Bridging and Nonbridging Oxygen in Tellurites
J. Phys. Chem. A, Vol. 109, No. 33, 2005 7637
2.1.2. NMR Spectroscopy. Spectra at 9.4 T (54.5 MHz 17
O
space of about 0.05 Å-1). For Na2Si2O5 this approach amounted
to a 4 × 2 × 4 Monkhorst-Pack grid, and for Na2Te4O9, a 3 ×
2 × 3 Monkhorst-Pack grid.25 The other samples have more
complex primitive unit cells and so have more complex
descriptions. All grids used were offset from the origin by 0.5
units in reciprocal space. Such optimal grids are computed by
the ABINIT code. The energies were computed using the
experimentally determined crystal structures.
XPS results were modeled using a thermodynamic cycle
approach.26,27 In this approach, it is noted first that extraction
of a core electron results in a solid with a core-ionized atom at
a specific site. The energy required to extract the electron is
the quantity observed in the XPS measurement. On the other
hand, the cohesive energy of the resulting defective solid relative
to free atoms can be computed by the planewave pseudopotential
method. This is done by representing the defective atom with a
pseudopotential constructed from an atom with a core hole. In
a second calculation, the defect is placed at a chemically distinct
site. The free atom reference state is the same in both cases.
Furthermore, in both cases the original, defect-free solid as
probed by XPS is the same. Therefore, one has
resonance frequency were acquired on a Bruker DSX spec-
trometer, under magic angle spinning conditions (12.0 kHz). A
Hahn echo sequence was used, with 4 and 8 µs times for the
90 and 180° pulses, respectively. A 500 s recycle delay was
used, and each spectrum consists of 2048 scans.
17O NMR spectra at 16.4 T (17O Larmor frequency of 94.9
MHz) were acquired on a Bruker Avance NMR spectrometer,
using 2.5 mm rotors and magic angle spinning at 30.0 kHz.
We employed a 2-dimensional multiple rotor-assisted population
transfer (RAPT) pulse sequence with Hahn echo detection.13
The RAPT transfer was repeated 21 times followed by acquisi-
tion of the free induction decay. 64 blocks of these spectra were
acquired in rapid succession and saved as a 2-dimensional data
set. A total of 724 scans (10% and 30% Na2O) or 1272 scans
(20% Na2O), respectively, were accumulated with a repetition
delay of 350 s. The spectra shown below are center slices after
Fourier transformation in both dimensions.
2.2. Computational Methods. 2.2.1. Molecular Modeling.
Modeling of molecular TeF4 and SiF4 was carried out with the
Amsterdam density functional code (ADF).14-16 Because the
object of this part of the study was only to develop a qualitative
Walsh diagram relating molecular shape to orbital energies, a
small basis set, double-ú STO, was used, together with frozen
core orbitals. Generalized gradient corrections to the local
density approximation as proposed by Becke,17 for exchange,
and Perdew,18 for correlation, were employed.
EB + EC ) E′ + E′
(1)
B
C
where EB is the binding energy of the core electron at the first
site and EC the cohesive energy of the resulting defective solid,
and the primed quantities refer to the defect appearing at the
second site. The shift between the binding energies can then be
computed as
2.2.2. Modeling Solids, XPS Data, and NMR Spectra.
Results relating to simulation of the XPS data were obtained
through use of the ABINIT code, which is based on pseudo-
potentials and planewaves.19 This is a density functional theory
approach to finding the energies of periodic solids, in which
the valence electron wave functions are expanded in terms of
planewaves, and the effect of the core electrons are ap-
proximated through the use of pseudopotentials. Pseudopoten-
tials were generated with the FHI98PP code.20 For the cases
discussed below, the pseudopotentials used were of Troullier-
Martins type,21 in separable form. For all atomic species studied
(Te, O, Na, Si), we used a maximum angular momentum value
of 2 for generation of the pseudopotentials, and also l ) 2 for
the local potential. For all elements, only the outer s and p
electrons were treated as valence electrons; in addition, for Na,
nonlinear core corrections22 were used to account for the core-
valence overlap from the relatively diffuse 2p orbitals.
EB - E′ ) -(EC - E′ )
(2)
B
C
Thus, the chemical shifts of an XPS spectrum can be computed,
despite the fact that the absolute values of the binding energies
cannot.
Replacing normal oxygen by a core hole oxygen lowers the
symmetry of the crystal, and this is taken into account in
constructing the k-space grid by ABINIT. Moreover, the
interactions between defects (in neighboring unit cells) should
be considered. We found however that for the relatively large
unit cells studied here, and at the 0.5 eV resolution necessary
for distinguishing different XPS shifts, replacing the unit cell
by a larger supercell made no significant difference in the energy
shifts.
The NMR parameters were computed using the NMR
module28,29 of the CASTEP code.30 This code also uses a density
functional theory approach within the planewave/pseudopotential
formalism. Additionally it includes code to calculate the
magnetic field response and the electric field gradient tensors.
This method has been validated recently on a variety of oxide
and glassy materials.31 The calculations were performed using
Troullier-Martins21 pseudopotentials. Pseudopotentials for Na
and O were generated using parameters given in ref 31 and for
Te using parameters given in ref 32. All calculations used the
experimental crystal structures. The PBE23 exchange-correlation
functional was used and the wave functions expanded in
planewaves with a maximum energy of 50 Ha.
For both the pseudopotentials and the calculations on the
periodic solids, the generalized gradient approximation for the
exchange and correlation terms due to Perdew, Burke, and
Enzerhof was used.23 For oxygen, an additional pseudopotential
with valence configuration 1s2s22p5 was generated, for use in
simulating oxygen 1s XPS data. All pseudopotentials constructed
were checked for existence of “ghost” states24 through the tests
available in the FHI98PP package and examination of the
logarithmic derivatives. Transferability tests were performed by
checking that the eigenvalues of the pseudoatoms and the all-
electron atoms agreed for a variety of test configurations, in
which partial charges were transferred from lower lying to higher
lying valence states or ionized completely.
The output of an ab initio NMR calculation is the absolute
chemical shielding tensor, σjiso(r) defined as the ratio between
a uniform external magnetic field, B, and the induced magnetic
field Bin(r)
As discussed below, the ab initio computations used here are
of the total energy of the model crystals, with defects at different
locations. In all cases, a planewave cutoff energy of 30 Ha (816
eV) was used. The necessary integration over reciprocal space
was performed by using an optimum grid, in the sense of fewest
k-points, for which the shortest vector in real space not included
was about 18.5 Å (this corresponded to a spacing in reciprocal
Bin(r) ) -σjiso(r)B
(3)
The isotropic shielding σiso(r), is one-third of the trace of