working on intro
This commit is contained in:
Emmanuel Giner
parent
dc21d85b4c
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@ -18,19 +18,18 @@
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\citation{alex_thom,piotr}
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\citation{scuseria}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{Bender_1969,Whitten_1969,Huron_1973,ShBuPeyChemPhys78,BuePeyButMolPhys78,Evangelisti_1983,Cimiraglia_1985,Cimiraglia_1987,Illas_1988,Povill_1992,EngHanLenCompChem01,Abrams_2005,Bunge_2006,MusEngelsJCC06,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018a,Scemama_2018b,Loos_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Loos_2019}
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\newlabel{FirstPage}{{}{1}{}{section*.1}{}}
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\@writefile{toc}{\contentsline {title}{Mixing density functional theory and wave function theory for strong correlation: the best of both worlds}{1}{section*.2}}
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\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}}
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\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}{section*.3}}
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\@writefile{toc}{\contentsline {section}{\numberline {II}Theory}{1}{section*.4}}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{G2,excited}
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\citation{kato}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\@writefile{toc}{\contentsline {section}{\numberline {II}Theory}{2}{section*.4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Basic formal equations}{2}{section*.5}}
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\newlabel{sec:basic}{{II\tmspace +\thinmuskip {.1667em}A}{2}{}{section*.5}{}}
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\newlabel{eq:levy}{{1}{2}{}{equation.2.1}{}}
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@ -38,14 +37,17 @@
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\newlabel{eq:e0approx}{{5}{2}{}{equation.2.5}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {B}Definition of an effective interaction within $\mathcal {B}$}{2}{section*.6}}
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\newlabel{sec:wee}{{II\tmspace +\thinmuskip {.1667em}B}{2}{}{section*.6}{}}
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\newlabel{eq:wbasis}{{6}{2}{}{equation.2.6}{}}
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\newlabel{eq:fbasis}{{8}{2}{}{equation.2.8}{}}
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\newlabel{eq:cbs_wbasis}{{10}{2}{}{equation.2.10}{}}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\bibdata{srDFT_SCNotes,srDFT_SC}
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\bibcite{GinPraFerAssSavTou-JCP-18}{{1}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
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\bibstyle{aipnum4-1}
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\citation{REVTEX41Control}
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\citation{aip41Control}
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\newlabel{eq:wbasis}{{6}{3}{}{equation.2.6}{}}
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\newlabel{eq:fbasis}{{8}{3}{}{equation.2.8}{}}
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\newlabel{eq:cbs_wbasis}{{10}{3}{}{equation.2.10}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {C}Definition of an range-separation parameter varying in real space}{3}{section*.7}}
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\newlabel{sec:mur}{{II\tmspace +\thinmuskip {.1667em}C}{3}{}{section*.7}{}}
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\newlabel{eq:weelr}{{11}{3}{}{equation.2.11}{}}
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@ -55,7 +57,7 @@
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{3}{section*.10}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{3}{section*.11}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{3}{section*.12}}
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\newlabel{LastBibItem}{{0}{3}{}{figure.7}{}}
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\newlabel{LastBibItem}{{1}{3}{}{figure.7}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{4}{figure.1}}
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\newlabel{fig:N2_avdz}{{1}{4}{N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.1}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{5}{figure.2}}
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@ -6,7 +6,7 @@
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%Control: page (0) single
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%Control: year (1) truncated
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%Control: production of eprint (0) enabled
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\begin{thebibliography}{0}%
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\begin{thebibliography}{1}%
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\makeatletter
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\providecommand \@ifxundefined [1]{%
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\@ifx{#1\undefined}
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@ -50,4 +50,18 @@
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\providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}%
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\let\auto@bib@innerbib\@empty
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%</preamble>
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\bibitem [{\citenamefont {Giner}\ \emph {et~al.}(2018)\citenamefont {Giner},
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\citenamefont {Pradines}, \citenamefont {Fert\'e}, \citenamefont {Assaraf},
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\citenamefont {Savin},\ and\ \citenamefont
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{Toulouse}}]{GinPraFerAssSavTou-JCP-18}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
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{Giner}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Pradines}},
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\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Fert\'e}}, \bibinfo
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{author} {\bibfnamefont {R.}~\bibnamefont {Assaraf}}, \bibinfo {author}
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{\bibfnamefont {A.}~\bibnamefont {Savin}}, \ and\ \bibinfo {author}
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{\bibfnamefont {J.}~\bibnamefont {Toulouse}},\ }\href@noop {} {\bibfield
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{journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume}
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{149}},\ \bibinfo {pages} {194301} (\bibinfo {year} {2018})}\BibitemShut
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{NoStop}%
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\end{thebibliography}%
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@ -11,6 +11,50 @@ Reallocated singl_function (elt_size=4) to 100 items from 50.
