Parameters

kmat	Kohn-Sham matrix
state	electronic state
occ	occupation numbers
wfn	wavefunctions
basis	atomic basis set
hfx_pot	properties of the Hartree-Fock potential

History

• 01.2009 created [Juerg Hutter]

Definition at line 1306 of file atom_utils.F.

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atom_trace()

pure real(kind=dp) function, public atom_utils::atom_trace	(	real(kind=dp), dimension(:, :, 0:), intent(in)	opmat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat
	)

Compute Trace[opmat * pmat] == Trace[opmat * pmat^T] .

Parameters

opmat	operator matrix (e.g. Kohn-Sham matrix or overlap matrix)
pmat	density matrix

Returns

value of trace

History

• 08.2008 created [Juerg Hutter]

Definition at line 1821 of file atom_utils.F.

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numpot_matrix()

subroutine, public atom_utils::numpot_matrix	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	imat,
		real(kind=dp), dimension(:), intent(in)	cpot,
		type(atom_basis_type), intent(inout)	basis,
		integer, intent(in)	derivatives
	)

Calculate a potential matrix by integrating the potential on an atomic radial grid.

Parameters

imat	potential matrix
cpot	potential on the atomic radial grid
basis	atomic basis set
derivatives	order of derivatives

History

• 08.2008 created [Juerg Hutter]

Definition at line 1838 of file atom_utils.F.

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ceri_contract()

pure subroutine, public atom_utils::ceri_contract	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	jmat,
		type(eri), dimension(:), intent(in)	erint,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat,
		integer, dimension(0:), intent(in)	nsize,
		logical, intent(in), optional	all_nu
	)

Contract Coulomb Electron Repulsion Integrals.

Parameters

jmat	...
erint	...
pmat	...
nsize	...
all_nu	...

History

• 08.2008 created [Juerg Hutter]

Definition at line 1898 of file atom_utils.F.

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eeri_contract()

pure subroutine, public atom_utils::eeri_contract	(	real(kind=dp), dimension(:, :, 0:), intent(inout)	kmat,
		type(eri), dimension(:), intent(in)	erint,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat,
		integer, dimension(0:), intent(in)	nsize
	)

Contract exchange Electron Repulsion Integrals.

Parameters

kmat	...
erint	...
pmat	...
nsize	...

History

• 08.2008 created [Juerg Hutter]

Definition at line 1972 of file atom_utils.F.

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err_matrix()

pure subroutine, public atom_utils::err_matrix	(	real(kind=dp), dimension(:, :, 0:), intent(out)	emat,
		real(kind=dp), intent(out)	demax,
		real(kind=dp), dimension(:, :, 0:), intent(in)	kmat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	pmat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	umat,
		real(kind=dp), dimension(:, :, 0:), intent(in)	upmat,
		integer, dimension(0:), intent(in)	nval,
		integer, dimension(0:), intent(in)	nbs
	)

Calculate the error matrix for each angular momentum.

Parameters

emat	error matrix
demax	the largest absolute value of error matrix elements
kmat	Kohn-Sham matrix
pmat	electron density matrix
umat	transformation matrix which reduce overlap matrix to its unitary form
upmat	transformation matrix which reduce density matrix to its unitary form
nval	number of linear-independent contracted basis functions
nbs	number of contracted basis functions

History

• 08.2008 created [Juerg Hutter]

Definition at line 2049 of file atom_utils.F.

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slater_density()

subroutine, public atom_utils::slater_density	(	real(kind=dp), dimension(:), intent(out)	density1,
		real(kind=dp), dimension(:), intent(out)	density2,
		integer, intent(in)	zcore,
		type(atom_state), intent(in)	state,
		type(grid_atom_type), intent(in)	grid
	)

Calculate Slater density on a radial grid.

Parameters

density1	alpha-spin electron density
density2	beta-spin electron density
zcore	nuclear charge
state	electronic state
grid	atomic radial grid

History

• 06.2018 bugfix [Rustam Khaliullin]
• 02.2010 unrestricted KS and HF methods [Juerg Hutter]
• 12.2008 created [Juerg Hutter]

Note

An initial electron density to guess atomic orbitals.

Definition at line 2092 of file atom_utils.F.

