determine local structure in those cases where the muffin-tin approximation used in most full multiple ... Keywords: XANES, 3D local structure, non muffin-tin.
New Approach for 3D Local Structure Refinement Using Non-Muffin-Tin XANES Analysis Grigory Smolentsev*, Alexander V. Soldatov* and Martin C. Feiters¶ *
¶
Faculty of Physics, Rostov State University, Rostov-on-Don, 344090, Russia Institute of Molecules and Materials, University of Nijmegen, Nijmegen, The Netherlands
Abstract. A new technique of 3D local structure refinement using full-potential X-ray absorption near edge structure (XANES) analysis is proposed and demonstrated in application to metalloorganic complexes of Ni. It can be applied to determine local structure in those cases where the muffin-tin approximation used in most full multiple scattering schemes fails. The method is based on the fitting of experimental XANES data using multidimensional interpolation of spectra as a function of structural parameters, recently proposed by us [1], and ab-initio full potential calculations of XANES using finite difference method [2]. The small number of required ab-initio calculations is the main advantage of the approach, which allows one to use computationally time-expensive non-muffin-tin finite-difference method. The possibility to extract information on bond angles in addition to bond-lengths accessible to standard EXAFS is demonstrated and it opens new perspectives of quantitative XANES analysis as a 3D local structure probe. Keywords: XANES, 3D local structure, non muffin-tin. PACS: 61.10.Ht
INTRODUCTION X-ray Absorption Near Edge Structure (XANES) is a well known technique, which can be used to probe bond lengths and angles. A few methods for the extraction of structural parameters from XANES were developed. In particular XANES fitting using full multiple scattering (FMS) calculations based on the muffin-tin (MT) approximation for the potential was recently applied using the MXAN [3] and FitIt [1] codes. Alternatively, simultaneous analysis of EXAFS and XANES taking into account a limited number of multiple scattering paths, sometimes gives angularsensitive data [4]. In this paper, we present the first example of local structure determination from quantitative XANES fitting on the basis of fullpotential approach, which can be applied in those cases where the MT approximation used in most FMS schemes fails As a system for the application of the method we have selected a complex of Ni with acetylacetonate (acacR, where R is a para-tertiarybutylbenzyl group attached to the acetylacetonate in the 3-position). Schematically it is shown in Fig. 2 Non-MT effects could be important for systems with large empty holes or interstitial regions [5] between atoms and sometimes in planar molecules [6]. Thus Ni(acacR)2 is
a system where one can expect non-MT effects to be important.
METHOD OF CALCULATION The proposed method of local structure determination is based on a combination of quantitative XANES fitting using a multidimensional interpolation approach [1] and full-potential calculations of XANES on the basis of the finite difference method [2]. The main idea is to minimize the number of required time-consuming FDM calculations using the following expansion of the spectrum as a function of structural parameters μi ( E , p1 + δp1 , p2 + δp2 ,..., pn + δpn ) = μ ( E , p1 , p2 ,..., pn ) + +
∑ A (E)δp + ∑ B n
n
n
Here
mn
( E )δpmδpn + ...
m, n
μ i (E )
coefficient,
is the interpolated X-ray absorption whereas
μ (E )
coefficient calculated via FDM,
is
the
absorption
( p1 , p 2 ,... p n )
is a
δp n
is a
starting set of structural parameters, and
deviation of parameter p n from the starting value. The energy dependent coefficients An ( E ), Bmn ( E )... are deduced from the results of
FDM calculations. A general description of the multidimensional interpolation and finite difference method can be found in Ref. 1, 7 and Ref. 2, respectively.
the best-fit structural parameters are the following: NiO distance 1.83±0.02 Å, O-C1 distance 1.28±0.02 Å, C1-C2 distance 1.39±0.035 Å, and O-Ni-O angle 93±1°.
RESULTS AND DISCUSSION As one can see from Fig. 1, the comparison of MT FMS and non-MT FDM calculations clearly demonstrates the importance of non-MT effects in the XANES of Ni(acacR)2. This is due to the presence of large interstitial regions inside the rings (marked as A in Fig. 2) in which the molecule potential cannot be considered as a constant. Absorption (norm. un.)
2.0
B 1.8
A
1.6 1.4
C D
1.2 1.0 0.8
MS FDM
P
FIGURE 2. Comparison of the experimental Ni K edge XANES (solid line), interpolated (dashed line) and FDM calculated (dotted line) spectra for the best fit of parameters. Inset: Structural model of Ni(acacR)2.
0.6 0.4 0.2 0.0
8320
8340
8360
8380
8400
Energy (eV) FIGURE 1. Comparison of theoretical MT FMS (top) and non-MT FDM calculations (bottom) spectra for the same set of structural parameters.
During local structure refinement structural parameters shown in the inset of Fig. 2 were varied within the following limits: Ni-O distance 1.76-1.92 Å, O-C1 distance 1.22-1.38 Å, C1-C2 distance 1.301.46 Å, and O-Ni-O angle 80°-100°. The C1-C3 distance and the O-C1-C3 and O-C1-C2 angles were fixed to 1.49 Å, 120°, and 120°, respectively. Using the strategy of interpolation polynomial construction described elsewhere [1] we found that only 21 spectra need to be calculated ab-initio to reproduce results of FDM calculations for any considered geometry. The final step of the XANES fitting is the minimization of the discrepancy between experimental and interpolated spectra. Interpolated and FDM calculated spectra for the best-fit geometry as well as experimental spectrum are shown in Fig. 2 and the agreement between them is quite good. A slight overestimation of the intensity of the pre-edge peak is systematic and cannot be reduced by variation of the local structure. The discrepancy between interpolated and FDM calculated spectra, due to uncertainties typical for a multidimensional interpolation approximation, is very small and it does not affect the results of the geometry determination. The values of
In conclusion, for the first time we have demonstrated a quantitative determination of 3D local structural parameters on the basis of full-potential XANES calculations. The field of future applications of the method is not limited to organometallic compounds since non-MT effects can be important for different materials with large interstitial regions between the atoms. Consideration of non-MT effects in these systems is crucial for correct determination of structural properties from XANES.
ACKNOWLEDGMENTS Grant RNP 2.1.1.1038 is kindly acknowledged.
REFERENCES 1. G. Smolentsev and A. V. Soldatov, J. Synchrotron Rad. 13, 19 (2006). 2. Y. Joly, Phys. Rev. B 63, 125120 (2001). 3. M. Benfatto, S. Della Longa, and C. R. Natoli, J. Synchrotron Rad. 10, 51 (2003). 4. A. Levina, R. S. Armstrong, and P. A. Lay, Coord. Chem. Rev. 249, 141 (2005). 5. M. Ogura and H. Akai, J. Phys.: Condens. Matter 17, 5741 (2005); T. Huhne and H. Ebert, Solid State Commun. 209, 577 (1999). 6. A. L. Ankudinov and J. J. Rehr, Physica Scripta T115, 24 (2005); D. L. Foulis, Phys. Rev. A 70, 022706 (2004). 7. G. Smolentsev and A. V. Soldatov, J. Phys: Cond. Matter 18, 759 (2006).
