Communication: Rigidity of the molecular ion ${\rm H}_5^+$H5+

Abstract

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.

Rotation/Torsion Coupling in H5+, D5+, H4D+, and HD4+ Using Diffusion Monte Carlo

“…Finally, in both cases, (9) where V represents the ensemble average of the potential energy and W tot (τ) provides the sum of the weights of the walkers at that time. The second term in the expression for E ref adjusts the value of E ref to ensure that the value of W tot is roughly constant.…”

“…One of the first systems of this type to be investigated spectroscopically was dimethylacetylene. 7,8 Other molecules and molecular ions with similarly low-energy torsion barriers include H 5 + , 9,15,16 CH 5 + , 10,17 and the NH 4 + ·(H 2 O) complex. 12,13 In studying systems that contain a large amplitude internal rotor, it is common to develop an effective Hamiltonian that treats the torsion as a fourth rotational coordinate:…”

Modelling rotations, vibrations, and rovibrational couplings in astructural molecules – a case study based on the H+5 molecular ion

“…Considerable attention has been placed in developing such model Hamiltonians for molecules like methanol, that include a large-amplitude internal rotor [19][20][21], as well as for molecules that contain virtually no barrier to internal rotation [22,23]. As to the spectra of these molecules, the small barriers lead to rotation/vibration structure that deviates substantially from the RRHO model and from those used to describe semirigid molecules, and to very surprising rotational structures [18,24,25].…”

“…An example of such an astructural molecule, and one which recently attracted considerable experimental and theoretical attention [18,[26][27][28][29][30][31], is H + 5 . This molecular ion with five hydrogen atoms lacks the usual central atom that can form multiple strong bonds, which is typical of virtually all other small molecular species.…”

“…There is a special class of molecules where the simple RRHO picture as well as its low-order PT corrections [1] provide an incorrect zeroth-order description and one must consider new models with 'unusual' characteristics to understand the high-resolution spectra of these molecules even at very low excitation energies. We call these molecules astructural [18].…”