The structure and dynamics of liquid water continue to
be debated,
with insight provided by, among others, X-ray emission spectroscopy
(XES), which shows a split in the high-energy 1b1 feature.
This split is yet to be reproduced by theory, and it remains unclear
if these difficulties are related to inaccuracies in dynamics simulations,
spectrum calculations, or both. We investigate the performance of
different methods for calculating XES of liquid water, focusing on
the ability of time-dependent density functional theory (TDDFT) to
reproduce reference spectra obtained by high-level coupled cluster
and algebraic-diagrammatic construction scheme calculations. A metric
for evaluating the agreement between theoretical spectra termed the
integrated absolute difference (IAD), which considers the integral
of shifted difference spectra, is introduced and used to investigate
the performance of different exchange-correlation functionals. We
find that computed spectra of symmetric and asymmetric model water
structures are strongly and differently influenced by the amount of
Hartree–Fock exchange, with best agreement to reference spectra
for ∼40–50%. Lower percentages tend to yield high density
of contributing states, resulting in too broad features. The method
introduced here is useful also for other spectrum calculations, in
particular where the performance for ensembles of structures are evaluated.