Interactions of Si+(2PJ) and Ge+ (2PJ) with rare gas atoms (He-Rn): interaction potentials, spectroscopy, and ion transport coefficients.

Accurate interatomic potentials were calculated for the interaction of a singly-charged silicon cation, Si+, with a single rare gas atom, RG (RG = Kr-Rn), as well as a singly-charged germanium cation, Ge+, with a single rare gas atom, RG (RG = He-Rn). The RCCSD(T) method and basis sets of quadruple-ζ and quintuple-ζ quality were employed; each interaction energy is counterpoise corrected and extrapolated to the basis set limit. The lowest electronic term (2P) of each 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. Variations in several spectroscopic parameters with the increasing atomic number of RG were examined. The presence of incipient chemical interaction was also examined via Birge-Sponer-like plots and various population analyses across the series. In the cases of heavier RG, these were consistent with a small amount of electron transfer from the heavier RG atom to the cation, rationalizing the spin-orbit splittings. This was also supported by the observed larger-than-expected spin-orbit splittings for the Si+-RG complexes. Finally, each set of RCCSD(T) potentials including spin-orbit coupling was employed to calculate transport coefficients for the cation moving through a bath of the RG. The calculated ion mobilities showed significant differences for the two atomic spin-orbit states, arising from subtle changes in the interaction potentials.

Electronic, vibrational, and torsional couplings in N-methylpyrrole: Ground, first excited, and cation states.

The electronic spectrum associated with the S1 ← S0 (Ã1A2←X̃1A1) one-photon transition of jet-cooled N-methylpyrrole is investigated using laser-induced fluorescence (LIF) and (1 + 1) resonance-enhanced multiphoton ionization (REMPI) spectroscopy; in addition, the (2 + 2) REMPI spectrum is considered. Assignment of the observed bands is achieved using a combination of dispersed fluorescence (DF), two-dimensional LIF (2D-LIF), zero-electron-kinetic energy (ZEKE) spectroscopy, and quantum chemical calculations. The spectroscopic studies project the levels of the S1 state onto those of either the S0 state, in DF and 2D-LIF spectroscopy, or the ground state cation (D0 +) state, in ZEKE spectroscopy. The assignments of the spectra provide information on the vibrational, vibration-torsion (vibtor), and torsional levels in those states and those of the S1 levels. The spectra are indicative of vibronic (including torsional) interactions between the S1 state and other excited electronic states, deduced both in terms of the vibrational activity observed and shifts from expected vibrational wavenumbers in the S1 state, attributed to the resulting altered shape of the S1 surface. Many of the ZEKE spectra are consistent with the largely Rydberg nature of the S1 state near the Franck-Condon region; however, there is also some activity that is less straightforward to explain. Comments are made regarding the photodynamics of the S1 state.

Comment on "Electronic, vibrational and torsional couplings in N-methylpyrrole: Ground, first excited and cation states" [J. Chem. Phys. 154, 224305 (2021)].

Two-color (1 + 1') zero-electron-kinetic-energy (ZEKE) and photoionization efficiency (PIE) spectra are reported via different levels in the S1 ← S0 (Ã1A2←X̃1A1) one-photon transition of jet-cooled N-methylpyrrole. The laser radiation is produced using two dye lasers, one with an 1800 l/mm grating and one with 2400 l/mm. We report spectra where the excitation and ionization radiation are produced with both combinations of the dye lasers; these spectra differ markedly. This is attributed to Wood's anomalies with the 2400 l/mm grating: one aspect is a loss in light intensity over a range of wavelengths, attributed to a resonance anomaly. Another is the appearance of a "shadow" ZEKE spectrum and PIE curve at apparently higher ionization wavenumbers; under some conditions, a third ZEKE spectrum was observed-these latter observations arise from higher-order dispersion effects, likely caused by a Rayleigh anomaly. We comment on these observations and report more representative ZEKE and PIE spectra than those presented in a recent paper by our group [A. R. Davies, D. J. Kemp, and T. G. Wright, J. Chem. Phys. 154, 224305 (2021)] for four intermediate S1 levels.

Torsions, low-frequency vibrations, and vibration-torsion ("vibtor") levels in the m-chlorotoluene cation.

Zero-electron-kinetic-energy (ZEKE) spectra are presented for m-chlorotoluene (mClT), employing different low-lying torsional and vibration-torsional ("vibtor") levels of the S1 state as intermediates. The adiabatic ionization energy is determined to be 71 319 cm-1 ± 5 cm-1 (8.8424 ± 0.0006 eV). It is found that the activity in the ZEKE spectra varies greatly for different levels and is consistent with the assignments of the S1 levels of m-fluorotoluene (mFT) deduced in the recent fluorescence study of Stewart et al. [J. Chem. Phys. 150, 174303 (2019)] and the ZEKE study from Kemp et al. [J. Chem. Phys. 151, 084311 (2019)]. As with mFT, the intensities in the ZEKE spectra of mClT are consistent with a phase change in the torsional potential upon ionization, allowing a large number of torsions and vibtor levels to be observed for the cation. Vibration-induced modifications of the torsional potential are discussed. Calculated vibrational wavenumbers for the S0, S1, and D0 + states are also presented.

Variations in Duschinsky rotations in m-fluorotoluene and m-chlorotoluene during excitation and ionization.

