added paragraph for mu(r)

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Emmanuel Giner 2019-05-09 00:48:21 +02:00
parent 7ff03c87ce
commit f3bb7ee298

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@ -468,8 +468,10 @@ In most cases, the basis-set corrected triple-$\zeta$ atomization energies are o
\label{fig:N2}}
\end{figure}
\titou{Figure \ref{fig:N2} shows $\rsmu{}{}(z)$ along the molecular axis ($z$) for \ce{N2} in various basis sets.
Short discussion to be added by Manu.}
\manu{A fundamental quantity for the present basis set correction is shape of the function $\rsmu{}{\Bas}(\br{})$ in space. As $\rsmu{}{\Bas}(\br{})$ should tend to infinity in any points in space when reaching the CBS, the local value of $\rsmu{}{\Bas}(\br{})$ can be used to quantify quality of a given basis set in a given point in space. Indeed, the larger the value of $\rsmu{}{\Bas}(\br{})$, the closer it is to the CBS limit, and therefore the smaller will be the energetic correction.
In order to qualitatively illustrate how the basis set correction operates, we report in Figure \ref{fig:N2} $\rsmu{}{\Bas}(z)$ along the molecular axis ($z$) for \ce{N2} and $\Bas=\{\text{cc-pVDZ, cc-pVTZ, cc-pVQZ}\}$.
This figure illustrates several general trends: i) the global value of $\rsmu{}{\Bas}(z)$ is much larger 0.5 which is the standard value used in RS-DFT ii) the local value of $\rsmu{}{\Bas}(z)$ systematically grows when improving the basis set $\Bas$, which means that the total DFT correction will diminish while improving the basis set, iii) the value of $\rsmu{}{\Bas}(z)$ are highly non uniform in space, illustrating the non homogeneity of the basis sets, iv) the value of $\rsmu{}{\Bas}(z)$ are signigicantly larger close to the nucleis, a signature that atom-centered basis sets describe better these regions than the bonding region.
}
%%% TABLE II %%%
\begin{table}