Protonated methane, CH₅⁺, is the prototype of an extremely floppy molecule. To the best of our knowledge all barriers are surmountable in the rovibrational ground state; the large amount of zero-point vibrational energy leads to large amplitude motions for many degrees of freedom. Low resolution but broad band vibrational spectroscopy [1] revealed an extremely wide range of C-H stretching vibrations. Comparison with theoretical IR spectra supported the structural motif of a CH₃ tripod and an H₂ moiety, bound to the central carbon atom by a 3c2e bond. In a more dynamic picture the five protons surround the central carbon atom without significant restrictions on the H-C-H bending or H_n-C torsional motions. The large-amplitude internal motions preclude a simple theoretical description of the type possible for more conventional molecules, such as the related spherical-top methane molecule. Recent high-resolution ro-vibrational spectra obtained in cold ion trap experiments [2] show that the observed CH₅⁺ transitions belong to a very well-defined energy level scheme describing the lowest rotational and vibrational states of this enigmatic molecule. Here we analyse the experimental ground state combination differences and associate them with the motional states of CH₅⁺ allowed by Fermi-Dirac statistics. A model Hamiltonian for unrestricted internal rotations in CH₅⁺ yields a simple analytical expression for the energy eigenvalues, expressed in terms of new quantum numbers describing the free internal rotation. These results are compared to the experimental combination differences and the validity of the model will be discussed together with the underlying assumptions. [1] O. Asvany, P. Kumar, I. Hegemann, B. Redlich, S. Schlemmer and D. Marx, Science 309, (2005) 1219-1222 [2] O. Asvany, K.M.T. Yamada, S. Brünken, A. Potapov, S. Schlemmer, Science 347 (2015) 1346-1349

Protonated methane CH₅⁺ is unique: It is an extremely fluxional molecule. All attempts to assign quantum numbers to the high-resolution transitions obtained over the last 20 years have failed because molecular rotation and vibration cannot be separated in the conventional waySchmiedt, H., et al.; J. Chem. Phys. 143 (15), 154302 (2015)Wodraszka, R. et al.; J. Phys. Chem. Lett. 6, 4229-4232 (2015). The first step towards a theoretical description is to include internal rotational degrees of freedom into the overall ones, which can be used to formulate a fundamentally new zero order approximation for the (now) generalized rotational states and energies. Predictions from this simple five-dimensional rotor model compare very favorably with the combination differences of protonated methane found in recent low temperature experimentsAsvany, O. et al.; Science, 347, (6228), 1346-1349 (2015) This talk will focus on symmetry aspects and implications of permutation symmetry for the generalized rotational states. Furthermore, refinements of the theory will be discussed, ranging from the generalization to even higher-dimensional rotors to explicit symmetry breaking and corresponding energy splittings. The latter includes the link to well-known theories of internal rotation dynamics and will show the general validity of the presented theory.

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Footnotes:

Schmiedt, H., et al.; J. Chem. Phys. 143 (15), 154302 (2015)

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Footnotes:

Asvany, O. et al.; Science, 347, (6228), 1346-1349 (2015).

In this talk we present the first steps in the design of an effective Hamiltonian for the vibration-rotation energy levels of CH₅⁺. Such a Hamiltonian would allow calculation of energy level patterns anywhere along the path travelled by a hypothetical CH₅⁺ (or CD₅⁺) molecule as it passes through various coupling cases, and might thus provide some hints for assigning the observed high-resolution spectra. The steps discussed here, which have not yet addressed computational problems, focus on mapping the vibration-rotation problem in CH₅⁺ onto the five-electron problem in the boron atom, using ideas and mathematical machinery from Condon and Shortley’s book on atomic spectroscopy. The mapping ideas are divided into: (i) a mapping of particles, (ii) a mapping of coordinates (i.e., mathematical degrees of freedom), and (iii) a mapping of quantum mechanical interaction terms. The various coupling cases along the path correspond conceptually to: (i) the analog of a free-rotor limit, where the H atoms see the central C atom but do not see each other, (ii) the low-barrier and high-barrier tunneling regimes, and (iii) the rigid-molecule limit, where the H atoms remain locked in some fixed molecular geometry. Since the mappings considered here often involve significant changes in mathematics, a number of interesting qualitative changes occur in the basic ideas when passing from B to CH₅⁺, particularly in discussions of: (i) antisymmetrization and symmetrization ideas, (ii) n,l,m_l,m_s or n,l,j,m_j quantum numbers, and (iii) Russell-Saunders computations and energy level patterns. Some of the mappings from B to CH₅⁺ to be discussed are as follows. Particles: the atomic nucleus is replaced by the C atom, the electrons are replaced by protons, and the empty space between particles is replaced by an “electron soup.” Coordinates: the radial coordinates of the electrons map onto the five local C-H stretching modes, the angular coordinates of the electrons map onto three rotational degrees of freedom and seven bending vibrational degrees of freedom. The half-integral electron spins map onto half-integral proton spins or onto integral deuterium spins (for CD₅⁺). Interactions: the Coulomb attraction between nucleus and electrons maps onto a Morse-oscillator C-H stretching potential, spin-orbit interaction maps onto proton-spin-overall-rotation interaction, and Coulomb repulsion between electrons maps onto some kind of proton repulsion that leads to the equilibrium geometry.

