Accurate and Facile Approximation for Vibrational Energy-Level Sums

Whitten, G.Z.; Rabinovitch, B. S.

doi:10.1063/1.1733526

Cited by 528 publications

(167 citation statements)

References 10 publications

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“…2 ͑which was based upon the Whitten-Rabinovitch expression͒ 34 is the total and not the symmetry accessible density of vibrational states. In general, for two states to couple by anharmonic interaction, they must be close in energy, have the same J-value, be of the same parity and symmetry with respect to exchange of identical nuclei, and have the same l quantum number.…”

Section: H 2 Results-density Of States Analysismentioning

confidence: 99%

Rovibrational spectroscopy of the v=6 manifold in C212H2 and C213H2

Srivastava

Conjusteau

Mabuchi

et al. 2000

The Journal of Chemical Physics

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We recorded rovibrational spectra of the 006 ϩ level of 12 C 2 H 2 and the 2131 1 1 Ϫ1 level of 13 C 2 H 2 in the ground electronic state using a two-photon sequential double resonance technique with a resolution of 15 MHz. Owing to the g/u symmetry of acetylene, the levels that we observe are inaccessible from the ground state by single photon techniques, and observation of these levels is reported here for the first time. Upper state rotational constants were derived from whole band fits of the observed lines, and compare favorably with expected values. Both spectra exhibit signs of local perturbations, and a density of states analysis leads us to believe that we are observing couplings to the full density of vibrational states one would expect from acetylene in this energy region. Despite the high resolution of our spectrometer, and the high excitation energy, no evidence for acetylene hydrogen permutation exchange isomerization ͑which is predicted to proceed through the vinylidene minimum on the potential͒ has been observed, implying that the rate of exchange isomerization is more than four orders-of-magnitude below the rate predicted by RRKM ͑Rice, Ramsperger, Kassel, and Marcus͒ theory.

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Section: H 2 Results-density Of States Analysismentioning

confidence: 99%

Rovibrational spectroscopy of the v=6 manifold in C212H2 and C213H2

Srivastava

Conjusteau

Mabuchi

et al. 2000

The Journal of Chemical Physics

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“…It should be stressed that this covers a very important region of the spectrum, since there is extensive empirical evidence to suggest that, for multidimensional molecular systems, the classical approximation to the density of states will be accurate once the sum of states has climbed to this order of magnitude. 4,[33][34][35] Hence, evaluation of the classical trace in Eq. ͑2͒ is likely to prove quite acceptable at higher energies.…”

Section: Discussionmentioning

confidence: 99%

“…In this way, analytic formulas for the density of states of collections of classical oscillators and rotors can be derived and have been the staple in unimolecular rate theory for many years. [32][33][34][35] The quantum mechanical trace in Eq. ͑1͒ is most readily carried out for separable Hamiltonians.…”

Section: Introductionmentioning

confidence: 99%

On the calculation of absolute spectral densities

Smith

Jeffrey

1996

The Journal of Chemical Physics

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On the relation of protein dynamics and exciton relaxation in pigment-protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra J. Chem. Phys. 116, 9997 (2002) A new method of calculating the absolute spectral density of a Hamiltonian operator is derived and discussed. The spectral density is expressed as the solution of an integral equation in which the kernel is a renormalized one-sided energy correlation function of the full microcanonical density operator and a microcanonical density operator for a reference Hamiltonian. The integral operator associated with this equation transforms a known spectral density function for the reference Hamiltonian into the spectral density of the full Hamiltonian. The integral equation, by virtue of its formulation in energy space, is inherently one-dimensional and offers no storage difficulties, and the elements of its kernel may be computed by applying the Lanczos algorithm to randomly selected eigenfunctions of the reference Hamiltonian. This spectral density correlation method offers a number of advantages over variational methods. In particular, it has the potential for overcoming the hitherto largely insurmountable problem of tracing over a multidimensional Hilbert space in order to compute the spectral density of a nonseparable molecular Hamiltonian.

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“…When applied to protein dissociation, the rate constants at low internal energy were found to be larger than the corresponding BS results by orders of magnitude as reported. The fact that some parameters used in calculation proposed by Whitten and Rabinovitch [21] were not adequate for proteins at low internal energy was found to be responsible for the overestimation. Improvement [27] of these parameters using the frequency set obtained in our previous work reduced the error to a factor Ͻ 2.…”

mentioning

confidence: 94%

“…Direct counting of states [17][18][19] was attempted from the early days of study together with the computationally less demanding version of using grouped frequencies [20] and approximate methods such as the Whitten-Rabinovitch (WR) semiclassical method [21] and the steepest-descent method [22]. It was observed that all the approximate methods provided erroneous results at low internal energy [4,20,23].…”

mentioning

confidence: 99%

Efficient and reliable calculation of rice-ramsperger—kassel-marcus unimolecular reaction rate constants for biopolymers: Modification of beyer-swinehart algorithm for degenerate vibrations

Moon

Sun

Kim

2007

J. Am. Soc. Mass Spectrom.

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The Beyer-Swinehart (BS) algorithm, which calculates vibrational state density and sum, was modified for simultaneous treatment of degenerate vibrations. The modified algorithm was used in the grouped-frequency mode of the Rice-Ramsperger-Kassel-Marcus (RRKM) unimolecular reaction rate constant calculation for proteins with relative molecular mass as large as 100,000. Compared to the original BS method, reduction in computation time by a factor of around 3000 was achieved. Even though large systematic errors arising from frequency grouping were observed for state densities and sums, they more or less canceled each other, thus enabling reliable rate constant calculation. The present method is thought to be adequate for efficient and reliable RRKM calculations for any macromolecule in the gas phase such as the molecular ions of proteins, nucleic acids, and carbohydrates generated inside a mass spectrometer. The algorithm can also be used to calculate the internal energy distribution of a macromolecule at thermal

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Accurate and Facile Approximation for Vibrational Energy-Level Sums

Cited by 528 publications

References 10 publications

Rovibrational spectroscopy of the v=6 manifold in C212H2 and C213H2

Rovibrational spectroscopy of the v=6 manifold in C212H2 and C213H2

On the calculation of absolute spectral densities

Efficient and reliable calculation of rice-ramsperger—kassel-marcus unimolecular reaction rate constants for biopolymers: Modification of beyer-swinehart algorithm for degenerate vibrations

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