Toward Automated Variational Computation of Rovibrational Resonances, Including a Case Study of the H2 Dimer

Room temperature detection of the (H2)2 dimer

The hydrogen dimer, (H2)2, is among the most weakly bound van der Waals complexes and a prototype species for first principles ab initio studies. The detection of the (H2)2 infrared absorption spectrum was reported more than sixty years ago at a temperature of 20 K. Due to the sharp decrease of the (H2)2 abundance with temperature, detection at room temperature was generally considered hardly achievable. Here we report the first room temperature detection of partly resolved rotational structures of (H2)2 by cavity ring down spectroscopy at sub-atmospheric pressures, in the region of the first overtone band of H2 near 1.2 μm. The quantitative analysis of the absorption features observed around ten allowed or forbidden transition frequencies of the monomer provides insight on the structure of this elusive species and a benchmark for future theoretical studies.

Vibrational Raman Shifts of Spin Isomer Combinations of Hydrogen Dimers and Isotopologues

Binding energies for para-para, ortho-para, and ortho-ortho hydrogen dimers (H₂)₂ are calculated using the six-dimensional (6D) interaction potential developed by Hinde [ J. Chem. Phys. 2008, 128, 154308]. The eigenstates of the dimers are computed by diagonalization using, as a basis, products of the rovibrational states of the monomers, a radial grid for the distance between the monomers, and spherical harmonics for the end-over-end rotation of the dimer. We describe the overall nuclear spin symmetry and use these properties to determine the relative population of various states, making use of a Boltzmann factor for each spin isomer to assess the effect of temperature. A predicted Raman spectrum in the Q(0) and Q(1) region of the hydrogen dimer is produced. To assess the accuracy of our model, we verify our produced shifts with experimental results obtained previously by Montero et al. [ Eur. Phys. J. D 2009, 52, 31-34] and find good agreement. These results are extended to other cases involving the deuterium (D₂)₂ and tritium dimer (T₂)₂ isotopologues, to predict Raman shifts.

Rotational-vibrational resonance states

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational-vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational-vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational-vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L², square integrable) or non-Hermitian (non-L²) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational-vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational-vibrational resonances of polyatomic molecular systems.

Full-dimensional (12D) variational vibrational states of CH4·F-: Interplay of anharmonicity and tunneling

The complex of a methane molecule and a fluoride anion represents a 12-dimensional (12D), four-well vibrational problem with multiple large-amplitude motions, which has challenged the quantum dynamics community for years. The present work reports vibrational band origins and tunneling splittings obtained in a full-dimensional variational vibrational computation using the GENIUSH program and the Smolyak quadrature scheme. The converged 12D vibrational band origins and tunneling splittings confirm complementary aspects of the earlier full- and reduced-dimensionality studies: (1) the tunneling splittings are smaller than 0.02 cm^-1; (2) a single-well treatment is not sufficient (except perhaps the zero-point vibration) due to a significant anharmonicity over the wells; and thus, (3) a full-dimensional treatment appears to be necessary. The present computations extend to a higher energy range than earlier work, show that the tunneling splittings increase upon vibrational excitation of the complex, and indicate non-negligible "heavy-atom" tunneling.