A b i n i t i o effective core potentials including relativistic effects. V. SCF calculations with ω-ω coupling including results for Au2 +, TlH, PbS, and PbSe A b i n i t i o effective core potentials for molecular calculations. II. Allelectron comparisons and modifications of the procedure J. Chem. Phys. 68, 3059 (1978); 10.1063/1.436172 Relativistic effects in a b i n i t i o effective core potentials for molecular calculations. Applications to the uranium atom A b i n i t i o effective core potentials: Reduction of allelectron molecular structure calculations to calculations involving only valence electronsWe have investigated the sources of error in bond lengths and dissociation energies computed from ab initio effective potentials derived from Phillips-Kleinman type pseudo-orbitals. We propose an alternate pseudo-orbital, effective potential treatment with the primary objective of agreement with all-electron molecular calculations. This new treatment forces the pseudo-orbitals to match precisely the Hartree-Fock orbitals in the valence region and thereby eliminates the major cause of error in the earlier calculations. Effective core potentials derived from these revised pseudo-orbitals were used to compute potential energy curves for the ground states of F 2 , Cl 2 , and LiCI and the results are compared with previous all-electron and effective potential calculations. Our effective potentials yield dissociation energies and bond lengths which are in excellent agreement with the all-electron values. Furthermore, in contrast to other procedures, our revised effective potentials result in an excellent description of the inner repulsive walls of the dissociation curves.

The coupled-cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions. The detailed equations for triple excitation amplitudes are presented, and a simplified version implemented that retains the dominant terms. The model presented, CCSDT-1, provides the energy correct through fourth order and the wave function through second order. The CCSDT-1 model is illustrated by comparing with full CI results for HF, BH, and H2O, the latter at several geometries.

Articles you may be interested inA b i n i t i o effective core potentials including relativistic effects. V. SCF calculations with ω-ω coupling including results for Au2 +, TlH, PbS, and PbSe Relativistic effects in a b i n i t i o effective core potential studies of heavy metal compounds. Application to HgCl2, AuCl, and PtH A b i n i t i o effective core potentials including relativistic effects. IV. Potential energy curves for the ground and several excited states of Au2 A b i n i t i o effective core potentials including relativistic effects. II. Potential energy curves for Xe2, Xe+ 2, and Xe*2 An effective core potential system has been developed for heavy atoms in which relativistic effects are included in the effective potentials (EP). The EP's are based on numerical Dirac-Hartree-Fock calculations for atoms and on the Phillips-Kleinman transformation with other aspects similar to the treatments of Goddard and Melius and Kahn, Baybutt, and Truhlar. The EP's may be writtenwhere Iljm> is a two-component angular basis function that is a product of a two-component Pauli spinor and spherical harmonics. The numerical functions UIjEP(r) are approximated as expansions in terms of Gaussian or exponential functions. The use of these EP's enables one to use the .ii -coupling scheme for subsequent applications in all-valence-electron calculations on heavy atoms and their molecules. A standard atomic SCF program has been modified to accommodate these EP's and Gaussian and exponential basis sets having the proper j angular dependence. Energy levels for many atomic states of Xe and Au were calculated. The study of Xe excited states indicates that the spin-orbit splittings are reasonably approximated and that the numerical DHF calculations are adequately reproduced. Au has been treated as an atom with I, 11, 17, 19, or 33 valence electrons to investigate the effects of redefinition of the core. P is the momentum operator (-iV). Also, .. (~ ~)with r:r being a Pauli matrix and

The unusual potential energy curve for the 1∑+g ground state of Be2 is investigated using many-body perturbation theory (MBPT) and coupled-cluster (CC) methods. The curve, which has a ∼2 kcal/mol inner minimum at ∼2.6Å and a van der Waals minimum at ∼5.0 Å, is very difficult to describe accurately with even high-level ab initio correlated methods. To resolve uncertainties in previous MBPT/CC studies, we have generalized CC theory to include effects of triple excitations. The present calculations are compared with recent full CI results to assess the relative importance of different contributions of electron correlation. MBPT (4) is found to be qualitatively correct, but to slightly exceed the correct full CI binding energy, while CC theory even with triple excitations, has no inner minimum. The latter follows from CC theory being exact for separated Be atoms (with frozen core) but to have a 1% correlation energy error in the binding region. Yet this 1% accounts for the ∼2 kcal/mol inner well. The possibility of the remaining 1% arising from connected quadruple excitations T4 is discussed.

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