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wigner_slater_functional()

pure subroutine, public atom_utils::wigner_slater_functional	(	real(kind=dp), dimension(:), intent(in)	rho,
		real(kind=dp), dimension(:), intent(out)	vxc
	)

Calculate the functional derivative of the Wigner (correlation) - Slater (exchange) density functional.

Parameters

rho	electron density on a radial grid
vxc	(output) exchange-correlation potential

History

• 12.2008 created [Juerg Hutter]

Note

A model XC-potential to guess atomic orbitals.

Definition at line 2157 of file atom_utils.F.

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atom_consistent_method()

pure logical function, public atom_utils::atom_consistent_method	(	integer, intent(in)	method,
		integer, intent(in)	multiplicity
	)

Check that the atomic multiplicity is consistent with the electronic structure method.

Parameters

method	electronic structure method
multiplicity	multiplicity

Returns

consistency status

History

• 11.2009 unrestricted KS and HF methods [Juerg Hutter]

Definition at line 2187 of file atom_utils.F.

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get_rho0()

subroutine, public atom_utils::get_rho0	(	type(atom_type), intent(in)	atom,
		real(kind=dp), intent(out)	rho0
	)

Calculate the total electron density at R=0.

Parameters

atom	information about the atomic kind
rho0	(output) computed density

History

• 05.2016 created [Juerg Hutter]

Definition at line 2217 of file atom_utils.F.

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atom_condnumber()

subroutine, public atom_utils::atom_condnumber	(	type(atom_basis_type), pointer	basis,
		real(kind=dp)	crad,
		integer, intent(in)	iw
	)

Print condition numbers of the given atomic basis set.

Parameters

basis	atomic basis set
crad	atomic covalent radius
iw	output file unit

History

• 05.2016 created [Juerg Hutter]

Definition at line 2308 of file atom_utils.F.

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atom_completeness()

subroutine, public atom_utils::atom_completeness	(	type(atom_basis_type), pointer	basis,
		integer, intent(in)	zv,
		integer, intent(in)	iw
	)

Estimate completeness of the given atomic basis set.

Parameters

basis	atomic basis set
zv	atomic number
iw	output file unit

Definition at line 2343 of file atom_utils.F.

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atom_basis_condnum()

subroutine, public atom_utils::atom_basis_condnum	(	type(atom_basis_type)	basis,
		real(kind=dp), intent(in)	rad,
		real(kind=dp), intent(out)	cnum
	)

Calculate the condition number of the given atomic basis set.

Parameters

basis	atomic basis set
rad	lattice constant (e.g. doubled atomic covalent radius)
cnum	(output) condition number

Definition at line 2478 of file atom_utils.F.

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contract2()

subroutine, public atom_utils::contract2	(	real(dp), dimension(:, :), intent(inout)	int,
		real(dp), dimension(:, :), intent(in)	omat,
		real(dp), dimension(:, :), intent(in)	cm
	)

Transform a matrix expressed in terms of a uncontracted basis set to a contracted one.

Parameters

int	(output) contracted matrix
omat	uncontracted matrix
cm	matrix of contraction coefficients

Definition at line 2611 of file atom_utils.F.

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contract2add()

subroutine, public atom_utils::contract2add	(	real(dp), dimension(:, :), intent(inout)	int,
		real(dp), dimension(:, :), intent(in)	omat,
		real(dp), dimension(:, :), intent(in)	cm
	)

Same as contract2(), but add the new contracted matrix to the old one instead of overwriting it.

Parameters

int	(input/output) contracted matrix to be updated
omat	uncontracted matrix
cm	matrix of contraction coefficients

Definition at line 2637 of file atom_utils.F.

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contract4()

subroutine, public atom_utils::contract4	(	real(dp), dimension(:, :), intent(inout)	eri,
		real(dp), dimension(:, :), intent(in)	omat,
		real(dp), dimension(:, :), intent(in)	cm1,
		real(dp), dimension(:, :), intent(in)	cm2
	)

Contract a matrix of Electron Repulsion Integrals (ERI-s).

Parameters

eri	(output) contracted ERI-s
omat	uncontracted ERI-s
cm1	first matrix of contraction coefficients
cm2	second matrix of contraction coefficients

Definition at line 2663 of file atom_utils.F.

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