Effects of symmetry, methyl groups and serendipity on intramolecular vibrational energy dispersal.

We consider two key parameters that have been proposed to be important for vibrational energy delocalization, closely related to intramolecular vibrational redistribution (IVR), in molecules. These parameters are the symmetry of the molecule, and the presence of torsional (internal rotor) modes of a methyl group. We consider four para-disubstituted benzene molecules and examine their vibrational character. The molecules selected are para-difluorobenzene, para-chlorofluorobenzene, para-fluorotoluene, and para-xylene. This set of molecules allows the above parameters to be assessed in a systematic way. The probe we use is zero-electron-kinetic-energy (ZEKE) spectroscopy, which is employed in a resonant scheme, where the intermediate levels are selected vibrational levels of the S1 excited electronic state, with wavenumbers up to 1300 cm-1. We conclude that symmetry, and the presence of a methyl groups, do indeed have a profound effect on "restricted" IVR at low energies. This is underpinned by serendipitous coincidences in the energies of the levels, owing to small shifts in vibrational wavenumbers between molecules, so bringing levels into resonance. Additionally, methyl groups play an important role in opening up new routes for coupling between vibrations of different symmetry, and this is critical in the transition to "statistical" IVR at lower energies for molecules that contain them. Further, the presence of two methyl groups in the symmetrically-substituted p-xylene causes more widespread IVR than does the single methyl group in the asymmetrically-substituted p-fluorotoluene.

Identification of separate isoenergetic routes for vibrational energy flow in p-fluorotoluene.

A deceptively simple feature in the S1 ← S0 spectrum of p-fluorotoluene (pFT), 1013 cm-1 above the origin, is studied using both zero-electron-kinetic-energy (ZEKE) and two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy. It is found to consist of a cornucopia of overlapped transitions to eigenstates that arise from numerous interacting levels. A significant variation in the activity is seen employing both the ZEKE and 2D-LIF techniques. Detailed insight into the complicated spectra can be achieved, owing to the large number of vibrational wavenumbers that have been previously determined for the S0, S1, and D0 + states, summarized herein. It is found that the activity is dominated by two overtones, which are individually interacting with other levels, so providing largely independent routes for vibrational energy flow at the same internal energy. Additionally, other weak features located 900-1050 cm-1 above the origin are examined.

Complexity surrounding an apparently simple Fermi resonance in p-fluorotoluene revealed using two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy.

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is a powerful tool allowing overlapped features in an electronic spectrum to be separated, and interactions between vibrations and torsions to be identified. Here the technique is employed to assign the 790-825 cm-1 region above the origin of the S1 ← S0 transition in para-fluorotoluene, which provides insight into the unusual time-resolved results of Davies and Reid [Phys. Rev. Lett. 109, 193004 (2012)]. The region is dominated by a pair of bands that arise from a Fermi resonance; however, the assignment is complicated by contributions from a number of overtones and combinations, including vibration-torsion ("vibtor") levels. The activity in the 2D-LIF spectra is compared to the recently reported zero-electron-kinetic-energy spectra [Tuttle et al., J. Chem. Phys. 146, 244310 (2017)] to arrive at a consistent picture of the energy levels in this region of the spectrum.

Interactions of C+(2PJ ) with rare gas atoms: incipient chemical interactions, potentials and transport coefficients.

Accurate interatomic potentials were calculated for the interaction of a singly charged carbon cation, C+, with a single rare gas atom, RG (RG = Ne-Xe). The RCCSD(T) method and basis sets of quadruple-ζ and quintuple-ζ quality were employed; each interaction energy was counterpoise corrected and extrapolated to the basis set limit. The lowest C+(2P) electronic term of the carbon cation was considered, and the interatomic potentials calculated for the diatomic terms that arise from these: 2Π and 2Σ+ Additionally, the interatomic potentials for the respective spin-orbit levels were calculated, and the effect on the spectroscopic parameters was examined. In doing this, anomalously large spin-orbit splittings for RG = Ar-Xe were found, and this was investigated using multi-reference configuration interaction calculations. The latter indicated a small amount of RG → C+ electron transfer and this was used to rationalize the observations. This is taken as evidence of an incipient chemical interaction, which was also examined via contour plots, Birge-Sponer plots and various population analyses across the C+-RG series (RG = He-Xe), with the latter showing unexpected results. Trends in several spectroscopic parameters were examined as a function of the increasing atomic number of the RG atom. Finally, each set of RCCSD(T) potentials was employed, including spin-orbit coupling to calculate the transport coefficients for C+ in RG, and the results were compared with the limited available data.This article is part of the theme issue 'Modern theoretical chemistry'.

