Function qsym2::angmom::sh_conversion::complexcinv

pub fn complexcinv(
    lcartqns: (u32, u32, u32),
    lpureqns: (u32, i32),
    csphase: bool,
) -> Complex<f64>

Computes the inverse complex coefficients $c^{-1}(l_x, l_y, l_z, l, m_l, l_{\mathrm{cart}})$ based on Equation 18 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, but more generalised for $l \leq l_{\mathrm{cart}} = l_x + l_y + l_z$.

Let $\tilde{g}(\alpha, l, m_l, l_{\mathrm{cart}}, \mathbf{r})$ be a complex solid harmonic Gaussian as defined in Equation 1 of the above reference with $n = l_{\mathrm{cart}}$, and let $g(\alpha, l_x, l_y, l_z, \mathbf{r})$ be a Cartesian Gaussian as defined in Equation 2 of the above reference. The inverse complex coefficients $c^{-1}(l_x, l_y, l_z, l, m_l, l_{\mathrm{cart}})$ effect the inverse transformation

g(\alpha, l_x, l_y, l_z, \mathbf{r})
= \sum_{l \le l_{\mathrm{cart}} = l_x+l_y+l_z} \sum_{m_l = -l}^{l}
    c^{-1}(l_x, l_y, l_z, l, m_l, l_{\mathrm{cart}})
    \tilde{g}(\alpha, l, m_l, l_{\mathrm{cart}}, \mathbf{r}).

Arguments

• lcartqns - A tuple of $(l_x, l_y, l_z)$ specifying the exponents of the Cartesian components of the Cartesian Gaussian.
• lpureqns - A tuple of $(l, m_l)$ specifying the quantum numbers for the spherical harmonic component of the solid harmonic Gaussian.
• csphase - If true, the Condon–Shortley phase will be used as defined in complexc. If false, this phase will be set to unity.

Returns

$c^{-1}(l_x, l_y, l_z, l, m_l, l_{\mathrm{cart}})$.