Rotation-vibration Coupling Research Articles

Incorporating reduced axis system embedding into ab initio tunnelling-rotation Hamiltonians with curvilinear vibrational Møller–Plesset perturbation theory

Large-amplitude vibrational motion influences the rovibrational structure of molecules that tunnel between multiple wells. Reaction path (RP) Hamiltonians, and curvilinear coordinates more generally, are useful for modelling pure vibrational motion in these systems and provide a practical framework for calculating accurate ab initio anharmonic vibrational energies and tunnelling splittings with perturbation theory. These computational tools also offer the means to address rotation-vibration coupling associated with large-amplitude motion in rotating molecules. In this paper, we incorporate the reduced axis system (RAS) frame embedding with RP Hamiltonians and second-order vibrational Møller-Plesset perturbation theory (VMP2). Because the RP-RAS Hamiltonian eliminates rotation-vibration momentum coupling everywhere along a one-dimensional reaction path, it is well suited for rovibrational VMP2 methods, the convergence of which relies critically on approximate vibration-vibration and vibration-rotation separability. The accuracy of this combined RP-RAS-VMP2 scheme is demonstrated by comparisons with numerically exact variational calculations and VMP2 parameters based on traditional Eckart embeddings for reduced-dimension models of torsional tunnelling in hydrogen peroxide and inversion tunnelling in cyclopropyl radical. The favourable computational scaling of VMP2 makes it a promising strategy for calculating accurate tunnelling-rotation parameters for medium-sized and larger molecules in full dimensionality.

A Note on Stability of a Dopant for Perovskite Solar Cells: Dimerization of 2,2′-bis(trifluoromethyl)-[1,1′-biphenyl]-4,4′-diamine Iodine

The note continues with the density-functional theory (DFT) quantum-chemical understanding of perovskite solar cells at molecular level. In particular, 2,2′-bis(trifluoromethyl)-[1,1′-biphenyl]-4,4′-diamine iodine (or BFBAI2, stoichiometry C14H12F6I2N2) is further calculated—the species is known to improve the power conversion efficiency and device stability. The thermodynamic-stability calculations are performed at the M06-2X/3-21G level with anharmonic vibrational analysis (including vibrational-rotational coupling) for construction of the vibrational-rotational partition functions. The dimerization is shown to be an essential feature of BFBAI2 (it is based on the formation of two hydrogen bonds). The BFBAI2 dimerization is described in the terms of the standard Gibbs energy and the related dimerization equilibrium constant. Comparisons are made with the water dimer, commonly used as a model system for hydrogen-bond formation. The equilibrium constants for the water dimerization are consistently lower than for the dimerization of BFBAI2 - as the presence of two hydrogen bonds in the BFBAI2 dimer contributes to the larger stabilization. The dimerization of BFBAI2 upon higher surface coverages represents an additional factor for the layer stabilization as there is decrease in the standard Gibbs energy at moderate temperatures. The dimerization also brings additional features for modulation of surface conditions.

Improved Geometries and Frequencies with the PFD-3B DFT Method.

Bond lengths have been calculated for a test set of 120 diatomic species, including all homonuclear diatomics, hydrides, fluorides, and oxides for elements H through Kr for which experimental data is available for comparison. The performance of the PFD-3B functional is significantly better than competitive DFT methods. The rms error in bond lengths is reduced to 0.01 Å using a moderate size 3Za1Pa + f triple-ζ basis set, with the rms error in harmonic vibrational constants, ωe, equal to 38 cm-1. A very small 2ZP0H basis set is sufficient to calculate anharmonic constants, ωeXe, within ±4 cm-1. The rotational constants, Be, agree with experiment to within ±2%, and the vibration-rotation coupling constants, αe, agree within 10%. The calculated vibrational zero-point energy, ZPE, agrees with experiment to within ±0.06 kcal mol-1 for the diatomic test set, and the error increases to just ±0.11 kcal mol-1 for a set of 12 small polyatomic species. Comparison of a detailed anharmonic analysis of the twisted ethylene cation to the PFI-ZEKE experimental data illustrates the reliability of the PFD-3B for atypical structures.

