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Pierre-Francois Loos 2020-08-02 17:50:00 +02:00
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@ -69,16 +69,16 @@ exact solution is recovered.
Hence, the accuracy of a FCI calculation can be systematically improved by increasing the size of the one-electron basis set.
Nevertheless, its exponential scaling with the number of electrons and with the size of the basis is prohibitive for most chemical systems.
In recent years, the introduction of new algorithms \cite{Booth_2009} and the
revival \cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016}
revival \cite{Abrams_2005,Bytautas_2009,Roth_2009,Giner_2013,Knowles_2015,Holmes_2016,Liu_2016,Garniron_2018}
of selected configuration interaction (sCI)
methods \cite{Bender_1969,Huron_1973,Buenker_1974} pushed the limits of
the sizes of the systems that could be computed at the FCI level.
the sizes of the systems that could be computed at the FCI level. \cite{Daday_2012,Chien_2018,Loos_2018a,Loos_2019,Loos_2020b,Loos_2020c}
However, the scaling remains exponential unless some bias is introduced leading
to a loss of size consistency. % CITE CIPSI 3-CLASS AND INITIATOR APPROXIMATION.
Diffusion Monte Carlo (DMC) is a numerical scheme to obtain
the exact solution of the Schr\"odinger equation with a different
constraint. In DMC, the solution is imposed to have the same nodal hypersurface
constraint. In DMC, the solution is imposed to have the same nodes (or zeroes)
as a given trial (approximate) wave function.
Within this so-called \emph{fixed-node} (FN) approximation,
the FN-DMC energy associated with a given trial wave function is an upper
@ -93,6 +93,9 @@ sets because the constraints imposed by the FN approximation
are less severe than the constraints imposed by the finite-basis
approximation.
\alert{However, it is usually harder to control the FN error in DMC, and this might affect energy differences such as atomization energies.
Moreover, improving systematically the nodal surface of the trial wave function can be a tricky job as there is no variational principle for the nodes.}
The qualitative picture of the electronic structure of weakly
correlated systems, such as organic molecules near their equilibrium
geometry, is usually well represented with a single Slater
@ -102,7 +105,7 @@ DMC with a single-determinant trial wave function can be used as a
single-reference post-Hatree-Fock method, with an accuracy comparable
to coupled cluster.\cite{Dubecky_2014,Grossman_2002}
The favorable scaling of QMC, its very low memory requirements and
its adequation with massively parallel architectures make it a
its adequacy with massively parallel architectures make it a
serious alternative for high-accuracy simulations on large systems.
As it is not possible to minimize directly the FN-DMC energy with respect