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Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the H$_3^+$ molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of H$_3^+$ and other polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.

Full-dimensional (12D) vibrational states of the methanol molecule (CH$_3$OH) have been computed using the GENIUSH-Smolyak approach and the potential energy surface from Qu and Bowman (2013). All vibrational energies are converged better than 0.5 cm$^{-1}$ with respect to the basis and grid size up to the first overtone of the CO stretch, ca. 2000 cm$^{-1}$ beyond the zero-point vibrational energy. About seventy torsion-vibration states are reported and assigned. The computed vibrational energies agree with the available experimental data within less than a few cm$^{-1}$ in most cases, which confirms the good accuracy of the potential energy surface. The computations are carried out using curvilinear normal coordinates with the option of path-following coefficients which minimize the coupling of the small- and large-amplitude motions. It is important to ensure tight numerical fulfilment of the $C_{3\mathrm{v}}$(M) molecular symmetry for every geometry and coefficient set used to define the curvilinear normal coordinates along the torsional coordinate to obtain a faithful description of degeneracy in this floppy system. The reported values may provide a computational reference for fundamental spectroscopy, astrochemistry, and for the search of the proton-to-electron mass ratio variation using the methanol molecule.

Benchmark-quality rovibrational data are reported for the methane dimer from variational nuclear motion computations using an ab initio intermolecular potential energy surface reported by [M. P. Metz et al., Phys. Chem. Chem. Phys., 2019, 21, 13504-13525]. A simple polarizability model is used to compute Raman transition moments that may be relevant for future direct observation of the intermolecular dynamics. Non-negligible $\Delta K\neq 0$ transition moments arise in this symmetric top system due to strong rovibrational couplings.

All vibrational energies of the (trans-, cis-, delocalized-) formic acid molecule are converged up to 4500 cm$^{-1}$ beyond the zero-point vibrational energy with the GENIUSH-Smolyak variational approach and using an ab initio potential energy surface [D. P. Tew and W. Mizukami, J. Phys. Chem. A, 120, 9815-9828 (2016)]. Full-dimensional dipole and polarizability surfaces are fitted to points computed at the CCSD/aug-cc-pVTZ level of theory. Then, body-fixed vibrational dipole and polarizability transition moments are evaluated and used to simulate jet-cooled infrared and Raman spectra of HCOOH. The benchmark-quality vibrational energy, transition moment, and wave function list will be used in further work in comparison with vibrational experiments, and in further rovibrational computations.

Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over surfaces are important types of molecular motions. Their fundamentally correct and detailed description can be obtained by solving the nuclear Schr\"odinger equation on a potential energy surface. Many of the chemically interesting processes involve quantum nuclear motions which are `delocalized' over multiple potential energy wells. These `large-amplitude' motions in addition to the high dimensionality of the vibrational problem represent challenges to the current (ro)vibrational methodology. A review of the quantum nuclear motion methodology is provided, current bottlenecks of solving the nuclear Schr\"odinger equation are identified, and solution strategies are reviewed. Technical details, computational results, and analysis of these results in terms of limiting models and spectroscopically relevant concepts are highlighted for selected numerical examples.

The automated development of a new ab initio full-dimensional potential energy surface (PES) is reported for the CH$_4\cdot$F$^-$ complex using the ROBOSURFER program package. The new potential provides a near-spectroscopic quality description over a broad configuration range including the methane-ion dissociation, as well as isolated methane vibrations. In particular, it improves upon the earlier [Czak\'o, Braams, Bowman (2008)] PES over intermediate methane-fluoride distances. Full-dimensional (12D) variational vibrational computations using the new PES and the GENIUSH-Smolyak algorithm show that tunneling splittings larger than 0.1 cm$^{-1}$ appear below the top of the interconversion barrier of the four equivalent minima of the complex.