In Vitro and In Silico Vibrational-Rotational Spectroscopic Characterization of the Next-Generation Refrigerant HFO-1123.

Very short-lived substances have recently been proposed as replacements for hydrofluorocarbons (HFCs), in turn being used in place of ozone-depleting substances, in refrigerant applications. In this respect, hydro-fluoro-olefins (HFOs) are attracting particular interest because, due to their reduced global warming potential, they are supposed to be environmentally friendlier. Notwithstanding this feature, they represent a new class of compounds whose spectroscopic properties and reactivity need to be characterized to allow their atmospheric monitoring and to understand their environmental fate. In the present work, the structural, vibrational, and ro-vibrational properties of trifluorothene (HFO-1123, F2C = CHF) are studied by state-of-the-art quantum chemical calculations. The equilibrium molecular structure has an expected error within 2 mÅ and 0.2° for bond lengths and angles, respectively. This represents the first step toward the computation of highly accurate rotational constants for both the ground and first excited fundamental vibrational levels, which reproduce the available experimental data well within 0.1%. Centrifugal distortion parameters and vibrational–rotational coupling terms are computed as well and used to solve some conflicting experimental results. Simulation of the vibrational transition frequencies and intensities beyond the double harmonic approximation and up to three quanta of vibrational excitation provides insights into the couplings ruling the vibrational dynamics and guides the characterization of the gas-phase infrared spectrum experimentally recorded in the range of 200–5000 cm–1. The full characterization of the IR features is completed with the experimental determination of the absorption cross sections over the 400–5000 cm–1 region from which the radiative forcing and global warming potential of HFO-1123 are derived.

Full quantum time-dependent simulations for the two-body breakups of H2Ar2+ and N2Ar2+

We developed a full quantum time-dependent wave-packet evolution method to simulate the multibody breakups of polyatomic molecular ions. The interaction picture theory was used to propagate the wave packet, where the effects of strong and long-range interactions are considered by basis functions and the weak and short-range interactions are included in the perturbation term. In this method, the Coulomb interactions, polycentric interactions, vibration-rotation coupling of molecular fragments, and the rotation-rotation coupling between molecular fragment and parent molecule are considered accurately. Using this method, we simulate the two-body breakups of ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}$ and ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$. The simulated results show that the ultrafast rotation of the molecular fragment generally exists in the breakup of the polyatomic molecular ion. For ${\mathrm{H}}_{2}{\mathrm{Ar}}^{2+}, {\mathrm{H}}_{2}^{+}$ can rotate from an initial broad distribution around ${35}^{\ensuremath{\circ}}$ and ${145}^{\ensuremath{\circ}}$ to a narrow distribution around ${75}^{\ensuremath{\circ}}$ and ${105}^{\ensuremath{\circ}}$ within 30 fs. For ${\mathrm{N}}_{2}{\mathrm{Ar}}^{2+}$, the initial sine-shaped angular distribution ($j$ = 0) shrinks to a narrow range (${90}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{20}^{\ensuremath{\circ}}$) within 120 fs and then spreads to an approximately random distribution within 300 fs. Such ultrafast rotations are dominated by the polycentric interaction between fragments and impacted by the vibration-rotation and rotation-rotation couplings.

Semi-experimental equilibrium (re SE) and theoretical structures of hydrazoic acid (HN3).

Hydrazoic acid (HN3) is used as a case study for investigating the accuracy and precision by which a molecular structure-specifically, a semi-experimental equilibrium structure (re SE)-may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration-rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN3 allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent re SE structure determination. The re SE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained re SE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that re SE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational re structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding re SE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born-Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation.

