Theory of Stereomutation Dynamics and Parity Violation in Hydrogen Thioperoxide Isotopomers 1,2,3HSO1,2,3H

We present quantitative calculations of the mode‐selective stereomutation tunneling and parity violation in chiral hydrogen thioperoxide (‘oxadisulfane') isotopomers XSOY with X, Y=H, D, and T. The torsional tunneling stereomutation dynamics are 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 predict how stereomutation is catalyzed or inhibited by excitation of various vibrational modes compared to the corresponding stereomutation dynamics of the vibrational ground state. Parity‐violating potentials were calculated with our recent multiconfiguration linear response (MC‐LR) approach in the random phase approximation (RPA). We find that, in agreement with general scaling expectations, the parity‐violating energy difference for the equilibrium structures of the two HSOH enantiomers (ca. 5×10^?12J mol^?1) is situated intermediate between HOOH and HSSH. Our results on the stereomutation dynamics and the influence of parity violation on these are discussed in relation to investigations for the analogous molecules H₂O₂, H₂S₂, and Cl₂S₂. As expected in XSOY (X, Y=H, D, and T), this influence is much larger than in the corresponding H₂O₂ isotopomers, but smaller than in H₂S₂ or Cl₂S₂.     

Mode Selective Stereomutation and Parity Violation in Disulfane Isotopomers H2S2, D2S2, T2S2

We report quantitative calculations of stereomutation tunneling in the disulfane isotopomers H₂S₂, D₂S₂, and T₂S₂, which are chiral in their equilibrium geometry. The quasi‐adiabatic channel, quasi‐harmonic reaction path Hamiltonian approach used here treats stereomutation including all internal degrees of freedom. The torsional motion is handled as an anharmonic reaction coordinate in detail, whereas all the remaining degrees of freedom are taken into account approximately. We predict how stereomutation is catalyzed or inhibited by excitation of the various vibrational modes. The agreement of our theoretical results with spectroscopic data from the literature on H₂S₂ and D₂S₂ is excellent. We furthermore predict the influence of parity violation on stereomutation as characterized approximately by the ratio (ΔE_pv/ΔE_±) of the (local or vibrationally averaged) parity violating potential ΔE_pv and the tunneling splittings ΔE_± in the symmetrical case. This ratio is exceedingly small for the reference molecules H₂O₂ and D₂O₂, and still very small (2⋅10⁻⁶ cm⁻¹) for H₂S₂, which, thus, all exhibit essentially parity conservation in the dynamics. However, for D₂S₂ it is ca. 0.002, and for T₂S₂ it is ca. 1, which seems to be the first case where such intermediate mixing through parity violation is quantitatively predicted for spectroscopically accessible molecules. The consequences for the spectroscopic detection of molecular parity violation are discussed briefly also in relation to other molecules.     

Steps towards molecular parity violation in axially chiral molecules. I. Theory for allene and 1,3-difluoroallene

In view of exploring possibilities for an experimental investigation of molecular parity violation we report quantum-chemical calculations of the parity-conserving and parity-violating potentials in the framework of electroweak quantum chemistry in allene C3H4 and 1,3-difluoroallene C3H2F2, which is nonplanar and axially chiral in the electronic ground state but expected to be nearly planar and achiral in several electronically excited states. The parity-violating potentials Epv for allene and 1,3-difluoroallene calculated with the multiconfiguration linear-response (MC-LR) approach of Berger and Quack [J. Chem. Phys. 112, 3148 (2000)] show qualitatively similar behavior as a function of torsional angle tau with maximum values of about 0.5 pJ mol(-1) for C3H4 and 2 pJ mol(-1) for C3H2F2. However, in the latter case they are asymmetrically shifted around tau=90 degrees , with a nonzero value at the chiral equilibrium geometry resulting in a parity-violating energy difference between enantiomers DeltapvE=Epv(P)-Epv(M)=1.2 pJ mol(-1) (equivalent to about 10(-13) cm(-1)). The calculated barrier heights corresponding to the nonrigid (multiple, and in part chiral) transition states in 1,3-difluoroallene fall in the range of 180-200 kJ mol(-1). These high barriers result in hypothetical tunneling splittings much smaller than DeltapvE and thus parity violation dominates over tunneling for the stereomutation dynamics in 1,3-difluoroallene. Therefore, DeltapvE is predicted to be a spectroscopically measurable energy difference. Two of the lower excited electronic states of C3H2F2 (1A and 3A) are calculated to be planar or quasiplanar, allowing, in principle, for spectroscopic state selection of states of well-defined parity. The results are discussed in relation to possible schemes of measuring parity violation in chiral molecules.     

