ai_cartesian_operators Module Reference

Coordinate and basis-center derivative ladders for Cartesian Gaussian integrals. Derivatives act on a basis function with the integral operator held fixed. Electronic-coordinate derivatives have the opposite sign. More...

Data Types
interface	cartesian_ladder
interface	apply_cartesian_1d

Functions/Subroutines
subroutine, public	cartesian_ladder_map (lmax, lmin, axis, map, source_lmin)
	Construct base, raised, lowered and degree indices for a Cartesian ladder.
subroutine, public	apply_cartesian_operator (la_max, la_min, npgfa, lb_max, lb_min, npgfb, ab, values, right, derivative, exponents, origin)
	Apply a Cartesian operator on either side of a primitive integral block. The input includes one extra shell on both sides. Coordinate multiplication uses the supplied shell-range layout; derivative inputs extend the lowest shell by one on the selected side for lowering. Screened primitive blocks must be zero in the input, including their raised and lowered functions.
subroutine, public	cartesian_polynomial_1d (source, values, la_max, lb_max, powers, origin)
	Form requested coordinate powers from separable Cartesian integral tables. Only requested powers are stored. With the origin on A, each power is a direct shift of the bra degree; other origins use the binomial expansion.

Detailed Description

Coordinate and basis-center derivative ladders for Cartesian Gaussian integrals. Derivatives act on a basis function with the integral operator held fixed. Electronic-coordinate derivatives have the opposite sign.

Function/Subroutine Documentation

cartesian_ladder_map()

subroutine, public ai_cartesian_operators::cartesian_ladder_map	(	integer, intent(in)	lmax,
		integer, intent(in)	lmin,
		integer, intent(in)	axis,
		integer, dimension(:, :), intent(out)	map,
		integer, intent(in), optional	source_lmin )

Construct base, raised, lowered and degree indices for a Cartesian ladder.

Parameters

lmax	highest output shell or one-dimensional degree
lmin	lowest output shell (zero for one-dimensional tables)
axis	Cartesian axis, or zero for a one-dimensional table
map	rows contain base, raised, lowered and degree indices
source_lmin	optional lowest input shell; defaults to lmin for Cartesian blocks

Definition at line 45 of file ai_cartesian_operators.F.

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apply_cartesian_operator()

subroutine, public ai_cartesian_operators::apply_cartesian_operator	(	integer, intent(in)	la_max,
		integer, intent(in)	la_min,
		integer, intent(in)	npgfa,
		integer, intent(in)	lb_max,
		integer, intent(in)	lb_min,
		integer, intent(in)	npgfb,
		real(kind=dp), dimension(:, :), intent(in)	ab,
		real(kind=dp), dimension(:, :, :), intent(out)	values,
		logical, intent(in)	right,
		logical, intent(in)	derivative,
		real(kind=dp), dimension(:), intent(in), optional	exponents,
		real(kind=dp), dimension(3), intent(in), optional	origin )

Apply a Cartesian operator on either side of a primitive integral block. The input includes one extra shell on both sides. Coordinate multiplication uses the supplied shell-range layout; derivative inputs extend the lowest shell by one on the selected side for lowering. Screened primitive blocks must be zero in the input, including their raised and lowered functions.

Parameters

la_max	highest output shell on A
la_min	lowest output shell on A
npgfa	number of primitives on A
lb_max	highest output shell on B
lb_min	lowest output shell on B
npgfb	number of primitives on B
ab	input integral block with raised shells
values	three Cartesian components in the output shell-range layout
right	act on the ket rather than the bra
derivative	select a basis-center derivative
exponents	Gaussian exponents on the selected side, required for derivatives
origin	displacement of the selected center from the coordinate reference point

Definition at line 190 of file ai_cartesian_operators.F.

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cartesian_polynomial_1d()

subroutine, public ai_cartesian_operators::cartesian_polynomial_1d	(	real(kind=dp), dimension(0:, 0:, :), intent(in)	source,
		real(kind=dp), dimension(0:, 0:, 0:, :), intent(out)	values,
		integer, intent(in)	la_max,
		integer, intent(in)	lb_max,
		integer, dimension(0:), intent(in)	powers,
		real(kind=dp), dimension(3), intent(in)	origin )

Form requested coordinate powers from separable Cartesian integral tables. Only requested powers are stored. With the origin on A, each power is a direct shift of the bra degree; other origins use the binomial expansion.

Parameters

source	input tables with enough raised bra degrees for the largest power
values	tables indexed by bra degree, ket degree, requested power and axis
la_max	highest output degree on A
lb_max	highest output degree on B
powers	nonnegative coordinate powers to evaluate
origin	displacement of A from the coordinate reference point

Definition at line 321 of file ai_cartesian_operators.F.

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