The fourth-age quantum chemical code GENIUSH is used for the variational determination of rotational-vibrational energy levels corresponding to reduced- and full-dimensional models of H(+)(5), a molecular ion exhibiting several strongly coupled large-amplitude motions. The computations are supplemented with one- and two-dimensional analytic results which help to understand the peculiar rovibrational energy-level structure computed correctly for the first time. An unusual aspect of the results is that the canonical Eckart-embedding of molecule-fixed axes, a cornerstone of the computational spectroscopy of semirigid molecules, is found to be inadequate. Furthermore, it is shown that while the 1D "active torsion" model provides proper results when compared to the full, 9D treatment, models excluding the torsion have limited physical significance. The structure of the rovibrational energy levels of H(+)(5) proves that this is a prototypical astructural molecule: the rotational and vibrational level spacings are of the same order of magnitude and the level structure drastically deviates from that computed via perturbed rigid-rotor and harmonic-oscillator models.

Rovibrational quantum nuclear motion computations, with J = 0, 1, and 2, are reported for the intermolecular degrees of freedom of the methane-water dimer, where J is the quantum number describing the overall rotation of the complex. The computations provide the first explanation of the far-infrared spectrum of this complex published in J. Chem. Phys., 1994, 100, 863. All experimentally reported rovibrational transitions, up to J = 2, can be assigned to transitions between the theoretically computed levels. The deviation of the experimental and computed rovibrational transitions is 0.5 cm(-1) for the ortho and 2 cm(-1) for the para species with a variance of 0.005 cm(-1). In addition to a lower systematic error, the overall agreement of theory and experiment is also better for the ortho species (involving ortho-H2O). Most importantly, for this species all levels of the 24-fold tunneling splitting manifold corresponding to the zero-point vibration (ZPV) are involved in at least one experimentally reported transition. For the para species there are a few energy levels in the computed ZPV manifold that are not involved in the reported experimental transitions. Furthermore, computed energy levels are identified that correspond to the ZPV tunneling splitting manifold of the secondary minimum structure of the dimer, which presumably appear in rovibrational transitions in the same energy regime as the observed transitions, but have not been experimentally reported.

One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H + 5 . Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H + 5 , this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H + 5 is gained via variational nuclear motion and diffusion Monte Carlo computations and by the analysis of the wavefunctions they provide. The modelling results describing the transition from the zero barrier limit to the large barrier limit should prove to be useful for the important class of molecules and molecular ions that contain two weakly coupled internal rotors. IntroductionThe simplest and exactly solvable quantum chemical models that are traditionally employed to understand highresolution spectra of gas-phase molecules are based on the harmonic oscillator (HO) and rigid rotor (RR) approximations of the vibrations and the rotations, respectively. In cases when the results based on the RRHO approximation, perhaps after a slight extension based on second-order perturbation theory [1][2][3][4][5], provide a good qualitative and even a semiquantitative understanding of spectral regularities, the molecule of interest can be considered to be 'semirigid'. These are molecules for which the electronic state that is being investigated contains a single, well-defined, and relatively deep minimum. For semirigid molecules, the timescales for the vibrational and rotational motions are sufficiently different to allow their approximate separation, the vibrational spacing decreases as the vibrational excitation increases, the vibrational states have well-defined symmetries provided by the point group characterising the unique equilibrium structure, and the rotational states can be assigned to a certain vibrational state. The RRHO treatment is familiar to most chemists as excellent textbooks exist which describe slightly anharmonic molecular vibrations [6,7] as

Matrix-isolation experiments near 3 K and state-of-the-art quantum chemical computations demonstrate that oxalic acid [1, (COOH)2] exhibits a sequential quantum mechanical tunneling phenomenon not previously observed. Intensities of numerous infrared (IR) bands were used to monitor the temporal evolution of the lowest-energy O-H rotamers (1cTc, 1cTt, 1tTt) of oxalic acid for up to 19 days following near-infrared irradiation of the matrix. The relative energies of these rotamers are 0.0 (1cTc), 2.6 (1cTt), and 4.0 (1tTt) kcal mol(-1). A 1tTt → 1cTt → 1cTc isomerization cascade was observed with half-lives (t1/2) in different matrix sites ranging from 30 to 360 h, even though the sequential barriers of 9.7 and 10.4 kcal mol(-1) are much too high to be surmounted thermally under cryogenic conditions. A general mathematical model was developed for the complex kinetics of a reaction cascade with species in distinct matrix sites. With this model, a precise, global nonlinear least-squares fit was achieved simultaneously on the temporal profiles of nine IR bands of the 1cTc, 1cTt, and 1tTt rotamers. Classes of both fast (t(1/2) = 30-50 h) and slow (t(1/2) > 250 h) matrix sites were revealed, with the decay rate of the former in close agreement with first-principles computations for the conformational tunneling rates of the corresponding isolated molecules. Rigorous kinetic and theoretical analyses thus show that a "domino" tunneling mechanism is at work in these oxalic acid transformations.

Variational nuclear motion computations, employing an exact kinetic energy operator and two different potential energy surfaces, are performed to study the first 60 vibrational states of the molecular ion H5 (+)≡ [H2-H-H2](+) and all of its deuterated isotopologues and isotopomers, altogether 12 species. Detailed investigation of the vibrational wavefunctions mostly results in physically intuitive labels not only for the fundamentals but also for the overtone and combination states computed. The torsional motion associated with the left and right diatomics appears to be well separated from the other vibrational degrees of freedom for all species. The unusual structure of the higher-lying bending states and the heavy mixing of the internal motions is partly due to the astructural character of all these molecular ions. The existence of distinct isotopomers in the H5-nDn (+), n = 1-4 cases, in the energy range studied, is confirmed. Two rules determine the stability order of the isotopomers: first, when possible, H prefers to stay in the middle of the ions rather than at the sides, and, second, the isotopomer with a homonuclear diatomic at the side is always lower in energy. The large number of precise vibrational energies of the present study, as well as the detailed assignment of the states, should serve as benchmarks for future studies by more approximate nuclear-motion treatments, such as diffusion Monte Carlo and multiconfiguration time-dependent Hartree.