Determination of the proton tunneling splitting of the vinyl radical in the ground state by millimeter-wave spectroscopy combined with supersonic jet expansion and ultraviolet photolysis

Twins in rotational spectroscopy: Does a rotational spectrum uniquely identify a molecule?

Rotational spectroscopy is the most accurate method for determining structures of molecules in the gas phase. It is often assumed that a rotational spectrum is a unique "fingerprint" of a molecule. The availability of large molecular databases and the development of artificial intelligence methods for spectroscopy make the testing of this assumption timely. In this paper, we pose the determination of molecular structures from rotational spectra as an inverse problem. Within this framework, we adopt a funnel-based approach to search for molecular twins, which are two or more molecules, which have similar rotational spectra but distinctly different molecular structures. We demonstrate that there are twins within standard levels of computational accuracy by generating rotational constants for many molecules from several large molecular databases, indicating that the inverse problem is ill-posed. However, some twins can be distinguished by increasing the accuracy of the theoretical methods or by performing additional experiments.

Fourier transform microwave spectroscopy of the 13C- and 18O-substituted tropolone. Proton tunneling effect for the isotopic species with the asymmetric potential wells

Fourier-transform microwave spectroscopy has been applied for the 13C/18O-substituted tropolone to observe tunneling-rotation transitions as well as pure rotational transitions. The tunneling-rotation transitions were observed between the 13C-4 and -6 forms as well as between 13C-3 and -7, between 13C-1 and -2, and between 18O-8 and -9 (we denote these tunneling pairs as 13C-46, etc., below) although they have an asymmetric tunneling potential due to the difference in the zero point energy (ZPE). From the observed tunneling splittings ΔEij (0.9800-1.6824 cm-1), the differences in ZPE Δij for the 13C-46, -37, -12, and 18O-89 species are derived to be -0.1104, 0.5652, -1.3682, and 1.3897 cm-1 to agree well with the DFT calculation. The state mixing ratio of the tunneling states decreases drastically from (44%:56%) to (8.7%:91.3%) for 13C-46 and 18O-89 with an increase in the asymmetry Δij of the tunneling potential function. The observed tunneling-rotation interaction constants Fij decrease from 16.001 to 9.224 cm-1 as the differences in ZPE Δij increase, while the diagonal tunneling-rotation interaction constants Fu increase from 1.767 to 13.70 cm-1, explained well by the mixing ratio of the tunneling states.

Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical

Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method.

Fine and hyperfine coupling constants of the cis-β-cyanovinyl radical, HCCHCN

A Fourier-transform microwave spectrum of the cis-β-cyanovinyl radical is re-measured for the K_a = 0 ladder of the a-type transitions up to 30 GHz and the 2₁₂-1₁₁ transition at 19.85 GHz. Four b-type transitions are also observed using a MW-MW double-resonance technique. Fine and hyperfine components observed for each rotational transition are fully assigned in the present study, and the precise molecular constants are determined for the radical. From the comparisons of the hyperfine coupling constants with those of the vinyl radicals, it is concluded that the substitution of one of the β-hydrogens by the cyano group has little effect on the electronic structure of the vinyl radical.

Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach

A combined approach that uses the vibrational configuration interaction (VCI) and semiclassical instanton theory was developed to study vibrational tunneling spectra of molecules with multiple wells in full dimensionality. The method can be applied to calculate low-lying vibrational states in the systems with an arbitrary number of minima, which are not necessarily equal in energy or shape. It was tested on a two-dimensional double-well model system and on malonaldehyde, and the calculations reproduced the exact quantum mechanical (QM) results with high accuracy. The method was subsequently applied to calculate the vibrational spectrum of the asymmetrically deuterated malonaldehyde with nondegenerate vibrational frequencies in the two wells. The spectrum is obtained at a cost of single-well VCI calculations used to calculate the local energies. The interactions between states of different wells are computed semiclassically using the instanton theory at a comparatively negligible computational cost. The method is particularly suited to systems in which the wells are separated by large potential barriers and tunneling splittings are small, for example, in some water clusters, when the exact QM methods come at a prohibitive computational cost.

