Vibrationally averaged structures

Bound state calculations with J = 0 are carried out for the above CCSD(T) surface. The linear He-Br-Br structure is found to be the most stable isomer with a binding energy of Do=16.02 cm , while the T-shaped isomer is predicted to lie only 1.1 cm above, indicates the coexistence of them even at low temperatures. The vibrationally averaged structures for these isomers are determined to be (R=4.88 A, 0= 0°) and (R=4.14 A, 0=90°), respectively. The above values are in good accordance with earlier experimental observations and in excellent agreement with recent LIF experimental data available. ... 

Table 7. Vibrationally averaged structural parameters for rare gas, hydrogen halide complexes. R is the heavy atom separation and the y s are effective RG—X—H angles based on .

So far the effect of nonadditivity in water has been studied in the context of various structural properties, vibrationally averaged structures, O-H frequency shifts [89], zero-point energies, rotational constants, cluster predissociation dynamics and tunneling splittings [58],... 

E/eRiCRjdR Cubic force constant part of the anharmonic contribution to vibrational frequencies anharmonic contribution to vibrationally averaged structures... 

The barrier of the H(out-of-ring) flipping motion below and above the plane is predicted to be low (approximately 0.04 kcal [95Woo]) so the vibrationally averaged structure has Q symmetry. 

There is naturally a close connection between the different pictures provided by the various time scales. The vibration-averaged structure differs at every position at a given instant, and at every instant at a given position. In both cases, however, its average value gives the diffusion-averaged structure. 

The results on crystal structures are not the only experimental evidences of the existence of X-H- - - k interactions. There are numerous gas-phase experimental studies. For example, the high-resolution optical and microwave spectra on the benzene-ammonia complex were presented [9]. It was found that in the vibrationally averaged structure, the C3 symmetry axis of ammonia is tilted by approximately 58° relative to the Ce benzene axis. In such a way the N-H bonds interact with rr-electrons of benzene through N-H- - - k hydrogen bonds. The resonance-enhanced two-photon ionization, the microwave spectroscopy and the other spectroscopic techniques were used to analyze such complexes as C6H6-H2O [10], CeHe-HF [11], CeHs-HCl [12] and also T-shaped complexes where rr-electrons of acetylene act as the proton acceptor while such moieties as HF, HCl or HCN are the proton donors [13-15]. 

The predicted vibrationally averaged structures are consistent with experimental observations. The predicted HF vibrational (red) shifts for the pairwise-additive potential energy surfaces are close to the experimental values but differ in a systematic fashion. The agreement is improved by the inclusion of three-body nonpairwise terms. The results from one study are listed for comparison with experiment in Table 5. 

Figure 10.4 Schematic representation of equilibrium (R ) structure corresponding to the minimum on PES ( bottom of the well") and vibrationally averaged structure (/ q)...

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