Open versus Cyclic Trimers

One likely geometry for a trimer would contain a pair of dimer structures as in Fig. 5.9a, where each H-bond is linear, or nearly so, and the H X—H angle is in the 100-130° range. As in some of the cases already described, a third H-bond can be formed if the proton on the last molecule is brought near the X atom of the first, forming a cyclic structure as in Fig. 5.9b. Of course the price paid for this third H-borid is some angular distortion of all three. 

Some early studies of the comparative stability of these two arrangements of the HF trimer with small basis sets had yielded ambiguous answers. In 1983, Karpfen et al. applied more extended basis sets and optimized the geometries with gradient procedures. They found the cyclic trimer more stable than the open one by 2.2 kcal/mol. Their results confirm the greater strain in each of the three H-bonds of the trimer the interaction energy per H-bond is 3.9 kcal/mol in the cyclic structure, as compared to the 4.7 kcal/mol in each of the two bonds of the open form. Soon thereafter, another study of the same system focused on the vibrational frequencies of the cychc structure. Each of the three H-bonds was calculated to contribute 5.0 kcal/mol, slightly more than computed earlier by Karpfen et al. 

Calculations in 1986 confirmed the greater stability of the cyclic geometry, as well as its planar nature, and suggested that the open form could convert to this geometry with little or no energy barrier. (Indeed, other calculations in the same year dispensed with the notion that the open form of the HF trimer represents a real minimum on the potential energy surface . ) It was also pointed out that all experimental measurements were indicative of the existence of the cyclic structure. It was found here that the H-bond energy per bond 

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Karpfen, A., Beyer, A., and Schuster, R, Ab initio studies on clusters of polar molecules. Stability of cyclic versus open-chain trimers of hydrogen fluoride, Chem. Phys. Lett. 102, 289-291 (1983). 

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