Trimers vibrational frequencies

Several schemes have been applied to overcome these problems. However, sublimation energies can be determined by measuring the temperature dependence of ion intensities, largely unaffected by the aforementioned problems. These measurements enable one to compute heats of formation, heats of dimerization, etc. for the neutral species. In addition, matrix-isolation techniques have yielded infrared active vibrational frequencies of dimers (and possibly one trimer) and geometrical structures of monomers and some dimers have been obtained from a combination of microwave spectra and electron diffraction. 

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. 

Table 5.18 Harmonic vibrational frequencies (cm ) of the water trimer, computed at SCF and corrrelated level, with DZP+diff basis set, along with percentage change. ...

Table 5.21 Shifts in harmonic intramolecular vibrational frequencies (cm ) of dimer and trimer of methanol, relative to the monomer, computed at SCF/6-311 + +G(2d,2p) level .

The shortness and equality of the P-N bonds in the trimeric and in the tetrameric chloride have been demonstrated in Section IV,B. The thermochemical evidence for a bond order greater than unity in the trimeric chloride is confirmed by the high value of the observed P-N stretching frequency, which is maintained or even increased as the series is ascended. The effect of mass on ring vibration frequencies is not large m, 25), so that the higher and lower infra-red absorption frequencies characteristic of the phosphonitrilic fluorides and bromides, respectively, are indications of their relative bond strengths, and are consistent with the aromatic theory. 

The molecular structure is assumed to be the same as that of the BeO trimer. The Li-F bond distance is taken from that of the 2 2 determined by Akishin and Rambidi (6). Four vibrational frequencies, A " and three E, are reported by Snelson (7)... 

The MoFg(g) monomer vibrational frequencies were used, with triple the degeneracy, for the trimer, the 12... 

We have extended the previous MD/DF calculations on neutral sulphur clusters [54] to sulphur anions up to S9. The results for the dimer and trimer, e.g. vibration frequencies for the anions Sj and SJ and for the neutral systems, agree well with previous work. Of particular interest is the prediction of stable chain structures in addition to the ring structures familiar from the neutral clusters (see above). Fig. 10 shows the most stable isomers of the former and representative isomem of the latter, of which there are many for n > 5. Of particular interest are chains with a planar tetramer at one or both ends, because such structures had not been found in the neutral chains. The most stable structures are generally opened or puckered rings of the neutral clusters, where at least one bond is strained or broken by the presence of the additional electron. The ground states of S5, Sf, Sg and S9 belong to this family. 

The corresponding effects in structural relaxations and vibrational frequency shifts are calculated to be of comparable magnitude in (HBr) complexes [243] as well. From the (HBr)2 dimer to the molecular HBr crystal, the experimentally determined intermolecular Br—Br distance contracts from 4.13A [241] to 3.93A [31], or by 0.20A. The calculated reductions of r(Br—Br) from the dimer to the trimer and tetramer amount to 0.09 and 0.12 A, respectively [243]. The vibrational frequency shift from the monomer to the in-phase H—Br stretching frequency of solid HBr amounts to —154 cm [273]. The calculated shifts to the dimer and trimer are —88, and —91 and —117cm, respectively, and that to the tetramer amount to —96, —128, and — 158cm [243]. 

Scuseria and Schaefer [202a] followed up some earlier work by attempting to determine whether the open trimer of HF represents a true minimum in the potential energy surface. Within the context of their double-C basis set, it was found that the cis open trimer is indeed a minimum (Hessian matrix has all positive eigenvalues), whereas the trans structure is a transition state. However, the situation is decidedly different when polarization functions are added to the basis set wherein the trans geometry becomes a transition state and the cis type does not correspond to a stationary point of any order. Nor does relaxing the fully planar restraint lead to a cis stationary point. Vibrational frequencies and intensities were reported for the stationary points. 

Vibrational frequencies and intensities were calculated for the cyclic trimers of both HF and HCl [103]. As noted earlier by Gaw et al. [95], the red shifts of the HF stretchers are much larger in the trimer than in the dimer. This trend extends to the HCl analogues although the numerical values of the shifts are uniformly smaller. The intensities of the HX stretches, too, exhibit a marked increase in the trimer as compared to the dimer. Similar comparisons extend to the intermolecular modes as well in that both the frequencies and intensities are considerably greater in the trimers. Kolenbrander et al. [202b] have provided evidence of separability of the in-plane and out-of-plane molecular vibrations in (HF)3. They estimate a barrier of at least 30 kJ/mol separates two equivalent conformations of this trimer, some 10 times higher than the interconversion barrier in (HF)2. 

Kofranek et al. [219] also examined cyclic geometries of the trimer and tetramer of HCN. In contrast to (HF)3 where the cyclic geometry is most stable, the linear trimer of HCN is preferred by 4.6 kJ/mol with the larger basis set. Nevertheless, the authors noted that the cyclic structure represents a true minimum on the potential energy surface of (HCN)3 with all vibrational frequencies real. (This finding is... 

ABSTRACT Ground state properties of several conceivable hydrogen bonded trimers composed of HCN and HP molecules have been evaluated at the SCP level. The most stable ones of these trimeric complexes have subsequently been reinvestigated with electron correlation methods (ACPP). We provide a survey of stabilization energies, dipole moments, selected harmonic vibrational frequencies and corresponding infrared intensities. We also discuss various aspects of the non-additivity of intermolecular interaction taking place in these clusters. 

In most vapor phase infrared spectroscopic investigations only the high-lying C-H and F-H stretching vibrations could be observed. Computed monomer, dimer and trimer harmonic vibrational frequencies in this region and the corres-... 

Table 4 Length (L/ A) and harmonic vibrational frequencies (v/cm" ) of the C—H bond for the monomer (M), and those in the C—interactions of dimer (D1,D2 and D3) and trimer (Tl) of VC, calculated with the B3LYP/6-311++G (d,p) method. Reproduced [44] with permission of Am. Chem. Soc.

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