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Pierre-Francois Loos 2019-04-07 23:22:32 +02:00
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18
Manuscript/G2-srDFT.tex
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@ -42,7 +42,7 @@
\newcommand{\IneV}[1]{#1 eV}
\newcommand{\InAU}[1]{#1 a.u.}
\newcommand{\InAA}[1]{#1 \AA}
\newcommand{\kcal}{kcal.mol$^{-1}$}
\newcommand{\kcal}{kcal/mol}
% methods
\newcommand{\D}{\text{D}}
@ -124,7 +124,11 @@
\affiliation{\LCT}
\begin{abstract}
We report a universal density-based basis set incompleteness correction that can be applied to any wave function theory method.
We report a universal density-based basis set incompleteness correction that can be applied to any wave function method.
The present correction relies on short-range correlation functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis set incompleteness error.
Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separated \textit{parameter} $\mu$, the key ingredient here is a basis-dependent, range-separated \textit{function} $\mu(\bf{r})$ which is dynamically determined to catch the missing short-range correlation due to the lack of electron-electron cusp in standard wave function methods.
As illustrative examples, we show how this density-based correction allows to obtain near-complete basis set CCSD(T) atomization energies for the G2 set of molecules with compact Gaussian basis sets.
For example, CCSD(T)+LDA/cc-pVTZ and CCSD(T)+PBE/cc-pVTZ return mean absolute deviations of \titou{X.XX} and \titou{X.XX} kcal/mol, respectively, compared to CBS atomization energies.
\end{abstract}
\maketitle
@ -160,7 +164,6 @@ Range-separated hybrids, i.e.~single-determinant approximations of RS-DFT, corre
Other basis set corrections are cool too, \cite{TorVal-JCP-09, KonVal-JCP-10, KonVal-JCP-11, BooCleAlaTew-JCP-2012, IrmHumGru-arXiv-2019, IrmGru-arXiv-2019} but not as cool as ours.
%The present manuscript is organized as follows.
Unless otherwise stated, atomic used are used.
@ -171,7 +174,6 @@ The present basis set correction relies on the RS-DFT formalism to capture the m
Here, we only provide the main working equations.
We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} for a more formal derivation.
%=================================================================
%\subsection{Correcting the basis set error of a general WFT model}
%=================================================================
@ -486,7 +488,7 @@ In order to correct such a defect, we propose here a new ECMD functional inspire
\label{eq:epsilon_cmdpbe}
\be{\PBE}{\sr}(\n{}{},\nabla \n{}{},\rsmu{}{}) = \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{1 + \beta(n,\nabla n, \rsmu{}{})\rsmu{}{3} },
\\
\label{eq:epsilon_cmdpbe}
\label{eq:beta_cmdpbe}
\beta(n,\nabla n,\rsmu{}{}) = \frac{3}{2\sqrt{\pi} (1 - \sqrt{2} )} \frac{\e{\PBE}{}(\n{}{},\nabla \n{}{})}{\n{\UEG}{(2)}(\n{}{})}.
\end{gather}
\end{subequations}
@ -494,7 +496,7 @@ The difference between the ECMD PBE functional defined in Ref.~\onlinecite{FerGi
This represents a major computational saving without loss of performance as we eschew the computation of $\n{}{(2)}$.
Therefore, the PBE complementary functional reads
\begin{equation}
\label{eq:def_lda_tot}
\label{eq:def_pbe_tot}
\bE{\PBE}{\sr}[\n{}{}(\br{}),\rsmu{}{}(\br{})] = \int \be{\PBE}{\sr}[\n{}{}(\br{}),\nabla \n{}{}(\br{}),\rsmu{}{}(\br{})] \n{}{}(\br{}) \dbr{}.
\end{equation}
Depending on the functional choice, the complementary functional $\bE{}{\Bas}[\n{\wf{}{\Bas}}{}]$ is then equal to $\bE{\LDA}{\sr}[\n{\wf{}{\Bas}}{}(\br{}),\rsmu{\wf{}{\Bas}}{}(\br{})]$ or $\bE{\PBE}{\sr}[\n{\wf{}{\Bas}}{}(\br{}),\rsmu{\wf{}{\Bas}}{}(\br{})]$ where $\rsmu{\wf{}{\Bas}}{}(\br{})$ is given by Eq.~\eqref{eq:mu_of_r}.
@ -678,8 +680,8 @@ Defining $\n{\wf{}{\Bas}}{\Val}$ as the valence one-electron density, the valenc
%\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5).
In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.
\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 test set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11}
In a second time, we compute the entire atomization energies of the G2 test set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family.
\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11}
In a second time, we compute the entire atomization energies of the G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family.
This molecular set has been exhausively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08,Gro-JCP-09,FelPet-JCP-09,NemTowNee-JCP-10,FelPetHil-JCP-11,PetTouUmr-JCP-12,FelPet-JCP-13,KesSylKohTewMar-JCP-18}).
%The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$.
As a method $\modX$ we employ either CCSD(T) or exFCI.