From c348e8170defbc729d75b7691b285fed61bca5fb Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Mon, 18 Nov 2019 16:55:09 +0100 Subject: [PATCH] numerical values --- FarDFT.nb | 70 ++++++++++++++++++++++++++++++++----------- Manuscript/FarDFT.tex | 33 ++++++++++---------- 2 files changed, 70 insertions(+), 33 deletions(-) diff --git a/FarDFT.nb b/FarDFT.nb index b19c4d9..bc08359 100644 --- a/FarDFT.nb +++ b/FarDFT.nb @@ -10,10 +10,10 @@ NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] -NotebookDataLength[ 549900, 10641] -NotebookOptionsPosition[ 539584, 10477] -NotebookOutlinePosition[ 539920, 10492] -CellTagsIndexPosition[ 539877, 10489] +NotebookDataLength[ 551363, 10677] +NotebookOptionsPosition[ 540821, 10509] +NotebookOutlinePosition[ 541158, 10524] +CellTagsIndexPosition[ 541115, 10521] WindowFrame->Normal*) (* Beginning of Notebook Content *) @@ -1705,6 +1705,38 @@ Cell[BoxData[ 3.7827277718121433`*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"8d489c13-936e-4272-b8f6-29963888bb9f"], +Cell[CellGroupData[{ + +Cell[BoxData[ + RowBox[{"SetAccuracy", "[", + RowBox[{ + RowBox[{"-", + RowBox[{"ES", "\[LeftDoubleBracket]", + RowBox[{";;", ",", "2"}], "\[RightDoubleBracket]"}]}], ",", "7"}], + "]"}]], "Input", + CellChangeTimes->{{3.783081024944618*^9, 3.7830810452646837`*^9}, { + 3.783081103856196*^9, 3.783081104302329*^9}}, + CellLabel->"In[12]:=",ExpressionUUID->"61dfa35c-e342-4dc8-903c-d82259a516b7"], + +Cell[BoxData[ + RowBox[{"{", + RowBox[{ + "0.0144967970908660851`5.16127206020633", ",", + "0.0145228596955837123`5.162052141689678", ",", + "0.0145605323788148646`5.16317725443819", ",", + "0.0145122400271831991`5.161734452848537", ",", + "0.0141416030960858222`5.150498643995601", ",", + "0.0123339467474009694`5.091102069000304", ",", + "0.0097155464204599512`4.987467231154754", ",", + "0.0067438074727065987`4.828905163227798", ",", + "0.0035844891476832362`4.554427269864077", ",", + "0.0020591325343476973`4.313684300519664", ",", + "0.0014581793704013584`4.163810949759818"}], "}"}]], "Output", + CellChangeTimes->{{3.7830810227244043`*^9, 3.783081045700563*^9}, + 3.783081105143827*^9}, + CellLabel->"Out[12]=",ExpressionUUID->"717b8b96-8077-4690-8e3e-3c1a5238ccd1"] +}, Open ]], + Cell[BoxData[{ RowBox[{ RowBox[{"GS", "=", @@ -1932,7 +1964,7 @@ Cell[BoxData[{ 3.782710858528974*^9}, {3.7827275396833487`*^9, 3.7827275687159843`*^9}, { 3.7827276811573753`*^9, 3.782727703059353*^9}, {3.7830130259268627`*^9, 3.783013037428529*^9}}, - 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The construction of these two functionals is described below. -Here, we restrict our study to spin-unpolarized systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$. +Here, we restrict our study to spin-unpolarised systems, \ie, $\n{\uparrow}{} = \n{\downarrow}{} = \n{}{}/2$ (where $\n{\uparrow}{}$ and $\n{\downarrow}{}$ are the spin-up and spin-down electron densities). +Extension to spin-polarised systems will be reported in future work. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Weight-dependent exchange functional} @@ -349,22 +350,22 @@ Combining these, we build a two-state weight-dependent correlation functional: $-\e{\co}{(I)}$ as a function of the radius of the glome $R = 1/(\pi \n{}{})^{1/3}$ for the ground state ($I=0$), and the first doubly-excited state ($I=1$) of the (spin-unpolarized) two-electron glomium system. } \begin{ruledtabular} - \begin{tabular}{ldd} + \begin{tabular}{lcc} & \tabc{Ground state} & \tabc{Doubly-excited state} \\ $R$ & \tabc{$I=0$} & \tabc{$I=1$} \\ \hline - $0$ & & \\ - $1/10$ & & \\ - $1/5$ & & \\ - $1/2$ & & \\ - $1$ & & \\ - $2$ & & \\ - $5$ & & \\ - $10$ & & \\ - $20$ & & \\ - $50$ & & \\ - $100$ & & \\ - $150$ & & \\ + $0$ & $0.023818$ & $0.014463$ \\ + $0.1$ & $0.023392$ & $0.014497$ \\ + $0.2$ & $0.022979$ & $0.014523$ \\ + $0.5$ & $0.021817$ & $0.014561$ \\ + $1$ & $0.020109$ & $0.014512$ \\ + $2$ & $0.017371$ & $0.014142$ \\ + $5$ & $0.012359$ & $0.012334$ \\ + $10$ & $0.008436$ & $0.009716$ \\ + $20$ & $0.005257$ & $0.006744$ \\ + $50$ & $0.002546$ & $0.003584$ \\ + $100$ & $0.001399$ & $0.002059$ \\ + $150$ & $0.000972$ & $0.001458$ \\ \end{tabular} \end{ruledtabular} \end{table} @@ -380,8 +381,8 @@ Combining these, we build a two-state weight-dependent correlation functional: & \tabc{$I=0$} & \tabc{$I=1$} \\ \hline $a_1$ & $-0.0238184$ & $-0.0144633$ \\ - $a_2$ & $+0.00575719$ & $-0.0504501$ \\ - $a_3$ & $+0.0830576$ & $+0.0331287$ \\ + $a_2$ & $+0.00540994$ & $-0.0506019$ \\ + $a_3$ & $+0.0830766$ & $+0.0331417$ \\ \end{tabular} \end{ruledtabular} \end{table}