. Can. J. Chem. 70, 6 12 (1992). Relativistic compact effective potentials (RCEP), which replace the atomic core electrons in molecular calculations, have been derived from numerical Dirac-Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional. Potentials are presented for the third-, fourth-, and fifthrow atoms of the Periodic Table (excluding the lanthanide series). The efficiency of molecular calculations is enhanced by using compact Gaussian expansions (no more than three terms) to represent the radial components of the potentials, and energy-optimized, shared-exponent, contracted-Gaussian atomic orbital basis sets. Transferability of the potentials has been tested by comparing calculated atomic excitation energies and ionization potentials with values obtained from numerical relativistic Hartree-Fock calculations. For the alkali and alkaline earth atoms, core polarization potentials (CPP) have been derived which may be added to the RCEP to make possible accurate molecular calculations without explicitly including core-valence correlating configurations in the wavefunction. Introduction two rows (Li-Ar) of the Periodic Table ( 5 ) . We designatedThe use of atomic effective core potentials (ECP) and model potentials (MP) to eliminate chemically inactive atomic core electrons from quantum mechanical calculations has become routine in the past decade. The development of such potentials in the early 1970's and applications through the mid-1980's have been reviewed previously (1). The use of such potentials in molecular calculations has gained widespread acceptance, and sets of effective potentials are included in widely distributed quantum chemistry programs such as HONDO ( 2 ) , GAMESS (3), and GAUSSIAN (4). We previously published accurate compact effective potentials (CEP) and matching basis sets for the atoms of the first '~u t h o r to whom correspondence may be addressed. 'NRC-NAS Postdoctoral Fellow, NIST, 1984NIST, -1986. Current address: California State University, San Marcos, CA 92096, U.S.A.Primed in Canada -the potentials "compact" because they are represented analytically by small Gaussian expansions and, therefore, offer significant economy in molecular calculations where the computer time required to construct the electronic integrals is proportional to the complexity of the potentials. In this report, we present effective potentials and basis sets of similar quality for the third, fourth, and fifth rows of the Periodic Table derived from numerical, relativistic, Dirac-Fock atomic wavefunctions. The analytic expansions of these POtentials are also limited to a few Gaussian terms (three or less), so we have designated them as "relativistic compact effective potentials" (RCEP).Recently, several compilations of model potentials and effective core potentials for use in molecular calculations have appeared in the literature. For the heavier atoms, relativistic effects have been incorporated by deriving the potentials ...

Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular-dependent components of these potentials are represented by compact one- and two-term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy-optimized Gaussian basis set expansions of the atomic pseudo-orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all-electron calculations.

An effective fragment model is developed to treat solvent effects on chemical properties andreactions. The solvent, which might consist of discrete water molecules, protein, or othermaterial, is treated explicitly using a model potential that incorporates electrostatics,polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully abinitio calculations. An effective fragment model is developed to treat solvent effects on chemical properties and reactions. The solvent, which might consist of discrete water molecules, protein, or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives ͑hessians͒ for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully ab initio calculations.

Abstract:We present refinements of the SIBFA molecular mechanics procedure to represent the intermolecular interaction energies of Zn(II). The two first-order contributions, electrostatic (E MTP ), and short-range repulsion (E rep ), are refined following the recent developments due to Piquemal et al. (Piquemal et al. J Phys Chem A 2003, 107, 9800; and Piquemal et al., submitted). Thus, E MTP is augmented with a penetration component, E pen , which accounts for the effects of reduction in electronic density of a given molecular fragment sensed by another interacting fragment upon mutual overlap. E pen is fit in a limited number of selected Zn(II)-mono-ligated complexes so that the sum of E MTP and E pen reproduces the Coulomb contribution E c from an ab initio Hartree-Fock energy decomposition procedure. Denoting by S, the overlap matrix between localized orbitals on the interacting monomers, and by R, the distance between their centroids, E rep is expressed by a S 2 /R term now augmented with an S 2 /R 2 one. It is calibrated in selected monoligated Zn(II) complexes to fit the corresponding exchange repulsion E exch from ab initio energy decomposition, and no longer as previously the difference between (E c ϩ E exch ) and E MTP . Along with the reformulation of the first-order contributions, a limited recalibration of the second-order contributions was carried out. As in our original formulation (Gresh, J Comput Chem 1995, 16, 856), the Zn(II) parameters for each energy contribution were calibrated to reproduce the radial behavior of its ab initio HF counterpart in monoligated complexes with N, O, and S ligands. The SIBFA procedure was subsequently validated by comparisons with parallel ab initio computations on several Zn(II) polyligated complexes, including binuclear Zn(II) complexes as in models for the Gal4 and ␤-lactamase metalloproteins. The largest relative error with respect to the RVS computations is 3%, and the ordering in relative energies of competing structures reproduced even though the absolute numerical values of the ab initio interaction energies can be as large as 1220 kcal/mol. A term-to-term identification of the SIBFA contributions to their ab initio counterparts remained possible even for the largest sized complexes.

