P. A. Christiansen

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.

Ab initio relativistic effective potentials with spin‐orbit operators. I. Li through Ar

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 atoms Li through Ar. These are tabulated in analytic form. Small optimized Gaussian basis sets with expansion coefficients for the lowest energy state for each atom are given and the reliability of the potentials relative to all electric calculations is discussed. Finally a procedure for computing molecular moments and Breit corrections is suggested.

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.

Simple one-electron quantum capping potentials for use in hybrid QM/MM studies of biological molecules

Calculations demonstrate that with a minor modification conventional ab initio effective potentials can be employed in place of link atoms to truncate quantum regions in hybrid quantum mechanics/molecular mechanics calculations. Simple quantum capping potentials are formed by replacing excess valence electrons in conventional effective potentials by spherical shielding and Pauli terms chosen to duplicate all-electron molecular structures and charge distributions. Tests involving truncated histidine show errors in charge and protonation energy to be reduced as compared to the link atom approach. Because of the use of conventional effective potential expansions, this approach can be implemented with minimal or no program modifications. Indeed, in its simplest form it requires the addition of only a single Gaussian and adjustable parameter to a conventional effective potential expansion. The parametrization requires little effective potential expertise or effort.

Relativistic effective potentials in quantum Monte Carlo calculations

The frozen‐core approximation was introduced into quantum Monte Carlo calculations by means of relativistic effective potentials. The conventional semilocal effective potentials were converted to local form using the same trial wave function used for importance sampling. Test calculations on Li, K, and their negative ions were readily carried out on a MicroVAX computer. The errors in the computed electron affinities (due to the effective potential and local potential approximations) were well under 0.1 eV.

Accurate relativistic effective potentials for the sixth-row main group elements

Errors in predicted bond lengths in effective potential calculations involving heavy main-group elements are shown to be the result of the poor representation of the f-shell space. Test calculations for PbO and the hydrides of thallium, lead, and bismuth demonstrate that with the inclusion of the 5d, 6s, and 6p subshells in the valence space and the proper partitioning of the f-shell valence spinors to form pseudospinors, accurate bond lengths are attainable. The previous reasonable bond lengths from 6s6p potentials appear to be the result of fortuitous error cancellations. New relativistic effective potentials in standard form are provided for Tl, Pb, Bi, At, and Rn in electronic format at www.clarkson.edu/∼pac/reps.html.

Separability of spin–orbit and correlation energies for the sixth-row main group hydride ground states

The spin–orbit energy contributions to the ground state potential energy curves for the main group hydrides, TIH through AtH are estimated by differencing multireference, single promotion, configuration interaction (MRS-CI) energies with and without the spin–orbit operator. The spin–orbit contributions are then summed into the energies determined at the λ−s MRSD-CI level (both single and double promotions). The agreement between the resultant curves and those obtained using intermediate coupling MRSD-CI is within 1.2 kcal/mol over a range of internuclear separations. This suggests that, contrary to previous arguments, spin–orbit coupling and correlation energies are very nearly separable for the main group hydride ground states. Furthermore, the computational effort expended by this separate evaluation is up to 12 times less than that for a comparable intermediate coupling CI. The analysis of some properties of these hydrides indicates that bond length shifts due to spin–orbit coupling are small (0.03 A) ...

Relativistic effective potential Cl calculations including spin—orbit coupling for the ground state of Bi2

Abstract The dissociation curve and spectroscopic properties for the O g + ground state of Bi 2 have been computed from configuration interaction calculations including relativistic effects. The D e and ω e values are in good agreement with experiment. The spin—orbit coupling mixes in substantial 3 ?? g character (about 25%) which results in a lower bond order, a slightly higher vibrational frequency and a slightly shorter bond length than one would get from separate 1 Σ g + or 3 π g calculations.

Effective potentials and multiconfiguration wave functions in quantum Monte Carlo calculations

Using relativistic effective potentials to eliminate the electron density in the core region we have computed quantum Monte Carlo (QMC) atomic energies for Be which accurately reproduce the experimental values in the range from the ground state to the first ionization energy. These calculations required only a few hours on a MicroVAX computer to obtain statistical errors smaller than a millihartree. For the ground state we found that it was absolutely essential to employ a multiconfiguration trial wave function to define the local potential. In contrast with an all‐electron QMC study, we find that the multiconfiguration trial wave function greatly reduces the statistical error for a given amount of sampling. Our work indicates that multiconfiguration wave functions should be used routinely in the context of effective potential QMC.

LOW-LYING

Abstract Test calculations for BiH 0+ ground and excited states using a CI configuration selection procedure, including the effective spin-orbit operator in the selection process (intermediate coupling CI), are compared with previous work in which the spin-orbit operator was included only in a final CI over λ−s selected configurations. While the lowest states are well described by the latter procedure, our results show an error in previous work in an upper state due to the failure to detect a charge transfer avoided crossing in their final intermediate coupling CI.