gamma Module Reference

Calculation of the incomplete Gamma function F_n(t) for multi-center integrals over Cartesian Gaussian functions. More...

Functions/Subroutines
subroutine, public	deallocate_md_ftable ()
	Deallocate the table of F_n(t) values. More...
subroutine, public	fgamma_0 (nmax, t, f)
	Calculation of the incomplete Gamma function F(t) for multicenter integrals over Gaussian functions. f returns a vector with all F_n(t) values for 0 <= n <= nmax. More...
real(kind=dp) function, dimension(0:nmax), public	fgamma_ref (nmax, t)
	Calculation of the incomplete Gamma function F_n(t) using a spherical Bessel function expansion. fgamma_ref returns a vector with all F_n(t) values for 0 <= n <= nmax. For t values greater than 50 an asymptotic formula is used. This function is expected to return accurate F_n(t) values for any combination of n and t, but the calculation is slow and therefore the function may only be used for a pretabulation of F_n(t) values or for reference calculations. More...
subroutine, public	init_md_ftable (nmax)
	Initialize a table of F_n(t) values in the range 0 <= t <= 12 with a stepsize of 0.1 up to n equal to nmax for the Taylor series expansion used by McMurchie-Davidson (MD). More...

Detailed Description

Calculation of the incomplete Gamma function F_n(t) for multi-center integrals over Cartesian Gaussian functions.

History

• restructured and cleaned (24.05.2004,MK)

Author

Matthias Krack (07.01.1999)

Function/Subroutine Documentation

deallocate_md_ftable()

subroutine, public gamma::deallocate_md_ftable

Deallocate the table of F_n(t) values.

Date

24.05.2004

Author

MK

Version

1.0

Definition at line 120 of file gamma.F.

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fgamma_0()

subroutine, public gamma::fgamma_0	(	integer, intent(in)	nmax,
		real(kind=dp), intent(in)	t,
		real(kind=dp), dimension(0:nmax), intent(out)	f
	)

Calculation of the incomplete Gamma function F(t) for multicenter integrals over Gaussian functions. f returns a vector with all F_n(t) values for 0 <= n <= nmax.

Parameters

nmax	...
t	...
f	...

Date

08.01.1999,

History

09.06.1999, MK : Changed from a FUNCTION to a SUBROUTINE

Literature

L. E. McMurchie, E. R. Davidson, J. Comp. Phys. 26, 218 (1978)

Parameters

• f : The incomplete Gamma function F_n(t).
• nmax: Maximum n value of F_n(t).
• t : Argument of the incomplete Gamma function.
• kmax: Maximum number of iterations.
• expt: Exponential term in the upward recursion of F_n(t).

Author

MK

Version

1.0

Definition at line 153 of file gamma.F.

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fgamma_ref()

real(kind=dp) function, dimension(0:nmax), public gamma::fgamma_ref	(	integer, intent(in)	nmax,
		real(kind=dp), intent(in)	t
	)

Calculation of the incomplete Gamma function F_n(t) using a spherical Bessel function expansion. fgamma_ref returns a vector with all F_n(t) values for 0 <= n <= nmax. For t values greater than 50 an asymptotic formula is used. This function is expected to return accurate F_n(t) values for any combination of n and t, but the calculation is slow and therefore the function may only be used for a pretabulation of F_n(t) values or for reference calculations.

Parameters

nmax	...
t	...

Returns

...

Date

07.01.1999

Literature

F. E. Harris, Int. J. Quant. Chem. 23, 1469 (1983)

Parameters

• expt : Exponential term in the downward recursion of F_n(t).
• factor : Prefactor of the Bessel function expansion.
• nmax : Maximum n value of F_n(t).
• p : Product of the Bessel function quotients.
• r : Quotients of the Bessel functions.
• sumterm: One term in the sum over products of Bessel functions.
• t : Argument of the incomplete Gamma function.

Author

MK

Version

1.0

Definition at line 422 of file gamma.F.

init_md_ftable()

subroutine, public gamma::init_md_ftable

(

integer, intent(in)

nmax

)

Initialize a table of F_n(t) values in the range 0 <= t <= 12 with a stepsize of 0.1 up to n equal to nmax for the Taylor series expansion used by McMurchie-Davidson (MD).

Parameters

nmax

...

Date

10.06.1999

Parameters

• nmax : Maximum n value of F_n(t).

Author

MK

Version

1.0

Definition at line 539 of file gamma.F.

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