Tunneling and Parity Violation in Trisulfane (HSSSH): An Almost Ideal Molecule for Detecting Parity Violation in Chiral Molecules

Measuring the parity‐violating energy difference Δ_pvE between the enantiomers of chiral molecules is a major challenge of current physical‐chemical stereochemistry. An important step towards this goal is to identify suitable molecules for such experiments by means of theory. This step has been made by calculations for the complex dynamics of tunneling and electroweak quantum chemistry of parity violation in the “classic” molecule trisulfane, HSSSH, which satisfies the relevant conditions for experiments almost ideally, as the molecule is comparatively simple and parity violation clearly dominates over tunneling in the ground state. At the same time, the barrier for stereomutation is easily overcome by the S?H infrared chromophore.     

Radiative excitation of the harmonic oscillator with applications to stereomutation in chiral molecules

We present theoretical considerations and quantitative numerical simulations of the coherent radiative excitation of chiral molecules exhibiting a double well potential in the electronic ground state (with stable enantiomers) and a harmonic oscillator potential with achiral minimum geometry in the excited electronic state following a scheme proposed in [33]. The one-dimensional short time dynamics is presented on the femtosecond time scale. We demonstrate the phenomena of quasiexponential, radiationless decay of the survival probability in the excited electronic state by simple harmonic oscillator wave packet motion, as well as coherent periodic chiral stereomutation. The differences and similarities of the excited state harmonic oscillator dynamics with two quite different ground state potentials are discussed. A designed pulse sequence allows for chemically efficient laser controlled stereomutation with high enantiomeric specificity. The results are discussed in relation to Friedrich Hund's early work on stereomutation by tunneling and in relation to our current understanding of chiral molecules including dynamical chirality and anharmonic vibrational dynamics on the femtosecond time scale and the violation of parity and other fundamental symmetries.     

Parity‐Violating Potentials for the Torsional Motion of Methanol (CH3OH) and Its Isotopomers (CD3OH, 13CH3OH,CH3OD,CH3OT,CHD2OH,and CHDTOH)

We present calculations on the parity‐conserving and the parity‐violating potentials in several MeOH isotopomers for the torsional motion by the newly developed methods of electroweak quantum chemistry from our group. The absolute magnitudes of the parity‐violating potentials for MeOH are small compared to H₂O₂ and C₂H₄, but similar to C₂H₆, which is explained by the high (threefold) symmetry of the torsional top in MeOH and C₂H₆. ‘Chiral’ and ‘achiral’ isotopic substitutions in MeOH lead to small changes only, but vibrational averaging is discussed to be important in all these cases. Simple isotopic sum rules are derived to explain and predict the relationships between parity‐violating potentials in various conformations and configurations of the several isotopomers investigated. The parity‐violating energy difference Δ_pvE=E_pv(R)?E_pv(S) between the enantiomers of chiral CHDTOH, first synthesized by Arigoni and co‐workers, is for two conformers ca. ?3.66?10^?17 and for the third one +7.32?10^?17 hc cm^?1. Thus, for Δ_pvE, the conformation is more important than the configuration (at the equilibrium geometries, without vibrational averaging). Averaging over torsional tunneling may lead to further cancellation and even smaller values.     

