J. C. Browne

Quantum‐Mechanical Integrals over Gaussian Atomic Orbitals

Formulas for the one‐, two‐, three‐, and four‐center energy integrals are derived using the general class of single‐particle Gaussian atomic orbitals χ=xiyjzk exp[−(α1x2+α2y2+α3z2)]. The overlap, kinetic energy, and dipole moment integrals are given in closed form. The potential energy integrals require a one‐dimensional numerical quadrature. A technique due to Singer was used in obtaining these latter formulas.

Configuration interaction studies of the HeH+ molecular ion. I Singlet sigma states

The method of superposition of configurations is applied to the singlet sigma states of HeH+ which correlate to the separated atom states of principal quantum number less than or equal to 3. The calculations are carried out for internuclear separations in the ranges 0(.1)34.5, 35.0(.5)50.0 bohr. Energy eigenvalues and the expectation values of the electron coordinate along the internuclear line are discussed in this paper. Dipole transition matrix elements and radial coupling matrix elements are presented in a companion paper. The quality of the calculations is exhibited by comparisons of the length and velocity forms of the dipole matrix elements, by the Hellmann‐Feynman theorem, and by the approach to atomic properties at large internuclear separations. Supplementary calculations of higher quality wavefunctions for the lowest states are also reported. These are used to help estimate the extent to which the results of the main calculations have converged toward the exact values. Comparisons with other wo...

Some Excited States of the Hydrogen Molecule. I. 1Πu(1s2pΠ) and 3Πu(1s2pΠ)

Theoretical potential curves, spectroscopic constants, and expectation values for some one‐electron operators are given for the 3Πu(1s2pΠ) (metastable) and 1Πu(1s2pΠ) states of the hydrogen molecule. Total energies of 0.7145 and 0.7334 a.u. are obtained for 1Πu and 3Πu, respectively. The experimental total energies are 0.7186 and 0.7381 a.u. for 1Πu and 3Πu, respectively. The maximum in the potential curve of the 1Πu state is found to be much smaller and to occur at a larger internuclear separation (0.02 eV at R≈8.5 a.u.) than estimated by previous theoretical calculations (0.1 eV at R≈4.5 a.u.). Our 1Πu curve is reasonably consistent with the observed data of Herzberg and Monfils.

Binding Energy of LiH+ and the Ionization Potential of LiH: Mixed Basis Set Calculation

A rigorous lower bound of 0.038 eV for the binding energy of LiH+ has been obtained via an ab initio quantum mechanical calculation using a generalized valence‐bond wavefunction with a mixed basis set of elliptic and Slater‐type orbitals. The probable error in the total energy given by this calculation is of the order of 0.1 eV, so that a probable upper bound for the binding energy of LiH+ is 0.15 eV. This invalidates the conclusion of a previous SCF—MO calculation which gave a substantial minimum in the LiH+ potential curve. A rigorous upper bound of 7.91 eV for the ionization potential of LiH is found by the relation E(LiH+, calculated) — E(LiH, experimental) ≥I.P. (LiH). A probable lower bound for I.P. (LiH) is 7.8 eV. Potential curves for the system Li++H from several wavefunctions are tabulated.

The computation of nuclear motion and mass polarization adiabatic energy corrections for several states of the hydrogen molecule

This paper reports the computation of the diagonal matrix elements of the nuclear motion and mass polarization operators (often referred to as adiabatic corrections) for several electronic states of the hydrogen molecule. It is observed that reasonably simple wavefunctions will yield accurate expectation values for the nuclear motion operators. The present calculation covers a greater range of R for the X 1Σ+g and B 1Σ+u states than is covered in the very accurate work of Kolos and Wolniewicz, and includes computations for the C 1Πu and D 1Πu states for which no theoretical results have been previously reported. For the latter states the present diagonal corrections have been used in conjunction with the very recent Born–Oppenheimer potential energy curves of Kolos and Rychlewski [J. Mol. Spectrosc. 62, 109 (1976)] to compute vibrational level energies for both H2 and D2. The diagonal corrections largely remove the mass‐dependent part of the discrepancy between theory and experiment for these vibrational ...

Adiabiatic ab initio potential curves for the B′ 1Σ+u state of H2

There is reported here an accurate ab initio calculation of the fixed nuclei potential curve for the B′ 1Σ+u state of H2 together with approximate values of the adiabatic corrections to the potential curve for this state. The state is observed to have two minima in its potential with the very small maxima occurring at approximately, R=5.5a0. Dipole transition moments and oscillator strengths for X 1Σ+g ↔ B 1Σ+u transitions are given for a wide range of internuclear separations.

Quantum‐Mechanical Potential‐Energy Curve for the Lowest 1Σu+ State of He2

The potential‐energy curve of the lowest 1Σu+ state of He2 is computed in a valence bond scheme using a 17‐term wavefunction of Slater orbitals. A maximum in the potential curve occurs at 5.22 a0 with a computed height of 0.153 eV. A rigorous upper bound of 0.364 eV is found for the potential maximum. The rationalized dissociation energy for the best wavefunction is 1.719 eV at Re=2.11 a0, and a rigorous lower bound on the dissociation energy is 1.508 eV.

Configuration interaction studies of HeH+ molecular ion. II Dipole and radial coupling matrix elements for the singlet sigma states

Configuration interaction calculations of the dipole, gradient, and radial coupling matrix elements among the lowest 10–12 1Σ states of HeH+ are reported for internuclear separations in the range 0≤R≤50 a.u. The forms 〈n|∂/∂R|m〉 and (Em − En)−1 〈n|∂V/∂R|m〉 of the radial coupling element are compared. The results are compared with those of other investigators. The accurate evaluation of these matrix elements in the present work demonstrates the feasibility of a quantitative ab initio treatment of low‐energy collisions between light atoms.

Some Excited States of the Helium Molecule. I. The Lowest 1Σu+ and 3Σg+ States and the First Excited 1Σg+ States

We report here some theoretical potential curves for the 1Σu+(2s, 1S0), 1Σg+(2s, 1S0), 1Σg+(2p0, 1S0), 3Σg+(2s, 3S1), and 3Σg+(2p0, 3S1) states of the helium molecule. We find, using a two‐term wavefunction with a mixed basis of Slater‐type orbitals and elliptic orbitals, that the 1Σu+ potential curve has a maximum of about 0.174 eV at R=5.0a0 and a minimum at R=2.07a0 with a rationalized binding energy, EB=E (calc., Re) − E (calc., R=∞) of EB=1.9 eV. We find, in agreement with the recent suggestions of R. S. Mulliken, that the lowest bound state of the helium molecule of symmetry 3Σg+ and the first bound excited state of symmetry 1Σg+ arise from the interactions He(1S0, 1s2)+He(3S0, 1s2s), 3Σg+(2s, 3S1), and He(1S0, 1s2)+He(1S0, 1s2s), 1Σg+(2s, 1S0), respectively. The 1Σg+(2s, 1S0) and 3Σg+(2s, 3S1) states were also found to have maxima in their computed potential curves. The computed maxima are: 1Σg+≈0.7 eV, R=4.5a0; 3Σg+≈0.8 eV, R=3.75a0.

Translational Absorption of HeH

There is reported here the calculation of the translational absorption spectrum of a system of a helium atom and a ground state hydrogen atom. We report also values of calculated potential curves for the ground state of the molecular system HeH and the dipole moment of the ground molecular state of HeH as a function of internuclear separation. The behavior of the dipole moment is of particular interest as it passes through zero at about R=7a0. This change of sign follows from and correlates with the known long range behavior of the dipole moment of this system.