Coupling response of flow-induced oscillating cylinder with a pair of flow-induced rotating impellers

An innovative device transforming the active control of rotating rods to passive control with a pair of impellers is proposed and numerically examined in this paper. The coupling response of a vortex-induced vibrating (VIV) circular cylinder symmetrically equipped with two impellers that are free to rotate is analyzed based on the results of computations that carried out for a reduced velocity range of Ur = 2–14 at a low Reynolds number of 150. In comparison with the bare cylinder, both the in-line and cross-flow responses are significantly augmented in the VIV initial branch with the introduction of a pair of passively rotating impellers, which is mainly attributed to the unstable rotation response in both direction and speed and the wake adjustment including the reduction in vortex formation length and broadening of flow wake. In the VIV lower branch, although the response amplitude is close to that of a bare cylinder, the strong interaction between two directional responses occurs with the same dominant frequency locking on the natural one. Nevertheless, the coexistence of multiple vibration frequencies leads to irregular oscillation trajectories and irregular vortex shedding. Moreover, the secondary vortex street is observed in the whole Ur range, but the number of merged vortices for the formation of secondary vortex street varies with Ur, depending on the response amplitude and the interaction between the shear layers of the main cylinder and impellers. In terms of time-averaged rotation, the symmetrical inward counter-rotating pattern is achieved despite the intermittent alteration of rotation direction. Furthermore, the vibration–rotation coupling is demonstrated from the variation of time-averaged rotation speed that closely follows the variation of vibration amplitude against Ur.

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone.

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers 16O18O16O and 16O16O18O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Structure, Stability, and Spectroscopic Properties of Small Acetonitrile Cation Clusters.

Ionization and fragmentation pathways induced by ionizing agents are key to understanding the formation of complex molecules in astrophysical environments. Acetonitrile (CH3CN), the simplest organic nitrile, is an important molecule present in the interstellar medium. In this work, DFT and MP2 calculations were performed in order to obtain the low energy structures of the most relevant cations formed from electron-stimulated ion desorption of CH3CN ices. Selected reaction pathways and spectroscopic properties were also calculated. Our results indicate that the most stable acetonitrile cation structure is CH2CNH+ and that hydrogenation can occur successively without isomerization steps until its complete saturation. Moreover, the stability of distinct cluster families formed from the interaction of acetonitrile with small fragments, such as CHn+, C2Hn+, and CHnCNH+, is discussed in terms of their respective binding energies. Some of these molecular clusters are stabilized by hydrogen bonds, leading to species whose infrared features are characterized by a strong redshift of the N-H stretching mode. Finally, the rotational spectra of CH3CN and protonated acetonitrile, CH3CNH+, were simulated using distinct computational protocols based on DFT, MP2, and CCSD(T) considering centrifugal distortion, vibrational-rotational coupling, and vibrational anharmonicity corrections. By adopting an empirical scaling procedure for calculating spectroscopic parameters, we were able to estimate the rotational frequencies of CH3CNH+ with an expected average error below 1 MHz for J values up to 10.

Simulations of Infrared Radiation Measurements in Shock and Expansion Tubes

This Paper presents the simulations of and CO infrared radiation behind shock waves and in expansion flows. This work is motivated by the little amount of characterizations of infrared radiation in these expansion flows and thermodynamic regimes, whereas carbon dioxide infrared radiation is deemed to contribute significantly to the afterbody heating withstood by a Martian spacecraft. Japan Aerospace Exploration Agency (JAXA) shock-tube facilities were operated at conditions generating flow velocities ranging from 2.8 to . Absolute infrared spectra of and CO were obtained under equilibrium and nonequilibrium conditions and used to assess the performances of the spectral solvers. Specifically, this Paper introduces the recent enhancements brought to JAXA in-house codes to compute nonequilibrium infrared radiation. Schemes to split the level energy into its pure vibrational, rotational, and vibration–rotation coupling and interactions contributions are proposed and implemented. The implementation was evaluated with comparison with literature data and recent measurements. Infrared radiation behind shock waves and under expansion regimes was analyzed with a newly developed model to infer the vibrational and rotational temperatures and determine the degree of thermal nonequilibrium. The latter outlines the highly complicated vibrational energy distribution of carbon dioxide during expansion and the subsequent radiation, as well as the possible shortcomings of the multitemperature models. Therefore, these studies of carbon dioxide nonequilibrium radiation during expansion pose new challenges to the community and will enable the upgrade and validation of the multitemperature and state-to-state models currently in use.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (18O16O18O) and asymmetric (18O18O16O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (16O18O16O) and asymmetric (16O16O18O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