An alternative route to detect parity violating energy differences through Bose-Einstein condensation of chiral molecules

Interactions which do not conserve parity might influence chiral compounds giving rise to a parity violating energy difference (PVED) that might have affected the evolution towards homochirality. However, this tiny effect predicted by electroweak-quantum chemistry calculations is easily masked by thermal effects, making it desirable to reach cold regimes in the laboratory. As an alternative route to the detection of the PVED, we study a simplified model of Bose-Einstein condensation of a sample of non-interacting chiral molecules, showing that it leads to a nonzero optical activity of the condensate and also to a subcritical temperature in the heat capacity, due to the internal structure of the molecule characterized by tunneling and parity violation. This predicted singular behavior found for the specific heat, below the condensation temperature, might shed some light on the existence of the thus far elusive PVED between enantiomers.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of biohomochirality. We have proposed the observation of molecular parity violation using the two-photon Ramsey fringes technique on a supersonic beam. As a first step in this direction, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for a parity violation experiment. For the (187)Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO(2) laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the ν(as) antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO is synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. The first high resolution spectra of jet-cooled MTO, obtained on a set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.     

Quantum stochastic resonance in parity violating chiral molecules

In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.     

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.     

Recent experimental and theoretical developments towards the observation of parity violation (PV) effects in molecules by spectroscopy

Parity violation (PV) at the molecular level is known to be responsible for a tiny energy difference between the two enantiomers of a chiral molecule. This parity violation energy difference (PVED) has not yet been detected by experiment. In the last few years, the search for PV effects in molecules has made important steps ahead for several reasons. On one hand, very accurate infra-red spectroscopy measurements were performed by metrologists on bromochlorofluoromethane (CHFClBr) with a 10 Hz accuracy, which so far is the most precise. On the other hand, relativistic calculations were used for the evaluation of DeltaE(PV) allowing for a screening of favorable molecules for future measurements. The synthesis of such chiral molecules with high parity violation effects is currently being investigated. In memory of Professor Jean-Bernard Robert.     

Jet cooled spectroscopy of H2DO+: Barrier heights and isotope-dependent tunneling dynamics from H3O+ to D3O+

The first high resolution spectroscopic data for jet cooled H2DO+ are reported, specifically via infrared laser direct absorption in the OH stretching region with a slit supersonic jet discharge source. Transitions sampling upper (0-) and lower (0+) tunneling states for both symmetric (nu1+ <-- 0+, nu1- <-- 0-, and nu1- <-- 0+) and antisymmetric (nu3+ <-- 0+ and nu3- <-- 0-) OH stretching bands are observed, where +/- refers to wave function reflection symmetry with respect to the planar umbrella mode transition state. The spectra can be well fitted to a Watson asymmetric top Hamiltonian, revealing band origins and rotational constants for benchmark comparison with high-level ab initio theory. Of particular importance are detection and assignment of the relatively weak band (nu1- <-- 0+) that crosses the inversion tunneling gap, which is optically forbidden in H3O+ or D3O+, but weakly allowed in H2DO+ by lowering of the tunneling transition state symmetry from D(3h) to C(2v). In conjunction with other H2DO+ bands, this permits determination of the tunneling splittings to within spectroscopic precision for each of the ground [40.518(10) cm(-1)], nu1 = 1 [32.666(6) cm(-1)], and nu3 = 1 [25.399(11) cm(-1)] states. A one-dimensional zero-point energy corrected potential along the tunneling coordinate is constructed from high-level ab initio CCSD(T) calculations (AVnZ, n = 3,4,5) and extrapolated to the complete basis set limit to extract tunneling splittings via a vibrationally adiabatic treatment. Perturbative scaling of the potential to match splittings for all four isotopomers permits an experimental estimate of DeltaV0 = 652.9(6) cm(-1) for the tunneling barrier, in good agreement with full six-dimensional ab initio results of Rajamaki, Miani, and Halonen (RMH) [J. Chem. Phys. 118, 10929 (2003)]. (DeltaV0 (RMH) = 650 cm(-1)). The 30%-50% decrease in tunneling splitting observed upon nu1 and nu3 vibrational excitations arises from an increase in OH stretch frequencies at the planar transition state, highlighting the transition between sp2 and sp3 hybridizations of the OHD bonds as a function of inversion bending angle.     

