Torsional Tunneling Splittings Research Articles

Torsional Tunneling Splitting in a Water Trimer

Using a full-dimensional quantum method for nuclei and a new first-principles water potential, we show that the torsional tunneling splitting in a water trimer can be reproduced with accuracy up to ∼1 cm-1. We quantify the coupling constants of the nuclear quantum states between nonadjacent wells and show that they are the main reason for shifting the quartet-split levels in spectra from a 1:2:1 spacing. This demonstrates the limitation of treatments using simplified models such as the Hückel model and emphasizes the nonlocal nature of the quantum interactions in this system. With such an ab initio endeavor, we examine the quality of the water potential developed and provide a rigorous scheme to decipher the experimental spectra with unprecedented accuracy, which is applicable to more general systems.

A periodic Numerov approach applied to the torsional tunneling splitting in hydrogen peroxide, aliphatic alcohols and phenol

Abstract The adapted Numerov approach was extended to periodic problems and applied to the torsional tunneling splitting of six increasingly complex target systems carrying a hydroxy-group. The deviations from experiment remained on the order of 1 cm−1, except for phenol in which the exceptionally small ground-state tunneling-splitting of 0.0017 cm−1 was found in very good agreement with the experimental value of 0.0019 cm−1. Overall, the accuracy of the periodic Numerov approach for the treatment of torsional tunneling is on the same order as alternative approaches, but at a substantially reduced computational demand due to the restriction of the problem to the respective degree of freedom.

Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives.

In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.

Single and double resonance spectroscopy of methanol embedded in superfluid helium nanodroplets.

Methanol is one of the simplest molecules that undergo torsional oscillations, and so it has been extensively studied in the gas phase by various spectroscopic techniques. At 300 K, a large number of rotational, torsional, and vibrational energy levels is populated, and this makes for a rather complicated spectrum, which is still not fully understood. It is expected that in going from 300 K to 0.4 K (the temperature of helium nanodroplets) the population distribution of methanol will mainly collapse into two states; the JK = 00 state for the A1 nuclear spin symmetry species (with ICH3 = 3/2), and the JK = 1-1 state for the E species (ICH3 = 1/2). This results in a simplified spectrum that consists of narrow a-type (ΔK = 0) lines and broader b- and c-type (ΔK = ±1) lines. We have recorded the rotovibrational spectrum of CH3OH in the OH stretching, CH3 stretching and bending, CH3 rocking, and CO stretching regions, and have firmly assigned five bands (v1, v2, v3, v7, and v8), and tentatively assigned five others (v9, 2v4, v4 + v10, 2v10, and v4 + v5). To our knowledge, the transitions we have assigned within the v4 + v10, 2v10, and v4 + v5 bands have not yet been assigned in the gas phase, and we hope that considering the very small "matrix" shift in helium nanodroplets (<1 cm(-1) for most subband origins of CH3OH), those made here can aid in their gas phase identification. Microwave-infrared double resonance spectroscopy was used to confirm the initially tentative a-type infrared assignments in the OH stretching (v1) band of A1 species methanol, in addition to revealing "warm" b-type lines. From a rotovibrational analysis, the B rotational constant is found to be reduced quite significantly (56%) with respect to the gas phase, and the torsional tunneling splittings are relatively unaffected and are at most reduced by 16%. While most rovibrational peaks are Lorentzian shaped, and those which are significantly perturbed by vibrational coupling in the gas phase are additionally broadened, the narrowest ΔJ = +1 peaks are asymmetric, and a skew-type analysis suggests that the response time of the helium solvent upon excitation is of the order of 1 ns.

Full-dimensional quantum calculations of the vibrational states of ${\rm H}_5^+$H5+

Full-dimensional quantum calculations of the vibrational states of H5(+) have been performed on the accurate potential energy surface developed by Xie et al. [J. Chem. Phys. 122, 224307 (2005)]. The zero point energies of H5(+), H4D(+), D4H(+), and D5(+) and their ground-state geometries are presented and compared with earlier theoretical results. The first 10 low-lying excited states of H5(+) are assigned to the fundamental, overtone, and combination of the H2-H3(+) stretch, the shared proton hopping and the out-of-plane torsion. The ground-state torsional tunneling splitting, the fundamental of the photon hopping mode and the first overtone of the torsion mode are 87.3 cm(-1), 354.4 cm(-1), and 444.0 cm(-1), respectively. All of these values agree well with the diffusion Monte Carlo and multi-configuration time-dependent Hartree results where available.