An ab initio study of the photodissociation of the vinyl radical

Photodissociation of the vinyl radical through pathways CH₂CH → CH₂C + H, CH₂CH → CHCH + H, and CH₂CH → CH₂ + CH is investigated by means of high-level ab initio calculations. Potential-energy curves (PECs) along the corresponding dissociating bond distance associated with the ground and several excited electronic states involved in the above fragmentation pathways, as well as the nonadiabatic couplings connecting the different states, are obtained. The findings of several experiments on vinyl photodissociation performed at different excitation wavelengths are analyzed and explained qualitatively in the light of the present PECs. A two-dimensional representation (consisting of radial and angular coordinates to represent one of the H atoms of the CH₂ group) is also used to calculate the electronic states. The surfaces obtained reflect a rich variety of conical intersections, exit barriers, and nonadiabatic couplings leading to predissociation in different regions of energy and of the two coordinates, suggesting a complex photodissociation dynamics of the CH₂CH → CHCH + H pathway, with rather different fragmentation mechanisms involved. The two-dimensional results also provide interesting information on the mechanism of in-plane hydrogen migration from the CH₂ group to the CH one through a high-lying transition state.

Spectroscopic detection of gas-phase HOSO2

The HOSO₂ radical was detected by microwave spectroscopy in a discharge plasma of a SO₂/H₂O gas mixture. The observed spectrum shows tunneling splittings due to the OH torsional motion. A least-squares analysis considering interactions between the two torsional sublevels of the ground vibronic state, 0⁺ and 0^-, reproduces the observed transition frequencies with a standard deviation of ca. 3 kHz. The splitting between the two torsional sublevels is accurately determined to be 24.3 MHz for HOSO₂ and 0.08 MHz for DOSO₂. The potential barrier for the OH torsional motion is estimated to be 1150 cm^-1 from a one-dimensional hindered rotor model.

A variational calculation of vibrational levels of vinyl radical

We report the vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and a contracted basis. Many of the levels of the two previous VR variational calculations differ significantly and differ also from those reported in this paper. We identify the source of and correct symmetry errors on the potential energy surfaces used in the previous calculations. VR has two equivalent equilibrium structures. By plotting wavefunction cuts, we show that two tunneling paths play an important role. Using the computed wavefunctions, it is possible to assign many states and thereby to determine tunneling splittings that are compared with their experimental counterparts. Our computed red shift of the hot band at 2897.23 cm^-1, observed by Dong et al. [J Chem. Phys. 128, 044305 (2008)], is 4.47 cm^-1, which is close to the experimental value of 4.63 cm^-1.

The ionization energy of the vinyl radical: a Mexican standoff with a happy ending

Theoretical approaches and experimental spectra are confirmed as the origin transition is shown to be forbidden in vinyl photoionization.

Rovibrational quantum dynamics of the vinyl radical and its deuterated isotopologues

Rotational–vibrational states up to 3200 cm⁻¹, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H₂C_βC_αH, and the following deuterated isotopologues of VR: CH₂CD, CHDCH, and CD₂CD.

Millimeter-wave spectroscopy of H(2)C=CD: Tunneling splitting and ortho-para mixing interaction

The H(2)C=CD isotopic species of vinyl radical produced in a supersonic jet expansion by ultraviolet laser photolysis was studied by millimeter-wave spectroscopy. Due to the tunneling motion of the α deuteron, the ground state is split into two components, 0(+) and 0(-). Tunneling-rotation transitions connecting the lower (0(+)) and upper (0(-)) components of the tunneling doublet were observed in the frequency region of 184-334 GHz, including three R- and two Q-branch transitions. Three and two pure rotational transitions in the K(a)=0 and 1 stacks, respectively, were also observed for each of the 0(+) and 0(-) states in the frequency region of 52-159 GHz. Least-squares analysis of the observed frequencies for the tunneling-rotation and pure rotational transitions with well resolved hyperfine structures yielded a set of precise molecular constants, among which the tunneling splitting in the ground state was determined to be ΔE(0)=1187.234(17) MHz, which is 1/14 that for H(2)C=CH. The potential barrier height derived from the observed tunneling splitting by an analysis of the tunneling dynamics using a one-dimensional model is 1545 cm(-1), consistent with the value 1568 cm(-1) obtained for the normal vinyl. The observed spectrum was found to be perturbed by a hyperfine interaction connecting ortho and para levels. The constant for the interaction, which we call the ortho-para mixing Fermi contact interaction, has been determined to be δa(F) ((β))=68.06(53) MHz. This is believed to be the first definite detection of such an interaction. By this interaction the ortho and para states of H(2)C=CD are mixed up to about 0.1%. The constant is more than 1000 times larger than spin-rotation interaction constants that cause ortho-para mixing in closed shell molecules and suggests extremely rapid conversion between the ortho and para nuclear spin isomers of H(2)C=CD.