Torsion-vibration coupling in methanol: the adiabatic approximation and intramolecular vibrational redistribution scaling

The four-dimensional model Hamiltonian of Wang and Perry [J. Chem. Phys. 109, 10795 (1998)] is used to compare the approximate adiabatic separation of the torsion and CH stretches in methanol to an exact solution of the same Hamiltonian. The adiabatic approximation accounts for the pattern of the energy levels in the lowest torsional states, including the inverted tunneling splittings, but does not account for the pattern of systematic two- and four-fold near degeneracies at high torsional excitation. In the adiabatic basis, the nonadiabatic couplings mix the torsional and vibrational degrees of freedom and hence are a source for intramolecular vibrational redistribution (IVR). These IVR matrix elements are found to decrease by only a factor of 2 or 3 with each higher coupling order, in agreement with the results of Pearman and Gruebele [Z. Phys. Chem. Munich 214, 1439 (2000)]. This gentle scaling behavior, which contrasts with a steeper falloff with coupling order in more rigid molecules, points to a more important role for direct high-order couplings in torsional molecules. In this model, the scaling behavior derives from a single coupling term that is low order in the torsional angular momentum in combination with one-dimensional torsional functions that include contributions from many torsional angular momenta.     

Supersonically cooled hydronium ions in a slit-jet discharge: high-resolution infrared spectroscopy and tunneling dynamics of HD2O+

Jet-cooled high-resolution infrared spectra of partially deuterated hydronium ion (HD2O+) in the O-H stretch region (nu3 band) are obtained for the first time, exploiting the high ion densities, long absorption path lengths, and concentration modulation capabilities of the slit-jet discharge spectrometer. Least-squares analysis with a Watson asymmetric top Hamiltonian yields rovibrational constants and provides high level tests of ab initio molecular structure predictions. Transitions out of both the lower (nu3(+)<--0(+)) and the upper (nu3(-)<--0(-)) tunneling levels, as well as transitions across the tunneling gap (nu3(-)<--0(+)) are observed. The nu3(-)<--0(+) transitions in HD2O+ acquire oscillator strength by loss of D(3h) symmetry, and permit both ground-state-[27.0318(72) cm(-1)] and excited-state-[17.7612(54) cm(-1)]-tunneling splittings to be determined to spectroscopic precision from a single rovibrational band. The splittings and band origins calculated with recent high level ab initio six-dimensional potential surface predictions for H3O+ and isotopomers [X. C. Huang, S. Carter, and J. M. Bowman, J. Chem. Phys. 118, 5431 (2003); T. Rajamaki, A. Miani, and L. Halonen, J. Chem. Phys. 118, 10929 (2003)] are in very good agreement with the current experimental results.     

Large parity violation effects in the vibrational spectrum of organometallic compounds

Large parity violation effects of the order of 1 Hz are predicted for the vibrational spectrum of two organometallic species, Os(eta5-C5H5)(=CCl2)Cl(PH3) and Re(eta5-Cp*)(=O)(CH3)Cl. It should therefore be possible to detect such effects in molecules by high-resolution spectroscopy for the first time.     

Implications of comparative spectral doublets observed for neon-isolated and gaseous tropolone(OH) and tropolone(OD)

Spectral doublet separations reported for gas phase and neon matrix-isolated samples of tropolone(OH) and tropolone(OD) are found to support recent work suggesting the possibility that tropolone has a slightly nonplanar geometry in the S1 (A 1B2) (pi*-pi) electronic state. Tautomerizations of gaseous tropolones in the S0 and S1 states are governed by equal double-minimum potential energy functions (PEFs), but interactions in the neon matrix environment transform the tautomerization PEFs of the slightly nonplanar S1 tropolones into unequal double-minimum PEFs. The spectral doublets reported for the zero-point S1-S0 transitions imply energy minima for the nonplanar S1 state in a neon matrix are offset by about 7 cm-1, and tunneling splittings in the symmetric double minimum PEFs of the gaseous molecules are damped about 2 cm-1 by the matrix environment. This means gas phase tunneling splittings smaller than 2 cm-1 are fully quenched in the neon matrix, and gas phase tunneling splittings near 20 cm-1 are damped by only 10%.     