Vibrations of the p-chlorofluorobenzene cation.

The vibrations of the ground state cation (X[combining tilde]2B1) of para-chlorofluorobenzene (pClFB) have been investigated using zero-electron-kinetic-energy (ZEKE) spectroscopy. ZEKE spectra were recorded using different vibrational levels of the S1 state as intermediate levels, for which assignments were put forward in an earlier paper [W. D. Tuttle, A. M. Gardner, and T. G. Wright, Chem. Phys. Lett., 2017, 684, 339]. These different intermediate levels dramatically modify the Franck-Condon factors for the ionization step. The adiabatic ionization energy (AIE) for pClFB was measured as 72 919 ± 5 cm-1, and analysis of the vibrational structure in the ZEKE spectra allowed further interrogation of the assignments of the REMPI spectrum. Assignment of the vibrational structure has been achieved by comparison with corresponding spectra of related molecules, via quantum chemical calculations, and via shifts in bands between the spectra of the 35Cl and 37Cl isotopologues. In this way it was possible to assign twenty out of the thirty vibrational modes of the ground state pClFB+ cation. Additionally, evidence for Fermi resonances between some vibrational levels was found in the S1 state, but no large-scale intramolecular vibrational redistribution (IVR) was seen in the spectra here. Finally, we discuss trends in AIE shifts for benzenes with one or two halogen atoms or methyl substituents.

Hybridization and Covalency in the Group 2 and Group 12 Metal Cation/Rare Gas Complexes.

We provide a consistent set of interaction energy curves for the group 2 (IIA) and group 12 (IIB) metal cation/rare gas complexes, M+-RG, where M+ = Be+-Ra+ and Zn+-Hg+ and RG = He-Rn. We report spectroscopic constants derived from these, compare them with available data, and discuss trends in the values. We gain insight into the interactions that occur using a range of approaches: reduced potential energy curves; charge and population analyses; molecular orbital diagrams and contour plots; and Birge-Sponer plots. Although sp hybridization occurs in the Be+-RG, Mg+-RG and group 12 M+-RG complexes, this appears to be minimal and covalency is the main aspect of the interaction. However, major sd hybridization occurs in the heavier group 2 M+-RG systems, which increases their interaction energies but there is minimal covalency. Examination of Birge-Sponer plots reveals significant curvature in many cases, which we ascribe to the changing amounts of hybridization or covalency as a function of internuclear separation. This suggests why the use of a simple electrostatics-based model potential to describe the interactions is inadequate.

Identifying complex Fermi resonances in p-difluorobenzene using zero-electron-kinetic-energy (ZEKE) spectroscopy.

The vibrations of the ground state cation ( X̃2B2g) of para-difluorobenzene (pDFB) have been investigated using zero-electron-kinetic-energy (ZEKE) spectroscopy. A comprehensive set of ZEKE spectra were recorded via different vibrational levels of the S1 state (<00 + 1300 cm-1). The adiabatic ionization energy for pDFB was measured as 73 869 ± 5 cm-1. Use of different intermediate levels allows different cationic vibrational activity to be obtained via the modification of the Franck-Condon factors for the ionization step, allowing the wavenumbers of different vibrational levels in the cation to be established. In addition, assignment of the vibrational structure in the ZEKE spectra allowed interrogation of the assignments of the S1 ← S0 transition put forward by Knight and Kable [J. Chem. Phys. 89, 7139 (1988)]. Assignment of the vibrational structure has been aided by quantum chemical calculations. In this way, it was possible to assign seventeen of the thirty vibrational modes of the ground state pDFB+ cation. Evidence for complex Fermi resonances in the S1 state, i.e., those that involve more than two vibrations, was established. One of these was investigated using picosecond time-resolved photoelectron spectroscopy. In addition, we discuss the appearance of several symmetry-forbidden bands in the ZEKE spectra, attributing their appearance to a Rydberg state variation of an intrachannel vibronic coupling mechanism.