On neglecting Coriolis and related couplings in first-principles rovibrational spectroscopy: considerations of symmetry, accuracy, and simplicity

The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy levels is investigated, employing triatomic AB{}_{2} molecules as models. In particular, calculations are performed for H{}_{2}{}^{16}O, across a range of vibrational and rotational excitations, both with and without the Coriolis contribution. A variety of different embedding choices are considered, together with a hierarchy of increasingly severe approximations culminating in a generalized version of the so-called “centrifugal sudden” method. Several surprising and remarkable conclusions are found, including that the Eckart embedding is not the best embedding choice.

Molecular structure determination: Equilibrium structure of pyrimidine (m-C4H4N2) from rotational spectroscopy (re SE) and high-level ab initio calculation (re) agree within the uncertainty of experimental measurement.

The pure rotational spectrum of pyrimidine (m-C4H4N2), the meta-substituted dinitrogen analog of benzene, has been studied in the millimeter-wave region from 235 GHz to 360 GHz. The rotational spectrum of the ground vibrational state has been assigned and fit to yield accurate rotational and distortion constants. Over 1700 distinct transitions were identified for the normal isotopologue in its ground vibrational state and least-squares fit to a partial sextic S-reduced Hamiltonian. Transitions for all four singly substituted 13C and 15N isotopologues were observed at natural abundance and were likewise fit. Deuterium-enriched samples of pyrimidine were synthesized, giving access to all eleven possible deuterium-substituted isotopologues, ten of which were previously unreported. Experimental values of rotational constants and computed values of vibration-rotation interaction constants and electron-mass corrections were used to determine semi-experimental equilibrium structures (re SE) of pyrimidine. The re SE structure obtained using coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] corrections shows exceptional agreement with the re structure computed at the CCSD(T)/cc-pCV5Z level (≤0.0002 Å in bond distance and ≤0.03° in bond angle). Of the various computational methods examined, CCSD(T)/cc-pCV5Z is the only method for which the computed value of each geometric parameter lies within the statistical experimental uncertainty (2σ) of the corresponding semi-experimental coordinate. The exceptionally high accuracy and precision of the structure determination is a consequence of the large number of isotopologues measured, the precision and extent of the experimental frequency measurements, and the sophisticated theoretical treatment of the effects of vibration-rotation coupling and electron mass. Taken together, these demanding experimental and computational studies establish the capabilities of modern structural analysis for a prototypical monocyclic aromatic compound.

Nuclear collectivity in the even–even $$^{164{-}178}$$ 164 - 178 Yb along the yrast line

The collective properties along the yrast line in well-deformed even–even $$^{164{-}178}$$ Yb isotopes are investigated by pairing self-consistent total Routhian surface (TRS) calculations and extended E-gamma over spin (E-GOS) curves. The calculated results from ground-state deformations, e.g., $$\beta _2$$ , are in agreement with previous theoretical predictions and available experimental data. The basic behaviors of moment of inertia are reproduced by the present TRS calculations and discussed based on the aligned angular momenta. The centipede-like E-GOS curves indicate that the non-rotational components appear along the yrast sequences in these nuclei, which can explain the discrepancy in the moment of inertia between theory and experiment to some extent. The further extended E-GOS curves, which include the first-order rotation–vibration coupling, appear to provide possible evidence of vibrational effects in the well-deformed nuclei of $$^{164{-}178}$$ Yb.