Rotational spectrum and inversion motions in the neon-dimethyl sulfide complex

The rotational spectra of the (20)Ne and (22)Ne isotopomers of the Ne-dimethyl sulfide (DMS) rare gas dimer have been measured by Fourier transform microwave spectroscopy. MP2/6-311++G(2d,2p) calculations, and the experimental spectroscopic data, suggest a structure of C(s) symmetry in which the Ne atom lies above the heavy atom plane of the DMS (in the sigma(v) plane which bisects the CSC angle). Experimental rotational constants are consistent with a S...Ne distance of 3.943(6) Angstroms and a (cm...S...Ne) angle of 63.2(6) degrees (where cm is the center of mass of DMS). A motion of the Ne atom from one side of the DMS to the other gives rise to inversion splittings of around 3 MHz in the c-type transitions. An ab initio potential energy surface calculation has allowed examination of several possible tunneling pathways, and suggests a barrier of between 20 and 40 cm(-1) for the inversion motion, depending on the tunneling pathway taken by the Ne. Dipole moment measurements are consistent with both the experimental and ab initio structures.     

Ab initio studies on hydrogen-transfer tunneling for Cl + HCl abstraction hydrogen reaction

This article presents a treatment scheme of the tunneling of hydrogen between two molecular centers (Cl…Cl). The purpose is to calculate the tunneling probabilities of hydrogen atom transfer from the initial (the proceeding complex) to the final-state energy minima (the succeeding complex) in two anharmonic vibrational states (0 → 0 and 1 → 1) in terms of the time-dependent perturbation theory expression and to see whether spectroscopic signatures of tunneling persist in the form of splittings of the vibrational modes. The analysis uses the realistic potential energy function calculated at the HF/6−31 + G** self-consistent-field basis-set level for the interaction between transferred hydrogen and its molecular skeleton (Cl…H…Cl). This potential energy surface is calibrated by comparing its properties with those from sf-POLCI and the LEPS potential-energy surfaces. The anharmonic vibrational state is characterized by the corrected vibrational energy levels and a set of linear combination coefficients obtained via perturbation theory. The tunneling probabilities for two transitions (0 → 0 and 1 → 1) were calculated and compared with those from Gamow's equation. Applicability of the time-dependent perturbation theory expression and Gamow's equation to the [Cl BOND H…Cl] system is discussed. The vibrational splitting energies are obtained, and a spectroscopic signature caused by tunneling is expected and should be observable. © 1996 John Wiley & Sons, Inc.     

Ne3-NH3 van der Waals tetramer: rotational spectra and ab initio study of the microsolvation of NH3 with rare gas atoms

Microwave rotational spectra of eleven isotopomers of the Ne(3)-NH(3) van der Waals tetramer were measured using a pulsed jet, Balle-Flygare type Fourier transform microwave spectrometer. The transitions measured fall between 4 and 17 GHz and correspond to the ground internal rotor state of the weakly bound complex. The (20)Ne(3)- and (22)Ne(3)-containing species are symmetric top molecules while the mixed (20)Ne(2)(22)Ne- and (20)Ne(22)Ne(2)-isotopomers are asymmetric tops. For each of the deuterium-containing isotopomers, a tunneling splitting was observed due to the inversion of NH(3) within the tetramer. The (14)N nuclear quadrupole hyperfine structures were resolved and included in the spectroscopic fits of the various isotopomers. The rotational constants obtained from the fits were used to estimate the van der Waals bond lengths of the tetramer while the (14)N nuclear quadrupole coupling contants and the observed inversion tunneling splittings provided information about the internal dynamics of the NH(3) moiety. The experimental results were complemented by the construction of three ab initio potential energy surfaces [CCSD(T)] for the Ne(3)-NH(3) complex, each corresponding to a different internal geometry of NH(3) ( 90 degree angle HNH = 106.67 degrees, 90 degree angle HNH = 113.34 degrees, and 90 degree angle HNH = 120.00 degrees ). The topologies of the surfaces are related to the structures and dynamics of the tetramer. Extensive comparisons are made between the results obtained for the Ne(3)-NH(3) tetramer in this work and previous experimental and ab initio studies of related Rg(n)-NH(3) van der Waals clusters.