H₅⁺ has been proposed to be the intermediate of the astrochemically interesting proton transfer reaction H₃⁺ + H₂ → H₂ + H₃⁺. The scrambling of five protons in this floppy, "structureless" ion introduces complications to its high-resolution rovibrational spectroscopy and the proton transfer dynamics between H₃⁺ and H₂. Quantum chemical studies are performed to predict and interpret the spectroscopic and dynamical properties of H₅⁺, with special consideration paid to the group theoretical aspects. If the full permutation of protons were allowed in H₅⁺, just like in CH₅⁺, the system should have been characterized by the G₂₄₀ complete permutation-inversion group. X.-G. Wang and T. Carrington Jr., J. Chem. Phys., 129, 234102 (2008). However, our diffusion Monte Carlo calculations indicate that such a full permutation is not allowed for most of the molecular configurations sampled by the reaction path of the proton transfer process in question, and the energetically accessible permutations are functions of the distance between the H₃⁺ and H₂ fragments.Z. Lin and A. B. McCoy, J. Phys. Chem. A, 119, 12109 (2015).In the present study, we investigate two extreme geometries of H₅⁺, the [H₂-H-H₂]⁺ shared-proton intermediate and the H₃⁺… H₂ long-range complex, using two subgroups of G₂₄₀, G₁₆ and G₂₄, respectively. In these two limiting circumstances, we derive the symmetry-adapted basis functions for the energy levels that describe the nuclear spins and the rovibrational motions of H₅⁺. Based on the results of these derivations, we discuss the spectroscopic properties of H₅⁺, including the coupling between different rovibrational degrees of freedom in the effective nuclear motion Hamiltonian, the electric-dipole selection rules for rovibrational spectroscopy, and correlations of energy levels between [H₂-H-H₂]⁺ and H₃⁺… H₂. Our study can be considered as the first step towards the implementation of future quantitative theoretical investigations for comparison with spectroscopic and dynamical experiments. Z. Lin, submitted to J. Mol. Spec.

Footnotes:

X.-G. Wang and T. Carrington Jr., J. Chem. Phys., 129, 234102 (2008). Z. Lin and A. B. McCoy, J. Phys. Chem. A, 119, 12109 (2015). Z. Lin, submitted to J. Mol. Spec.

In the CH₄ − F⁻ complex, an adiabatic separation of the CH stretch frequencies from the CH₄ orientational coordinates allows the calculation of the four adiabatic CH stretch surfaces. These ab initio calculations reveal (i) a large variation of CH stretch frequencies ( 100 cm⁻¹) in the orientational space and (ii) the existence of four symmetrically equivalent sets of vibrational conical intersections (CIs). Two sets of symmetry-allowed CIs are identified in addition to the symmetry-required CIs at the front- and back-side C_3v geometries. These results have implications for the evolution of excited CH vibrations in methane during its approach to a potentially reactive surface.

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the energy levels and wave functions of the potential energy surface.

Transition state theory is central to our understanding of chemical reaction dynamics. We demonstrate here a method for extracting transition state energies and properties from a characteristic pattern found in frequency domain spectra of isomerizing systems. This pattern, a dip in the spacings of certain barrier-proximal vibrational levels, can be understood using the concept of effective frequency, ω^eff. The method is applied to the cis-trans conformational change in the S₁ state of C₂H₂ and the bond-breaking HCN-HNC isomerization. In both cases, the barrier heights derived from spectroscopic data agree extremely well with previous ab initio calculations. We also show that it is possible to distinguish between vibrational modes that are actively involved in the isomerization process and those that are passive bystanders. (This work has been published in J. H. Baraban, P. B. Changala, G. Ch. Mellau, J. F. Stanton, A. J. Merer, and R. W. Field. Spectroscopic characterization of isomerization transition states. Science, 350(6266):1338-1342, 2015.)

