diff --git a/trex.org b/trex.org index c9824ea..7b93fdf 100644 --- a/trex.org +++ b/trex.org @@ -684,13 +684,19 @@ power = [ \] where $i$ is the atomic orbital index, $P$ refers to either - polynomials or spherical harmonics, and $s(i)$ specifies the shell - on which the AO is expanded. + polynomials in $x,y,z$ or real solid harmonics + \[ + S^m_{\ell}(\mathbf{r}) \equiv \sqrt{\frac{4\pi}{2\ell+1}}\; r^\ell + Y^m_{\ell}(\theta,\varphi) + \] + (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 - expressed using real spherical harmonics or polynomials in Cartesian - coordinates. In the case of real spherical 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 + expressed using real solid harmonics or polynomials in Cartesian + coordinates. In the case of real solid harmonics, the AOs are + ordered as $0, +1, -1, +2, -2, \dots, + m, -m$). In the case of polynomials, the canonical (or alphabetical) ordering is used,