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Vibrational energy relaxation
Overtone band
Vibrational partition function
The concept of characterizing normal vibrational modes lμ in terms of internal vibrational modes vn typical of molecular fragments or structural subunits is developed. Essential for this concept is the amplitude 𝒜nμ that provides the basis for a quantitative comparison of modes lμ and vn and, by this, facilitates the extraction of chemical information out of vibrational spectra. Twelve possibilities of defining amplitude 𝒜 are tested with regard to (a) the physical basis of the definition of 𝒜, (b) the dependence of 𝒜 on the set of internal parameters chosen to describe the molecule, and (c) the amount of chemical information transferred by 𝒜. The two most promising candidates for a generally applicable amplitude 𝒜 are based on adiabatic internal modes and a comparison of lμ and vn with the help of mass or force constant matrix. For the practical testing of amplitude 𝒜, three different criteria are developed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 29–40, 1998
Vibrational partition function
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Overtone band
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The theory presented in this paper investigates the vibrational correlation functions of dense molecular fluids, taking into account all vibrational transition and depopulation modes of the electronic ground state. Particular attention is paid to dynamic coupling of relevant excitations (coupled Raman bands, coupled rate equations), and to the significance of distinct vibrational correlations (i.e. correlations between adjacent molecules). Various collision induced relaxation mechanisms are included: pure dephasing arising from transition frequency fluctuations, intramolecular depopulation and resonant as well as non-resonant vibrational energy transfer. The coupling of the molecular vibrators is assumed to be weak. As a result the following conclusions apply. First the relaxation constants of the depopulation modes need not be given by the vibrational exciton annihilation rates. Second, weakly-separated or overlapping transition bands can show a significant dynamic coupling. Third, distinct vibrational correlations, although negligible at time zero, can be significant at finite times, as a result of resonant and non-resonant vibrational transfer processes. Fourth, the contribution of the depopulation process on the dephasing constant of a collective μ → v transition cannot be related to the annihilation rates of the involved vibrational excitons, μ and v.
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Chemical reactions occur due to energy accumulation in specific vibrational intramolecular degrees of freedom (dofs). Thus, vibrational energy redistribution among different dofs inside a molecule as well as intermolecular vibrational energy transfer to external dofs is of particular importance for chemical reactions. In many cases these processes take place on a picosecond time scale such that short pulse lasers may be used to excite vibrations and analyze microscopic vibrational processes in a media. The process of photodissociation of organic peroxides carbon dioxide is formed with a broad vibrational energy distribution disposed mainly in the bend and symmetric stretch vibrational degrees of freedom. The highest frequency asymmetric stretch mode seems to remain unexcited because in all the solvents its vibrational relaxation is very slow. Comparatively fast vibrational cooling of CO/sub 2/ is insured by the Fermi resonance between the bend and symmetric stretch vibrations and proceeds through V-V near resonant energy transfer to solvent molecules.
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Over many years, we have published vibrational spectra of molecular materials at extreme pressure and temperature obtained using shock compression and coherent Raman spectroscopy methods. For diatomic molecules, we were able to extract vibrational temperatures from the intensities of spectrally resolved vibrational hot bands. Larger molecules in the condensed phase suffer band broadening effects that obscure the vibrational hot bands as the anharmonicities are typically smaller than the widths of the bands. This inability to resolve the hot bands inhibits the extraction of vibrational temperature and the measurement of the vibrational frequency of the fundamental. Here, we use a hot band model based on gas-phase anharmonic coupling coefficients to fit coherent anti-Stokes Raman spectra of the ν1 vibrational mode of shock compressed condensed phase N2O with shock pressures and temperatures estimated from literature equations of state and compare to fits from a model using a single Gaussian peak. We report the resulting vibrational frequency shifts with shock pressure.
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Diatomic molecule
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Two-dimensional infrared spectroscopy
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In this work a fully symmetrized quantum mechanical description of vibrational motion in terms of complex vibrational coordinates and complex basis wavefunctions is outlined, designed for studying vibrational level mixing and intramolecular vibrational energy redistribution (IVR) around CH stretch overtone states in benzene. Symmetrized local mode (LM) formalism has been applied to the CH stretch system, while the remaining benzene vibrations (including out-of-plane modes) were treated as normal modes (NM). Using the outlined approach a model calculation of the absorption spectrum of the first overtone state CH (n=2) at ∼6000 cm−1 has been carried out.
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The vibrational level mixing at the second CH stretch overtone state CH(v=3) in benzene has been studied quantum mechanically using a completely symmetrized vibrational basis set in terms of a combined local mode/normal mode description. The employed symmetrized approach has helped to reduce the dimensionality of coupling Hamiltonian matrices and thus allowed for the inclusion of all 30 vibrational modes in the calculations. The absorption spectrum and dynamical intramolecular vibrational redistribution characteristics for initial excitation of a symmetrized local mode “bright” state in the CH(v=3) overtone manifold have been calculated and analyzed in connection with the degree of localization of the CH stretch overtone vibrational system in benzene.
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Hamiltonian (control theory)
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Vibrational partition function
Two-dimensional infrared spectroscopy
Overtone band
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Quantum chemical
Overtone band
Vibrational partition function
Vibrational spectrum
Harmonic
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Overtone band
Overtone
Vibrational partition function
Vibrational energy relaxation
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Vibrational energy relaxation
Vibrational partition function
Vibrational energy
Overtone band
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