We investigate Duschinsky rotation/mixing between three vibrations for both m-fluorotoluene (mFT) and m-chlorotoluene (mClT), during electronic excitation and ionization. In the case of mFT, we investigate both the S1 → S0 electronic transition and the D0 + ← S1 ionization, by two-dimensional laser-induced fluorescence (2D-LIF) and zero-electron-kinetic energy (ZEKE) spectroscopy, respectively; for mClT, only the D0 + ← S1 ionization was investigated, by ZEKE spectroscopy. The Duschinsky mixings are different in the two molecules, owing to shifts in vibrational wavenumber and variations in the form of the fundamental vibrations between the different electronic states. There is a very unusual behavior for two of the mFT vibrations, where apparently different conclusions for the identity of two S1 vibrations arise from the 2D-LIF and ZEKE spectra. We compare the experimental observations to the calculated Duschinsky matrices, finding that these successfully pick up the key geometric changes associated with each electronic transition and so are successful in qualitatively explaining the vibrational activity in the spectra. Experimental values for a number of vibrations across the S0, S1, and D0 + states are reported and found to compare well to those calculated. Assignments are made for the observed vibration-torsion ("vibtor") bands, and the effect of vibrational motion on the torsional potential is briefly discussed.

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.

Vibration-modified torsional potentials and vibration-torsion ("vibtor") levels in the m-fluorotoluene cation.

Zero-kinetic-energy (ZEKE) spectra are presented for m-fluorotoluene, employing different low-lying (<350 cm-1) intermediate torsional and vibration-torsional ("vibtor") levels of the S1 state. The adiabatic ionization energy (AIE) is found to be 71 997 ± 5 cm-1 (8.9265 ± 0.0006 eV). It is found that the activity in the ZEKE spectra varies greatly for different levels and is consistent with the assignments of the S1 levels deduced in the recent fluorescence study of Stewart et al. [J. Chem. Phys. 150, 174303 (2019)]. For cation torsional levels, the most intense band corresponds to changes in the torsional quantum number, in line with the known change in the phase of the torsional potential upon ionization. This leads to the observation of an unprecedented number of torsions and vibtor levels, with the pronounced vibtor activity involving out-of-plane vibrations. Interactions between levels involving torsions are discussed, with evidence presented, for the first time it is believed, for modification of a torsional potential induced by a vibration. Also, we discuss the possibility of distortion of the methyl group leading to a change from G6 molecular symmetry to Cs point group symmetry.

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.

Quantum chemical study of the structure, spectroscopy and reactivity of NO+.(H2O) n=1-5 clusters.

Quantum chemical methods including Møller-Plesset perturbation (MP2) theory and density functional theory (DFT) have been used to study the structure, spectroscopy and reactivity of NO+(H2O) n=1-5 clusters. MP2/6-311++G** calculations are shown to describe the structure and spectroscopy of the clusters well. DFT calculations with exchange-correlation functionals with a low fraction of Hartree-Fock exchange give a binding energy of NO+(H2O) that is too high and incorrectly predict the lowest energy structure of NO+(H2O)2, and this error may be associated with a delocalization of charge onto the water molecule directly binding to NO+ Ab initio molecular dynamics (AIMD) simulations were performed to study the NO+(H2O)5 [Formula: see text] H+(H2O)4 + HONO reaction to investigate the formation of HONO from NO+(H2O)5 Whether an intracluster reaction to form HONO is observed depends on the level of electronic structure theory used. Of note is that methods that accurately describe the relative energies of the product and reactant clusters did not show reactions on the timescales studied. This suggests that in the upper atmosphere the reaction may occur owing to the energy present in the NO+(H2O)5 complex following its formation.This article is part of the theme issue 'Modern theoretical chemistry'.

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'.

Reactivity of the O2+·(H2O)n and NO+·(H2O)n cluster ions in the D-region of the ionosphere.

The protonated water clusters present in the D-region of the ionosphere have been postulated to be formed from cluster ions such as O2+·(H2O)n and NO+·(H2O)n, although the detailed mechanism of the underlying reactions is not understood. Second order Møller-Plesset perturbation theory based Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations of the reactions of the O2+·(H2O)n and NO+·(H2O)n cluster ions to form protonated water clusters reveal different mechanisms for the O2+ and NO+ based ions. AIMD simulations of O2+·(H2O)n=2-5 with initial velocities of the atoms sampled from the Maxwell-Boltzmann distribution at 220 K show that following charge transfer, a reaction to form a protonated water cluster and OH occurs rapidly where the neutral O2 molecule is just a spectator. In contrast, the reaction of NO+·(H2O)n=4,5 has been hypothesised to involve an intracluster reaction, but no reaction is observed in AIMD simulations using thermal initial velocities. However, it is shown that reactions to form protonated water clusters do occur in simulations when a water molecule collides with a NO+·(H2O)4 cluster.

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.

Transport coefficients of He(+) ions in helium.

This paper demonstrates that the transport coefficients of (4)He(+) in (4)He can be calculated over wide ranges of E/N, the ratio of the electrostatic field strength to the gas number density, with the same level of precision as can be obtained experimentally if sufficiently accurate potential energy curves are available for the X(2)Σu (+) and A(2)Σg (+) states and one takes into account resonant charge transfer. We start by computing new potential energy curves for these states and testing their accuracy by calculating spectroscopic values for the separate states. It is established that the potentials obtained by extrapolation of results from d-aug-cc-pVXZ (X = 6, 7) basis sets using the CASSCF+MRCISD approach are each in exceptionally close agreement with the best potentials available and with experiment. The potentials are then used in a new computer program to determine the semi-classical phase shifts and the transport cross sections, and from these the gaseous ion transport coefficients are determined. In addition, new experimental values are reported for the mobilities of (4)He(+) in (4)He at 298.7 K, as a function of E/N, where careful consideration is given to minimizing various sources of uncertainty. Comparison with previously measured values establishes that only one set of previous data is reliable. Finally, the experimental and theoretical ion transport coefficients are shown to be in very good to excellent agreement, once corrections are applied to account for quantum-mechanical effects.

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.