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Reallocated wiz_functions (elt_size=4) to 6000 items from 3000.
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Database file #1: srDFT_SCNotes.bib
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Database file #2: srDFT_SC.bib
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Warning--I didn't find a database entry for "alex_thom"
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Warning--I didn't find a database entry for "Bender_1969"
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Warning--I didn't find a database entry for "ShBuPeyChemPhys78"
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control{REVTEX41Control}, control.key{N/A}, control.author{N/A}, control.editor{N/A}, control.title{N/A}, control.pages{N/A}, control.year{N/A}, control.eprint{N/A},
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control{aip41Control}, control.key{N/A}, control.author{N/A}, control.editor{N/A}, control.title{}, control.pages{0}, control.year{N/A}, control.eprint{N/A},
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Warning--jnrlst (dependency: not reversed) set 1
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@ -23,45 +67,45 @@ Control: production of article title (-1) disabled
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You've used 2 entries,
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You've used 3 entries,
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(There was 1 warning)
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(There were 45 warnings)
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@ -239,7 +239,7 @@ Therefore, although constant efforts are performed to reduce the computational c
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From the theoretician point of view, the complexity of description of a given chemical system can be roughly
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categorized by the strength of the electronic correlation appearing in its electronic structure.
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Weakly correlated systems, such as closed-shell organic molecules near their equilibrium geometry, are typically dominated by the avoidance effects when electron are near the electron coalescence point, which are often called short-range correlation effects,
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or far, typically dispersion forces. The theoretical description of weakly correlated systems is one of the more concrete achievement
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or far from each other, typically dispersion forces. The theoretical description of weakly correlated systems is one of the more concrete achievement
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of quantum chemistry, and the main remaining issue for these systems is to push the limit in terms of the size of the chemical systems that can be treated.
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The case of the so-called strongly correlated systems, which are ubiquitous in chemistry, is much more problematic as they exhibits
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a much more exotic electronic structure.
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@ -254,17 +254,22 @@ ii) the quantitative description of the systems must take into account weak corr
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other electronic configurations with typically much smaller weights in the wave function.
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Fulfilling these two objectives is a rather complicated task, specially if one adds the requirement of size-extensivity and additivity of the computed energy in the case of non interacting fragments, which is a very desirable property for any approximated method.
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To tackle this complicated problem, many methods have been proposed and an exhaustive review of the zoology of methods for strong correlation goes beyond the scope and purpose of this article.
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To tackle this problem, many WFT methods have emerged which can be categorized in two branches: the single-reference (SR)
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and multi-reference (MR) methods.
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The SR methods rely on a single electronic configuration as a zeroth-order wave function, typically Hartree-Fock (HF).
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Then the electron correlation is introduced by increasing the rank of multiple hole-particle excitations,
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preferably treated in a coupled-cluster fashion for the sake of compactness of the wave function and extensivity of the computed energies.
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preferably treated in a coupled-cluster (CC) fashion for the sake of compactness of the wave function and extensivity of the computed energies.
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The advantage of these approaches rely on the rather straightforward way to improve the level of accuracy,
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which consists in increasing the rank of the excitation operators used to generate the CC wave function.