An improved model to calculate equilibrium constants for formation of peroxy radical–water complexes

Recent experimental results show that the kinetics of some radical–radical reactions important for atmospheric pollution formation are faster when a radical–molecule complex forms as one step in the reaction mechanism. Calculated radical–molecule equilibria are needed to accurately describe the concentrations of complexes formed in these experiments as well as in the atmosphere. Here we report calculation of the equilibrium constant for complexation of hydroperoxy (HO2·) and 2-hydroxyethylperoxy radicals (HOCH2CH2O2·) with one water molecule by directly calculating the canonical partition function of the reactant and product species. We demonstrate the accuracy of the calculation using formation of the water dimer as a test case. Ab initio calculations provide the binding energy, rotational constants, and vibrational frequencies of both monomers and complexes. We demonstrate the failure of the harmonic approximation in the partition function for describing the low-frequency vibrational modes of the complexes. Instead, we model one dissociative hydrogen bond mode using a Lennard-Jones 6–3 potential and the other low-frequency vibrational modes using one- and twofold hindered rotors. The contributions of weakly bound states of the long-range dipole–dipole potential (Lennard-Jones 6–3) and of vibration–rotation coupling are not as important as the contribution of twofold hindered rotors. We also discuss methods for including multiple hydrogen-bonding configurations (local minima) when calculating equilibrium constants for formation of complexes.

Direct Molecular Simulation of Nonequilibrium Dilute Gases

This paper summarizes research performed over the past decade on the direct molecular simulation of dilute gas flows. Similar to the molecular dynamics method, a potential energy surface is the sole model input to a direct molecular simulation calculation. However, instead of simulating the motion of all atoms in the system deterministically, the direct molecular simulation method uses stochastic techniques and assumptions, adopted from the well-established direct simulation Monte Carlo method, which are accurate for dilute gases. Using the same potential energy surface as input, the direct molecular simulation method is verified to exactly reproduce pure molecular dynamics results for shock-wave flows. The direct molecular simulation method is then used to investigate nonequilibrium flows such as strong shock waves and dissociating nitrogen systems involving rotation–vibration coupling and coupling between internal energy and dissociation. Direct molecular simulation algorithms are detailed, and a number of new results relevant to hypersonic flows are presented along with a summary of other recent results in the literature.

Microwave Spectra, Structure, and Ring-Puckering Vibration of Octafluorocyclopentene.

The rotational spectra of octafluorocyclopentene (C5F8) has been measured for the first time using pulsed jet Fourier transform microwave spectroscopy in a frequency range of 6 to 16 GHz. As in the molecule cyclopentene, the carbon ring is nonplanar, and inversion through the plane results in an inversion pair of ground state vibrational energy levels with an inversion splitting of 18.4 MHz. This large amplitude motion leads to the vibration-rotation coupling of energy levels. The symmetric double minimum ring-puckering potential function was calculated, resulting in a barrier of 222 cm-1. The rotational constants A0 = 962.9590(1) MHz, B0 = 885.1643(4) MHz, C0 = 616.9523(4) MHz, A1 = 962.9590(1) MHz, B1 = 885.1643(4) MHz, C1 = 616.9528(4) MHz, and two centrifugal distortion constants for each state were determined for the parent species and all 13C isotopologues. A mixed coordinate molecular structure was determined from a least-squares fit of the ground state rotational constants of the parent and each 13C isotopologue combined with the equilibrium bond lengths and angles from quantum chemical calculations.

Equilibrium clumped-isotope effects in doubly substituted isotopologues of ethane

We combine path-integral Monte Carlo methods with a new intramolecular potential energy surface to quantify the equilibrium enrichment of doubly substituted ethane isotopologues due to clumped-isotope effects. Ethane represents the simplest molecule to simultaneously exhibit 13C–13C, 13C–D, and D–D clumped-isotope effects, and the analysis of corresponding signatures may provide useful geochemical and biogeochemical proxies of formation temperatures or reaction pathways. Utilizing path-integral statistical mechanics, we predict equilibrium fractionation factors that fully incorporate nuclear quantum effects, such as anharmonicity and rotational-vibrational coupling which are typically neglected by the widely used Urey model. The magnitude of the calculated fractionation factors for the doubly substituted ethane isotopologues indicates that isotopic clumping can be observed if rare-isotope substitutions are separated by up to three chemical bonds, but the diminishing strength of these effects suggests that enrichment at further separations will be negligible. The Urey model systematically underestimates enrichment due to 13C–D and D–D clumped-isotope effects in ethane, leading to small relative errors in the apparent equilibrium temperature, ranging from 5K at 273.15K to 30K at 873.15K. We additionally note that the rotameric dependence of isotopologue enrichment must be carefully considered when using the Urey model, whereas the path-integral calculations automatically account for such effects due to configurational sampling. These findings are of direct relevance to future clumped-isotope studies of ethane, as well as studies of 13C–13C, 13C–D, and D–D clumped-isotope effects in other hydrocarbons.

