Walter C. Ermler

Ab initio relativistic effective potentials with spin–orbit operators. IV. Cs through Rn

A refined version of the ‘‘shape consistent’’ effective potential procedure of Christiansen, Lee, and Pitzer was used to compute averaged relativistic effective potentials (AREP) and spin–orbit operators for the elements Rb through Xe. Particular attention was given to the partitioning of the core and valence space and, where appropriate, more than one set of potentials is provided. These are tabulated in analytic form. Gaussian basis sets with contraction coefficients for the lowest energy state of each atom are given. The reliability of the transition metal AREPs was examined by comparing computed atomic excitation energies with accurate all‐electron relativistic values. The spin–orbit operators were tested in calculations on selected atoms.

Spin-Orbit Coupling and Other Relativistic Effects in Atoms and Molecules

Publisher Summary This chapter focuses on the recommended method for the inclusion of spin-orbit coupling and other relativistic effects for molecules containing heavy elements, considering computational complexity and accuracy factors that is one based on ab initio REPS. The calculation of accurate wave functions for systems containing heavy elements requires addressing the difficulties of the treatment of large numbers of electrons and the subtleties of electron correlation. This is not intended as a general review of relativity in chemistry or quantum mechanics, nor even of effective potential procedures, but is rather a critical discussion, including a limited number of applications, of the background, approximations, and implications of techniques developed by the present authors and collaborators and colleagues. The underlying assumption behind all methods for defining effective core potentials (EP) is the frozen core approximation. That is, the intrinsic reliability of core-valence separability. However, substantial savings are not realized by this approximation alone because of the radical oscillations of the valence orbitals in the region near the nuclei. An accurate procedure for performing calculations that incorporate spinorbit and other relativistic effects, and that represents intermediate coupling states for molecules containing heavy atoms, is based on A-S coupling in conjunction with the use of the ab initio REP-based spin-orbit operator and extended configuration interaction.

AB initio effective core potentials including relativistic effects. A procedure for the inclusion of spin-orbit coupling in molecular wavefunctions

Abstract The first ab initio procedure for the treatment of spin-orbit coupling in molecules based on the use of relativistic effective potentials derived from Dirac-Fock atomic wavefunctions is presented. A rigorous definition for the spin-orbit operator is given and its use in molecular calculations discussed.

Ab initio relativistic effective potentials with spin-orbit operators. VII. Am through element 118

Ab initio averaged relativistic effective core potentials (AREP) and spin-orbit (SO) operators are reported for the elements Am through element 118. Two sets have been calculated for certain elements to provide AREPs with varying core/valence space definition, thereby permitting the treatment of core/valence correlation interactions. The AREPs and SO operators are tabulated as expansions in Gaussian-type functions (GTF). GTF valence basis sets are derived for the lowest energy state of each atom. The reliability of the AREPs and SO operators is gauged by comparing calculated atomic orbital eigenvalues and SO splitting energies with all-electron relativistic values.

The quartic force field of H2O determined by many‐body methods. II. Effects of triple excitations

Ab initio coupled cluster and many‐body perturbation theory methods that include triple excitation effects are applied to the determination of the quartic force field of the water molecule using an extended Slater‐type basis set. Predictions of fundamental, overtone, and combination vibrational frequencies, rotational constants, and vibration–rotation coupling constants are reported for H2O and its isotopomers. The best predicted harmonic frequencies for the stretching modes of H2O are accurate to 3 cm−1, while the bending mode has an error of 28 cm−1. The mean absolute error for all frequencies reached by two quanta is 0.6%, while the anharmonic constants xiu2009j have a mean absolute error of less than 3%. The important role of triple excitation effects in the surface determination is discussed, and is compared with the effects of quadruple excitations.

