3. Results and discussion

This established empirical relationship also makes it possible to calculate the vibrational zero-point energies of the aromatic derivatives with accuracy, provided

This adjustment can be explained by the fact that in aromatic compounds, the bonds in the aromatic nucleus are all identical because of the conjugation, whereas in our model it has been assumed that there are three C—C single bonds and three

Eq. (5) was used to calculate the ZPEs of several organic compounds belonging to different classes of compounds (hydrocarbons, oxygen compounds, nitrogen compounds, chlorinated compounds, brominated compounds, fluorinated compounds, sulfur compounds, aromatic compounds, etc.). Thus, the contributions of the bonds C—H, N—H, O—H, S—H, C—O, C—C, C—N, C—S, N—N, C—F, C—Cl, C=C, C=N, C=O, C=S, C☰C, and C☰N have been determined. To extend our model to brominated compounds, we have determined in 2004 the contribution of the C—Br bond [39] and incorporated it into our empirical formula. The calculated vibrational zero-point energies for 38 compounds containing this bond (C—Br) correlate well with experimental values. In addition, we have extended the field of application of this empirical model to organophosphorus compounds (III). The bond contributions of P—F, P—C, P—H, P—Cl, P—S, P—N, and P—O were determined [29]. The results obtained for 101 chemical systems containing these bonds are in good agreement with experimental values. The estimated ZPEs were compared with the results obtained by application of quantum chemistry methods at the level ab initio (HF/

ZPE ¼ 1:08:ZPE empirical ð Þ� 1:07 kcal ð Þ =mol (6)

), in all cases with satisfactory results.

) and

More recently [40], to calculate vibrational zero-point energies (ZPEs) of organophosphorus compounds (V), we determined the contributions of the bonds P=O and P=S and incorporated them into our empirical formula. Comparison of the results obtained for more than 80 organophosphorus compounds (V) with

) shows the reliability of the empirical approach. In this chapter, we describe the results obtained in the case of organosilicon compounds. We present the values obtained for the contributions of the Si—H, Si—C, Si—Cl, Si—O, and Si—Si bonds which make it possible to calculate the vibrational zero-point energies of the silicon compounds. The results thus obtained are compared firstly with the available experimental values, secondly to the values obtained by the methods of the quantum chemistry at the semiempirical (AM1) and

) level, and finally to the results derived from a similar

The theoretical calculations were performed at the semiempirical [41] and den-

sity functional theory [42, 43] levels using, respectively, the AM1 method and B3LYP [44–46] with 6-31G\* basis set which were implemented in the Gaussian03W program [47, 48]. The molecular geometries were optimized without any symmetry constraints, and the harmonic frequencies were calculated to ensure that the structures really corresponded to a true local minimum energy on the potential energy surface in the first time and to determine the vibrational zero-point energies in the

the reported values and with those obtained by ab initio (HF/6-31G\*

that the empirical values are adjusted by the following equation:

Modern Spectroscopic Techniques and Applications

C=C double bonds.

6-31G\*

DFT(B3LYP/6-31G\*

DFT(B3LYP/6-31G\*

second time.

42

) and DFT(B3LYP/6-31G\*

approach based on simple atom additivity.

2. Computational methods
