Rotational-vibrational correlations

INTRAMOLECULAR ROTATION-VIBRATION CORRELATIONS IN DILUTED SOLUTIONS. NON-DEGENERATE VIBRATIONS. 

The third theory of this group is the recent theory by Tarjus and Bratos (12). It describes the rotation-vibration correlation effects arising from intermolecular forces but neglects the role of the centrifugal interaction. This contribution is thus complementary to those reviewed earlier. The basic assumptions of the theory are as follows, (i) Active diatomic molecule is executing... 

Spectral effect of the rotation-vibration correlation is particularly important for degenerate transitions. The Coriolis interaction, frequently envisaged in this context, was studied in a long series of papers due to Muller and Kneubiihl (14,17,19), Muller, Etique et al. (15,16) and Muller (18). Other important papers were published by Eagles and Me Clung (20), Levi, Marsault... 

It is probably fair to say, in appreciating the actual situation in the field, that spectral manifestations of the Coriolis interaction are, in essence, adequately interpreted. Still, the description remains entirely quatitative. From the other side, the effects of intermolecular rotation-vibration correlations on degenerate vibrations are, at the present time, practically unexplored this problem certainly merits attention. Here again, the computer simulation techniques will be useful. However, their use can only be envisaged once the quantum-mechanical part of this problem has been solved. This problem refers to the study of degenerate vibrations perturbed by random solvent-solute interactions. 

The rotation-vibration correlation effects in pure liquids have been much less explored than those occuring in diluted solutions. The early work is due to Van Woerkom, de Bleyser et al. (27) and to Lynden-Bell (28). Recent progress of the theory is described in papers by Wang and Me Hale (29), Me Hale (30), Levesque, Weis and Oxtoby (31,32). See also Bratos and Tarjus (33). These papers are discussed in what follows. 

The last group of papers are relative to the computer-simulation study of the rotation-vibration correlations in pure liquids. The main authors are Levesque, Weis and Oxtoby (31,32) who examined liquid and HCl in much detail. A molecular dynamics simulation was carried out using 500 molecules for N2 and 256 for HCl periodic boundary conditions were imposed It was found that, in the isotropic Raman spectrum of liquid N2>intermolecular rotation-vibration interactions are mainly due to short range repulsion and dispersion forces the role of centrifugal forces seems secondary which is an unexpected result. The presence of important interference effects makes any partition illusory. Only intermolecular rotation-vibration correlation effects were examined in the case of infrared and anisotropic Raman spectra of liquid HCl. It results from this calculation that the simple product correlation function is indistinguishable from the total correlation function within the uncertainty of the simulation. This conclusion is similar to that reached by Tarjus and Bratos (12). It should not be forgotten, however, that the latter theory applies to diluted solutions whereas the function determined by Levesque, Weis and Oxtoby is an approximate correlation function of a pure liquid. 

The theory of the rotation-vibration correlation in pure liquids is much less advanced then that relative to diluted solutions. 

All. Rotation-Vibration Correlation in Infrared and Anisotropic Spectra of. diluted Van der Waals Solutions. Effect of Intermolecular Forces. 

Using the impact approximation presented in Chapter 6, they may easily be found for any rotational band even if rotational-vibrational interaction is nonlinear in J. In 1954 R W. Anderson proved as a theorem [104] that expansion of the spectral wings in inverse powers of frequency is controlled by successive odd derivatives of the correlation function at the origin. In impact approximation the lowest non-zero derivative of this type is the third and therefore asymptotics G/(co) is described by the power expansion [20]... 

Without regard for deformational and rotational vibrations of unit vectors e(ij, the qualitative behavior of the time dependence of the correlation function for two-dimensional reorientations is describable by the following relation ... 

Brouard, M., Martinez, M.T., and O Mahony, J. (1990). Fragment pair correlations in the vibrationally mediated photodissociation of H2O2 Rotation-vibration coupling in the third OH stretching overtone, Mol. Phys. 71, 1021-1041. 

The solution of the simultaneous differential Equations 11 and 12 has already been discussed in detail in Reference 16. Only the four lowest rotational-vibrational energies, as a function of y and D, for all of the isotopic hydrogens have been calculated and tabulated. These are the states which correlate, in the case of the free molecule, with the states... 

Fig. 4. Time dipole correlation functions C(t) of water in critical state (left top), in bulk liquid water at 30°C (left center), in a monolayer on fluorophlogopite mica (left bottom), in LTA bonded to the first 4 Na+ ions (right top), in SB A-15 heated to 300°C for 2 hrs (right center), and in fully hydrated SBA-15 (right bottom). The normalized total correlation functions, obtained according to Eq. (9) involve vibrations of the transition dipole of the (v+5) band displayed as rapid oscillations. Rotational correlations including angular perturbations appear as envelopes of the vibrational correlation functions. The inertial rotational motion about the least rotational axis of the water molecule is indicated as a quadratic decay C(t) - (kT/I) t2 at times 0 - 0.05 psec in each C(t) vs. t graph. The graphs on the left are reproduced from ref. 18.

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