ao_util Module Reference

All kind of helpful little routines. More...

Functions/Subroutines
real(kind=dp) function, public	gauss_exponent (l, radius, threshold, prefactor)
	The exponent of a primitive Gaussian function for a given radius and threshold is calculated. More...
real(kind=dp) function, public	exp_radius (l, alpha, threshold, prefactor, epsabs, epsrel, rlow)
	The radius of a primitive Gaussian function for a given threshold is calculated. g(r) = prefactor*r**l*exp(-alpha*r**2) - threshold = 0. More...
real(kind=dp) function, public	exp_radius_very_extended (la_min, la_max, lb_min, lb_max, pab, o1, o2, ra, rb, rp, zetp, eps, prefactor, cutoff, epsabs)
	computes the radius of the Gaussian outside of which it is smaller than eps More...
real(dp) function, public	gaussint_sph (alpha, l)
	... More...
pure real(dp) function, public	trace_r_axb (A, lda, B, ldb, m, n)
	... More...

Detailed Description

All kind of helpful little routines.

History

• Cleaned (22.04.2021, MK)

Author

CJM & JGH

Function/Subroutine Documentation

gauss_exponent()

real(kind=dp) function, public ao_util::gauss_exponent	(	integer, intent(in)	l,
		real(kind=dp), intent(in)	radius,
		real(kind=dp), intent(in)	threshold,
		real(kind=dp), intent(in)	prefactor
	)

The exponent of a primitive Gaussian function for a given radius and threshold is calculated.

Parameters

l	...
radius	...
threshold	...
prefactor	...

Returns

...

Date

07.03.1999

Variables

• exponent : Exponent of the primitive Gaussian function.
• l : Angular momentum quantum number l.
• prefactor: Prefactor of the Gaussian function (e.g. a contraction coefficient).
• radius : Calculated radius of the Gaussian function.
• threshold: Threshold for radius.

Author

MK

Version

1.0

Definition at line 59 of file ao_util.F.

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exp_radius()

real(kind=dp) function, public ao_util::exp_radius	(	integer, intent(in)	l,
		real(kind=dp), intent(in)	alpha,
		real(kind=dp), intent(in)	threshold,
		real(kind=dp), intent(in)	prefactor,
		real(kind=dp), intent(in), optional	epsabs,
		real(kind=dp), intent(in), optional	epsrel,
		real(kind=dp), intent(in), optional	rlow
	)

The radius of a primitive Gaussian function for a given threshold is calculated. g(r) = prefactor*r**l*exp(-alpha*r**2) - threshold = 0.

Parameters

l	Angular momentum quantum number l.
alpha	Exponent of the primitive Gaussian function.
threshold	Threshold for function g(r).
prefactor	Prefactor of the Gaussian function (e.g. a contraction coefficient).
epsabs	Absolute tolerance (radius)
epsrel	Relative tolerance (radius)
rlow	Optional lower bound radius, e.g., when searching maximum radius

Returns

Calculated radius of the Gaussian function

Variables

• g : function g(r)
• prec_exp: single/double precision exponential function
• itermax : Maximum number of iterations
• contract: Golden Section Search (GSS): [0.38, 0.62] Equidistant sampling: [0.2, 0.4, 0.6, 0.8] Bisection (original approach): [0.5] Array size may trigger vectorization

Definition at line 95 of file ao_util.F.

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exp_radius_very_extended()

real(kind=dp) function, public ao_util::exp_radius_very_extended	(	integer, intent(in)	la_min,
		integer, intent(in)	la_max,
		integer, intent(in)	lb_min,
		integer, intent(in)	lb_max,
		real(kind=dp), dimension(:, :), optional, pointer	pab,
		integer, optional	o1,
		integer, optional	o2,
		real(kind=dp), dimension(3), intent(in)	ra,
		real(kind=dp), dimension(3), intent(in)	rb,
		real(kind=dp), dimension(3), intent(in)	rp,
		real(kind=dp), intent(in)	zetp,
		real(kind=dp), intent(in)	eps,
		real(kind=dp), intent(in)	prefactor,
		real(kind=dp), intent(in)	cutoff,
		real(kind=dp), optional	epsabs
	)

computes the radius of the Gaussian outside of which it is smaller than eps

Parameters

la_min	...
la_max	...
lb_min	...
lb_max	...
pab	...
o1	...
o2	...
ra	...
rb	...
rp	...
zetp	...
eps	...
prefactor	...
cutoff	...
epsabs	...

Returns

...

History

03.2007 new version that assumes that the Gaussians origante from spherical Gaussians

Note

can optionally screen by the maximum element of the pab block

Definition at line 207 of file ao_util.F.

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gaussint_sph()

real(dp) function, public ao_util::gaussint_sph	(	real(dp), intent(in)	alpha,
		integer, intent(in)	l
	)

...

Parameters

alpha	...
l	...

Returns

...

Definition at line 298 of file ao_util.F.

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trace_r_axb()

pure real(dp) function, public ao_util::trace_r_axb	(	real(dp), dimension(lda, *), intent(in)	A,
		integer, intent(in)	lda,
		real(dp), dimension(ldb, *), intent(in)	B,
		integer, intent(in)	ldb,
		integer, intent(in)	m,
		integer, intent(in)	n
	)

...

Parameters

A	...
lda	...
B	...
ldb	...
m	...
n	...

Returns

...

Definition at line 330 of file ao_util.F.

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