Documentation for module gamma

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

source: gamma.F
Loading...

public Subroutines/Functions:

Deallocate the table of F_n(t) values.
SUBROUTINE
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.
FUNCTION
REAL(dp)
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.
SUBROUTINE
init_md_ftable (nmax)
Initalize 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).

SUBROUTINEdeallocate_md_ftable()

Deallocate the table of F_n(t) values.

SUBROUTINEfgamma_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.

Arguments:
INTEGER,
INTENT(in)
:: nmax ...
REAL(dp),
INTENT(in)
:: t ...
REAL(dp),
INTENT(out)
:: f(0:nmax) ...

FUNCTIONfgamma_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.

Return Value ::
REAL(dp)
Arguments:
INTEGER,
INTENT(in)
:: nmax ...
REAL(dp),
INTENT(in)
:: t ...

SUBROUTINEinit_md_ftable(nmax)

Initalize 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).

Arguments:
INTEGER,
INTENT(in)
:: nmax ...