M. Krauss

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.

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.

The electronic structure of nitrogen dioxide. I. Multiconfiguration self‐consistent‐field calculation of the low‐lying electronic states

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 X 2A1, A 2B2, B 2B1, C 2A2, 4B2, 4A2, and 2Σ+g electronic states of NO2. The minima of the A 2B2, B 2B1, and C 2A2 states have all been found to be within 2 eV of the minimum of the X 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‐polarizatio...

Interaction Potential between He and H2

The interaction potential of He with H2 has been determined in the Hartree—Fock approximation. An analytic expression for the interaction potential has been determined in a form suitable for consideration of energy‐transfer problems. The expression is V(X, R, θ)=C exp{‐α0X+α1Xr} {A(θ)+B(θ)r}, which is valid for 0≤R≤2 a.u., 2.5≤X≤3.8 a.u., where R=r+Re, Re=1.4 a.u. and C=198.378 eV, α0=1.86176 a.u.−1, α1=0.3206 a.u.−2, A(θ)=1.10041 {1+0.18250 P2(cosθ)}, B(θ)=−0.52151 {1−0.27506 P2(cos(θ)} a.u.−1. X is the distance between the He and H2 centers of charge, R is the H2 bond distance, and XR cosθ=X·R. From this result we see that the force exerted on the oscillator is comparable for both a collision along the line of centers and one along the molecular bisector.

Pseudonatural Orbitals as a Basis for the Superposition of Configurations. I. He2

The use of pseudonatural orbitals (PNO) is proposed to improve the rate of convergence in the superposition of configurations (SOC). Natural orbitals are determined for selected electron pairs in the Hartree—Fock field of the n−2 electron core and are then used as the basis for the total SOC calculation. Since these natural orbitals are not natural for the n‐electron system they are considered false or pseudonatural orbitals when used in the n‐electron problem.The PNO basis has been applied to He2+ and H3 to test the convergence. Complete results are reported here only for He2+. The PNOs are quite successful in speeding up the convergence of the SOC and rendering the calculation of correlation energy quite practical in general. Gaussian‐type orbitals (GTO) are used throughout and were not a serious impediment to obtaining quantitative accuracy. In fact the large number of unoccupied Hartree—Fock orbitals consequent upon the use of a GTO basis permit a straightforward determination of the PNO orbitals.

Predissociation of the Schumann-Runge bands of O2

Abstract The predissociation line broadening in the Schumann-Runge bands of O2 is interpreted through an ab initio calculation of the pertinent repulsive potential energy curves and spin-orbit matrix elements. The ab initio results provide an overall qualitative picture of the predissociation which is further refined through a detailed comparison of calculated level shifts and widths with experimental data. The position of the dominant repulsive curve is also deduced by a deperturbation of the level shift in the second vibrational difference. The predissociation is dominated by the 5Πu state crossing the B 3 Σ u − state around 1.875 A with a spin-orbit matrix element of 65 cm−1. The 1Πu and 3Πu states have small spin-orbit matrix elements and play only minor roles in the predissociation. The calculated and experimental widths are in good agreement for low and high vibrational levels. The apparent experimental widths between v = 5 and 11 are shown to be inconsistent with the theoretical analysis, the difference probably being due to line blending.

Photoionization and Absorption Spectrum of Formaldehyde in the Vacuum Ultraviolet

Absorption and photoionization coefficients have been measured for H2CO in the 600–2000‐A region. Integrated oscillator strengths were determined for a number of strong Rydberg transitions above 1200 A. From the photoionization curve the first adiabatic ionization potential was found to be 10.87±0.01 eV. As an aid in interpreting the absorption spectrum, theoretical calculations were made using a single‐configuration self‐consistent field procedure for the Rydberg states and a model which included mixing between the Rydberg and valence states. On this basis, weak absorption features between 1340 and 1430 A have been assigned to the 1B1(σ → π *) valence state. The 1A1(π → π *) valence state is deduced to be strongly autoionized just above the 2B2 ionization limit.

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.

Multiconfiguration self‐consistent‐field calculation of the dipole moment function of CO(X1Σ+)

The dipole moment function for the 1Σ+ ground state of CO in the vicinity of the equilibrium internuclear distance has been calculated by the optimized valence configurations (OVC) multiconfiguration self‐consistent‐field method. The results are compared with existing Hartree‐Fock and configuration interaction treatments of this molecule at single points and also the dipole moment function deduced from experimental infrared intensities. At the experimental equilibrium separation, the calculated dipole moment is −0.167 D (C−O+) which is in reasonable agreement with the microwave value of −0.112 D (C−O+). The vibrationally averaged expectation value of the dipole moment based on the computed moment function and accurate vibrational wavefunctions is −0.151 D (C−O+) which is in better agreement with the observed microwave quantity and illustrates that the effect of vibrational averaging is not negligible in systems such as CO that possess small permanent dipole moments. A general prescription for constructing...

Interaction Energy Curves of LiHe and NaHe (X 2Σ+, A 2Π, B 2Σ+) and X 1Σ+ Ions

Hartree–Fock interaction energy curves have been calculated for the X 2Σ+, A 2Π, and B 2Σ+ states of neutral LiHe and NaHe as well as for the ground state X 1Σ+ ions over a range of distances from 3 to 10 a.u. Since it is intended to apply these results to scattering problems, the variation of the dipole and quadrupole moments and the electronic transition probabilities with internuclear distance were also obtained. Both Slater‐type functions and Gaussian‐type functions were used as variational trial functions with the intention of gauging the efficacy of the Gaussian basis. Except for situations involving small energy minima the Gaussian basis yielded results accurate relative to the Slater basis. The features of the Hartree–Fock interaction energy curves can be summarized as follows:(1) The X 2Σ+ interaction energy is purely repulsive for both molecules to the accuracy of the present calculation.(2) The A 2Π and X 1Σ+ curves are strikingly similar for both Li and Na confirming the penetration of the He ...