We present quantum scattering calculations for the collisional relaxation rate coefficient of spin-polarized 87Rb(f = 2,m = 2) atoms, which determines the loss rate of cold Rb atoms from a magnetic trap. Unlike the lighter alkali atoms, spin-polarized 87Rb atoms can undergo dipolar relaxation due to both the normal spin-spin dipole interaction and a second-order spin-orbit interaction with distant electronic states of the dimer. We present ab initio calculations for the second-order spin-orbit terms for both Rb2 and Cs2. The corrections lead to a reduction in the relaxation rate for 87Rb. Our primary concern is to analyze the sensitivity of the 87Rb trap loss to the uncertainties in the ground state molecular potentials. Since the scattering length for the a3Σ+u state is already known, the major uncertainties are associated with the X1Σ+g potential. After testing the effect of systematically modifying the short-range form of the molecular potentials over a reasonable range, and introducing our best estimate of the second-order spin-orbit interaction, we estimate that in the low temperature limit the rate coefficient for loss of Rb atoms from the f = 2,m = 2 state is between 0.4 × 10−15 cm3/s and 2.4 × 10−15 cm3/s (where this number counts two atoms lost per collision). In a pure condensate the rate coefficient would be reduced by 1/2.

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Traditional spectroscopic analysis of the complex and irregular absorption spectrum of NO2 has provided a relatively small amount of information concerning the nature of the excited states. An extensive ab initio investigation has been undertaken, therefore, to provide a basis for interpretation of the experimental results. Multiconfiguration self-consistent-field (MC–SCF) wavefunctions have been computed for the low-lying X̃ 2A1, Ã 2B2, B̃ 2B1, C̃ 2A2, 4B2, 4A2, and 2Σ+g electronic states of NO2. The minima of the Ã 2B2, B̃ 2B1, and C̃ 2A2 states have all been found to be within 2 eV of the minimum of the X̃ 2A1 ground state; for these states, C2v potential surfaces have been constructed for purposes of a spectral interpretation. The 4B2, 4A2, and 2Σ+g states are all more than 4 eV above the minimum of the ground state and have been examined in less detail. The study described here significantly improves on previous NO2 ab initio calculations in three important areas: (1) The double-zeta-plus-polarization quality basis set is larger and more flexible; (2) the treatment of molecular correlation is more extensive; and (3) the electronic energies have been calculated for several different bond lengths and bond angles in each state. For the four lowest doublet states the following spectral data have been obtained:     The ground state experimental constants are included in parentheses. The estimated accuracy of the various parameters is ±0.02 Å for bond length, ±2° for bond angle, ±10% for the vibrational frequencies, ±0.10 D for dipole moments, and ±0.3 eV for the adiabatic excitation energies. An unusual feature has been found for the 2Σ+g state. The equilibrium geometry of this linear state has two unequal bond lengths of 1.20 Å and 1.42 Å and the inversion barrier is approximately 800 cm−1.

Photoionization e ffi c ien cy curves are obtained for h ydroge n c hloride and several methyl ha lid es, both ordll1ary and de ute rated, from ion izat ion thres h old to 600 A. Di sc uss ion is o-iven on elec troni c s tru cture of ions, au toionizing Rydbe rg s tates, and lin e-s hape behavior. Ionization'" e n ergies, heats of ~o rm at i o n of ion s, and bond dis sociati on e ne rgi es are tabulated without regard to di s tribution of e nergy 111 II1ternal modes, 111 relallve kll1e tlc energy, o r other poss ib le modes.Key Words: Di ssoc iation e ne rgi es : He l: ionization; mass s pec trometry; me thyl hali des; vac uum ultravi o let s pec trosco py.