IR and FTMW-IR Spectroscopy and Vibrational Relaxation Pathways in the CH Stretch Region of CH3OH and CH3OD

Infrared spectra of jet-cooled CH(3)OD and CH(3)OH in the CH stretch region are observed by coherence-converted population transfer Fourier transform microwave-infrared (CCPT-FTMW-IR) spectroscopy (E torsional species only) and by slit-jet single resonance spectroscopy (both A and E torsional species, CH(3)OH only). Twagirayezu et al. reported the analysis of ν(3) symmetric CH stretch region (2750-2900 cm(-1); Twagirayezu et al. J. Phys. Chem. A 2010, 114, 6818), and the present work addresses the more complicated higher frequency region (2900-3020 cm(-1)) containing the two asymmetric CH stretches (ν(2) and ν(9)). The additional complications include a higher density of coupled states, more extensive mixing, and evidence for Coriolis as well as anharmonic coupling. The overall observed spectra contain 17 interacting vibrational bands for CH(3)OD and 28 for CH(3)OH. The sign and magnitude of the torsional tunneling splittings are deduced for three CH stretch fundamentals (ν(3), ν(2), ν(9)) of both molecules and are compared to a model calculation and to ab initio theory. The number and distribution of observed vibrational bands indicate that the CH stretch bright states couple first to doorway states that are binary combinations of bending modes. In the parts of the spectrum where doorway states are present, the observed density of coupled states is comparable to the total density of vibrational states in the molecule, but where there are no doorway states, only the CH stretch fundamentals are observed. Above 2900 cm(-1), the available doorway states are CH bending states, but below, the doorway states also involve OH bending. A time-dependent interpretation of the present FTMW-IR spectra indicates a fast (∼200 fs) initial decay of the bright state followed by a second, slower redistribution (about 1-3 ps). The qualitative agreement of the present data with the time-dependent experiments of Iwaki and Dlott provides further support for the similarity of the fastest vibrational relaxation processes in the liquid and gas phases.

Ro-torsional energy correlation between the high barrier and free-internal-rotor limits: The case of the skew chain molecule HSOH

Skew-chain molecules, such as HSOH, exhibit exotic behavior due to coupling of torsion and rotation. In particular, the torsional tunneling splittings vary cyclically in magnitude with axial rotational quantum number, K, with a period depending on the ratio of the moments of inertia for their end moieties. Although successfully modeled using a variety of approaches (algebraic, reduced-dimensional, and full-dimensional) a conceptual understanding of this cyclic variation for HSOH has not been presented. We do this here, using the reduced-dimension Generalized Semi-Rigid Bender (GSRB) approach to establish the correlation between states at the free-rotor (zero-barrier) limit and those at the more physical high-barrier limit. In this context we present the symmetries and appropriate quantum numbers for the states in these two limiting cases. We show that the cyclic variation of the magnitude of the torsional splittings originates in the energy level-structure in the zero-barrier limit combined with the correlation to the high-barrier limit. This allows us to give a simple recipe for calculating the period of this cyclic variation in any such skew-chain molecule, based only on the moments of inertia of the two end moieties.

The rotational spectrum of HS32OH and HS34OH above 1 THz

Accurate spectral data of H(32)SOH and H(34)SOH at 1.3 THz were recorded using a synthesizer based multiplier spectrometer. The spectra were analyzed together with data from an earlier study which contain measurements at 1.9 THz. The combination of both data sets allows to determine experimentally the tunneling splitting of energy levels with K(a) = 4 and 5 for the first time. The obtained results are essential to test a novel model on torsional tunneling splitting in HSOH. Transitions with K(a) = 1 <-- 0, K(a) = 2 <-- 1, and K(a) = 3 <-- 2 all exhibit strong c-type and somewhat weaker b-type transitions. In contrary, transitions with K(a) = 4 <-- 3 display only c-type but no b-type transitions. The absence of b-type transitions is completely unexpected and yet not well understood. For the H(34)SOH isotopolog the data set has been substantially extended by the new measurements of (r)Q(3)-branch transitions at 1.3 THz. Based on the new data the accuracy of the H(34)SOH molecular parameters has been significantly improved.

