Real space multiple scattering calculations of the electronic density of states and x-ray spectra in solids typically scale as the cube of the system and basis set size, and hence are highly demanding computationally. For example, x-ray absorption near edge structure (XANES) calculations in solids typically require clusters of order NR atoms and s, p, and d states for convergence, with NR between about 10 2-10 3 ; for this case about 10 2 inversions of 9NR × 9NR matrices are needed, one for each energy point. We discuss here two ways to speed up these calculations: 1) message passing interface (MPI) parallel processing, and 2) fast, Lanczos multiple scattering algorithms. Together these algorithms can reduce computation times typically by two orders of magnitude. These are both implemented in a generalization of the ab initio self-consistent FEFF8 code, which thus makes XANES calculations in complex systems with of order 10 3 atoms practical. The Lanczos algorithm also yields a natural crossover between full and finite-order multiple scattering with increasing energy, thus differentiating the extended and near-edge regimes.

A method is proposed for the accurate determination of atomic wave functions and energies by the explicit introduction of interelectronic coordinates into a configuration-interaction wave function. This is accomplished by choosing the configurations in the wave function to be antisymmetrized projected products of one-electron functions with powers of interelectronic coordinates. A 107-configuration wave function for the ground state of the beryllium atom was constructed from a basis set consisting of s and p Slater-type orbitals and powers of interelectronic coordinates: r~& (g, =0, 1, 2). The energy obtained from this wave function (E = -14.666 54 a.u. ) is an upper bound to the "exact" nonrelativistic energy of this state and it is believed to be within 0.0002 a.u. of the "exact" value. The advantages that the present method offers for extending accurate Hylleraas-method calculations to atomic systems with N &3 are discussed.

Hylleraas-configuration

Expressions are derived for the integrals which arise in calculations of atomic wavefunctions of four or more electrons, utilizing the method of explicit introduction of interelectronic distances rij into a configuration interaction wavefunction (subject to the restriction of at most one rij per configuration). The approach followed in the derivations is similar to one followed by Öhrn and Nordling for three electron integrals; however, in extending the Öhrn and Nordling scheme to four electrons for a basis of s, p, and d Slater-type orbitals, numerical snags are encountered which have been obviated by an Euler transformation on certain of the auxiliary integrals.

Born-Oppenheimer approximation Hylleraas variational calculations with up to 7034 expansion terms are reported for the 1sigma(g)+ ground state of neutral hydrogen at various internuclear distances. The nonrelativistic energy is calculated to be -1.174 475 714 220(1) hartree at R = 1.4 bohr, which is four orders of magnitude better than the best previous Hylleraas calculation, that of Wolniewicz [J. Chem. Phys. 103, 1792 (1995)]. This result agrees well with the best previous variational energy, -1.174 475 714 216 hartree, of Cencek (personal communication), obtained using explicitly correlated Gaussians (ECGs) [Cencek and Rychlewski, J. Chem. Phys. 98, 1252 (1993); Cencek et al., ibid. 95, 2572 (1995); Rychlewski, Adv. Quantum Chem. 31, 173 (1998)]. The uncertainty in our result is also discussed. The nonrelativistic energy is calculated to be -1.174 475 931 399(1) hartree at the equilibrium R = 1.4011 bohr distance. This result also agrees well with the best previous variational energy, -1.174 475 931 389 hartree, of Cencek and Rychlewski [Rychlewski, Handbook of Molecular Physics and Quantum Chemistry, edited by S. Wilson (Wiley, New York, 2003), Vol. 2, pp. 199-218; Rychlewski, Explicitly Correlated Wave Functions in Chemistry and Physics Theory and Applications, edited by J. Rychlewski (Kluwer Academic, Dordrecht, 2003), pp. 91-147.], obtained using ECGs.