Relativistic effective core potentials (ECP) are derived for Au and Hg atoms, where the ECP incorporates the Coulomb and exchange contributions of the core orbitals, the core-orthogonality terms for the valence orthogonality terms for the valence orbitals, and the effect of the ’’mass–velocity’’ and ’’Darwin’’ relativistic effects on the valence orbitals. The results of atomic valence-electron (VE) calculations with the ECP’s compare favorably with relativistic Hartree–Fock and Dirac–Hartree–Fock calculations and with experiment, when the effects of spin–orbit coupling are included in the VE calculations. Nonrelativistic calculations, by contrast, lead to erroneous predictions and to differences in excitation energies of 1.5–3.5 eV. The large relativistic effects in the atoms carry over into the AuH, AuCl, and HgCl2 molecules, as they are important in determining correct bond lengths and bond energies and in influencing the charge distributions. Similarly large relativistic effects are encountered in ionization potentials calculated for HgCl2 from orbital energies and from SCF calculations. Spin–orbit coupling is introduced to compare with the experimental photoelectron spectrum. An extensive study of the lowest electronic states of HgH is presented, where the effects of spin–orbit coupling are critical in describing the potential energy curves of the excited 2Π1/2 and 22Σ+1/2 states.
A formalism is developed for obtaining ab initio effective core potentials from numerical Hartree–Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I. The effective core potentials enable one to eliminate the core electrons and the associated orthogonality constraints from electronic structure calculations on atoms and molecules. The effective core potentials are angular momentum dependent, basis set independent, and stable against variational collapse of their eigenfunctions to core functions. They are derived from neutral atom wavefunctions using a pseudo-orbital transformation which is motivated by considerations of the expected accuracy of their use and of basis set economy in molecular calculations. Then the accuracy is demonstrated by multiconfiguration Hartree–Fock calculations of potential energy curves for HF, HCl, HBr, HI, F2, Cl2, Br2, and I2 and one-electron properties for HF and HBr. The differences between valence-electron calculations employing the present effective core potentials and all-electron calculations are smaller than differences due to basis set choices, even though the basis sets are extended ones. Thus the effective core potentials are quite successful. In addition larger configuration mixing calculations are performed for HBr and Br2 (1637 and 3396 configurations, respectively) and again the effective core potentials are judged to perform well.
We have investigated the efficacy of ab initio effective potentials in replacing the core electrons of atoms for use in molecular calculations. The effective potentials are obtained from ab initio GI calculations on atoms and are unique and local. We find that the use of these effective potentials to replace the core orbitals of such molecules as LiH, Li2, BH, or LiH2, leads to wavefunctions in excellent agreement with all-electron ab initio results. The use of such effective potentials should allow ab initio quality wave-functions to be obtained for systems too large for the ab initio consideration of all the electrons.
Accurate ab initio potential energy curves for the classic Li-F ionic-covalent interaction by extrapolation to the complete basis set limit and modeling of the radial nonadiabatic couplingThe potential curves of the four lowest 1 ~ + states of LiF have been studied by ab initio configuration interaction methods, using a contracted Gaussian basis set of better than double-' quality, augmented with diffuse basis functions on the fluorine atom. The choice of orbitals and selection of configurations were carried out with the objective of obtaining a balanced treatment of the four states and of the different regions of the potential curves. "Generalized valence-bond" orbitals, obtained from ground-state MCSCF calculations, together with "improved virtual orbitals," were found suitable for the construction of the configuration functions. The latter were energy selected from all single and double excitations relative to a set of 12 "reference configurations," chosen to include all contributions found important for any of the four states at any internuclear distance. The expected avoided crossing between the lowest covalent and ionic structures is found at an internuclear distance of about 11 bohr, compared to the experimentally deduced value of 14 bohr, due to the considerable difficulty in obtaining a balanced description of the electron correlation of the separated species, particularly the F-ion. A set of diabatic potential curves was generated from the two lowest adiabatic curves by a novel procedure based on the Rittner model of the ionic state. A set of adjusted adiabatic potentials was obtained from the diabatic curves after shifting the ionic diabatic curve downward by 0.42 eV to correct for the error in the computed electron affinity of the fluorine atom, resulting in a shift of the avoided crossing to the correct internuclear distance of 14 bohr. The dipole moments of the four states were computed as a function of internuclear distance and were interpreted in terms of the electronic structure.culations on LiF, the Simplest of the alkali halide diatomics. Since there have been no rigorous calculations reported previously on these systems-except for ground states and often near the equilibrium geometry only4-6_ it has been the aim of this work to examine the full potential curves for a number of states, with emphasis on the nature of the avoided crossing.The ionic dissociation limit in LiF, Li+(lS) + F-(IS),
The procedure of deriving ab initio effective core potentials (ECP) to incorporate the Coulomb and exchange effects as well as orthogonality constraints from the inner core electrons is extended to include the dominant relativistic effects on the valence orbitals. An ab initio approach is then described which enables the valence electrons in heavy atoms to be treated in a standard nonrelativistic manner by including the effect of the relativistic core–valence interactions directly into the ECP. The starting point for this procedure is the Pauli Hartree–Fock relativistic treatment of Cowan and Griffin. The pseudo-orbital transformation and derivation of the l-dependent effective core potentials are analogous to the nonrelativistic case with certain modifications. Analytic forms for the pseudo-orbitals and ECP’s are derived for the U atom, and results of valence electron calculations are presented.
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