From d704b19c13c63417316625beb170aa92fb19f66e Mon Sep 17 00:00:00 2001 From: v1j4y Date: Mon, 6 Sep 2021 07:45:10 +0200 Subject: [PATCH] Some improvements to the description. --- org/qmckl_ao.org | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/org/qmckl_ao.org b/org/qmckl_ao.org index 647be4a..f78350c 100644 --- a/org/qmckl_ao.org +++ b/org/qmckl_ao.org @@ -14,10 +14,10 @@ Gaussian ($p=2$): \exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right). \] -In the case of Gaussian functions, $n_s$ is always zero. -The normalization factor $\mathcal{N}_s$ ensures that all the functions -of the shell are normalized to unity. Usually, basis sets are given -a combination of normalized primitives, so the normalization +In the case of Gaussian functions, $n_s$ is always zero. The +normalization factor $\mathcal{N}_s$ ensures that all the functions of +the shell are normalized (integrate) to unity. Usually, basis sets are +given a combination of normalized primitives, so the normalization coefficients of the primitives, $f_{ks}$, need also to be provided. Atomic orbitals (AOs) are defined as @@ -26,10 +26,11 @@ Atomic orbitals (AOs) are defined as \chi_i (\mathbf{r}) = \mathcal{M}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r}) \] -where $\theta(i)$ returns the shell on which the AO is expanded, -and $\eta(i)$ denotes which angular function is chosen. -Here, the parameter $\mathcal{M}_i$ is an extra parameter which allows -the normalization of the different functions of the same shell to be +where $\theta(i)$ returns the shell on which the AO is expanded, and +$\eta(i)$ denotes which angular function is chosen and $P$ are the +generating functions of the given angular momentum $\eta(i)$. Here, +the parameter $\mathcal{M}_i$ is an extra parameter which allows the +normalization of the different functions of the same shell to be different, as in GAMESS for example. In this section we describe first how the basis set is stored in the