for a SCO complex [Fe
II (tren(py) 3 )]
2+ , the TDDFT approach can predict the Fe
L 3 -edge XANES spectra of both the low-spin and high-spin complexes which agree
well with experiment [247–249]. However, such agreement depends on the system.
When the same procedure was applied to a variety of Fe
II and Fe
III complexes with
different spin states, the accuracy did not always persist (Hua et al., submitted).
Other post-HF methods have been employed for simulating the K-edge XES,
XAS, or RIXS spectra of very small molecules. The intentions are to examine the
effect of electron correlation, to include the effect of shake-up/shake-off processes,
and/or to consider the influence of bond breaking. Ågren and coworkers had
reported early CI studies of XAS [250, 251] and XES [252, 253] spectra of CO
and N 2 . Recently, Neese et al. [254] studied the vibrationally-resolved RIXS
spectra of CO 2 using the MRCI method. Coupled cluster (CC)-based methods
have been developed for core state calculations, including single-reference
equation-of-motion CC (EOM-CC) [255, 256], state-specific multireference CC
(SS-MRCC) [257], and open-shell symmetry-adapted cluster configuration interaction (SAC-CI) methods [258, 259].
4 Other Computational Issues
4.1 Density Functionals for Core Excitations
Core excitation energies are often underestimated by TDDFT. It is often necessary
to shift the TDDFT core excitation spectrum by tens of electronvolts for light atom
excitations and hundreds of electronvolts for heavy atom core excitations to match
experiment. The corresponding shifts for ΔSCF type methods are much smaller,
with typical values < 2 eV [57] for light atom core excitations. Both ΔSCF and
TDDFT have relativistic and basis set errors. The large differences between their
shifts come from the self-interaction error of energy density functionals and the
absence of orbital relaxation in TDDFT. A constant (even large) shift to a simulated
linear X-ray absorption spectrum does not change the relative positions of spectroscopic features. This may not be the case for nonlinear X-ray spectroscopy spectra
because core excitations may interact with each other, and those shifts cannot be
considered as constants. Thus a proper choice of energy density functional is
essential for a successful TDDFT simulation of nonlinear X-ray spectroscopy
signals.
The failure of common generalized gradient approximation (GGA) or hybrid
functionals to capture long-range charge transfer excited states was analyzed
thoroughly [94], and is attributed to the self-interaction error in the functionals
used. Surprisingly, a simple Perdew–Zunger self-interaction correction (SIC)
scheme [260] applied to ΔSCF or TDDFT does not correct the core excitation
energies in the right direction [261]. This SIC scheme has already been combined
with the CPP method (explained in the previous section) to produce improved core
322
Y. Zhang et al.
II (tren(py) 3 )]
2+ , the TDDFT approach can predict the Fe
L 3 -edge XANES spectra of both the low-spin and high-spin complexes which agree
well with experiment [247–249]. However, such agreement depends on the system.
When the same procedure was applied to a variety of Fe
II and Fe
III complexes with
different spin states, the accuracy did not always persist (Hua et al., submitted).
Other post-HF methods have been employed for simulating the K-edge XES,
XAS, or RIXS spectra of very small molecules. The intentions are to examine the
effect of electron correlation, to include the effect of shake-up/shake-off processes,
and/or to consider the influence of bond breaking. Ågren and coworkers had
reported early CI studies of XAS [250, 251] and XES [252, 253] spectra of CO
and N 2 . Recently, Neese et al. [254] studied the vibrationally-resolved RIXS
spectra of CO 2 using the MRCI method. Coupled cluster (CC)-based methods
have been developed for core state calculations, including single-reference
equation-of-motion CC (EOM-CC) [255, 256], state-specific multireference CC
(SS-MRCC) [257], and open-shell symmetry-adapted cluster configuration interaction (SAC-CI) methods [258, 259].
4 Other Computational Issues
4.1 Density Functionals for Core Excitations
Core excitation energies are often underestimated by TDDFT. It is often necessary
to shift the TDDFT core excitation spectrum by tens of electronvolts for light atom
excitations and hundreds of electronvolts for heavy atom core excitations to match
experiment. The corresponding shifts for ΔSCF type methods are much smaller,
with typical values < 2 eV [57] for light atom core excitations. Both ΔSCF and
TDDFT have relativistic and basis set errors. The large differences between their
shifts come from the self-interaction error of energy density functionals and the
absence of orbital relaxation in TDDFT. A constant (even large) shift to a simulated
linear X-ray absorption spectrum does not change the relative positions of spectroscopic features. This may not be the case for nonlinear X-ray spectroscopy spectra
because core excitations may interact with each other, and those shifts cannot be
considered as constants. Thus a proper choice of energy density functional is
essential for a successful TDDFT simulation of nonlinear X-ray spectroscopy
signals.
The failure of common generalized gradient approximation (GGA) or hybrid
functionals to capture long-range charge transfer excited states was analyzed
thoroughly [94], and is attributed to the self-interaction error in the functionals
used. Surprisingly, a simple Perdew–Zunger self-interaction correction (SIC)
scheme [260] applied to ΔSCF or TDDFT does not correct the core excitation
energies in the right direction [261]. This SIC scheme has already been combined
with the CPP method (explained in the previous section) to produce improved core
322
Y. Zhang et al.