Jahn-Teller effect in tetrahedral symmetry: Large-amplitude tunneling motion and rovibronic structure of CH4+ and CD4+

Few-femtosecond electronic and structural rearrangements of CH4+ driven by the Jahn-Teller effect

The Jahn-Teller effect (JTE) is central to the understanding of the physical and chemical properties of a broad variety of molecules and materials. Whereas the manifestations of the JTE in stationary properties of matter are relatively well studied, the study of JTE-induced dynamics is still in its infancy, largely owing to its ultrafast and non-adiabatic nature. For example, the time scales reported for the distortion of CH 4 + from the initial T d geometry to a nominal C 2 v relaxed structure range from 1.85 fs over 10 ± 2 fs to 20 ± 7 fs. Here, by combining element-specific attosecond transient-absorption spectroscopy and quantum-dynamics simulations, we show that the initial electronic relaxation occurs within 5 fs and that the subsequent nuclear dynamics are dominated by the Q2 scissoring and Q1 symmetric stretching modes, which dephase in 41 ± 10 fs and 13 ± 3 fs, respectively. Significant structural relaxation is found to take place only along the e-symmetry Q2 mode. These results demonstrate that CH 4 + created by ionization of CH 4 is best thought of as a highly fluxional species that possesses a long-time-averaged vibrational distribution centered around a D 2 d structure. The methods demonstrated in our work provide guidelines for the understanding of Jahn-Teller driven non-adiabatic dynamics in other more complex systems.

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic level insight into photochemistry. Herein, we performed a time-resolved study of ultrafast molecular symmetry breaking via geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft X-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry broken cation, which were detected in the X-ray signal. These oscillations were damped within 58 ± 13 femtoseconds, as vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens new avenues for exploring complex systems.

Multipole-moment effects in ion-molecule reactions at low temperatures: part III - the He+ + CH4 and He+ + CD4 reactions at low collision energies and the effect of the charge-octupole interaction

We present experimental and theoretical studies of the He+ + CH4 and He+ + CD4 reactions at collision energies in the kB·(0-10) K range. Helium atoms in a supersonic beam are excited to a low-field-seeking Rydberg-Stark state and merged with a supersonic beam of CH4 or CD4 using a curved surface-electrode deflector. The ion-molecule reactions are studied within the orbit of the helium Rydberg [He(n)] electron, which suppresses stray-electric-fields-induced heating and makes it possible to reach very low collision energies. The collision energy is varied by adjusting the velocity of the He(n) atoms with the surface deflector, keeping the velocity of the methane beam constant. The reaction product ions (C(H/D)p+ with p∈ {1,2,3}) are collected in a time-of-flight mass spectrometer and monitored as a function of the collision energy. No significant energy-dependence of the total reaction yields of either reactions is observed. The measured relative reaction rate coefficient for the He+ + CH4 reaction is approximately twice higher than the one for the He+ + CD4 reaction. The CH+, CH2+ and CH3+ (CD+, CD2+ and CD3+) ions were detected in ratios 0.28(±0.04) : 1.00(±0.11) : 0.11(±0.04) [0.35(±0.07) : 1.00(±0.16):0.04+0.09-0.04]. We also present calculations of the capture rate coefficients for the two reactions, in which the interaction between the charge of the helium ion and the octupole moment of the methane molecule is included. The rotational-state-specific capture rate coefficients are calculated for states with J = (0-3) at collision energies below kB·15 K. After averaging over the rotational states of methane populated at the rotational temperature of the supersonic beam, the calculations only predict extremely weak enhancements (in the order of ∼0.4%) of the rate coefficients compared to the Langevin rate constant kL over the collision-energy range considered.

Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds

Models for the quick estimation of energy splittings caused by coherent tunneling of hydrogen atoms are evaluated with available experimental data for alcohols and improvements are proposed. The discussed models are mathematically simple and require only results from routine quantum chemical computations, i.e. hybrid DFT calculation of the equilibrium geometry and the transition state within the harmonic approximation. A benchmark of experimental splittings spanning four orders of magnitude for 27 alcohol species is captured by three evaluated models with a mean symmetric deviation factor of 1.7, 1.5 and 1.4, respectively, i.e. the calculated values deviate on average by this factor in either direction. Limitations of the models are explored with alcohols featuring uncommon properties, such as an inverted conformational energy sequence, a very light molecular frame, an elevated torsional frequency, or a coupling with a second internal degree of freedom. If the splitting of either the protiated or deuterated form of an alcohol is already experimentally determined, the one of the second isotopolog can be estimated by three additional models with a mean symmetric deviation factor of 1.14, 1.19 and 1.15, respectively. It is shown that this can be achieved with a novel approach without any quantum chemical calculation by directly correlating experimental splittings of isotopologs across related species. This is also demonstrated for other classes of compounds with hydrogen tunneling, such as amines, thiols, and phenols. Furthermore, it is found that the isotope effect can even be anticipated without any further knowledge about the system solely from the size of either splitting with a mean symmetric deviation factor of 1.3. This is based on an extensive sample of 77 pairs of splittings spanning eight orders of magnitude for isotopologs of chemically diverse compounds.

Ultrafast imaging of spontaneous symmetry breaking in a photoionized molecular system

The Jahn-Teller effect is an essential mechanism of spontaneous symmetry breaking in molecular and solid state systems, and has far-reaching consequences in many fields. Up to now, to directly image the onset of Jahn-Teller symmetry breaking remains unreached. Here we employ ultrafast ion-coincidence Coulomb explosion imaging with sub-10 fs resolution and unambiguously image the ultrafast dynamics of Jahn-Teller deformations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{CH}}}_{4}^{+}$$\end{document}CH4+ cation in symmetry space. It is unraveled that the Jahn-Teller deformation from C_3v to C_2v geometries takes a characteristic time of 20 ± 7 fs for this system. Classical and quantum molecular dynamics simulations agree well with the measurement, and reveal dynamics for the build-up of the C_2v structure involving complex revival process of multiple vibrational pathways of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{CH}}}_{4}^{+}$$\end{document}CH4+ cation.

The Jahn-Teller effect is the spontaneous symmetry breaking of the molecular structure caused by the coupling of electrons and nuclei. Here the authors use ultrafast Coulomb explosion imaging to map the evolution of the fundamental symmetry lowering process in photoionized methane within around 20fs.

Structure and dynamics of the radical cation of ethane arising from the Jahn-Teller and pseudo-Jahn-Teller effects

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of C₂H₆ has been recorded in the region of the adiabatic ionization threshold. The partially rotationally resolved spectrum indicates the existence of several vibronic states of C₂H₆⁺ with less than 600 cm^-1 of internal excitation. The analysis of the rotational structures assisted by ab initio calculations enabled the determination of the adiabatic ionization energy of C₂H₆ and the investigation of the structure and dynamics of C₂H₆⁺ at low energies. The ground state of C₂H₆⁺ is found to be a ²A_g state of diborane-like structure with strongly mixed (a_1g)^-1 and (e_g)^-1 configurations. The vibrational structure reveals the importance of large-amplitude nuclear motions involving the diborane distortion modes, the C-C stretching motion, and the internal rotation at elongated C-C distances. The spectrum is analyzed in the light of the information obtained in earlier studies of C₂H₆⁺ by ab initio quantum chemistry, EPR spectroscopy and photoelectron spectroscopy.

A vacuum ultraviolet laser pulsed field ionization-photoion study of methane (CH4): determination of the appearance energy of methylium from methane with unprecedented precision and the resulting impact on the bond dissociation energies of CH4and CH4+

High-resolution VUV laser PFI-PI detection method for the study of quantum-state-selected unimolecular ion dissociation.