Molecular symmetry group analysis of the low-wavenumber torsions and vibration-torsions in the S1 state and ground state cation of p-xylene: An investigation using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy.

For the first time, a molecular symmetry group (MSG) analysis has been undertaken in the investigation of the electronic spectroscopy of p-xylene (p-dimethylbenzene). Torsional and vibration-torsional (vibtor) levels in the S1 state and ground state of the cation of p-xylene are investigated using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the present work, we concentrate on the 0-350 cm-1 region, where there are a number of torsional and vibtor bands and we discuss the assignment of this region. In Paper II [W. D. Tuttle et al., J. Chem. Phys. 146, 124309 (2017)], we examine the 350-600 cm-1 region where vibtor levels are observed as part of a Fermi resonance. The similarity of much of the observed spectral activity to that in the related substituted benzenes, toluene and para-fluorotoluene, is striking, despite the different symmetries. The discussion necessitates a consideration of the MSG of p-xylene, which has been designated G72, but we shall also designate [{3,3}]D2h and we include the symmetry operations, character table, and direct product table for this. We also discuss the symmetries of the internal rotor (torsional) levels and the selection rules for the particular electronic transition of p-xylene investigated here.

Vibration and vibration-torsion levels of the S1 state of para-fluorotoluene in the 580-830 cm-1 range: Interactions and coincidences.

A study of the vibration and vibration-torsion levels of para-fluorotoluene in the 580-830 cm-1 region is presented, where a number of features are located whose identity is complicated by interactions and overlap. We examine this region with a view to ascertaining the assignments of the bands; in particular, identifying those that arise from interactions involving various zero-order states (ZOSs) involving both vibrations and torsions. Resonance-enhanced multiphoton ionization (REMPI) is employed to identify the wavenumbers of the relevant transitions, and subsequently zero-kinetic-energy (ZEKE) spectra are recorded to assign the various eigenstates. In some cases, a set of ZEKE spectra are recorded across the wavenumber range of a REMPI feature, and we construct what we term a two-dimensional ZEKE (2D-ZEKE) spectrum, which allows the changing ZOS contributions to the eigenstates to be ascertained. Assignment of the observed bands is aided by quantum chemical calculations and all b1 and a2 symmetry vibrational wavenumbers are now determined in the S1 state and cation, as well as those of the D10 vibration. We also compare to the activity seen in the corresponding S1 ← S0 spectrum of para-difluorobenzene.

Vibrational and vibrational-torsional interactions in the 0-600 cm-1 region of the S1← S0 spectrum of p-xylene investigated with resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy.

We assign the 0-600 cm-1 region of the S1← S0 transition in p-xylene (p-dimethylbenzene) using resonance-enhanced multiphoton ionization (REMPI) and zero-kinetic-energy (ZEKE) spectroscopy. In the 0-350 cm-1 range as well as the intense origin band, there are a number of torsional and vibration-torsion (vibtor) features. The latter are discussed in more detail in Paper I [A. M. Gardner et al., J. Chem. Phys. 146, 124308 (2017)]. Here we focus on the origin and the 300-600 cm-1 region, where vibrational bands and some vibtor activity are observed. From the origin ZEKE spectrum, we derive the ionization energy of p-xylene as 68200 ± 5 cm-1. The assignment of the REMPI spectrum is based on the activity observed in the ZEKE spectra coupled with knowledge of the vibrational wavenumbers obtained from quantum chemical calculations. We assign several isolated vibrations and a complex Fermi resonance that is found to comprise contributions from both vibrations and vibtor levels, and we examine this via a two-dimensional ZEKE spectrum. A number of the vibrational features in the REMPI and ZEKE spectra of p-xylene that have been reported previously are reassigned and now largely consist of totally symmetric contributions. We briefly discuss the appearance of non-Franck-Condon allowed transitions. Finally, we find remarkably similar spectral activity to that in the related disubstituted benzenes, para-difluorobenzene, and para-fluorotoluene.

Torsion and vibration-torsion levels of the S1 and ground cation electronic states of para-fluorotoluene.

