Rovibrational Energies of Triatomic Molecules by Means of the Rayleigh-Schrödinger Perturbation Theory.

A Rayleigh-Schrödinger perturbation theory approach based on the adiabatic (Born-Oppenheimer) separation of vibrational motions was previously developed and used to evaluate for a system of coupled oscillators the adiabatic energy levels and their nonadiabatic corrections. This method is applied here to calculate rotation-vibration energies of the triatomic molecular ions HeH(+)(2) and ArNO(+) consisting of a strongly bound diatomic fragment and a relatively loosely bound rare gas atom. In these systems the high-frequency stretching motion of the diatomic fragment can be separated from the other two low-frequency motions without substantial loss of accuracy. Treating the diatomic fragment as a rigid rotor, the low-frequency stretching motion is decoupled from the bending motion in analogy to the concept of the adiabatic (Born-Oppenheimer) separation of motions and the strong nonadiabatic couplings between these two motions are accounted for perturbationally. Although the resulting perturbation series may show poor convergence, they turn out to be accurately summable by applying standard techniques for the summation of divergent series. Comparison with the results obtained from full-dimensional calculations for the two ions shows that the approach is capable of providing accurate energies for quite a few of the bound rotation-vibration states and that in the case of the HeH(+)(2) ion it is even able to predict the positions and widths of some low-lying resonance states with good accuracy. The perturbation approach yields zeroth-order energies and corrections in terms of the relevant quantum numbers. It thus allows a direct assignment of the energy levels without any reference to the corresponding eigenfunctions. The weak couplings between the high- and low-frequency motions can easily be treated by the same perturbative approach and numerically exact energies can finally be obtained. Copyright 2000 Academic Press.

Vibrational Dynamics of H5 + and Its Deuterated Isotopomers

The vibrational dynamics of the H5 + complex and its deuterated isotopomers H4 D+ , H3 D2 + , H2 D3 + , HD4 + , and D5 + are investigated using a model Hamiltonian which is based on the assumption that on the potential energy hypersurface the barriers for the internal rotation motions are infinitely high except for the practically free propeller-like motion. According to our previous studies on H5 + , the propeller-like rotation essentially does not interact with the remaining vibrations and is therefore neglected in the present calculations. Within the framework of the adiabatic approximation the resulting eight-dimensional vibrational problem is separated into two smaller subproblems which are solved numerically applying the same scheme as previously. The calculations are performed using a new extended potential energy function which also provides a reliable description of the interactions between the degenerate stretching motions and the remaining vibrations. As in our previous calculations, the high-frequency fundamentals obtained for H5 + are in good agreement with their experimental counterparts, whereas the reliability of the present results for the low-frequency motions is considerably improved as a result of the appropriate description of the relevant interactions. Predictions of the vibrational energies of the other deuterated isotopomers are made on the same accuracy level. The zero-point energies derived from the present calculations are believed to be accurate enough for a quantitative determination of the binding energies of the different isotopomers.

Symmetry Analysis of the Vibrational Dynamics of the H3 D2 + and H2 D3 + Complexes

A symmetry analysis of the H3 D2 + and H2 D3 + complexes in a model with one large amplitude motion, the propeller-like internal rotation, is presented. Symmetry coordinates and symmetry adapted polynomial expansions of the potential, dipole moment, and polarizability functions are derived within the framework of the extended molecular symmetry group G 3 (2, 2) using the projection operator and Molien function techniques.

Ab initio Calculated Rotation-Vibration Linestrengths for HeH2+

Together with the recently determined potential energy surface for the ground electronic state of HeH2+ [V. Spirko and W. P. Kraemer, J. Mol. Spectrosc. 172, 265-274 (1995)], the electric dipole moment components were calculated directly as expectation values with the corresponding length operators at the center of mass of the ion and using the variationally optimized configuration interaction wavefunctions. From the fitted potential energy and dipole moment functions all bound rotation-vibration energy levels and the line strengths of all dipole-allowed bound-bound transitions were evaluated variationally within the framework of the Sutcliffe-Tennyson Hamiltonian. Strong transitions, especially for the (He...H2)+ stretching motion, were obtained in the 500-800 cm-1 infrared frequency range. The present calculations demonstrate that the conditions for detecting the still unobserved rotation-vibration spectrum of HeH2+ are rather promising. Copyright 1997Academic Press

An ab Initio Study of the NH2+ Absorption Spectrum

In a previous publication (1997. P. Jensen, J. Mol. Spectrosc. 181, 207-214), rotation-vibration energy levels for the electronic ground state X3B1 of the amidogen ion, NH2+, were predicted using the MORBID Hamiltonian and computer program with an ab initio potential energy surface. In the present paper we calculate a new ab initio potential energy surface for the X3B1 state, and we calculate ab initio the potential energy surfaces of the a1A1 and b1B1 excited singlet electronic states (which become degenerate as a 1Delta state at linearity). We use the multireference configuration interaction (MR-CI) level of theory with molecular orbital bases that are optimized separately for each state by complete-active-space SCF (CASSCF) calculations. For the X state we use the MORBID Hamiltonian and computer program to obtain the rotation-vibration energies. For the a and b excited singlet electronic states we calculate the rovibronic energy levels using the RENNER Hamiltonian and computer program. We also calculate ab initio the dipole moment surfaces for the X, a, and b electronic states, and the out-of-plane transition moment surface for the b <-- a electronic transition. We use this information to simulate absorption spectra within X3B1 and a1A1 state and of the b1B1 <-- a1A1 transition in order to aid in the search for them. Copyright 1997 Academic Press. Copyright 1997Academic Press