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Some improvements to the description.

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v1j4y 2021-09-06 07:45:10 +02:00
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@ -14,10 +14,10 @@ Gaussian ($p=2$):
\exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right). \exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right).
\] \]
In the case of Gaussian functions, $n_s$ is always zero. In the case of Gaussian functions, $n_s$ is always zero. The
The normalization factor $\mathcal{N}_s$ ensures that all the functions normalization factor $\mathcal{N}_s$ ensures that all the functions of
of the shell are normalized to unity. Usually, basis sets are given the shell are normalized (integrate) to unity. Usually, basis sets are
a combination of normalized primitives, so the normalization given a combination of normalized primitives, so the normalization
coefficients of the primitives, $f_{ks}$, need also to be provided. coefficients of the primitives, $f_{ks}$, need also to be provided.
Atomic orbitals (AOs) are defined as 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}) \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, where $\theta(i)$ returns the shell on which the AO is expanded, and
and $\eta(i)$ denotes which angular function is chosen. $\eta(i)$ denotes which angular function is chosen and $P$ are the
Here, the parameter $\mathcal{M}_i$ is an extra parameter which allows generating functions of the given angular momentum $\eta(i)$. Here,
the normalization of the different functions of the same shell to be 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. different, as in GAMESS for example.
In this section we describe first how the basis set is stored in the In this section we describe first how the basis set is stored in the