r0pt Figure The nature of the isomerization process that turns vinylidene into acetylene has been awaiting advances in experimental methods, to better define fractionation widths beyond those available in the seminal 1989 photoelectron spectrum measurement.K. M. Ervin, J. Ho, and W. C. Lineberger, J. Chem. Phys. 91, 5974 (1989). doi:10.1063/1.457415his has proven a challenge. The technique of velocity-map imaging (VMI) is one avenue of approach. Images of electrons photodetached from vinylidene negative-ions, at various wavelengths, 1064 nm shown, provide more detail, including unassigned structure, but only an incremental improvement in the instrument line width. Intriguingly, the VMIs demonstrate a mode dependent variation in the electron anisotropy. Most notable in the figure, the inner-ring transition clusters are discontinuously, more isotropic. Electron anisotropy may provide an alternative key to examine the character of vinylidene transitions, mediating the necessity for an extreme resolution measurement. Vibrational dependent anisotropy has previously been observed in diatomic photoelectron spectra, associated with the coupling of electronic and nuclear motions.M. van Duzor et al. J. Chem. Phys. 133, 174311 (2010). doi:10.1063/1.3493349html:<hr /><h3>Footnotes: K. M. Ervin, J. Ho, and W. C. Lineberger, J. Chem. Phys. 91, 5974 (1989). doi:10.1063/1.457415T M. van Duzor et al. J. Chem. Phys. 133, 174311 (2010). doi:10.1063/1.3493349

The concept of Quantum Monodromy (QM) provides a fresh insight into the structure of rovibrational levels in those flexible molecules for which a bending mode can carry the molecule through the linear configuration. To confirm the existence of QM in a molecule required the fruits of several strands of development: the formulation of the abstract mathematical concept of monodromy, including the exploration of its relevance to systems described by classical mechanics and its manifestation in quantum molecular applications; the development of the required spectroscopic technology and computer-aided assignment; and the development of a theoretical model to apply in fitting to the observed data. We present a timeline for each of these strands, converging in our initial confirmation of QM in NCNCS from pure rotational data alone.B. P. Winnewisser et al., Phys. Rev. Lett. 95, 243002 (2005).n that work a Generalised SemiRigid Bender (GSRB) Hamiltonian was fitted to the experimental rotational structure. Rovibrational energies calculated from the fitted GSRB parameters allowed us to construct an "Energy-Momentum" map and confirm the presence of QM in NCNCS. In further experimental work at the Canadian Light Source Synchrotron we have identified a network of transitions directly connecting the relevant energy levels and thereby have produced a refined Energy Momentum map for NCNCS from experimental measurements alone. This map extends from the ground vibrational level to well above the potential energy barrier, beautifully illustrating the characteristic signature of QM in a system uncomplicated by interaction with other vibrational modes.

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Footnotes:

B. P. Winnewisser et al., Phys. Rev. Lett. 95, 243002 (2005).I

r0pt Figure We use high Rydberg states to measure the properties of H₂⁺ and HD⁺ in the vicinity of their dissociation limits H⁺+H, H⁺+D and H+D⁺, with particular emphasis on quasibound rovibrational levels above the dissociation threshold of the X^{+ 2}Σ_g⁺ ground state. Although the existence of these quasibound levels has been predicted a long time ago, they have never been observed. Positions and widths of the lowest resonances have not been calculated either. Given the role that such states play in the three-body and radiative recombination of H(1s) and H⁺ to form H₂⁺, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels (shape resonances) of H₂⁺, located close to the top of the centrifugal barriers and which decay by quantum-mechanical tunneling. For HD⁺ we present measurements of rovibrational levels of the A^{+ 2}Σ_u⁺ state, located between the two dissociation limits. Because of the g-u-symmetry breaking in HD⁺, these levels are coupled to the H⁺+D continuum by nonadiabatic interactions (Feshbach resonances). The experimental results will be compared with the positions and widths we calculate for these levels using a potential model for the X⁺ and the A⁺ state of H₂⁺ and HD⁺ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer potential energies.