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Despite its appealing elegant simplicity, the computational cost of the CC methods increase drastically with the rank of the excitation
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operators, even if alternative approaches have been proposed using stochastic techniques\cite{alex_thom,piotr} or symmetry-broken approaches\cite{scuseria}.
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In the MR approaches, the zeroth order wave function consists in a linear combination of Slater determinants which are supposed to concentrate most of strong interactions and near degeneracies.
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On top of this zeroth-order wave function, weak correlation is introduced by the addition of other configurations
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operators, even if promising alternative approaches have been proposed using stochastic techniques\cite{alex_thom,piotr} or symmetry-broken approaches\cite{scuseria}.
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In the MR approaches, the zeroth order wave function consists in a linear combination of Slater determinants which are supposed to concentrate most of strong interactions and near degeneracies inherent in the structure of the Hamiltonian for a strongly correlated system. The usual approach is to perform a complete active space self consistent field (CASSCF) whose variational property prevent any divergence, and which can provide extensive energies. Of course, the choice of the active space is rather a subtle art and the CASSCF results might strongly depend on the level of chemical/physical knowledge of the user.
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On top of this zeroth-order wave function, weak correlation is introduced by the addition of other configurations through either configuration interaction (MRCI) or perturbation theory (MRPT) and even coupled cluster (MRCC), which have their strengths and weaknesses,
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The advantage of MRCI approaches rely essentially in their simple linear parametrisation for the wave function together with the variational property of their energies, whose inherent drawback is the lack of size extensivity of their energies unless reaching the FCI limit. On the other hand, MRPT and MRCC can provide extensive energies but to the price of rather complicated formalisms, and these approaches might be subject to divergences and/or convergence problems due to the non linearity of the parametrisation for MRCC or a too poor choice of the zeroth-order Hamiltonian.
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A natural alternative is to combine MRCI and MRPT, which falls in the category of selected CI (SCI) which goes back to the late 60's and who has received a revival of interest and applications during the last decade \cite{Bender_1969,Whitten_1969,Huron_1973,ShBuPeyChemPhys78,BuePeyButMolPhys78,Evangelisti_1983, Cimiraglia_1985, Cimiraglia_1987, Illas_1988, Povill_1992,EngHanLenCompChem01,Abrams_2005,Bunge_2006,MusEngelsJCC06,Bytautas_2009,Giner_2013,Caffarel_2014,Giner_2015,Garniron_2017b,Caffarel_2016a,Caffarel_2016b,Holmes_2016,Sharma_2017,Holmes_2017,Chien_2018,Scemama_2018a,Scemama_2018b,Loos_2018b,Garniron_2018,Evangelista_2014,Schriber_2016,Schriber_2017,Liu_2016,Per_2017,Ohtsuka_2017,Zimmerman_2017,Li_2018,Loos_2019}, and among which the CI perturbatively selected iteratively (CIPSI) can be considered as a pioneer. The main idea of the CIPSI and other related SCI algorithms is to iteratively select the most important Slater determinants thanks to perturbation theory in order to build a MRCI zeroth-order wave function which automatically concentrate the strongly interacting part of the wave function. On top of this MRCI zeroth-order wave function, a rather simple MRPT approach is used to recover the missing weak correlation and the process is iterated until reaching a given stopping criterion. It is important to notice that in the SCI algorithms, neither the SCI or the MRPT are size extensive \text{per se}, but the extensivity property is almost recovered by approaching the FCI limit.
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When the SCI are affordable, their clear advantage are they provide near FCI wave functions and energies, whatever the level of knowledge of the user on the specific physical/chemical problem considered. The drawback of SCI is certainly their \textit{intrinsic} exponential scaling due to their linear parametrisation. Nevertheless, such an exponential scaling is lowered by the smart selection of the zeroth-order wave function together with the MRPT calculation.
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A sensible advantage of WFT is its systematically improvable character to tend to the exact solution, which is the so-called full configuration interaction (FCI) in a complete basis set (CBS).
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