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Merge pull request #30 from v1j4y/ao_mo_vj

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AO and MO related functions.
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Anthony Scemama 2021-09-06 09:48:03 +02:00 committed by GitHub
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@ -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