A bactracking algorithm for exact counting of internal molecular energy levels

Kemper, Mjh Martin; Dijk, van J Jan; Buck, HM Henk

doi:10.1016/0009-2614(78)80405-9

Cited by 61 publications

(13 citation statements)

References 7 publications

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“…The vibrational state density of a molecule at a given excitation energy grows exceptionally rapidly with the number of vibrational degrees of freedom, and in particular, the number of low vibrational modes. − Due to the presence of 3 N – 6 = 27 vibrational normal modes, the phenyl radical might be expected to suffer substantial loss of spectral simplicity from IVR induced fragmentation of isolated eigenstates of the lower order and largely separable Hamiltonian. Note that such intramolecular vibrational dynamics does not necessarily imply any true homogeneous broadening of lines beyond the sub-Doppler line width, as could occur for the case of strong predissociative coupling with the continuum.…”

Section: Discussionmentioning

confidence: 99%

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

2013

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Phenyl radical has been studied via sub-Doppler infrared spectroscopy in a slit supersonic discharge expansion source, with assignments for the highest frequency b2 out-of-phase C-H symmetric stretch vibration (ν19) unambiguously confirmed by ≤6 MHz (0.0002 cm(-1)) agreement with microwave ground state combination differences of McMahon et al. [Astrophys. J. 2003, 590, L61-64]. Least squares analysis of over 100 resolved rovibrational peaks in the sub-Doppler spectrum to a Watson Hamiltonian yields precision excited-state rotational constants and a vibrational band origin (ν0 = 3071.8915(4) cm(-1)) consistent with a surprisingly small red-shift (0.9 cm(-1)) with respect to Ar matrix isolation studies of Ellison and co-workers [J. Am. Chem. Soc. 2001, 123, 1977]. Nuclear spin weights and inertial defects confirm the vibrationally averaged planarity and (2)A1 rovibronic symmetry of phenyl radical, with analysis of the rotational constants consistent with a modest C2v distortion of the carbon backbone frame due to partial sp rehybridization of the σ C radical-center. Most importantly, despite the number of atoms (N = 11) and vibrational modes (3N - 6 = 27), phenyl radical exhibits a remarkably clean jet cooled high-resolution IR spectrum that shows no evidence of intramolecular vibrational relaxation (IVR) phenomena such as local or nonlocal perturbations due to strongly coupled nearby dark states. This provides strong support for the feasibility of high-resolution infrared spectroscopy in other aromatic hydrocarbon radical systems.

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Section: Discussionmentioning

confidence: 99%

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

2013

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“…The Nature of the Near-Resonant Vibrational States. Using the model where the torsional motion is adiabatically separated from the normal-mode vibrations, we can determine the local density of cis, gauche, and delocalized torsional states using direct state-count methods. , In this calculation, we use the normal-mode frequencies that have been previously assigned . All normal-mode vibrational states are assumed to have the same torsional potential and the torsional states are calculated by diagonalizing the one-dimensional hindered rotation Hamiltonian using a free-rotor basis set .…”

Section: Methodsmentioning

confidence: 99%

Conformational Dependence of Intramolecular Vibrational Energy Redistribution in the EthylenicCH₂ Stretch Fundamental of Allyl Fluoride

McWhorter

Pate

1998

J. Phys. Chem. A

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The high-resolution (6 MHz) infrared spectra of the asymmetric ethylenic hydride stretches of both cis and gauche allyl fluoride have been measured. Rotational assignments of the eigenstates are made using the groundstate microwave-infrared double-resonance capabilities of an electric resonance optothermal spectrometer (EROS). The cis vibrational band near 3114 cm -1 is characterized by sparse, narrow IVR multiplets resulting from weak Coriolis or cross conformer interactions between the vibrational bath states. The IVR lifetime of the cis vibrational band is approximately 2 ns (2000 ps). The gauche vibrational band near 3100 cm -1 is qualitatively and quantitatively quite different from the cis band. The gauche band is characterized by significantly fragmented IVR multiplets with an average IVR lifetime of about 90 ps. The measured anharmonic state density of the gauche band is about 30 states/cm -1 . The disagreement between the measured state densities of the gauche vibrational band and the calculated values suggest that the gauche vibrational states do not interact with cis vibrational states. For two IVR multiplets of the gauche band, the transitions were assigned according to the parity of the rovibrational bright state. The two parity states show roughly the same dynamical behavior. Also, RRKM calculations of the unimolecular isomerization rate are performed and compared to experimental results. The RRKM calculations overestimate both the cis and gauche isomerization rates by orders of magnitude.

