Interpretation of the vibrational energy level structure of the astructural molecular ion H5+ and all of its deuterated isotopomers

Abstract

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.

Quasistructural molecules

“…For a quasistructural molecule, all of the following should hold (to a greater or lesser extent) at the same time: (a) consideration of a single minimum on the PES, even though the molecule may possess only one minimum determinable by methods of electronic‐structure theory (this is the case, for example, for the quasistructural H and CH molecular cations treated in detail below), is insufficient to interpret the structure and the dynamical behavior of the molecule and its observable (high‐resolution) spectra, (b) when the structure is averaged, principally over the vibrational ground state(s), it may be significantly (i.e., even qualitatively) different from the equilibrium BO one (“quasistructurality” manifests itself in the effective structure of the molecule, whereby the equilibrium and the ground‐state rotational constants may become drastically different), due to strongly anharmonic zero‐point motions and the significant occupancy of low‐energy (ro)vibrational states, (c) rotational and vibrational spacings are of the same order of magnitude (this is most easily satisfied for light, H‐containing molecules) and the internal nuclear dynamics is thus exceedingly complex, (d) spectroscopic characterization of the molecule must rely on MS groups involving permutation and inversion symmetry operations and feasible and unfeasible motions in the Longuet‐Higgins sense, and (e) the set of assigned rovibrational energies of the molecule exhibits unconventional (in the most striking cases “negative”) rotational‐energy contributions (this is one of the most clear signs of quasistructural behavior). Note right away that (1) case (b) can happen for molecules considered to be semirigid, and (2) in a few publications we called quasistructural molecules “astructural.” Nevertheless, we now believe that the new terminology proposed here should replace the old one. A feasible alternative would be to greatly extend the IUPAC definition of “fluxional molecules.”…”

“…As predicted by all sophisticated electronic‐structure computations, the equilibrium structure of the H ion resembles that of a solvated ion, with the core H ion, formed by a strong 3‐center–2‐electron (3c–2e) bond, solvated by a H 2 molecule, placed perpendicularly to the H plane. The height of the torsional barrier, hindering the internal turnaround of the seemingly loosely attached H 2 subunit, is rather low, ∼80 cm −1 …”

Rovibrational quantum dynamical computations for deuterated isotopologues of the methane–water dimer

“…The rovibrational computations reproduce fine details of and provide an assignment to many experimental features. Most interestingly, the experimentally observed reversed rovibrational sequences (whereby within the usual molecular picture one would assign a "negative" rotational energy to a vibrational state, a characteristic feature of certain floppy molecular systems [5][6][7][8][9][10][11]) were also obtained in the computations.…”

Using collocation and a hierarchical basis to solve the vibrational Schrödinger equation

“…In FBR and DVR calculations, it is common to use a direct product basis. 11,[16][17][18][19][20][21][22][23][24][25] .…”