Relativistic Atomic Wave Functions Research Articles

Relativistic coupled-cluster calculations of transition properties in highly charged inert-gas ions

We have carried out an extensive investigation of various spectroscopic properties of highly charged inert-gas ions using a relativistic coupled-cluster method through a one-electron detachment procedure. In particular, we have calculated the atomic states $2{s}^{2}2{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$, $2{s}^{2}2{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}$, and $2s2{p}^{6}\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}$ in F-like inert-gas ions; $3{s}^{2}3{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$, $3{s}^{2}3{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}$, and $3s3{p}^{6}\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}$ states in Cl-like Kr, Xe, and Rn; and $4{s}^{2}4{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{3/2}$, $4{s}^{2}4{p}^{5}\phantom{\rule{4pt}{0ex}}^{2}P_{1/2}$, and $4s4{p}^{6}\phantom{\rule{4pt}{0ex}}^{2}S_{1/2}$ states in Br-like Xe and Rn. Starting from a single-reference Dirac-Hartree-Fock wave function, we construct our exact atomic states by including the dynamic correlation effects in an all-order perturbative fashion. Employing this method, we estimate the ionization potential energies of three low-lying orbitals present in their respective closed-shell configurations. Since the considered highly charged inert-gas ions exhibit huge relativistic effects, we have taken into account the corrections due to Breit interaction as well as from the dominant quantum electrodynamic correction such as vacuum polarization and self-energy effects in these systems. Using our calculated relativistic atomic wave functions and energies, we accurately determine various transition properties such as wavelengths, line strengths, oscillator strengths, transition probabilities, and lifetimes of the excited states.

A case study in scalability: An ADI method for the two-dimensional time-dependent Dirac equation

The dynamics of relativistic atomic wave functions evolving under the influence of intense laser pulses is used as an example of a general class of applications employing the alternating direction implicit method. The method requires the solution of many tridiagonal systems of linear equations. A range of parallel algorithms for this setting are analyzed with respect to their scalability on large parallel machines.

Systematic generation of relativistic Gaussian basis sets

A method for the Gaussian basis set generation for molecular relativistic Dirac-Fock calculations is proposed. The basis set exponents are obtained in the process of stochastic optimization (a hybrid of simplex and simulated annealing optimization techniques has been employed) of a functional defined as the sum of squares of differences between the numerical relativistic atomic wave functions and the wave functions obtained using the Gaussian function expansion. After this pre-optimization step the exponents are refined by ordinary gradient energy-functional based procedure. The present method seems to be very effective and robust. As an example the optimized basis sets of atoms from H (Z=1) to Ar (Z=18) are presented. Results of the Dirac-Fock calculations for all atoms under study are presented and compared with the numerical Dirac-Fock results and results obtained using the Gaussian basis sets according to Okada et al.: J. Chem. Phys.93 (1990) 5013.

Nonlinear Least-Squares Fitting of Numerical Relativistic Atomic Wave Functions by a Linear Combination of Slater-Type Functions for Atoms withZ= 1–36

New relativistic atomic ground-state wave functions calculated by using the Dirac–Fock program package GRASP92 [Parpia et al. (1996). Comput. Phys. Commun. 94, 249–271; Su & Coppens (1997). Acta Cryst. A53, 749–762, (1998). Acta Cryst. A54, 357] for atoms H through Kr (Z = 1–36) have been fitted by a linear combination of Slater-type functions using a nonlinear least-squares procedure. These analytical expressions allow derivation of closed-form expressions for the X-ray scattering factors of the core and valence electrons and for the atomic densities and electrostatic properties of the pseudoatoms, the latter being required for the evaluation of physical properties from accurate X-ray diffraction data. All results are accessible via http://wings.buffalo.edu/~chem9982.

Calculation ofL 3 subshell alignment within a coupled-state formalism

Theoretical results for the impact parameter dependence of theA20 alignment parameter are compared with experimental data. The calculations have been performed within a coupled channel formalism, using relativistic atomic wave functions as basis states.

Induced magnetic form factor of NpO 2

A polarized neutron diffraction experiment has been performed at ILL on a single crystal of NpO 2 weighting only 5 mg. A moment of 0.07 μ B at 4.2 K was induced by an applied field of 4.6 T, in good agreement with recent magnetic susceptibility measurements. Corrections were made for the strong extinction. A new value of b Np has been determined ( b Np = 1.00 (3) × 10 −12 cm) and, in agreement with published data, reanalysed in a consistent fashion regarding stoichiometry. The form factor obtained is satisfactory fitted with the theoretical one for Np 4+ ions calculated from relativistic atomic wave functions.

Calculation of the unoccupied4flevel in europium metal

Hartree-Fock-Wigner-Seitz band calculations, employing crystal potentials constructed from relativistic atomic wave functions via the renormalized-atom method, are used to estimate ${\ensuremath{\Delta}}_{+}({f}^{7}\ensuremath{\rightarrow}{f}^{8})$, the unoccupied $4f$-level position relative to the Fermi level in Eu metal. It is found that ${\ensuremath{\Delta}}_{+}\ensuremath{\simeq}8.6$ eV, which, in conjunction with other calculations, leads to a value of 10.5 eV for the $4f$ Coulomb interaction energy $U$. Both results are consonant with recent measurements. Sensitivity of the ${\ensuremath{\Delta}}_{+}$ estimate to the choice of input atomic configurations is also examined.

Relativistic Calculations of Electron Binding Energies by a Modified Hartree-Fock-Slater Method

Relativistic atomic wave functions and electron binding energies have been calculated by a modified Hartree-Fock-Slater method. The local exchange approximation, originally introduced by Slater, is modified in such a way that the total energy of the system is minimized. Approximate expressions for the optimum exchange potential are suggested for all atoms and ions. The total atomic energies and electron binding energies obtained by this method agree extremely well with the corresponding Hartree-Fock results in the cases where such data are available. Various corrections to the theoretical binding energies are discussed, in particular the effect of rearrangement during the ionization process. It is found that this effect is of importance for inner shells in all elements and is responsible for the main discrepancy between experimental and previous theoretical results for light and medium-heavy elements. For heavy elements other effects are of importance, and various possible sources of the residual discrepancy between theory and experiments are discussed.