Multiconfigurational Approach to X-ray Spectroscopy …
189
general and have been applied to many standard quantum chemistry methods such as
density functional theory (DFT) [84], algebraic diagrammatic construction (ADC)
[38], and coupled cluster [17]. Yet, as is the case for ground state chemistry and
UV–visible spectroscopy, transition metal complexes are particularly challenging,
due to their open-shell electronic structures and strong correlation, and some of the
methods mentioned above cannot be trusted in this context.
Thanks to its low cost and reasonable accuracy, time-dependent density functional theory (TD-DFT) is widely used. DFT can also be used in conjunction with
wavefunction methods such as in the DFT/restricted open-shell CI singles (ROCIS),
where a CI with single excitations is built and DFT correlation is added using three
system-independent parameters [75]. These DFT-based methods typically fail if the
ground states have significant multi-reference character, which is frequent for firstrow transition metals. In addition, there is often a strong functional dependence,
reducing the predictive power of the method as different functionals can lead to
different conclusions. In particular, self-interaction error has a strong effect on the
calculated spectrum, the low spatial overlap between core and valence orbitals creating what can effectively be considered to be a charge-transfer excitation, which is
an important weakness of some DFT functionals and leads to a critical dependence
on the amount of Hartree–Fock exchange [65].
An electronic structure approach that is well suited for transition metal systems is
the multiconfigurational (MC) self-consistent field (SCF) method, among which the
complete active-space (CASSCF) version is the most widely used [76]. Multiconfigurational methods can be adapted to X-ray processes by including also core electrons
in the excitation space [1, 2, 40]. As the number of excitations from the core orbitals
can typically be restricted to one, it becomes convenient to use a restricted active
space (RAS) wavefunction [62]. This approach has become a leading method to simulate X-ray spectra of smaller transition metal complexes [10, 42, 43, 71, 72]. It can,
with minor adaptations, be applied to L-edge XAS and RIXS dominated by electric dipole transitions between bound states [6, 71, 92]. By including second-order
terms in the wave vector expansion, electric dipole forbidden transitions in metal
K pre-edge XAS and RIXS can be described [32, 33]. With these developments,
multiconfigurational methods have now been used to describe all X-ray processes
shown in Fig. 1. With recent extensions to continuum excitations, it is also possible
to calculate XPS [29, 43]. The combination of an ab initio philosophy with good
accuracy provides a powerful predictive tool for the analysis of X-ray spectra. In the
following section, we will discuss the basic principles of the multiconfigurational
approach, and how to design calculations to get accurate and reliable results.
3 Multiconfigurational Approach to X-ray Processes
The multiconfigurational active-space methods are based on the division of the orbital
space into a small set of so-called active orbitals and a larger set of inactive orbitals
[79]. Within the active orbitals, electron correlation is treated accurately with CI.
189
general and have been applied to many standard quantum chemistry methods such as
density functional theory (DFT) [84], algebraic diagrammatic construction (ADC)
[38], and coupled cluster [17]. Yet, as is the case for ground state chemistry and
UV–visible spectroscopy, transition metal complexes are particularly challenging,
due to their open-shell electronic structures and strong correlation, and some of the
methods mentioned above cannot be trusted in this context.
Thanks to its low cost and reasonable accuracy, time-dependent density functional theory (TD-DFT) is widely used. DFT can also be used in conjunction with
wavefunction methods such as in the DFT/restricted open-shell CI singles (ROCIS),
where a CI with single excitations is built and DFT correlation is added using three
system-independent parameters [75]. These DFT-based methods typically fail if the
ground states have significant multi-reference character, which is frequent for firstrow transition metals. In addition, there is often a strong functional dependence,
reducing the predictive power of the method as different functionals can lead to
different conclusions. In particular, self-interaction error has a strong effect on the
calculated spectrum, the low spatial overlap between core and valence orbitals creating what can effectively be considered to be a charge-transfer excitation, which is
an important weakness of some DFT functionals and leads to a critical dependence
on the amount of Hartree–Fock exchange [65].
An electronic structure approach that is well suited for transition metal systems is
the multiconfigurational (MC) self-consistent field (SCF) method, among which the
complete active-space (CASSCF) version is the most widely used [76]. Multiconfigurational methods can be adapted to X-ray processes by including also core electrons
in the excitation space [1, 2, 40]. As the number of excitations from the core orbitals
can typically be restricted to one, it becomes convenient to use a restricted active
space (RAS) wavefunction [62]. This approach has become a leading method to simulate X-ray spectra of smaller transition metal complexes [10, 42, 43, 71, 72]. It can,
with minor adaptations, be applied to L-edge XAS and RIXS dominated by electric dipole transitions between bound states [6, 71, 92]. By including second-order
terms in the wave vector expansion, electric dipole forbidden transitions in metal
K pre-edge XAS and RIXS can be described [32, 33]. With these developments,
multiconfigurational methods have now been used to describe all X-ray processes
shown in Fig. 1. With recent extensions to continuum excitations, it is also possible
to calculate XPS [29, 43]. The combination of an ab initio philosophy with good
accuracy provides a powerful predictive tool for the analysis of X-ray spectra. In the
following section, we will discuss the basic principles of the multiconfigurational
approach, and how to design calculations to get accurate and reliable results.
3 Multiconfigurational Approach to X-ray Processes
The multiconfigurational active-space methods are based on the division of the orbital
space into a small set of so-called active orbitals and a larger set of inactive orbitals
[79]. Within the active orbitals, electron correlation is treated accurately with CI.