Torsion−Vibration Coupling in Methanol: Diabatic Behavior in the CH Overtone Region

Through a fit to methanol CH overtone data, a previously developed 4-dimensional torsion-vibration Hamiltonian is extended to high CH stretch excitation as well as to high torsional excitation. The strength of the torsion-vibration coupling is found to increase with CH stretch excitation. Systematic patterns of near degeneracy (3-, 4-, and 6-fold) are found in different regions of quantum number space. In the region of the CH fundamentals, an approximate a diabatic separation of the torsion (slow degree of freedom) from the CH stretches (fast degrees of freedom) accounts for the pattern of the energy levels and for the signs of the torsional tunneling splittings. For the higher CH overtones (v(CH) > or = 4), a diabatic representation accounts for the torsional structure obtained from the fully coupled calculation and for certain trends found in the pattern of the energy levels.

Stereomutation Tunneling Switching Dynamics and Parity Violation in Chlorineperoxide Cl−O−O−Cl

In a search for efficient spectroscopic avenues toward experiments on molecular parity violation, we investigate the stereomutation tunneling processes in the axially chiral chlorine isotopomers of Cl2O2 by the quasi-adiabatic channel reaction path Hamiltonian (RPH) approach and the corresponding parity violating potentials by means of quantum chemical calculations including our recently developed Multiconfiguration linear response (MC-LR) approach to electroweak quantum chemistry. The calculated ground-state torsional tunneling splittings for all isotopomers of Cl2O2 are much smaller than the parity violating energy differences Delta(pv)E between the enantiomers of these molecules and therefore parity violation is predicted to dominate the quantum dynamics of stereomutation at low energies. We also compare these with torsional ground-state tunneling splittings and parity violating energy differences of the whole series of axially chiral HXYH(+) isotopomers (with X, Y= Cl(+), O, S, Se, Te). A comparison with our previous results for the homologous molecule Cl2S2 shows that for Cl2O2 a spectroscopic high-resolution analysis should be easier and the energy region of large tunneling splittings should be more easily accessible by IR excitation. We thus propose a scheme using "tunneling switching" with vibrational excitation in order to carry out the measurement of time-dependent parity violation in superposition states of initially well-defined parity. We discuss the advantages and drawbacks of such an experiment that can be carried out entirely in the IR spectral range (for Cl2O2 or related molecules).

Torsional tunneling splittings in the v4 = 1 excited torsional state of Si2H6: analysis of hot bands accompanying fundamental transitions in the high resolution infrared spectrum

The (ν4 + ν6) − ν4, (ν4 + ν8) − ν4 and (ν4 + ν9) − ν4 hot infrared systems of disilane (Si2H6) have been analysed at high resolution, and the values of the relative vibration–rotation–torsion parameters have been determined. The torsional splitting is about 0.500 cm−1 in the ν4 and ν4 + ν6 states, and decreases strongly in the vibrationally degenerate upper states ν4 + ν8 (about 0.0272 cm−1 on average) and ν4 + ν9 (about 0.3019 cm−1), consistent with theoretical predictions. Comparison between the vibrational wavenumbers of cold transitions and hot transitions originating in the excited torsional state v4 = 1 allows one to determine the change of the fundamental torsional frequency ν4 caused by the excitation of small amplitude vibrations. A remarkable increase in ν4 of about 8.599 cm−1 is found in the v9 = 1 state (E1d SiH3-rocking mode, asymmetric to inversion in the staggered geometry), and this corresponds to an increase in the torsional barrier height in this excited fundamental vibrational state by about 48.77 cm−1. The mechanism responsible for the decrease of the torsional splittings in the degenerate vibrational states is briefly outlined by means of second-order perturbation theory, using torsion-hindered vibrational basis functions of E1d and E2d symmetries for the degenerate modes.

Theoretical studies of the potential surface and vibrational spectroscopy of CH3OH and its deuterated analogs

A potential-energy force field for methanol is calculated at the coupled-cluster singles doubles and noniterative triples correction level using the correlation-consistent polarized valence triple zeta basis set. The force field describes the coupled molecular vibrations, including the cubic and quartic anharmonicites, as a function of the torsional coordinate. The resulting molecular eigenstates are calculated using a combination of perturbative and variation calculations following the approach of Castillo-Chará and Sibert [J. Chem. Phys. 119, 11671 (2003)]. The energies, including torsional tunneling splittings, are compared with available spectroscopic data for all the fundamentals. Excellent agreement is found. Varying the torsional mass, correlation plots are constructed in order to elucidate the complex role of torsion-vibration coupling.

