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@ 157,7 +157,7 @@ fixednode approximation is much more difficult to control than the


finitebasis approximation, especially to compute energy differences.


The conventional approach consists in multiplying the determinantal part of the trial wave


function by a positive function, the Jastrow factor, which main assignment is to take into


account the bulk of the dynamical electron correlation and reduce the statistical fluctuation without altering the location of the nodes.


account the bulk of the dynamical electron correlation and reduce the statistical fluctuations without altering the location of the nodes.


%electronelectron cusp and the shortrange correlation effects.


The determinantal part of the trial wave function is then stochastically reoptimized within variational


Monte Carlo (VMC) in the presence of the Jastrow factor (which can also be simultaneously optimized) and the nodal


@ 248,7 +248,7 @@ applicable to large systems with a multiconfigurational character is


still an active field of research. The present paper falls


within this context.




The central idea of the present work, and the launchpad for the remainder of this study, is that one can combine the various strengths of WFT, DFT, and QMC in order to create a new hybrid method with more attractive features and higher accuracy.


The central idea of the present work, and the launch pad for the remainder of this study, is that one can combine the various strengths of WFT, DFT, and QMC in order to create a new hybrid method with more attractive features and higher accuracy.


In particular, we show here that one can combine CIPSI and KSDFT via the range separation (RS) of the interelectronic Coulomb operator \cite{SavINC96a,Toulouse_2004}  a scheme that we label RSDFTCIPSI in the following  to obtain accurate FNDMC energies with compact multideterminant trial wave functions.


An important takehome message from the present study is that the RSDFT scheme essentially plays the role of a simple Jastrow factor by mimicking shortrange correlation effects.


Thanks to this, RSDFTCIPSI multideterminant trial wave functions yield lower fixednode energies with more compact multideterminant expansion than CIPSI, especially for small basis sets, and can be produced in a completely deterministic and systematic way, without the burden of the stochastic optimization.


@ 275,7 +275,7 @@ multideterminant wave function one can wish for  in a given basis set  is


FCI is the ultimate goal of postHF methods, and there exists several systematic


improvements on the path from HF to FCI:


i) increasing the maximum degree of excitation of CI methods (CISD, CISDT,


CISDTQ, \ldots), or ii) expanding the size of a complete active space


CISDTQ,~\ldots), or ii) expanding the size of a complete active space


(CAS) wave function until all the orbitals are in the active space.


SCI methods take a shortcut between the HF


determinant and the FCI wave function by increasing iteratively the


@ 409,11 +409,11 @@ An inner (microiteration) loop (blue) is introduced to accelerate the


convergence of the selfconsistent calculation, in which the set of


determinants in $\Psi^{\mu\,(k,l)}$ is kept fixed, and only the diagonalization of


$\hat{H}^{\mu\,(k,l)}$ is performed iteratively with the updated density $n^{(k,l)}$.


The inner loop is exited when the absolute energy difference between two successive microiterations $\Delta E^{(k,l)}$ is below a threshold $\tau_2$ that has been here set to $10^{2} \times \tau_1$ \hartree{}.


The inner loop is exited when the absolute energy difference between two successive microiterations $\Delta E^{(k,l)}$ is below a threshold $\tau_2$ that has been here set to $10^{2} \times \tau_1$.


The convergence of the algorithm was further improved


by introducing a direct inversion in the iterative subspace (DIIS)


step to extrapolate the oneelectron density both in the outer and inner loops. \cite{Pulay_1980,Pulay_1982}


Note that any rangeseparated postHF method can be


We emphasize that any rangeseparated postHF method can be


implemented using this scheme by just replacing the CIPSI step by the


postHF method of interest.


Note that, thanks to the selfconsistent nature of the algorithm,


@ 426,13 +426,15 @@ the final trial wave function $\Psi^{\mu}$ is independent of the starting wave f


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




All reference data (geometries, atomization


energies, zeropoint energy corrections, etc) were taken from the NIST


energies, zeropoint energy, etc) were taken from the NIST


computational chemistry comparison and benchmark database


(CCCBDB).\cite{nist}


In the reference atomization energies, the zeropoint vibrational


energy was removed from the experimental atomization energies.




All calculations have been performed using BurkatzkiFilippiDolg (BFD)


pseudopotentials \cite{Burkatzki_2007,Burkatzki_2008} with the associated double,


triple, and quadruple$\zeta$ basis sets (VXZBFD).


triple, and quadruple$\zeta$ basis sets (V$X$ZBFD).


The smallcore BFD pseudopotentials include scalar relativistic effects.


Coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] \cite{Scuseria_1988,Scuseria_1989} and KSDFT energies have been computed with


\emph{Gaussian09},\cite{g16} using the unrestricted formalism for openshell systems.


@ 459,9 +461,10 @@ calculations. Simple Jastrow factors were used to reduce the


fluctuations of the local energy (see Sec.~\ref{sec:rsdftj} for their explicit expression).


The FNDMC simulations are performed with allelectron moves using the


stochastic reconfiguration algorithm developed by Assaraf \textit{et al.},


\cite{Assaraf_2000} with a time step of $5 \times 10^{4}$ a.u.


\cite{Assaraf_2000} with a time step of $5 \times 10^{4}$ a.u. and a


projection time of $1$ a.u.




All the data related to the present study (geometries, basis sets, total energies, etc) can be found in the {\SI}.


All the data related to the present study (geometries, basis sets, total energies, \textit{etc}) can be found in the {\SI}.




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Influence of the rangeseparation parameter on the fixednode error}



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