The Dirac equation in the algebraic approximation. II. Extended basis set calculations for hydrogenic atoms

Benchmark values for molecular two-electron integrals arising from the Dirac equation

The two-center two-electron Coulomb and hybrid integrals arising in relativistic and nonrelativistic ab initio calculations on molecules are evaluated. Compact, arbitrarily accurate expressions are obtained. They are expressed through molecular auxiliary functions and evaluated with the numerical Global-adaptive method for arbitrary values of parameters in the noninteger Slater-type orbitals. Highly accurate benchmark values are presented for these integrals. The convergence properties of new molecular auxiliary functions are investigated. The comparison for two-center two-electron integrals is made with results obtained from single center expansions by translation of the wave function to a single center with integer principal quantum numbers and results obtained from the Cuba numerical integration algorithm, respectively. The procedures discussed in this work are capable of yielding highly accurate two-center two-electron integrals for all ranges of orbital parameters.

Ab initio fully relativistic molecular calculations: bonding in gold hydride

The electronic structure of gold hydride is investigated by ab initio fully relativistic extended basis set self-consistent field and configuration interaction calculations based on the Dirac equation. The gold 6p orbitals play only a very minor role in the bonding. The ten electrons occupying the 5d orbitals in the free gold atom are significantly affected by the formation of the molecule whose electronic structure exhibits substantial 5d‒6s hybridization. The extended-basis calculations show that relativity shortens the bond length by 0.45 a. u. (1 a. u. (atomic unit) of length = 1 bohr ≈ 0.529177 × 10 ‒10 m), substantially increases the fundamental vibration frequency and doubles the binding energy predicted by using a single determinant wavefunction. The bonding cannot be fully understood by using non-relativistic theory.