due to a dimerization along the chains. NaV
2
O
5
possesses an orthorhombic
crystal structure at room temperature and is centro-symmetric (Pmmn) with
only one distinct V ion in a mixed valence state (average valence V
+4.5
) [78].
The spins are carried by V-O-V molecular orbitals (rungs), the basic building
blocks of the electronic structure of this unconventional spin-Peierls material.
The electronic structure of insulating NaV
2
O
5
has been the subject of many
experimental and theoretical investigations [79, 80]. By comparing model
calculations of the electronic structure with experimental spectra from
conventional optical techniques the key parameters of the electronic structure
can be determined.
The molecular like V-O-V-rungs of NaV
2
O
5
that run along the chains build
up a ladder-like electronic system. Each of these rungs takes up one of the
electrons that the sodium atoms, separating the chains, donate. Formally this
leads to a V
4.5+
-valency and both the possibility of distinct V
4+
/V
5+
sites
(charge-ordering) and a delocalization of this electron (mixed valence) has
been discussed. X-ray diffraction studies [79] support the model of a mixed
valence structure. Density functional theory band structure calculations using
the local density approximation of this quarter-filled ladder system cannot
reproduce the insulating state but show that the lowest d-states are of xy-
character with considerable dispersion across the Fermi level. Moreover, the
bands belonging to the antibonding d
xy
-states are separated by about 1.2 eV
from the occupied d
xy
-orbital. LDA + U calculations show that the on-site
Coulomb interaction (correlation effect) actually splits the lowest d
xy
-bands
into a spin-up and spin-down component with a gap of less than 1 eV. The
remaining empty d-orbital states have energies of some 1.6 eV and more
above the occupied d
xy
-orbital. In a localized picture this can be described by
the crystal field splitting.
V 2p-RIXS of NaV
2
O
5
experiments show a rather strong energy loss peak
around 1.6 eV [80]. There exists a controversy regarding which orbital
symmetry the corresponding final states have and whether the energy loss
reflects the on-site correlation energy (Mott gap) or the crystal field splitting
10 Dq. Duda et al. [81] have shown that in O 1s-RIXS of NaV
2
O
5
there exists
an RIXS peak at 1.2 eV energy loss (see Figure 14.18), when excited into the
upper Hubbard band state (i.e., the hybridized O 2p-V 3d-state). This is a non-
local excitation that transfers a d-electron from the excited V site to the other
V site on the same rung (on-rung excitation) via an O 1s-excitation, i.e., an
excitation to the antibonding d
xy
-states. It is therefore likely that the spin-split
empty d
xy
-states are found at even lower excitation energies, i.e., less than
1 eV, in accord with theoretical predictions and optical measurements. Note
also that an excitation requiring the transfer of an electron from another rung
to the core-excited one (interrung hopping) entails a small overlap between
the involved wavefunctions and in turn a low excitation probability. It is
14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy 626