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# Representing Exact Electron Densities by a Single Slater Determinant in Finite Basis Sets

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posted on 2020-12-08, 09:03 authored by Philip Jakobsen, Frank JensenThe premise for Kohn–Sham
density functional theory is that
the exact electron density can be generated by a set of orbitals in
a single Slater determinant. While this is ensured in a complete basis
set, it has been shown that it cannot hold in small basis sets. The
present work probes how accurately a reference electron density of
the full-CI type can be reproduced by a set of orbitals in a single
Slater determinant, as a function of the basis set used for the fitting
electron density. The key finding is that the fitting error may be
significant for basis sets of double- or triple-ζ quality. It
is also shown that it is important that the fitting basis set includes
the same basis functions as used for generating the reference electron
density. The main limitation in a given basis set is the lack of higher
order polarization functions. The error for practical purposes becomes
insignificant for basis sets of quadruple-ζ or better quality,
and this should be the choice when assessing the accuracy of exchange-correlation
functionals by comparing electron densities to accurate reference
results generated by wave function methods. The methodology in the
present work can be used to transform an electron density from a multideterminant
wave function into a set of orbitals in a single Slater determinant,
and this may be useful for developing and testing new exchange-correlation
functionals.