tblite_integral_trafo Module Reference

Implementation of transformations from cartesian to spherical harmonic basis functions and adjoint transformation for contravariant vectors from spherical harmonic to cartesian basis functions, as well as the inverse of the latter. More...

Functions/Subroutines
pure subroutine, public	transform0 (lj, li, cart, sphr, bra, ket)
	Transformation from the cartesian to the spherical harmonic basis for a shell pair block.
pure subroutine, public	transform1 (lj, li, cart, sphr, bra, ket)
	Transformation from the cartesian to the spherical harmonic basis for a vector of shell pair block.
pure subroutine, public	transform2 (lj, li, cart, sphr, bra, ket)
	Transformation from the cartesian to the spherical harmonic basis for a matrix of shell pair block.
pure subroutine, public	adjoint_transform0 (lj, li, sphr, cart, bra, ket)
	Adjoint transformation from the spherical harmonic to the cartesian basis for a shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).
pure subroutine, public	adjoint_transform1 (lj, li, sphr, cart, bra, ket)
	Adjoint transformation from the spherical harmonic to the cartesian basis for a vector of shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).
pure subroutine, public	adjoint_transform2 (lj, li, sphr, cart, bra, ket)
	Adjoint transformation from the spherical harmonic to the cartesian basis for a matrix of shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).
pure subroutine, public	contravariant_transform0 (lj, li, cart, sphr, bra, ket)
	Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).
pure subroutine, public	contravariant_transform1 (lj, li, cart, sphr, bra, ket)
	Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a vector of shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).
pure subroutine, public	contravariant_transform2 (lj, li, cart, sphr, bra, ket)
	Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a matrix of shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Detailed Description

Implementation of transformations from cartesian to spherical harmonic basis functions and adjoint transformation for contravariant vectors from spherical harmonic to cartesian basis functions, as well as the inverse of the latter.

Spherical harmonics use standard ordering, i.e. [-l, ..., 0, ..., l].

Function/Subroutine Documentation

adjoint_transform0()

pure subroutine, public tblite_integral_trafo::adjoint_transform0	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :), intent(in)	sphr,
		real(wp), dimension(:, :), intent(out)	cart,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Adjoint transformation from the spherical harmonic to the cartesian basis for a shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	sphr	Spherical harmonic representation of the integral [bra j, ket i]
[out]	cart	Cartesian representation of the integral [bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

adjoint_transform1()

pure subroutine, public tblite_integral_trafo::adjoint_transform1	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :), intent(in)	sphr,
		real(wp), dimension(:, :, :), intent(out)	cart,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Adjoint transformation from the spherical harmonic to the cartesian basis for a vector of shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	sphr	Spherical harmonic representation of the integral [:, bra j, ket i]
[out]	cart	Cartesian representation of the integral [:, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

adjoint_transform2()

pure subroutine, public tblite_integral_trafo::adjoint_transform2	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :, :), intent(in)	sphr,
		real(wp), dimension(:, :, :, :), intent(out)	cart,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Adjoint transformation from the spherical harmonic to the cartesian basis for a matrix of shell pair block. Applies quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	sphr	Spherical harmonic representation of the integral [:, :, bra j, ket i]
[out]	cart	Cartesian representation of the integral [:, :, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

contravariant_transform0()

pure subroutine, public tblite_integral_trafo::contravariant_transform0	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :), intent(in)	cart,
		real(wp), dimension(:, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

contravariant_transform1()

pure subroutine, public tblite_integral_trafo::contravariant_transform1	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :), intent(in)	cart,
		real(wp), dimension(:, :, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a vector of shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [:, bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [:, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

contravariant_transform2()

pure subroutine, public tblite_integral_trafo::contravariant_transform2	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :, :), intent(in)	cart,
		real(wp), dimension(:, :, :, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Inverse of the adjoint transformation, from the cartesian back to the spherical harmonic basis for a matrix of shell pair block. Applies to quantities which behave contravariant w.r.t. the basis functions (i.e. MO expansion coefficients or the density matrix).

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [:, :, bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [:, :, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

transform0()

pure subroutine, public tblite_integral_trafo::transform0	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :), intent(in)	cart,
		real(wp), dimension(:, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Transformation from the cartesian to the spherical harmonic basis for a shell pair block.

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

transform1()

pure subroutine, public tblite_integral_trafo::transform1	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :), intent(in)	cart,
		real(wp), dimension(:, :, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Transformation from the cartesian to the spherical harmonic basis for a vector of shell pair block.

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [:, bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [:, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension

transform2()

pure subroutine, public tblite_integral_trafo::transform2	(	integer, intent(in)	lj,
		integer, intent(in)	li,
		real(wp), dimension(:, :, :, :), intent(in)	cart,
		real(wp), dimension(:, :, :, :), intent(out)	sphr,
		logical, intent(in)	bra,
		logical, intent(in)	ket )

Transformation from the cartesian to the spherical harmonic basis for a matrix of shell pair block.

Parameters

[in]	li	Angular momentum of ket shell i
[in]	lj	Angular momentum of bra shell j
[in]	cart	Cartesian representation of the integral [:, :, bra j, ket i]
[out]	sphr	Spherical harmonic representation of the integral [:, :, bra j, ket i]
[in]	bra	Flag for transformation of the bra dimension
[in]	ket	Flag for transformation of the ket dimension