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M. Lundberg and M. G. Delcey
paradigm [76]. After a short introduction to different X-ray modeling approaches,
we will give a step-by-step explanation of the multiconfigurational approach for
transition metal systems. This will be followed by examples of how the combination of theory and experiment can give new insights into transition metal chemistry,
in areas ranging from femtosecond spectroscopy to biological cofactors [39, 74].
The current limits of the multiconfigurational approach are systems with two transition metals and the final section describes potential improvements to handle more
complex systems.
2 Theoretical Simulations of X-ray Spectra
Modeling X-ray spectroscopy includes the same challenges involved in accurate
descriptions of valence states, but the presence of a core hole introduces further
complications. Taking the metal L-edge XAS spectra of an open-shell system as an
example, the final states are affected by both strong 3d-3d and 2p-3d correlation,
as well as 2p and 3d spin–orbit coupling (SOC). This complicates the mapping of
electronic structure to spectral shape.
On the other hand, due to the local nature of the core hole, atomic models can provide a very efficient description of many X-ray spectroscopies. A standard modeling
approach based on this idea is the charge-transfer multiplet (CTM) method [31, 87].
In this model, initial and final states are calculated from an atomic full configuration
interaction (CI) including 2p and 3d orbitals, i.e., taking into account all possible 3d
electron configurations. Ligands are described by an empirical ligand-field splitting
and to model more covalent interactions, ligand-to-metal charge-transfer (LMCT)
or metal-to-ligand charge-transfer (MLCT) configurations can be added in the CI.
This method is not only conceptually simple but also computationally inexpensive
and has historically been one of the dominant ways to theoretically reproduce Xray spectra of transition metals and to interpret them in intuitive terms. However,
the CTM method includes parameters that are fitted to the experimental spectrum,
which makes it less suitable for predictive purposes. Additionally, the number of
model parameters increases with decreasing symmetry, and the semiempirical CTM
approach thus works best for complexes with a high degree of symmetry.
If the aim is to predict the spectral fingerprint of a molecule and distinguish
between different electronic structure alternative, ab initio approaches are preferable
as they are independent from semiempirical parameters. A detailed review of ab initio
methods for X-ray spectroscopy simulation can be found in [67]; for our purpose
here, we will only provide a short overview. Formally, any quantum chemistry method
able to describe valence excitations can be extended to the X-ray regime. However,
most methods typically generate excited states in energy ordering, so the main change
needed in the formalism is a way to target the proper energy range without first having
to compute all valence states. Various ideas have been proposed and implemented
such as core–valence separation [14, 84], efficient energy-specific eigenvalue solvers
[54], and the complex polarization propagator (CPP) [22]. Those formalisms are
M. Lundberg and M. G. Delcey
paradigm [76]. After a short introduction to different X-ray modeling approaches,
we will give a step-by-step explanation of the multiconfigurational approach for
transition metal systems. This will be followed by examples of how the combination of theory and experiment can give new insights into transition metal chemistry,
in areas ranging from femtosecond spectroscopy to biological cofactors [39, 74].
The current limits of the multiconfigurational approach are systems with two transition metals and the final section describes potential improvements to handle more
complex systems.
2 Theoretical Simulations of X-ray Spectra
Modeling X-ray spectroscopy includes the same challenges involved in accurate
descriptions of valence states, but the presence of a core hole introduces further
complications. Taking the metal L-edge XAS spectra of an open-shell system as an
example, the final states are affected by both strong 3d-3d and 2p-3d correlation,
as well as 2p and 3d spin–orbit coupling (SOC). This complicates the mapping of
electronic structure to spectral shape.
On the other hand, due to the local nature of the core hole, atomic models can provide a very efficient description of many X-ray spectroscopies. A standard modeling
approach based on this idea is the charge-transfer multiplet (CTM) method [31, 87].
In this model, initial and final states are calculated from an atomic full configuration
interaction (CI) including 2p and 3d orbitals, i.e., taking into account all possible 3d
electron configurations. Ligands are described by an empirical ligand-field splitting
and to model more covalent interactions, ligand-to-metal charge-transfer (LMCT)
or metal-to-ligand charge-transfer (MLCT) configurations can be added in the CI.
This method is not only conceptually simple but also computationally inexpensive
and has historically been one of the dominant ways to theoretically reproduce Xray spectra of transition metals and to interpret them in intuitive terms. However,
the CTM method includes parameters that are fitted to the experimental spectrum,
which makes it less suitable for predictive purposes. Additionally, the number of
model parameters increases with decreasing symmetry, and the semiempirical CTM
approach thus works best for complexes with a high degree of symmetry.
If the aim is to predict the spectral fingerprint of a molecule and distinguish
between different electronic structure alternative, ab initio approaches are preferable
as they are independent from semiempirical parameters. A detailed review of ab initio
methods for X-ray spectroscopy simulation can be found in [67]; for our purpose
here, we will only provide a short overview. Formally, any quantum chemistry method
able to describe valence excitations can be extended to the X-ray regime. However,
most methods typically generate excited states in energy ordering, so the main change
needed in the formalism is a way to target the proper energy range without first having
to compute all valence states. Various ideas have been proposed and implemented
such as core–valence separation [14, 84], efficient energy-specific eigenvalue solvers
[54], and the complex polarization propagator (CPP) [22]. Those formalisms are