Multiconfigurational Approach to X-ray Spectroscopy …
209
bonds and more localized 3d orbitals, which is seen in a significantly larger width
of the e g resonance of ferrous tacn [58]. Notice that the individual states are actually
not resolved in the experiment. It is instead the differences in selection rules that
makes it possible to identify the different energy regions for T 1u and T 2u states.
5 Extensions to Metal Dimers and Complex Systems
All systems previously discussed in this chapter have been relatively small and
included no more than one transition metal atom. Many catalytic systems include two
or more metal atoms, but multiconfigurational calculations of X-ray processes for
such systems are challenging. Including two instead of one metal basically doubles
the number of core and valence orbitals and leads to large active spaces. This in turn
leads to a very large number of states within the energy range covered by the X-ray
spectra [74]. Here two different approaches to RAS modeling of metal dimers are
presented. First, a heme dimer with intermolecular coupling between metal atoms
is discussed, followed by a μ-oxo bridged metal dimer with covalent coupling [74,
81].
5.1 Intermolecular Coupling
Heme systems play important roles in many biological systems including oxygen
transport and catalysis. In many spectral probes, the intense transitions in the porphyrin obscure information about the electronic structure of the iron. This limitation
can be overcome with a suitable X-ray probe, and iron L-edge XAS has been successfully used to probe the electronic structure of the Fe–O 2 bond [95]. Another
interesting characteristic is that hemes are prone to complexation in solvent. This
gives rise to π -π interactions between the porphyrins, as well as resonant coupling of
close-lying electronic states of the monomers. These interactions should be detectable
in the X-ray signature [74].
RAS simulations have been made of hemin dimers that form in water solvent,
see Fig. 17. To avoid treating the full supermolecule, the relevant valence and corehole states of each monomer are calculated first. The configurations with energies
close to X-ray resonances are then extracted. XAS and RIXS correspond to one
and two-particle excitations correspondingly, and the full set of states necessary to
model these processes can at a first approximation be modeled using a configuration
interaction model including singles and doubles (CISD) [74]. After reduction of the
size of the interaction matrix by ignoring some contributions, diagonalization gives
the states of the full dimer from which X-ray intensities can be calculated.
The simulated spectra of three different dimer orientations are shown as CIE
cuts through the L-edge RIXS planes, see Fig. 17. Some resonances show distinct
changes, including the elastic peak at 0 eV energy transfer. The magnitude of these
209
bonds and more localized 3d orbitals, which is seen in a significantly larger width
of the e g resonance of ferrous tacn [58]. Notice that the individual states are actually
not resolved in the experiment. It is instead the differences in selection rules that
makes it possible to identify the different energy regions for T 1u and T 2u states.
5 Extensions to Metal Dimers and Complex Systems
All systems previously discussed in this chapter have been relatively small and
included no more than one transition metal atom. Many catalytic systems include two
or more metal atoms, but multiconfigurational calculations of X-ray processes for
such systems are challenging. Including two instead of one metal basically doubles
the number of core and valence orbitals and leads to large active spaces. This in turn
leads to a very large number of states within the energy range covered by the X-ray
spectra [74]. Here two different approaches to RAS modeling of metal dimers are
presented. First, a heme dimer with intermolecular coupling between metal atoms
is discussed, followed by a μ-oxo bridged metal dimer with covalent coupling [74,
81].
5.1 Intermolecular Coupling
Heme systems play important roles in many biological systems including oxygen
transport and catalysis. In many spectral probes, the intense transitions in the porphyrin obscure information about the electronic structure of the iron. This limitation
can be overcome with a suitable X-ray probe, and iron L-edge XAS has been successfully used to probe the electronic structure of the Fe–O 2 bond [95]. Another
interesting characteristic is that hemes are prone to complexation in solvent. This
gives rise to π -π interactions between the porphyrins, as well as resonant coupling of
close-lying electronic states of the monomers. These interactions should be detectable
in the X-ray signature [74].
RAS simulations have been made of hemin dimers that form in water solvent,
see Fig. 17. To avoid treating the full supermolecule, the relevant valence and corehole states of each monomer are calculated first. The configurations with energies
close to X-ray resonances are then extracted. XAS and RIXS correspond to one
and two-particle excitations correspondingly, and the full set of states necessary to
model these processes can at a first approximation be modeled using a configuration
interaction model including singles and doubles (CISD) [74]. After reduction of the
size of the interaction matrix by ignoring some contributions, diagonalization gives
the states of the full dimer from which X-ray intensities can be calculated.
The simulated spectra of three different dimer orientations are shown as CIE
cuts through the L-edge RIXS planes, see Fig. 17. Some resonances show distinct
changes, including the elastic peak at 0 eV energy transfer. The magnitude of these