Harmonic wavenumbers

Table 3 Predicted harmonic wavenumbers for the fundamental modes of two conformers of OSSO as calculated by quantum mechanical methods [34] values in parentheses from [57]...

For a precise determination of the structures, ab initio calculations on the energies of formation and characteristic harmonic wavenumbers have been performed at the HF and MP2/6-31G(d,p) level of theory with the Gaussian 92 program for the species of interest . The ab initio calculated energies and harmonic vibrational wavenumbers are given in Table 5. 

The accuracy of the harmonic BP86/RI/TZVP force field (104) permitted that all bands, which split upon photoisomerization, could be assigned to the two possible isomers 5(A) and 5(B). The accuracy of the harmonic wavenumbers is, in general, better than 6 cm-1 for these bands (with the exception of 12 cm-1 for the mode at 1270 cm-1). 

The conclusion is that if the spectrum can be analysed in terms of equations (3)—(7), then the force constants can be determined. The bond length re can be determined from the equilibrium rotational constant Bc then the quadratic force constant /3 can be determined either from the harmonic wavenumber centrifugal distortion constant De then the cubic force constant /3 can be determined from aB and finally the quartic force constant /4 can be determined from x. It is necessary to determine the force constants in this order since in each case we depend upon already knowing the preceding constants of lower order. The values of re,f2,f3, and /4 calculated in this way for a number of diatomic molecules are shown in Table 2. 

The observation of a large number of overtones of a fundamental under resonance Raman conditions makes it possible to determine the harmonic wavenumbers (coj) and the anharmonicity constants Xjj and Xjt. The vibrational terra for a polyatomic species is given by the expression... 

Results on a large number of linear-chain complexes of platinum are summarised in Table 11. Harmonic wavenumbers and anharmonicity constants have been determined in all cases. The normal coordinate seems to be related to the halogen movements involved in the proposed hopping process for the conductivity of these linear-chain mixed-valence complexes (95). The chain halogen atoms would need to move, on average, 0.54,0.38 and 0.22 A for chlorides, bromides and iodides, respectively, in order to reach the point midway between the two platinum atoms, i.e. to the situation of a platinum (III) chain. These values only differ by a factor of about two from the root-mean-square amplitudes of vibration of Vi in the Vj = 16 states these are calculated (91) to be 0.22 A for X = Cl (wi = 319.5 cm-i) and 0.20 A for X = Br (cji = 179.6 cm ). These distance changes are related to the shift in the equilibrium... 

The agreement is not exact because the observed wavenumbers were used rather than zero order harmonic wavenumbers. In a like manner for the E vibrations Eq. (3.54) becomes... 

Table 20 shows predicted and observed harmonic and anharmonic wavenumbers for (HF)2- The theoretical harmonic values reveal a serious discrepancy. The oh initio coj and (06 wavenumbers obtained from the MP2/aug-cc-pVQZ and CCSD(T)/TZ2P(f,d) methods are significantly larger than the harmonic wavenumbers obtained from the SQSBDE pair potential (or other semiempirical potentials based on the CPF calculations), Obviously, the SQSBDE potential yields harmonic wavenumbers that are comparable to the CPF/F 8s6p2d/... 

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