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Pierre-Francois Loos 2020-02-13 22:57:17 +01:00
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FarDFT.nb
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@ -547,8 +547,10 @@ Ensemble energies (in hartree) of \ce{H2} with $\RHH = 1.4$ bohr as a function o
\label{sec:res}
Here, we consider as testing ground the minimal-basis \ce{H2} molecule.
We select STO-3G as minimal basis, and study the behaviour of the total energy of \ce{H2} as a function of the internuclear distance $\RHH$ (in bohr).
This minimal-basis example is quite pedagogical as the molecular orbitals are fixed by symmetry.
Therefore, there is no density-driven error and the only error that we are going to see is the functional-driven error (and this is what we want to study).
This minimal-basis example is quite pedagogical as the molecular orbitals are fixed by symmetry.
We have then access to the individual densities of the ground and doubly-excited states (which is not usually possible in practice).
Therefore, thanks to the spatial symmetry and the minimal basis, the individual densities extracted from the ensemble density are equal to the \textit{exact} individual densities.
In other words, there is no density-driven error and the only error that we are going to see is the functional-driven error (and this is what we want to study).
The bonding and antibonding orbitals of the \ce{H2} molecule are given by
\begin{subequations}