From bbfdbdf3151d0373e55bf497a6e494b2c368949e Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Thu, 13 Feb 2020 22:57:17 +0100 Subject: [PATCH] NB --- FarDFT.nb | 3199 ++++++++++++++++++++++++++++++++++++----- Manuscript/FarDFT.tex | 6 +- 2 files changed, 2831 insertions(+), 374 deletions(-) diff --git a/FarDFT.nb b/FarDFT.nb index e563b9f..7fc7bd1 100644 --- a/FarDFT.nb +++ b/FarDFT.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 106735, 2807] -NotebookOptionsPosition[ 94731, 2617] -NotebookOutlinePosition[ 95068, 2632] -CellTagsIndexPosition[ 95025, 2629] +NotebookDataLength[ 196078, 5262] +NotebookOptionsPosition[ 178259, 4982] +NotebookOutlinePosition[ 178596, 4997] +CellTagsIndexPosition[ 178553, 4994] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -37,8 +37,7 @@ mathpazo,xcolor,bm,mhchem}\>\"", "}"}]}]}], "]"}], ";"}]}], "Input", InitializationCell->True, 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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}