Dissociative recombination of CH4(+)

CH4(+) is an important molecular ion in the astrochemistry of diffuse clouds, dense clouds, cometary comae, and planetary ionospheres. However, the rate of one of the common destruction mechanisms for molecular ions in these regions, dissociative recombination (DR), is somewhat uncertain. Here, we present absolute measurements for the DR of CH4(+) made using the heavy ion storage ring CRYRING in Stockholm, Sweden. From our collision-energy dependent cross-sections, we infer a thermal rate constant of k(Te) = 1.71(±0.02) × 10(–6)(Te/300)(−0.66(±0.02)) cm3 s(–1) over the region of electron temperatures 10 ≤ Te ≤ 1000 K. At low collision energies, we have measured the branching fractions of the DR products to be CH4 (0.00 ± 0.00); CH3 + H (0.18 ± 0.03); CH2 + 2H (0.51 ± 0.03); CH2 + H2 (0.06 ± 0.01); CH + H2 + H (0.23 ± 0.01); and CH + 2H2 (0.02 ± 0.01), indicating that two or more C–H bonds are broken in 80% of all collisions.

Jahn-Teller effects in molecular cations studied by photoelectron spectroscopy and group theory

The traditional "ball-and-stick" concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn-Teller (JT) effect which is very common in open-shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo-Jahn-Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of "antiaromaticity" are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential-energy surface are separated by substantial barriers.

Rovibronic analysis of the Jahn-Teller effect in CH2D2(+) at low energies

The Jahn-Teller effect in the ground state of CH(2)D(2)(+) has been studied by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy. The lowest three bands have been assigned to the three isomers CH([l])H([l])D(s)D(s)(+), CH([l])H(s)D([l])D(s)(+), and CH(s)H(s)D([l])D([l])(+), in which the deuterium atoms are attached to the central carbon atom by two short bonds, one short and one long bond, and two long bonds, respectively, and which have different zero-point vibrational energies. Whereas CH([l])H([l])D(s)D(s)(+) and CH(s)H(s)D([l])D([l])(+) can each be described by a single structure with C(2v) symmetry, CH([l])H(s)D([l])D(s)(+) corresponds to four equivalent C(1) structures that interconvert by tunneling. The rotational structure of these three bands is compared with predictions made on the basis of a tunneling Hamiltonian combined with a rotational Hamiltonian that incorporates the effects of the large-amplitude tunneling motion. The zero-point energies of CH([l])H(s)D([l])D(s)(+) and CH(s)H(s)D([l])D([l])(+) relative to that of CH([l])H([l])D(s)D(s)(+) are Delta = 123.6(5) cm(-1) and Delta(') = 243.2(5) cm(-1), respectively, and the tunneling matrix element sigma coupling the four C(2v) equilibrium structures of CH([l])H(s)D([l])D(s)(+) is -1.7(4) cm(-1).

Jahn-Teller effect in CH3D+ and CD3H+: Conformational isomerism, tunneling-rotation structure, and the location of conical intersections

High-resolution pulsed-field-ionization zero-kinetic-energy photoelectron spectra of CH(3)D and CD(3)H have been recorded at rotational resolution from the adiabatic ionization energy up to 600 cm(-1) of internal energy of the respective cations. The spectra are characterized by the effects of a large-amplitude pseudorotational motion exchanging the equivalent nuclei in each molecule. With increasing internal energy, a transition from the tunneling regime with splittings of the order of 1-10 cm(-1) to the free pseudorotation regime is observed. A theoretical model that treats the simultaneous rotational and pseudorotational motions and incorporates the effects of the geometric phase has been developed. The model provides the appropriate rovibronic symmetries in the C(3v)(M) molecular symmetry group and reaches a near-quantitative agreement with the experimental data. The complete group-theoretical analysis of the rovibronic problem is also given. The analysis of the spectra has revealed the existence of two different isomers for both CH(3)D(+) and CD(3)H(+), which differ in the bond length between the carbon atom and the unique ligand atom. All isomers are subject to a fast pseudorotational motion between three equivalent minima with a period of 3-5 ps in CH(3)D(+) and 18-28 ps in CD(3)H(+). The analysis has also provided the ordering of the tunneling sublevels for each isomer, which enables the location of the twofold conical intersections on the potential energy surface that could not be determined from experiments on CH(4) (+).