Function qsym2::angmom::sh_conversion::sh_cart2cl_mat
source · pub fn sh_cart2cl_mat(
l: u32,
lcart: u32,
cartorder: &CartOrder,
csphase: bool,
pureorder: &PureOrder,
) -> Array2<Complex<f64>>
Expand description
Obtains the matrix containing linear combination
coefficients of complex solid harmonic Gaussians of a specific degree in the expansion of
Cartesian Gaussians, i.e., briefly,
Let be a complex solid harmonic
Gaussian as defined in Equation 1 of Schlegel, H. B. & Frisch, M. J. Transformation between
Cartesian and pure spherical harmonic Gaussians. International Journal of Quantum Chemistry
54, 83–87 (1995), DOI with
, and let
be a
Cartesian Gaussian as defined in Equation 2 of the above reference. Here,
is a
single index labelling a complex solid harmonic Gaussian of spherical harmonic degree
and order
, and
a single index labelling a Cartesian
Gaussian of degrees
such that
.
We can then write
where is given by the inverse
complex coefficients
defined in complexcinv
.
We can order the rows of
that have the same
into rectangular blocks of dimensions
which give contributions from complex solid harmonic Gaussians of a particular degree
.
We denote these blocks
.
They contain only zero elements if
and
have different parities.
§Arguments
l
- The degree of the complex spherical harmonic factor in the solid harmonic Gaussian.lcart
- The total Cartesian degree for the Cartesian Gaussians and also for the radial part of the solid harmonic Gaussian.cartorder
- ACartOrder
struct giving the ordering of the components of the Cartesian Gaussians.csphase
- Set totrue
to use the Condon–Shortley phase in the calculations of thecoefficients. See
complexc
andcomplexcinv
for more details.pureorder
- APureOrder
struct giving the ordering of the components of the pure Gaussians.
§Returns
The block.