Clumped-isotope signatures at equilibrium of CH4, NH3, H2O, H2S and SO2

High precision Δi values at equilibrium determined by theoretical methods are imperatively needed as references for the development of new clumped-isotope thermometers (or tracers). In this study, quantum chemistry methods with corrections beyond the harmonic approximation are used to obtain the clumped-isotope signatures at equilibrium of several gas-phase molecules (i.e., CH4, NH3, H2O, H2S, and SO2). Here, we consider as many corrections to the traditional Bigeleisen–Mayer equation as possible to obtain accurate Δi values at equilibrium and their temperature dependences. The corrections include anharmonic correction for zero-point energy, anharmonic correction for vibrational excited states, vibration–rotation coupling correction for zero-point energy, vibration–rotation coupling correction for vibrational excited states, quantum mechanical correction to rotation, and centrifugal distortion correction, which are important for theoretical understanding of clumped-isotope signals. Specifically, molecular constants are calculated via second-order perturbative analysis at the MP2/aug-cc-pVTZ level. The CCSD/6-311+G(3df,3pd) and CCSD/aug-cc-pVTZ levels are further employed to ensure the precision of harmonic frequencies of methane. For methane, a polynomial fit of ΔCH313D values over the temperature range of from 273.15 to 1000K is obtained: ΔCH313D=0.002551000T4-0.116391000T3+1.013641000T2-0.436271000T Our results are slightly different from previous theoretical calculations, and may serve as new anchors for calibrating experimental observations.

Probing the Structure, Pseudorotation, and Radial Vibrations of Cyclopentane by Femtosecond Rotational Raman Coherence Spectroscopy.

Femtosecond time-resolved Raman rotational coherence spectroscopy (RCS) is employed to determine accurate rotational, vibration–rotation coupling constants, and centrifugal distortion constants of cyclopentane (C5H10). Its lowest-frequency vibration is a pseudorotating ring deformation that interconverts 10 permutationally distinct but energetically degenerate "twist" minima interspersed by 10 "bent" conformers. While the individual twist and bent structures are polar asymmetric tops, the pseudorotation is fast on the time scale of external rotation, rendering cyclopentane a fluxionally nonpolar symmetric top molecule. The pseudorotational level pattern corresponds to a one-dimensional internal rotor with a pseudorotation constant Bps ≈ 2.8 cm(-1). The pseudorotational levels are significantly populated up to l = ± 13 at 298 K; <10% of the molecules are in the l = 0 level. The next-higher vibration is the “radial” ν23 ring deformation mode at 273 cm–1, which is far above the pseudorotational fundamental. Femtosecond Raman RCS measurements were performed in a gas cell at T = 293 K and in a pulsed supersonic jet at T ≈ 90 K. The jet cooling reduces the pseudorotational distribution to l < ±8 and eliminates the population of ν23, allowing one to determine the rotational constant as A0 = B0 = 6484.930(11) MHz. This value is ∼300 times more precise than the previous value. The fit of the RCS transients reveals that the rotation–pseudorotation coupling constant αe,psB = −0.00070(1) MHz is diminutive, implying that excitation of the pseudorotation has virtually no effect on the B0 rotational constant of cyclopentane. The smallness of αe,psB can be realized when comparing to the vibration–rotation coupling constant of the ν23 vibration, αe,23B = -9.547(1) MHz, which is about 104 times larger.