[en] Let E(R) be a potential-energy function for a neutral or ionic diatom in the Born-Oppenheimer approximation. Then the approximation of E(R) for 0 < R < infinity starting from finite and typically small sets of given information is considered. The approach is based on the fact that the scaled potential curves F(R) = R²E(R) derive from an eigenvalue problem which depends linearly on R. The nature of the curves F(R) is examined in detail. The results include the discovery of various approximants, some of which display rigorous bounding properties and others, closely related, whose behavior with respect to the approximated function appears to be predictable. 36 references

[en] The recently introduced ''vibronic'' method of calculating dynamic dipole polarizabilities has been applied to HeH⁺. Because this molecule has a vibrational component to its polarizability, it is shown that special care has to be taken when the method is applied. The method has been modified and the calculations carried out more rigorously than before in order to avoid certain problems which were previously undetected. New and more accurate results are reported and these are compared with those that can be obtained by using the traditional clamped nucleus method

[en] Accurate photodissociation cross sections have been obtained for the A¹Σ⁺ <- X¹Σ⁺ electronic transition of HeH⁺ using ab initio potential curves and dipole transition moments. Partial cross sections have been evaluated for all rotational transitions from the vibrational levels v'' = 0-11 and over the entire accessible wavelength range λλ100-1129. Assuming a Boltzmann distribution of the rovibrational levels of the X¹Σ⁺ state, photodissociation cross sections are presented for temperatures between 500 and 12,000 K. A similar set of calculations was performed for the pure rovibrational photodissociation in the X¹Σ⁺ electronic ground state, but covering photon wavelengths into the far-infrared. Applications of the cross sections to the destruction of HeH⁺ in the early universe and in UV-irradiated environments such as primordial halos and protoplanetary disks are briefly discussed.

[en] A procedure for carrying out the Buenker--Peyerimhoff extrapolation using perturbation theory natural orbitals (PTNO's) is presented. This procedure is then applied to the H₂O and HeH₂⁺ systems within the framework of a configuration space comprising all single and double excitations from a single configuration. The results indicate that significantly smaller secular determinants need to be solved when PTNO's are used; the extrapolated CI energies are within 5 x 10^-4 a.u. of energy obtained from the full calculation within the same configuration space

[en] A calculation of the magnetic-susceptibility components and rotational g value of HeH⁺ is reported. Rovibronic wave functions, with explicit inclusion of the interelectronic coordinate, are used

[en] The variational method is used to find the ground state energy of the molecular hydrogen ion, H₂⁺ , by employing a linear combination of atomic orbitals (LCAO) of the Slater-type, all with the same exponential parameter ζ. For the equilibrium position, R = 2 a.u, eight digit accuracy was achieved using 21 orbitals on each nucleus, with the highest principal quantum number, N = 6. Beyond R = 50, thirteen digit accuracy is obtained. The wave function is given for various LCAO at the equilibrium position. The same method has also been applied to the HeH²⁺ molecular ion and a high degree of accuracy was achieved

[en] Recently, experimental evidence for the existence of a bound state of the HeH²⁺ molecular ion was reported by Ben-Itzhak, Gertner, Heber, and Rosner [Phys. Rev. Lett. 71, 1347 (1993)]. This three-body system was predicted by Bates and Carson to have bound vibrational states in the 2pσ electronic state despite the strong repulsion potential between the two nuclei. These 2pσ vibrational states decay via an electronic transition to the 1sσ repulsive ground state with a mean lifetime of about 1 nsec. We have used the ''fragment-fragment'' coincidence method to measure the mean lifetime of the HeH²⁺ molecular ions which dissociate in flight before reaching the detector. The yield of these molecular ions was measured as a function of the distance between the target cell and the analyzer exit. From this measurement a mean lifetime of 3.9±0.4 nsec was determined. The 2pσ→1sσ transition rates for all vibrational states have been calculated within the Born-Oppenheimer approximation using available oscillator strengths. It is shown that the transition rates decrease with increasing vibrational energy because of the ''stretch'' of the molecular ion. The distribution of 2pσ vibrational states populated by vertical transitions from stripping the HeH⁺ electronic ground state was evaluated, and the resulting decay curve compares well with the measured one

[en] The 1 ²Pi(1 ²B₁,1 ²A'') state of the helium dihydride ion HeH₂⁺ has been examined with ab initio electronic structure calculations. In particular, the potential energy hypersurface for this Rydberg state has been surveyed with an MCSCF/CI wavefunction involving orbital expansions in a double-zeta plus double polarization plus diffuse one-electron basis. The surface is essentially a trough falling monotonically from the atom--diatomic asymptote He(X ¹S) +H₂⁺(C ²Pi/sub u/), through the triatomic region, to the asymptote HeH(1 ²Pi)+H⁺. At some triatomic geometries the 1 ²Pi state is one of the lowest excited electronic states of this molecular ion system. The results obtained here are the first reported explicit treatment of HeH₂⁺ Rydberg states, and will contribute towards the elucidation of the manifolds of the lowest two Rydberg series arising from the (HeH,H)⁺ excited asymptotes

[en] A brief history of the development of ab initio calculations for the HeH₂ quasi-molecule energy surface, and the parametric fits to these ab initio calculations, is presented. The concept of 'physical reasonableness' of the parametric fit is discussed. Several new improved parametric fits for the energy surface, meeting these requirements, are then proposed. One fit extends the Russek-Garcia parametric fit for the deep repulsion region to include r-dependent parameters, resulting in a more physically reasonable fit with smaller average error. This improved surface fit is applied to quasi-elastic collisions of He on H₂ in the impulse approximation. Previous classical calculations of the scaled inelastic vibrorotational excitation energy distributions are improved with this more accurate parametric fit of the energy surface and with the incorporation of quantum effects in vibrational excitation. It is shown that Sigmund's approach in developing his scaling law is incomplete in the contribution of the three-body interactions to vibrational excitation of the H₂ molecule is concerned. The Sigmund theory is extended to take into account for r-dependency of three-body interactions. A parametric fit for the entire energy surface from essentially 0 ≤R≤∞ and 1.2≤r≤1.6 a.u., where R is the intermolecular spacing and r is the hydrogen bonding length, is also presented. This fit is physically reasonable in all asymptotic limits. This first, full surface parametric fit is based primarily upon a composite of ab initio studies by Russek and Garcia and Meyer, Hariharan and Kutzelnigg. Parametric fits for the H₂(1sσ_g)², H₂⁺(1sσ_g), H₂⁺(2pσ_u) and (LiH₂)⁺ energy surfaces are also presented. The new parametric fits for H₂, H₂⁺(1sσ_g) are shown to be improvements over the well-known Morse potentials for these surfaces

[en] The method of optimized expansions of the basis has been applied to the calculation of the dynamic polarizability of molecules in a Gaussian basis. The question of the form of the functions expanding the original basis has been examined in detail. A program has been compiled, and calculations are carried out for the molecules H₂⁺, H₂, He₂⁺⁺, and HeH⁺. The results show good agreement with the data obtained by other authors. It has been concluded that the method examined can be applied to large molecules