Mode-selective stereomutation tunneling and parity violation in HOClH+ and H2Te2 isotopomers

We investigate the stereomutation tunneling processes in the axially chiral prototype ion HOClH+ and in H2Te2 isotopomers in their relation to parity violation using quantum chemical calculations including our recently developed MC-LR approach to electroweak quantum chemistry and the quasiadiabatic channel reaction path Hamiltonian (RPH) approach. All the molecules dealt with here exhibit intermediate barriers to stereomutation (in the range from 0.1 to 0.3eV depending on the molecule and cis- or trans-type of transition structure considered). Whereas tunneling dominates the quantum dynamics of stereomutation in all isotopomers of HOClH+, the ground-state torsional tunneling splittings for hydrogen ditelluride isotopomers D2Te2 and T2Te2 are calculated to be much smaller than the parity violating energy differences ΔEpv between the enantiomers of these molecules. We present a systematic investigation of the dependence of tunneling splittings upon the excitation of various vibrational modes and we identify some strongly promoting and some weakly inhibiting modes as well as essentially inactive modes. A comparison of the new results for HOClH+ with our previous results for the isoelectronic HSOH shows some similarities but also some striking differences. HOClH+ is predicted to have sufficient kinetic stability for a spectroscopic observation, as a barrier of more than 1eV separates it from the more stable isomer H2OCl+. We also provide a summary comparing the whole series of axially chiral HXYH(+) isotopomers with X, Y=O, S, Se, Te, Cl and discuss the outlook for experiments on molecular parity violation in this series of molecular and ionic species. For the hydrogenic compounds D2Te2 is the only non-radioactive compound, in which parity violation is predicted to dominate over tunneling, similar to the chlorinated species Cl2S2, which we had investigated earlier.

Mode‐selective stereomutation tunneling as compared to parity violation in hydrogen diselenide isotopomers 1,2,3H280Se2

AbstractWe present quantitative calculations of the mode‐selective stereomutation tunneling in the chiral hydrogen diselenide isotopomers X2Se2 with X = H, D, and T. The torsional tunneling stereomutation dynamics were investigated with a quasi‐adiabatic channel quasi‐harmonic reaction path Hamiltonian approach, which treats the torsional motion anharmonically in detail and all remaining coordinates as harmonic (but anharmonically coupled to the reaction coordinate). We also investigated the influence of the excitation of fundamental modes on the stereomutation dynamics and predict which modes should be promoting or inhibiting. Our stereomutation dynamics results and the influence of parity violation on these are discussed in relation to our recent investigations for the analogous molecules H2O2, HSOH, H2S2, and Cl2S2. The electronic potential energy barrier heights for the torsional motion of hydrogen diselenide are similar to those of HSOH, whereas the torsional tunneling splittings are similar to the corresponding values of HSSH. The ground‐state torsional tunneling splittings calculated here for D2Se2 are of the same order as the parity‐violating energy difference reported by Laerdahl and Schwerdtfeger (Phys. Rev. A 1999, 60, 4439), whereas for T2Se2 the corresponding tunneling splitting is about three orders of magnitude smaller.

Full dimensional theoretical study of the torsion-vibration eigenstates and torsional splittings of CH3OH

The vibrations of methanol are studied theoretically via a fully coupled treatment of the small amplitude motions and the large amplitude torsional mode. Van Vleck perturbation theory is used to find a representation in which the coupling between the vibrational states is reduced. The full vibration-torsion eigenstates are obtained subsequently via matrix diagonalization. The convergence of the perturbation theory and variational calculations are discussed. The torsion-vibration energies and the torsional tunneling splittings are compared with available spectroscopic data for all the fundamentals. The unusual inverted E–A torsional tunneling splitting pattern observed spectroscopically for rotationless torsion-vibrational states is predicted by our calculation.

Semiclassical Calculations of Tunneling Splitting in Hydrogen Peroxide and Its Deuterated Isotopomers

Torsional tunneling splittings for the ground and selected vibrationally excited states of HOOH, HOOD, and DOOD are calculated using a semiclassical tunneling approach. The approach incorporates tunneling calculations into quasiclassical trajectory simulations and is thus practical for large systems. Comparisons with the experimental and quantum results show that the mode selectivity and isotope effects are generally reproduced in the semiclassical calculations. The causes for the quantitative discrepancies between the quantum and semiclassical calculations are discussed.

