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Introduced real solid harmonics in the documentation

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Anthony Scemama 2024-10-16 16:54:56 +02:00
parent b68fe5a18a
commit da62668b1f
1 changed files with 11 additions and 5 deletions
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@ -684,13 +684,19 @@ power = [
\] \]
where $i$ is the atomic orbital index, $P$ refers to either where $i$ is the atomic orbital index, $P$ refers to either
polynomials or spherical harmonics, and $s(i)$ specifies the shell polynomials in $x,y,z$ or real solid harmonics
on which the AO is expanded. \[
S^m_{\ell}(\mathbf{r}) \equiv \sqrt{\frac{4\pi}{2\ell+1}}\; r^\ell
Y^m_{\ell}(\theta,\varphi)
\]
(see [[https://en.wikipedia.org/wiki/Solid_harmonics][Wikipedia]]), and $s(i)$
specifies the shell on which the AO is expanded.
$\eta(i)$ denotes the chosen angular function. The AOs can be $\eta(i)$ denotes the chosen angular function. The AOs can be
expressed using real spherical harmonics or polynomials in Cartesian expressed using real solid harmonics or polynomials in Cartesian
coordinates. In the case of real spherical harmonics, the AOs are coordinates. In the case of real solid harmonics, the AOs are
ordered as $0, +1, -1, +2, -2, \dots, + m, -m$ (see [[https://en.wikipedia.org/wiki/Table_of_spherical_harmonics#Real_spherical_harmonics][Wikipedia]]). In ordered as $0, +1, -1, +2, -2, \dots, + m, -m$). In
the case of polynomials, the canonical (or alphabetical) ordering is the case of polynomials, the canonical (or alphabetical) ordering is
used, used,