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Some improvements to the description.
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@ -14,10 +14,10 @@ Gaussian ($p=2$):
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\exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right).
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\exp \left( - \gamma_{ks} | \mathbf{r}-\mathbf{R}_A | ^p \right).
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\]
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\]
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In the case of Gaussian functions, $n_s$ is always zero.
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In the case of Gaussian functions, $n_s$ is always zero. The
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The normalization factor $\mathcal{N}_s$ ensures that all the functions
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normalization factor $\mathcal{N}_s$ ensures that all the functions of
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of the shell are normalized to unity. Usually, basis sets are given
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the shell are normalized (integrate) to unity. Usually, basis sets are
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a combination of normalized primitives, so the normalization
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given a combination of normalized primitives, so the normalization
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coefficients of the primitives, $f_{ks}$, need also to be provided.
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coefficients of the primitives, $f_{ks}$, need also to be provided.
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Atomic orbitals (AOs) are defined as
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Atomic orbitals (AOs) are defined as
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@ -26,10 +26,11 @@ Atomic orbitals (AOs) are defined as
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\chi_i (\mathbf{r}) = \mathcal{M}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
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\chi_i (\mathbf{r}) = \mathcal{M}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
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\]
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\]
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where $\theta(i)$ returns the shell on which the AO is expanded,
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where $\theta(i)$ returns the shell on which the AO is expanded, and
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and $\eta(i)$ denotes which angular function is chosen.
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$\eta(i)$ denotes which angular function is chosen and $P$ are the
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Here, the parameter $\mathcal{M}_i$ is an extra parameter which allows
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generating functions of the given angular momentum $\eta(i)$. Here,
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the normalization of the different functions of the same shell to be
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the parameter $\mathcal{M}_i$ is an extra parameter which allows the
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normalization of the different functions of the same shell to be
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different, as in GAMESS for example.
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different, as in GAMESS for example.
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In this section we describe first how the basis set is stored in the
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In this section we describe first how the basis set is stored in the
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