The state-of-the-art empirical potential, and the state-of-the-art ab initio potential for the b(1³Π_2u) state of ^7,7Li₂ agree with each other that the (v=100,J=0) ro-vibrational state has an outer classical turning point larger than the diameter of most bacteria and many animal cells. The 2015 empirical potentialDattani (2015) http://arxiv.org/abs/1508.07184v1ased on a significant amount of spectroscopic data, predicts the (v=100,J=0) level to be bound by only 0.000 000 000 004 cm⁻¹ ( 0.2 Hz). The outer turning point of the vibrational wavefunction is about 671 000 Å  or 0.07 mm. Here, the two Li atoms are bound to each other, despite being nearly as far apart as the lines on a macroscopic ruler. The 2014 ab initio calculation based on a powerful Fock space MRCC methodMusial & Kucharski (2014) Journal of Chemical Theory and Computation, 10, 1200.nd with the long-range tail anchored by C₃^7Li/r³ with the ultra-high precision 2015 value of C₃^7Li, has this same level bound by 0.000 000 000 1 cm⁻¹ ( 3 Hz), with an outer turning point of > 0.01 mm. While this discovery occurred during a study of Li₂, the b(1³Π_2u) states of heavier alkali diatomics are expected to have even larger amplitude vibrational states. While it might be tempting to call these very large molecules "Rydberg molecules", it is important to remember that this term is already used to describe highly excited electronic states whose energy levels follow a formula similar to that for the famous Rydberg series. The highly delocalized vibrational states are a truly unfamiliar phenomenon.

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Footnotes:

Dattani (2015) http://arxiv.org/abs/1508.07184v1b Musial & Kucharski (2014) Journal of Chemical Theory and Computation, 10, 1200.a

r0pt Figure A potential energy surface (PES) is a fundamental tool and source of understanding for theoretical spectroscopy and for dynamical simulations. Making correct assignments for high-resolution rovibrational spectra of floppy polyatomic and van der Waals molecules often relies heavily on predictions generated from a high quality ab initio potential energy surface. Moreover, having an effective analytic model to represent such surfaces can be as important as the ab initio results themselves. For the one-dimensional potentials of diatomic molecules, the most successful such model to date is arguably the "Morse/Long-Range" (MLR) function developed by R. J. Le Roy and coworkers.Mol. Phys. 105, 663 (2007); J. Chem. Phys. 131, 204309 (2009); Mol. Phys. 109, 435 (2011).t is very flexible, is everywhere differentiable to all orders. It incorporates correct predicted long-range behaviour, extrapolates sensibly at both large and small distances, and two of its defining parameters are always the physically meaningful well depth D_e and equilibrium distance r_e. Extensions of this model, called the Multi-Dimension Morse/Long-Range (MD-MLR) function, have been applied successfully to atom-plus-linear molecule, linear molecule-linear molecule and atom-non-linear molecule systems.Phys. Chem. Chem. Phys. 10, 4128 (2008); J. Chem. Phys. 130, 144305 (2009); J. Chem. Phys. 132, 214309 (2010); J. Chem. Phys. 140, 214309 (2014); J. Chem. Phys. 144, 014301 (2016).owever, there are several technical challenges faced in modelling the interactions of general molecule-molecule systems, such as the absence of radial minima for some relative alignments, difficulties in fitting short-range potential energies, and challenges in determining relative-orientation dependent long-range coefficients. This talk will illustrate some of these challenges and describe our ongoing work in addressing them.

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Footnotes:

Mol. Phys. 105, 663 (2007); J. Chem. Phys. 131, 204309 (2009); Mol. Phys. 109, 435 (2011).I Phys. Chem. Chem. Phys. 10, 4128 (2008); J. Chem. Phys. 130, 144305 (2009); J. Chem. Phys. 132, 214309 (2010); J. Chem. Phys. 140, 214309 (2014); J. Chem. Phys. 144, 014301 (2016).H

The binary complex of rare gas atom and water is an ideal model to study the anisotropic potential energy surface of van der Waals interaction and the large amplitude motion. Although Xe-H₂O, Kr-H₂O, Ar-H₂O, Ar-D₂O and even Ne-D₂O complexes were studied by microwave or high resolution infrared spectroscopy, the lighter Ne-H₂O complex has remained unidentified. In this talk, we will present the theoretical and experimental investigation of the Ne-H₂O complex. A four-dimension PES for H₂O-Ne which only depended on the intramolecular (Q2) normal-mode coordinate of H2O monomer was calculated in this work to determine the rovibrational energy levels and mid-infrared transitions. Aided with the calculated transitions, we were able to assigned the high resolution mid-infrared spectra of both ²⁰Ne-H₂O and ²²Ne-H₂O complexes that are generated with a pulsed supersonic molecular beam in a multipass direct absorption spectrometer equiped with an external cavity quantum cascade laser at 6 μm. Several bands of both para and ortho Ne-H2O were assigned and fitted using the Hamiltonian with strong Coriolis and angular-radical coupling terms. The predicted groud state energy levels are then confirmed by the J=1-0 and J=2-1 transitions measurement using a cavity based Fourier transform microwave spectrometer.