Nonlinear Least-Squares Fitting of Numerical Relativistic Atomic Wave Functions by a Linear Combination of Slater-Type Functions for Atoms Z = 1 - 54. Zhengwei Su & Philip Coppens, Chemistry Department, State University of New York at Buffalo, Buffalo, NY 14260-3000

New relativistic atomic ground-state wave functions calculated by using the Dirac-Fock program package GRASP92 [1,2] for atoms H through Xe (Z = 1 - 54) have been fitted by a linear combination of Slater-type functions with a nonlinear least-squares procedure. [2] The initial parameters of the fitting functions were taken fromthe non-relativistic Roothaan-Hartree-Fock ground-state atomic wavefunctions[3] and the converged analytical pseudo wave functions are normalized. These analytical expressions enable one to express the orbital scattering factors in closed form. The availability of these fitted wave functions is crucial for the accurate charge density refinement and analysis of structures containing heavy atoms such as transition metals. We illustrate the use of these wave functions by presenting the results of the refinement, the evaluation of electrostatic properties, and the topological analysis of the charge density of FeS₂. Comparisons will be made of the X-ray scattering and electron scattering factors calculated directly from the numerical relativistic wave functions and those from the fitted wave functions.

[1] Parpia, F. A., Froese Fischer, C. & Grant, I. P. (1996). Comput.Phys. Comm.. 94, 249-271.

[2] Su, Z. & Coppens, P.(1997). Submitted to Acta Cryst. A. [3] Zhu, C., Byrd, R. H., Lu, P. & Nocedal, J. (1994). L-BFGS_B -Fortran Subroutines for Large-Scale Bound Constrained Optimization. Department of Electrical Engineering and Computer Science,,Northwestern University, IL, USA.

[4] Bunge, C. F., Barrientos, J. A. and Bunge, A. V. (1993).At. Data Nucl. Data Tables 53, 113-162.