Walter J. Stevens

Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms

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.

Effective core potential methods for the lanthanides

In this paper a complete set of effective core potentials (ECPs) and valence basis sets for the lanthanides (Ce to Lu) are derived. These ECPs are consistent not only within the lanthanide series, but also with the third‐row transition metals which bracket them. A 46‐electron core was chosen to provide the best compromise between computational savings and chemical accuracy. Thus, the 5s and 5p are included as ‘‘outer’’ core while all lower energy atomic orbitals (AOs) are replaced with the ECP. Generator states were chosen from the most chemically relevant +3 and +2 oxidation states. The results of atomic calculations indicate that the greatest error vs highly accurate numerical potential/large, even‐tempered basis set calculations results from replacement of the large, even‐tempered basis sets with more compact representations. However, the agreement among atomic calculations remains excellent with both basis set sizes, for a variety of spin and oxidation states, with a significant savings in time for th...

An Effective Fragment Method for Modeling Solvent Effects in Quantum Mechanical 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 (hessians) 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.

Frozen fragment reduced variational space analysis of hydrogen bonding interactions. Application to the water dimer

Abstract A reduced variational space method is presented for analyzing hydrogen bonding interactions in terms of Coulomb and exchange, polarizability, and charge-transfer components. The method relies on the use of SCF optimized monomer orbitais in dimer calculations in which the wavefunction of one monomer is held frozen while the other is optimized with a basis set including selected subsets of the unoccupied monomer orbitals. Freezing the monomer wavefunctions allows the polarizability and charge-transfer interactions to be ascribed to specific monomers. Applications are presented for the interaction energy and dipole moment of the water dimer.

Evaluation of Charge Penetration between Distributed Multipolar Expansions

A formula to calculate the charge penetration energy that results when two charge densities overlap has been derived for molecules described by an effective fragment potential (EFP). The method has been compared with the ab initio charge penetration, taken to be the difference between the electrostatic energy from a Morokuma analysis and Stone’s Distributed Multipole Analysis. The average absolute difference between the EFP method and the ab initio charge penetration for dimers of methanol, acetonitrile, acetone, DMSO, and dichloromethane at their respective equilibrium geometries is 0.32 kcal mol−1.

Theoretical determination of bound–free absorption cross sections in Ar+2

Ab initio calculations have been carried out for the potential energy curves and transition moments of the 2Σ+u, 2Πg, 2Πu, and 2Σ+g states of Ar+2 which arise from the 2P+1S ion–atom asymptote. These data have been used in a theoretical calculation of the dissociative absorption cross sections from the bound 2Σ+u state to the repulsive 2Πg and 2Σ+g states. The 2Σ+u→2Πg transition, which is dominated by spin–orbit effects, has a maximum absorption cross section of 2.6×10−19 cm2 centered at 716 nm with a full width at half‐maximum of 185 nm at room temperature. The 2Σ+u→2Σ+g transition is found to be much stronger with a maximum cross section of 0.5×10−16 cm2 centered at 300 nm with a full width at half‐maximum of 75 nm at room temperature.

Electronic structure of FeO and RuO

The electronic structure of FeO and RuO is examined using multiconfiguration self‐consistent‐field (MC‐SCF) wave functions that go asymptotically to minimally correlated fragment atoms. Core electrons are eliminated by the use of relativistic effective potentials (REP) which also are used to calculate the spin‐orbit coupling constant for the 5Δ, 5Π, and 5Φ states. The electronic structure of the FeO and RuO 5Δ states is described in terms of interacting singly charged ions, M+ and O−, which are bound primarily by a strong sigma bond. The natural orbitals are determined and evaluated in detail. The characteristics of these orbitals are used to hypothesize an aufbau for the ground states of most of the first and second row transition metal oxides. In addition to the 5Δ states, the 5Σ+, 5Π, 5Φ, 5Σ−, 5Γ, 7Σ+, 7Π, 7Φ, 3Δ, 3Σ+, 3Π, and 3Φ states were also studied. FeH and RuH 6Δ, 4Δ, and 4Φ states were also examined to evaluate the basis set.

Abinitio study of the hydrogen bonding interactions of formamide with water and methanol

Ab initio calculations of hydrogen bond energies for a number of water–formamide and methanol–formamide complexes are reported at both the SCF and correlated levels. Full gradient optimizations of these structures have been performed for basis sets of double zeta and double zeta plus polarization quality. For both water and methanol, the most stable 1:1 complex is found to be a cyclic double hydrogen bonded structure. Basis set effects on the calculated hydrogen bond energies were investigated as was the magnitude of the basis set superposition error. In all cases investigated, the addition of polarization functions to the basis set is found to decrease the calculated binding energy by approximately 2–4 kcal/mol, while correlation is found to increase the binding energy by ≂1 kcal/mol. Calculations on dihydrated formamide indicate a small three‐body contribution to the total binding energy.

Theoretical transition dipole moments and lifetimes for the A 1Σ+u→X Σ+g system of Na2

Multiconfiguration self‐consistent field (MCSCF) calculations have been carried out on the X 1Σ+g, A 1Σ+u, and B 1Πu states of Na2. The calculated potential energy curves are in good agreement with the experimental X and A RKR curves of Hessel and Kusch. Both the A→X and B→X transition moments have been calculated as a function of nuclear separation using MCSCF wavefunctions. These calculations are in excellent agreement with the recent experimental determinations of the B→X transition moment. A values and lifetimes of several A‐state vibrational and rotational levels for the A→X transition have been calculated using the theoretical transition moment and the experimental potential curves of Hessel and Kusch. These again are in excellent agreement with the recently measured lifetimes.

Effective core potentials and accurate energy curves for Cs2 and other alkali diatomics

Energy curves of Cs2 that correlate to the ground (SS) and first excited asymptote (SP) are calculated using compact effective potentials (CEP) and core polarization potentials (CPP) which reduce the alkali atom to a single valence electron. Dissociation energies and equilibrium internuclear separations are in good agreement with experimental values. The long‐range properties of the energy curves are analyzed to determine the region where the chemical interactions begin. Analogous energy curves and spectroscopic constants are obtained for the Rb2 molecule. The ground state singlet and triplet energy curves are also determined for K2. For completeness, the ground state spectroscopic constants are also reported for the Li and Na neutral and cation homonuclear diatomic molecules to illustrate the accuracy of the CEP and CPP for all the alkali atoms. Both doublet and quartet energy curves of the homonuclear anions also were examined. The dissociation energies and electron detachment energies of the doublet gr...