Vibrational states of the formic acid molecule are converged using the GENIUSH-Smolyak approach and the potential energy surface taken from [D. Tew and W. Mizukami, J. Phys. Chem. A 120, 9815 (2016)]. The quantum nuclear motion is described by using the $cis$-$trans$ torsional coordinate and eight curvilinear normal coordinates defined with respect to an instantaneous reference configuration changing as a function of the torsional degree of freedom. Harmonic oscillator basis functions are used for the curvilinear normal coordinates, a Fourier basis for the torsional coordinate, and a simple basis pruning condition is combined with a Smolyak integration grid. $Trans$, $cis$, and $delocalized$ vibrational states are reported up to and slightly beyond the isomerization barrier.

The present work intends to join and respond to the excellent and thoroughly documented rovibrational study of [X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 154, 124112 (2021)] that used an approach tailored for floppy dimers with an analytic dimer Hamiltonian and a non-product basis set including Wigner $D$ functions. It is shown in the present work that the GENIUSH black-box-type rovibrational method can approach the performance of the tailor-made computation for the example of the floppy methane-water dimer. Rovibrational transition energies and intensities are obtained in the black-box-type computation with `only' 2-3 times larger basis set sizes and in an excellent numerical agreement in comparison with the more efficient tailor-made approach.

Curvilinear kinetic energy models are developed for variational nuclear motion computations including the inter- and the low-frequency intra-molecular degrees of freedom of the formic acid dimer. The coupling of the inter- and intra-molecular modes is studied by solving the vibrational Schr\"odinger equation for a series of vibrational models, from two up to ten active vibrational degrees of freedom by selecting various combinations of active modes and constrained coordinate values. Vibrational states, nodal assignment, and infrared vibrational intensity information is computed using the the full-dimensional potential energy surface (PES) and electric dipole moment surface developed by Qu and Bowman [Phys. Chem. Chem. Phys. 18, 24835 (2016); J. Chem. Phys. 148, 241713 (2018)]. Good results are obtained for several fundamental and combination bands in comparison with with jet-cooled vibrational spectroscopy experiments, but the description of the $\nu_8$ and $\nu_9$ fundamental vibrations, which are close in energy and have the same symmetry, appears to be problematic. For further progress in comparison with experiment, the potential energy surface, and in particular, its multi-dimensional couplings representation, requires further improvement.

A full-dimensional \emph{ab initio} potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methane-argon complex using the GENIUSH computer program and the Smolyak sparse grid method. The full-dimensional computations make it possible to study fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly-bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm$^{-1}$ root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the $\langle r \rangle_0$ methane structure. Allowing 10 basis functions for the methane fragment, the rms of the bound state vibrational energies is reduced to 0.07 cm$^{-1}$, which is much better than the 3D models. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens the route for the study of the role of dispersion forces on the excited methane vibrations and the energy transfer from the intra- to the intermolecular vibrational modes.

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.

Methodological progress is reported in the challenging direction of a black-box-type variational solution of the (ro)vibrational Schr\"odinger equation applicable to floppy, polyatomic systems with multiple large-amplitude motions. This progress is achieved through the combination of (i) the numerical kinetic-energy operator (KEO) approach of [E. M\'atyus, G. Czak\'o, and A. G. Cs\'asz\'ar, J. Chem. Phys. 130, 134112 (2009)] and (ii) the Smolyak non-product grid method of [G. Avila and T. Carrington, Jr., J. Chem. Phys. 131, 174103 (2009)]. The numerical representation of the KEO makes it possible to choose internal coordinates and a body-fixed frame best suited for the molecular system. The Smolyak scheme reduces the size of the direct-product grid representation by orders of magnitude, while retaining some of the useful features of it. As a result, multi-dimensional (ro)vibrational states are computed with system-adapted coordinates, a compact basis- and grid-representation, and an iterative eigensolver. Details of the methodological developments and the first numerical applications are presented for the CH$_4\cdot$Ar complex treated in full (12D) vibrational dimensionality.