We investigate the low-energy transitions (0-570 cm-1) of the S1 state of para-fluorotoluene (pFT) using a combination of resonance-enhanced multiphoton ionization and zero-kinetic-energy (ZEKE) spectroscopy and quantum chemical calculations. By using various S1 states as intermediate levels, we obtain ZEKE spectra. The differing activity observed allows detailed assignments to be made of both the cation and S1 low-energy levels. The assignments are in line with the recently published work on toluene from the Lawrance group [J. R. Gascooke et al., J. Chem. Phys. 143, 044313 (2015)], which considered vibration-torsion coupling in depth for the S1 state of toluene. In addition, we investigate whether two bands that occur in the range 390-420 cm-1 are the result of a Fermi resonance; we present evidence for weak coupling between various vibrations and torsions that contribute to this region. This work has led to the identification of a number of misassignments in the literature, and these are corrected.

Assignment of the vibrations of the S0, S1, and D0 (+) states of perhydrogenated and perdeuterated isotopologues of chlorobenzene.

We report vibrationally resolved spectra of the S1←S0 transition of chlorobenzene using resonance-enhanced multiphoton ionization spectroscopy. We study chlorobenzene-h5 as well as its perdeuterated isotopologue, chlorobenzene-d5. Changes in the form of the vibrational modes between the isotopologues and also between the S0 and S1 electronic states are discussed for each species. Vibrational bands are assigned utilizing quantum chemical calculations, previous experimental results, and isotopic shifts, including those between the (35)Cl and (37)Cl isotopologues. Previous work and assignments of the S1 spectra are discussed. Additionally, the vibrations in the ground state cation, D0 (+), are considered, since these have also been used by previous workers in assigning the excited neutral state spectra.

Resonance-enhanced multiphoton ionization (REMPI) spectroscopy of bromobenzene and its perdeuterated isotopologue: Assignment of the vibrations of the S(0), S(1), and D(0)(+) states of bromobenzene and the S(0) and D(0)(+) states of iodobenzene.

We report vibrationally resolved spectra of the S1←S0 transition of bromobenzene using resonance-enhanced multiphoton ionization spectroscopy. We study bromobenzene-h5 as well as its perdeuterated isotopologue, bromobenzene-d5. The form of the vibrational modes between the isotopologues and also between the S0 and S1 electronic states is discussed for each species, allowing assignment of the bands to be achieved and the activity between states and isotopologues to be established. Vibrational bands are assigned utilizing quantum chemical calculations, previous experimental results, and isotopic shifts. Previous work and assignments of the S1 spectra are discussed. Additionally, the vibrations in the ground state cation, D0 (+), are considered, since these have also been used by previous workers in assigning the excited neutral state spectra. We also examine the vibrations of iodobenzene in the S0 and D0 (+) states and comment on the previous assignments of these. In summary, we have been able to assign the corresponding vibrations across the whole monohalobenzene series of molecules, in the S0, S1, and D0 (+) states, gaining insight into vibrational activity and vibrational couplings.

Vibrations of the S1 state of fluorobenzene-h5 and fluorobenzene-d5 via resonance-enhanced multiphoton ionization (REMPI) spectroscopy.

We report resonance-enhanced multiphoton ionization spectra of the isotopologues fluorobenzene-h5 and fluorobenzene-d5. By making use of quantum chemical calculations, the changes in the wavenumber of the vibrational modes upon deuteration are examined. Additionally, the mixing of vibrational modes both between isotopologues and also between the two electronic states is discussed. The isotopic shifts lead to dramatic changes in the appearance of the spectrum as vibrations shift in and out of Fermi resonance. Assignments of the majority of the fluorobenzene-d5 observed bands are provided, aided by previous results on fluorobenzene-h5.

Direct observation of vibrational energy dispersal via methyl torsions.

Explicit evidence for the role of methyl rotor levels in promoting energy dispersal is reported. A set of coupled zero-order vibration/vibration-torsion (vibtor) levels in the S1 state of para-fluorotoluene (pFT) are investigated. Two-dimensional laser-induced fluorescence (2D-LIF) and two-dimensional zero-kinetic-energy (2D-ZEKE) spectra are reported, and the assignment of the main features in both sets of spectra reveals that the methyl torsion is instrumental in providing a route for coupling between vibrational levels of different symmetry classes. We find that there is very localized, and selective, dissipation of energy via doorway states, and that, in addition to an increase in the density of states, a critical role of the methyl group is a relaxation of symmetry constraints compared to direct vibrational coupling.