Improved ab initio effective potentials for Ar, Kr, and Xe with applications to their homonuclear dimers

Effective core potentials for the Ar, Kr, and Xe atoms derived from numerical Hartree–Fock and Dirac–Hartree–Fock wave functions are applied in SCF and CI calculations of homonuclear diatomic potential energy curves. Detailed comparisons are made with the all‐electron calculations of Wadt for the ground and lowest positive states. Relativistic effects, excluding spin–orbit coupling, are seen to be relatively unimportant. Plots of the potential energy curves and computed spectroscopic constants show excellent agreement with the all‐electron results. On the other hand, comparisons with results obtained using effective potentials derived using varients of Phillips–Kleinman procedures show dramatic differences for Xe2 and Xe2+. From SCF calculations on Xe2 and Xe2+ it was found that the explicit inclusion of the spin–orbit operator in the SCF procedure (using ω–ω coupling) results in essentially the same potential curves obtained by adding the spin–orbit correction as a final semiempirical perturbation.

Polyatomic surface fitting, vibrational-rotational analysis, expectation value and intensity program

Abstract A computer program, SURVIBTM, has been developed for fitting multi-dimensional potential energy and property surfaces and calculating vibrational-rotational spectra of symmetric and asymmetric top polyatomic molecules. Given surfaces in the form of internal coordinates and energy or property points, the program performs seven main types of calculations. These include determining equilibrium and saddle point geometries, internal coordinate force fields, normal mode eigensolutions, normal coordinate force fields, spectroscopic constants, expectation values of properties, and transition dipole moments and intensities. Numerous options are available for each type of calculation. High-degree expansions for several forms of analytical expressions are implemented for the representations of force fields. The vibrational analysis and transition dipole results are presented in the form of spectroscopic constants, which include anharmonicity through quartic terms according to second-order perturbation theory. Point-group symmetry is utilized for reducing the length of internal coordinate expansions and for the analysis of selection rules in calculations of vibrational absorption intensities.

Ab initio calculations of potential energy curves of Hg2 and TlHg

Potential energy curves for electronic states of Hg2 and TlHg are presented and analyzed. They are derived using large scale configuration interaction procedures for the valence electrons, with the core electrons represented by ab initio relativistic effective potentials. The effect of spin‐orbit coupling are investigated for the low‐lying excimer states. It is determined that neither system possesses strongly bound electronic states for which transitions to the repulsive ground states are optically allowed.

Ab initio potential energy curves for the low-lying electronic states of the argon excimer

Configuration interaction calculations are reported for the potential energy curves of the argon excimer that arise due to excitation to the 4s and 4p Rydberg molecular orbitals. Effective core potentials were employed to replace the core electrons of the Ar atoms thereby reducing the computational procedure to one for a 16 valence system. Potential energy curves for three excimer states of each of the symmetries 1Σ+g, 1Σ+u, 3Σ+g, 3Σ+u, 1Πu, 3Πu, 1Πg, and 3Πg are reported and compared with those previously computed. Spectroscopic constants and curve maxima are reported where appropriate.

The effects of basis set quality and configuration mixing in ab initio calculations of the ionization potentials of the nitrogen molecule

Systematic configuration interaction calculations of the adiabatic ionization potentials of N2(1Σg+) to the Xu20092Σg+, Au20092Πu and Bu20092Σu+ states of N2+ give best results of 15.62, 16.41, and 18.93 eV compared with observed values of 15.576, 16.694, and 18.746 eV. The computed values are near the complete basis limit for a wave function containing single and double excitations from the Hartree–Fock configuration with the Langhoff–Davidson correction for unlinked cluster quadruple excitations. The critical dependence of ionization potentials on basis is demonstrated. Vertical ionization potentials at near the N2 ground state equilibrium internuclear separation are compared for a variety of basis sets using different computational methods. In particular, an important comparison is made with the EOM calculation of Herman, Yeager, Freed, and McKoy using a ’’double‐zeta+polarization’’ basis identical to one used in this study. We conclude that agreement to within ∼0.2 eV can be expected for ionization potentials bet...