Multiconfigurational Approach to X-ray Spectroscopy …
207
The multiplet splittings are directly related to the structure of the molecular
orbitals. The t 2g -e g interactions, and thus the multiplet splittings, are largest if both
orbitals are localized on the metal, i.e., if they are ionic. The size of the splitting is
thus related to the extent of orbital delocalization in the molecule. In practice, the
short lifetime of the 1s hole gives rise to large lifetime broadenings which can make
it difficult to accurately determine the energy of all the states. This limitation can be
overcome with the use of RIXS.
4.5 Metal–Ligand Covalency from Multiplet Splittings
RIXS can achieve higher resolution than XAS because the lifetime broadening in
the energy transfer direction is determined by the lifetime of the final state after
emission. L-edge RIXS can under the right experimental conditions resolve different
mutiplet states in the valence region [80], but this requires better resolution than in
the study discussed above [53]. Instead, multiplet splittings will be illustrated using
1s2p RIXS where the final state has a 2p core hole, see Fig. 1 [45, 58]. The same
approach has already been used to study how the metal ligands modulate electron
transfer in cytochrome c, a key component in cell respiration [44].
1s2p RIXS spectra of ferro- and ferricyanide are shown in Fig. 15 [32, 58, 68]. All
spectra have two separate regions, stretching roughly diagonally across the plane.
The region at lower energy transfer corresponds to states in the L 3 edge of the
XAS spectrum, while the upper region corresponds to the L 2 edge. The calculated
RAS spectra do not include the intense transitions in the rising edge, but reproduce
the structure of the pre-edge. The incident energy resonances are the same as in K
pre-edge XAS. In ferrocyanide, there are two pre-edge resonances, 1s → e g and
1s → e g /π
∗ , with the latter being hidden under the rising edge in the experimental
spectrum [33]. Ferricyanide also has a low-energy 1s → t 2g resonance, and a broad
e g peak split by multiplet interactions as shown in Fig. 14a.
It is most instructive to look at the e g resonance in ferrocyanide. Along the incident
energy axis, it does not contain much information because it corresponds to a single
state. More information can be obtained from the energy transfer direction. The
2 p → 1s emission from the intermediate state lead to 2 p
5 t
6
2g e
1
g final states, nominally
the same as in L-edge XAS. An L-edge-like spectrum is obtained by taking a vertical
cut along constant incident energy (CIE) through the maximum of the e g resonance,
see Fig. 15. With only a single incident energy resonance, it could be expected that
the e g part of the CIE cut and the L-edge XAS should look similar. Instead, the width
of the e g resonance increases from the 0.8 eV in the L-edge spectrum to 1.5 eV in
the CIE spectrum, see Fig. 16a. As the experimental broadenings are similar in the
two experiments, the explanation is instead the differences in selection rules [58].
The 2 p
5 t
6
2g e
1
g configuration gives T 1u and T 2u states. The single-photon electric
dipole transitions in XAS only reach T 1u states from the
1 A 1g ground state, while
the two-photon RIXS process reaches both T 1u and T 2u final states, see Fig. 16b.
207
The multiplet splittings are directly related to the structure of the molecular
orbitals. The t 2g -e g interactions, and thus the multiplet splittings, are largest if both
orbitals are localized on the metal, i.e., if they are ionic. The size of the splitting is
thus related to the extent of orbital delocalization in the molecule. In practice, the
short lifetime of the 1s hole gives rise to large lifetime broadenings which can make
it difficult to accurately determine the energy of all the states. This limitation can be
overcome with the use of RIXS.
4.5 Metal–Ligand Covalency from Multiplet Splittings
RIXS can achieve higher resolution than XAS because the lifetime broadening in
the energy transfer direction is determined by the lifetime of the final state after
emission. L-edge RIXS can under the right experimental conditions resolve different
mutiplet states in the valence region [80], but this requires better resolution than in
the study discussed above [53]. Instead, multiplet splittings will be illustrated using
1s2p RIXS where the final state has a 2p core hole, see Fig. 1 [45, 58]. The same
approach has already been used to study how the metal ligands modulate electron
transfer in cytochrome c, a key component in cell respiration [44].
1s2p RIXS spectra of ferro- and ferricyanide are shown in Fig. 15 [32, 58, 68]. All
spectra have two separate regions, stretching roughly diagonally across the plane.
The region at lower energy transfer corresponds to states in the L 3 edge of the
XAS spectrum, while the upper region corresponds to the L 2 edge. The calculated
RAS spectra do not include the intense transitions in the rising edge, but reproduce
the structure of the pre-edge. The incident energy resonances are the same as in K
pre-edge XAS. In ferrocyanide, there are two pre-edge resonances, 1s → e g and
1s → e g /π
∗ , with the latter being hidden under the rising edge in the experimental
spectrum [33]. Ferricyanide also has a low-energy 1s → t 2g resonance, and a broad
e g peak split by multiplet interactions as shown in Fig. 14a.
It is most instructive to look at the e g resonance in ferrocyanide. Along the incident
energy axis, it does not contain much information because it corresponds to a single
state. More information can be obtained from the energy transfer direction. The
2 p → 1s emission from the intermediate state lead to 2 p
5 t
6
2g e
1
g final states, nominally
the same as in L-edge XAS. An L-edge-like spectrum is obtained by taking a vertical
cut along constant incident energy (CIE) through the maximum of the e g resonance,
see Fig. 15. With only a single incident energy resonance, it could be expected that
the e g part of the CIE cut and the L-edge XAS should look similar. Instead, the width
of the e g resonance increases from the 0.8 eV in the L-edge spectrum to 1.5 eV in
the CIE spectrum, see Fig. 16a. As the experimental broadenings are similar in the
two experiments, the explanation is instead the differences in selection rules [58].
The 2 p
5 t
6
2g e
1
g configuration gives T 1u and T 2u states. The single-photon electric
dipole transitions in XAS only reach T 1u states from the
1 A 1g ground state, while
the two-photon RIXS process reaches both T 1u and T 2u final states, see Fig. 16b.