Classical versus quantum models

This works well for fhe fundamental vibrational frequency of simple diatomic molecules, and is not too far from the average value of a two-atom stretch within a polyatomic molecule. However, this approximation only gives the average or center frequency of the diatomic bond. In addition, one might expect that since the reduced masses of, for example, C-H, O-H, and N-H are 0.85, 0.89, and 0.87, respectively (these constitute the major absorption bands in the near-infrared spectrum), the ideal frequencies of all fhese pairs would be quife similar. 

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Notably, adiabatic chaimel models and variational transition state theory yield identical rate estimates as long as they employ the same assumptions for the energy levels. However, the implementations of the two theories generally employ different assumptions (e.g., classical versus quantum) and so jdeld modestly different rate estimates. Furthermore, the adiabatic models sometimes implement additional constraints such as an assumed conservation of the orbital angular momentum. 

Figure 9.3 Logarithm of the probability density versus t for an attractive delta potential having a zero energy resonance exact quantum numerical solution (solid line) classical model solution (squares). The long-time behavior is indistinguishable from Eq. (83). a = —1, T = 0.2, and other parameters as in Figure 9.2.

Classical molecular dynamics simulations of NACs in smectite interlayers predicted that inner-sphere K+-O2N— complexes would readily form between NACs and interlayer K" " (9,11). Therefore, in order to help rationalize the observed FTIR spectral shifts in terms of the proposed complexation reactions between —NO2 groups and interlayer cations, quantum calculations of some simple models (Fig. 1) for inner-sphere NAC-K" interactions were performed they are summarized in Table 3. The quantum results follow the experimental trends for complexed versus uncomplexed —NO2 stretching frequencies. That is, complexation by K+ results in a red shift (i.e., to lower frequency) of the Vasy,n(NO) band and a simultaneous blue shift of the Vsym(NO) band. Taken togetha-, the splitting between the two frequencies decreases upon complexation. The K-O2N interac-... 

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