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“…Since the CH 2 OH radical has only five atoms and nine vibrational modes, only six of which have energetically accessible frequencies, the vibrational state density near ν 3 is quite sparse. Indeed, we can calculate these state densities using the efficient Kemper backtracking algorithm, 61 based on the thorough diagonal/off-diagonal anharmonic frequency analysis by Marenich and Boggs. 29,30 It is worth stressing that diagonal anharmonicity in the internal rotation coordinate is large and therefore crucial to take into account.…”

Section: Negative Tunneling Splittings In the Upper Statementioning

confidence: 99%

Sub-Doppler infrared spectroscopy of CH2OH radical in a slit supersonic jet: Vibration-rotation-tunneling dynamics in the symmetric CH stretch manifold

Schuder

Wang

Chang

et al. 2017

The Journal of Chemical Physics

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The sub-Doppler CH-symmetric stretch (ν) infrared absorption spectrum of a hydroxymethyl (CHOH) radical is observed and analyzed with the radical formed in a slit-jet supersonic discharge expansion (T = 18 K) via Cl atom mediated H atom abstraction from methanol. The high sensitivity of the spectrometer and reduced spectral congestion associated with the cooled expansion enable first infrared spectroscopic observation of hydroxymethyl transitions from both ± symmetry tunneling states resulting from large amplitude COH torsional motion. Nuclear spin statistics due to exchange of the two methyl H-atoms aid in unambiguous rovibrational assignment of two A-type K = 0 ← 0 and K = 1 ← 1 bands out of each ± tunneling state, with additional spectral information obtained from spin-rotation splittings in P, Q, and R branch K = 1 ← 1 transitions that become resolved at low N. A high level ab initio potential surface (CCSD(T)-f12b/cc-pvnzf12 (n = 2,3)/CBS) is calculated in the large amplitude COH torsional and CH wag coordinates, which in the adiabatic approximation and with zero point correction predicts ground state tunneling splittings in good qualitative agreement with experiment. Of particular astrochemical interest, a combined fit of the present infrared ground state combination differences with recently reported millimeter-wave frequencies permits the determination of improved accuracy rotational constants for the ground vibrational state, which will facilitate ongoing millimeter/microwave searches for a hydroxymethyl radical in the interstellar medium.

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A bactracking algorithm for exact counting of internal molecular energy levels

Cited by 61 publications

References 7 publications

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

Conformational Dependence of Intramolecular Vibrational Energy Redistribution in the EthylenicCH₂ Stretch Fundamental of Allyl Fluoride

Sub-Doppler infrared spectroscopy of CH2OH radical in a slit supersonic jet: Vibration-rotation-tunneling dynamics in the symmetric CH stretch manifold

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A bactracking algorithm for exact counting of internal molecular energy levels

Cited by 61 publications

References 7 publications

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν19 Out-of-Phase Symmetric CH Stretch

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν19 Out-of-Phase Symmetric CH Stretch

Conformational Dependence of Intramolecular Vibrational Energy Redistribution in the EthylenicCH2 Stretch Fundamental of Allyl Fluoride

Sub-Doppler infrared spectroscopy of CH2OH radical in a slit supersonic jet: Vibration-rotation-tunneling dynamics in the symmetric CH stretch manifold

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High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

High-Resolution Rovibrational Spectroscopy of Jet-Cooled Phenyl Radical: The ν₁₉ Out-of-Phase Symmetric CH Stretch

Conformational Dependence of Intramolecular Vibrational Energy Redistribution in the EthylenicCH₂ Stretch Fundamental of Allyl Fluoride