The effects of the use of full potentials in the calculation of x-ray absorption near-edge structure by the multiple-scattered-wave x-alpha method

In this work we describe the effects of the relaxation of the muffin-tin (MT) potential approximation (and the consequent use of full potentials (FPs)) in the ab initio calculation of X-ray-absorption near-edge structure (XANES) by the multiple-scattered-wave (MSW) Xα method. In doing so we demonstrate the validity and computational feasibility of the extended FP-MSW theory due to Natoli et al. (1986). We describe certain refinements to this theory and the development of a practicable computational approach for its realization. With the results of the newly-developed computer programs for certain model systems we show that the FP-MSW method leads to much higher accuracies in both bound-state energy eigenvalues and in photoionization cross-sections near the threshold. Our FP-MSW XANES calculations for the chromium hexa-carbonyl (Cr(CO)₆) system therefore demonstrate, because the results are still significantly different from the experimental spectrum (although closer than the MT case), that there remain other deficiencies in the physical model. Although beyond the scope of this work, we strongly suspect that the bulk of the remaining error would be accounted for by a better treatment of inelastic loss and (to a lesser extent) exchange-correlation. Our final conclusion is that the use of FPs is necessary (and now feasible) for the accurate calculation of XANES. We begin with an introduction to X-ray absorption spectroscopy (XAS) and then concentrate on XANES giving the motivation in terms of its structural significance and describing the necessity and difficulty of accurate ab initio calculations. The central part of XANES calculations is the solution of Schrödinger’s equation for the initial and final molecular states in the absorption process, and we summarize the approximations to the full many-body equation that make it tractable. This leads to a discussion of the MT approximation and an illustration of its deficiences. We review various remedies that have been proposed and concentrate on the FP-MSW theory of Natoli et al. (1986). We then give a detailed presentation of the theory and develop the necessary representation of the potential in terms of spherical harmonic expansions (SHXs). It is shown that, for symmetric molecules with up to two coordinating shells of atoms, five to ten partial waves per prototype atom serve to make the SHX representation from one to three orders of magnitude more accurate than the MT case. The development of the FP-SW bound-state eigenvalue program ENESHX is described and the program tested with the hydrogen molecular ion (H₂⁺). By comparison with the MT results we find that the error is reduced to less than 12% in the worst case (the ground state) and less than 0.2% for the highest levels. Calculations for the Cr(CO)₆ system do show changes of as much as -O.4 Ryd. for the valence levels (stemming mostly from the better treatment of the interstitial region). The successfully-tested ENESHX is then adapted to produce the FP-SW continuum photoionization cross-section program CNTSHX which is then tested with a Li²⁺ ion pseudo-cluster whose exact analytic cross-sections are known. Above about 1 Ryd. from threshold, the CNTSHX cross-sections are within 1% of the exact values, compared to 7% for the MT case. Below 1 Ryd. the CNTSHX error remains less than 5%. CNTSHX is then run for Cr(CO)₆ with the results described above