Potential, intermolecular vibrational averages

The angular-dependent adiabatic potential energy curves of these complexes obtained by averaging over the intermolecular distance coordinate at each orientation and the corresponding probability distributions for the bound intermolecular vibrational levels calculated by McCoy and co-workers provide valuable insights into the geometries of the complexes associated with the observed transitions. The He - - IC1(X, v" = 0) and He + 1C1(B, v = 3) adiabatic potentials are shown in Fig. 3 [39]. The abscissa represents the angle, 9,... 

Figure 10. Linear equilibrium geometries for CO2-HF and CO2-HCI. The shallow angular potential gives rise to large, hinge-like zero-point excursions. The O—H distances shown are averaged over all intermolecular vibrations.

The intermolecular potential as it is given in Eq. (3) for example, does not depend explicitly on the (external) molecular displacements or on the (internal) normal coordinates as required by Eq. (10). The atom-atom potential in Eq. (5) does not even depend explicitly on the molecular orientations Q. All these dependencies have to be brought out, by expansion and transformation of the potentials in Eq. (3) and Eq. (5), before these can actually be used in lattice dynamics calculations. The way this is performed depends on the lattice dynamics method chosen (see below). If one is not interested in the internal molecular vibrations, the free-molecule Hamiltonians may be omitted from Eq. (10) and the potential may be averaged over the molecular vibrational states. The effective potential thus obtained no longer depends on the coordinates and Q. ... 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

To demonstrate the potential of two-dimensional nonresonant Raman spectroscopy to elucidate microscopic details that are lost in the ensemble averaging inherent in one-dimensional spectroscopy, we will use the Brownian oscillator model and simulate the one- and two-dimensional responses. The Brownian oscillator model provides a qualitative description for vibrational modes coupled to a harmonic bath. With the oscillators ranging continuously from overdamped to underdamped, the model has the flexibility to describe both collective intermolecular motions and well-defined intramolecular vibrations (1). The response function of a single Brownian oscillator is given as,... 

Table 4. Free energy components intermolecular harmonic vibration, g, and the potential energy, u, of structures at minimum potential energy. The differences defined as = 9w averaged over...

Similar reasoning was behind vibrational analysis in systems with hydrogen bonds [Y. Marechal and A. Witkowsld, Theor. Chim. Acta, 9, 116 (1967).] The authors selected a slow intermolecular motion proceeding in the potential energy averaged ovct fast intramolecular motions. 

Figure 1. Potential energy diagrams, a. external translation (gas phase) h. external translation (condensed phase) c. internal vibration (gas phase) d. internal vibration (condensed phase). In a, r denotes the average intermolecular distance in the gas phase, in b, r denotes the value of the intermolecular distance evaluated at the minimum, and in c and d, r denotes the value of the coordinate descril ng the molecular distortion evaluated at the minimum. Notice for the external motions the zero point energy change on condensation, (E — Ee) — E — EJ > 0, because E E 0, but for the internal motions it may be positive, negative, or zero depending on the effect of the intermolecular forces on the specific motion under consideration.

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