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@ 493,3 +493,107 @@ note={Gaussian Inc. Wallingford CT}


eprint = {2002.03107},


url = {https://arxiv.org/abs/2002.03107v2}


}




@article{Per_2012,


author = {Per, Manolo C. and Walker, Kelly A. and


Russo, Salvy P.},


title = {{How Important is Orbital Choice in SingleDeterminant Diffusion Quantum Monte


Carlo Calculations?}},


journal = {J. Chem. Theory Comput.},


volume = {8},


number = {7},


pages = {22552259},


year = {2012},


month = {Jul},


issn = {15499618},


publisher = {American Chemical Society},


doi = {10.1021/ct200828s}


}




@article{Petruzielo_2012,


author = {Petruzielo, F. R. and Toulouse, Julien and


Umrigar, C. J.},


title = {{Approaching chemical accuracy with quantum Monte Carlo}},


journal = {J. Chem. Phys.},


volume = {136},


number = {12},


pages = {124116},


year = {2012},


month = {Mar},


issn = {00219606},


publisher = {American Institute of Physics},


doi = {10.1063/1.3697846}


}




@misc{Caffarel_2016_2,


title = {{Recent Progress in Quantum Monte Carlo}},


journal = {ACS Symp. Ser.},


year = {2016},


month = {Jan},


note = {[Online; accessed 6. Jul. 2020]},


url = {https://pubs.acs.org/doi/abs/10.1021/bk20161234.ch002}


}




@article{Giner_2016,


author = {Giner, Emmanuel and Assaraf, Roland and


Toulouse, Julien},


title = {{Quantum Monte Carlo with reoptimised perturbatively selected configurationinteraction


wave functions}},


journal = {Mol. Phys.},


volume = {114},


number = {78},


pages = {910920},


year = {2016},


month = {Apr},


issn = {00268976},


publisher = {Taylor {\&} Francis},


doi = {10.1080/00268976.2016.1149630}


}




@article{Dash_2019,


author = {Dash, Monika and Feldt, Jonas and Moroni, Saverio and


Scemama, Anthony and Filippi, Claudia},


title = {{Excited States with Selected Configuration InteractionQuantum Monte Carlo:


Chemically Accurate Excitation Energies and Geometries}},


journal = {J. Chem. Theory Comput.},


volume = {15},


number = {9},


pages = {48964906},


year = {2019},


month = {Sep},


issn = {15499618},


publisher = {American Chemical Society},


doi = {10.1021/acs.jctc.9b00476}


}




@article{Dash_2018,


author = {Dash, Monika and Moroni, Saverio and Scemama, Anthony and


Filippi, Claudia},


title = {{Perturbatively Selected ConfigurationInteraction Wave Functions for Efficient


Geometry Optimization in Quantum Monte Carlo}},


journal = {J. Chem. Theory Comput.},


volume = {14},


number = {8},


pages = {41764182},


year = {2018},


month = {Aug},


issn = {15499618},


publisher = {American Chemical Society},


doi = {10.1021/acs.jctc.8b00393}


}




@article{Wang_2019,


author = {Wang, Ting and Zhou, Xiaojun and Wang, Fan},


title = {{Performance of the Diffusion Quantum Monte Carlo Method with a SingleSlaterJastrow


Trial Wavefunction Using Natural Orbitals and Density Functional Theory Orbitals


on Atomization Energies of the Gaussian2 Set}},


journal = {J. Phys. Chem. A},


volume = {123},


number = {17},


pages = {38093817},


year = {2019},


month = {May},


issn = {10895639},


publisher = {American Chemical Society},


doi = {10.1021/acs.jpca.9b01933}


}



@ 54,7 +54,7 @@ solution of the Schrödinger equation with an approximate Hamiltonian


expressed in a finite basis of Slater determinants.


The FCI wave function can be interpreted as the exact solution of the


true Hamiltonian obtained with the additional constraint that it


can only span the space provided by a given basis. At the complete


can only span the space provided by the basis. At the complete


basis set (CBS) limit, the constraint vanishes and the exact solution


is obtained.




@ 79,25 +79,72 @@ as a given trial wave function. This approximation is known as the


function coincide with the nodes of the exact wave function, the exact


energy and wave function are obtained.


The DMC method is attractive because its scaling is polynomial with


the number of electrons and the size of the trial wave


the number of electrons and with the size of the trial wave


function. Moreover, the total energies obtained are usually below


those obtained with FCI because the fixednode approximation imposes


less constraints on the solution than the finitebasis approximation.




In many cases, the systems under study are well described by a single


Slater determinant. Singledeterminant DMC can be used as a postHatreeFock


singlereference method with an accuracy comparable to coupled cluster.


The favorable scaling of QMC and its adequation with massively


parallel architectures makes it an attractive alternative for large


systems.


It has been shown that the nodal surfaces obtained with


KohnSham determinants are in general better than those obtained with


the HartreeFock determinant,\cite{Per_2012} and of comparable quality


to those obtained with natural orbitals of singledeterminant


correlated calculations.\cite{Wang_2019}


However, the fixednode approximation is much more difficult to


control than the finitebasis approximation.






% Single detrminant nodes improved with DFT


% Jastrow optimization > Better nodes


% Combination CIPSI/DMC > Water paper


control than the finitebasis approximation, as it is not possible


to minimize directly the DMC energy with respect to the variational


parameters of the trial wave function.


The conventional approach consists in multiplying the trial wave


function by a positive function, the \emph{Jastrow factor}, taking


account of the electronelectron cusp and the shortrange correlation


effects. The wave function is then reoptimized in the presence of the


Jastrow factor and the nodal surface is expected to be improved.


Using this technique, it has been shown that the chemical accuracy


could be reached within DMC.\cite{Petruzielo_2012}




Another approach consists in considering the DMC method as a


\emph{postFCI method}. The trial wave function is obtained by


approaching the FCI with a selected configuration interaction


method such as CIPSI for instance.\cite{Giner_2013,Caffarel_2016_2}


When the basis set is increased, the trial wave function tends to the


exact wave function, so the nodal surface can be systematically


improved.\cite{Caffarel_2016}


This technique has the advantage that using FCI nodes in a given basis


set is well defined and has a unique solution. The optimization of the


wave function is deterministic, so the calculations are reproducible


and don't require the expertise of a QMC expert. However,


this technique can't be applied to large systems because of the


exponential scaling of the size of the wave function. Extrapolation


techniques have been applied to estimate the DMC energy of a FCI


wave function in a large basis set,\cite{Scemama_2018} and other


authors have used a combination of the two approaches where CIPSI


trial wave functions are reoptimized under the presence of a Jastrow


factor.\cite{Giner_2016,Dash_2018,Dash_2019}








\section{Combining rangeseparated DFT with CIPSI}


\label{sec:rsdftcipsi}




Starting from a HartreeFock determinant in a small basis set,


we have seen that we can systematically improve the trial wave


function in two directions. The first one is by increasing the


size of the atomic basis set, and the second one is by


increasing the determinant expansion towards the FCI limit.


A third direction of improvement exists. It is the path which connects


the HartreeFock determinant to the KohnSham determinant, which


usually has a better nodal surface. This third path is obtained by


the socalled \emph{rangeseparated} DFT framework which splits the


electronelectron interaction in a longrange part and a shortrange


part. HELP MANU!








\subsection{CIPSI}




\emph{Configuration interaction using a perturbative selection made



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