Rotational and Torsional Analysis of the OH-Stretch Third Overtone in 13CH3OH

We record double resonance spectra of the 4ν1 band of jet-cooled 13C-methanol using single rotational state selection in the ν1 fundamental and subsequent promotion of the selected molecules to the fourth vibrational level. We then detect transitions to the final excited states by infrared laser assisted photofragment spectroscopy (IRLAPS). The assigned A symmetry transitions reach upper states with K=0 and 1, and J from 0 to 5. For E symmetry, the transitions reach levels with K in the range −3 to 2 and J from 1 to 7. The rotation–torsional analysis determines a value for the torsional tunneling splitting of 2.8±0.4 cm−1 at v1=4. In a previous paper (J. Chem. Phys.110, 11 359–11 367 (1999)), we reported a trend of monotonically decreasing tunneling splittings in 12CH3OH for v1=0, 3, and 6 that we explained by a model that incorporates a linear increase in the torsional barrier height with OH stretch excitation. The 13CH3OH tunneling splitting for the 4ν1 band is in quantitative agreement with the trend found for 12CH3OH.

Can a local mode picture account for vibration–torsion coupling? Ab initio test based on torsional variation of methyl stretching and bending frequencies in methanol

The torsional dependence of the CH3 stretching and bending modes of methanol has been explored in terms of a local mode internal coordinate picture [X. Wang and D. S. Perry, J. Chem. Phys. 109, 10795 (1998)]. First, the torsional variations of the small-amplitude vibrational frequencies along the mass weighted intrinsic reaction coordinate from the top to the bottom of the torsional potential barrier were calculated by means of ab initio frequency projection utilizing GAUSSIAN 98. The resulting curves for the three C–H stretch ab initio frequencies as functions of the torsional angle cannot be reproduced by the original 3×3 local mode model incorporating stretch–torsion and stretch–stretch couplings at lowest-order only, but are well-fitted if the model is extended to include higher-order coupling terms. For the CH-bending modes, with internal coordinates chosen to give a high degree of localization, bend–torsion and bend–bend coupling parameters were determined from the ab initio projected frequencies, and were then used to predict torsional tunneling splittings. Just as observed for the C–H stretch modes, the two higher-frequency asymmetric CH-bend modes are predicted to have inverted tunneling splittings with reduced amplitudes, while the splitting pattern for the lower frequency symmetric-bend mode is predicted to be normal.

Intramolecular energy transfer in highly vibrationally excited methanol. III. Rotational and torsional analysis

We report here torsional analysis of rotationally resolved spectra of the 3ν1, 5ν1, and 6ν1 (OH stretch) bands of jet-cooled methanol. The upper states are reached by a double resonance excitation scheme involving the selection of single rotational states in the ν1 fundamental band. Detection of the overtone transitions (nν1←ν1) is by infrared laser assisted photofragment spectroscopy (IRLAPS). The torsional tunneling frequency declines monotonically from 9.1 cm−1 in the vibrational ground state to 1.6 cm−1 at 6ν1. For the available rotational levels at 3ν1 (K=0–3) and 6ν1 (K=0,1), the pattern of torsional energies is approximately regular. To obtain the vibrational dependence of the torsional barrier V3, it was necessary to use the OH radical and HOOH as models for the vibrational dependence of the torsional inertial constant F. The assumed linear dependence of V3 on ν1 accounts for the torsional tunneling splittings at v1=0, 3, and 6 and for the pattern of the torsional energies. V3 increases by 40–45 cm−1 per quantum of OH excitation.

An internal coordinate model of coupling between the torsion and C–H vibrations in methanol

The torsional tunneling splittings of the asymmetric C–H stretches (ν2 and ν9) in methanol are inverted with the E level lower in energy than the A level, whereas the symmetric C–H stretch (ν3) is normal with A below E. An internal coordinate model, which treats the torsion and the three C–H stretches simultaneously, accounts for the observed tunneling splittings. The model parameters are the local stretching frequency ω=2934.0 cm−1, the direct local–local coupling λ=−42.2 cm−1, and a single stretch-torsion coupling parameter μ=12.9 cm−1. The torsion-vibration coupling is nonadiabatic in the sense that it is not consistent with a Born–Oppenheimer separation of the torsion from the other vibrations. The fact that the model is based largely on the G6 molecular symmetry suggests that tunneling inversion may be common in torsional molecules. The torsionally mediated couplings among the C–H stretches do not conserve symmetry in the Cs point group and are strong enough to contribute to rapid intramolecular vibrational redistribution (IVR).