Vibrational modes of the vinyl and deuterated vinyl radicals

Following the initial report of the detection of fundamental transitions of all nine vibrational modes of the vinyl radical [Letendre , L. ; Liu , D.-K. ; Pibel , C. D. ; Halpern , J. B. ; Dai , H.-L. J. Chem. Phys. 2000 , 112 , 9209] by time-resolved IR emission spectroscopy, we have re-examined the assignments of the vibrational modes through isotope substitution. Precursor molecules vinyl chloride-d3, vinyl bromide-d3, and 1,3-butadiene-d6 are used for generating vibrationally excited vinyl-d3 through 193 nm photolysis. The nondeuterated versions of these molecules along with vinyl iodide and methyl vinyl ketone are used as precursors for the production of vinyl-h3. IR emission following the 193 nm photolysis laser pulse is recorded with nanosecond time and approximately 8 cm(-1) frequency resolution. A room-temperature acetylene gas cell is used as a filter to remove the fundamental transitions of acetylene, a photolysis product, in order to reduce the complexity of the emission spectra. Two-dimensional cross-spectra correlation analysis is used to identify the emission bands from the same emitting species and improve the S/N of the emission spectra. Isotope substitution allows the identification of several low-frequency vibrational modes. For C2H3, the assigned modes are the nu4 (CC stretch) at 1595, nu5 (CH2 symmetric bend) at 1401, nu6 (CH2 asymmetric + alpha-CH bend) at 1074, nu8 (CH2 + alpha-CH symmetric out-of-plane (oop) bend) at 944, and nu9 (CH2 + alpha-CH asymmetric oop bend) at 897 cm(-1). For C2D3, the modes are the nu5 (CD2 symmetric bend) at 1060, nu6 (CD2 asymmetric + alpha-CD bend) at 820, and nu8 (CD2 + alpha-CD symmetric oop bend) at 728 cm(-1).

Ortho-para mixing interaction in the vinyl radical detected by millimeter-wave spectroscopy

Ortho-para mixing interaction due to the coupling of nuclear and electron spins was detected for the first time by millimeter-wave spectroscopy of the deuterated vinyl radical H(2)CCD. The ground state of H(2)CCD is split by the deuteron tunneling into two components 0(+) and 0(-) separated by DeltaE(0)=1186.794(16) MHz. Rotational levels in the 0(+) and 0(-) states, one being an ortho level and the other a para level, are coupled by the interaction expressed by 0(+/-)mid R:H(')mid R:0(-/+)=(deltaa(F)/2)S(I(1)-I(2)), where I(1) and I(2) are spins of the two protons and S is the electron spin. The deltaa(F) constant has been determined to be 68.06(52) MHz. The para to ortho conversion rate constant is predicted to be 1.2x10(5) s(-1) torr(-1).

Millimeter-wave spectroscopy of CoNO produced by UV laser photolysis of Co(CO)3NO

The rotational spectrum of cobalt mononitrosyl (CoNO) produced by ultraviolet photolysis of Co(CO)(3)NO was observed in the millimeter-wave region. Seven rotational transitions in the ground state ranging from J = 6-5 to 12-11, with hyperfine splittings due to the Co nucleus (I = 7/2), were detected in a supersonic jet environment, while higher-frequency transitions in the range from J = 29-28 to 35-34 were measured in the ground, nu(1), nu(2), nu(3), and 2nu(2) vibrational states using a free-space absorption cell. It was confirmed from the observed spectral pattern that the CoNO molecule has a linear structure with the electronic ground state of (1)Sigma(+) symmetry. The rotational lines in the 2nu(2)(Sigma) and nu(3) states were observed to be perturbed by Fermi resonance. The equilibrium rotational constant B(e) is determined to be 4682.207(15) MHz. The CoN bond length is derived to be 1.5842 A assuming the NO bond length of 1.1823 A. A large nuclear spin-rotation interaction constant, C(I) = 123.8(11) kHz, was determined, suggesting a (1)Pi electronic excited state lying close to the ground state.

Tunneling Splitting of Energy Levels and Rotational Constants in the Vinyl Radical C2H3

The instanton theory newly implemented by two of the authors (G.V.M. and H.N.) is applied to hydrogen tunneling transfer in a vinyl radical. The converged instanton trajectory is found on the CCSD(T)/aug-cc-pVTZ level of an ab initio potential energy surface. The calculated ground-state energy splitting agrees with the recent high-resolution experimental data within 3% of discrepancy. The semiclassical wave function is used to estimate the splitting of the principal rotational constants of the radical.