3.1 Estimation based on simple bond additivity

Using the least squares method, we have determined the contributions of the Si—H, Si—C, Si—Cl, Si—O, and Si—Si bond by correlating, for a population of molecules, the values of the vibrational zero-point energies obtained experimentally and those obtained by Eq. (5). The values of the contributions obtained for the studied bonds and those already established [29, 38–40, 49] are given in Table 1.

To test the reliability of the extended empirical model, we applied it to 91 silicon compounds different from those used in the compilation of contributions. This group of molecules contains different classes such as silanes, siloxanes, chlorosilanes, silyl ethers, silanols, silyl chlorides, cyclic organosilicon, and aromatic organosilicon.

The ZPEs obtained are recorded in Table 2. These results show a very good agreement between the calculated and the experimental values. Indeed, the average error is of the order of 1.51 kcal/mol for the 91 molecular systems for which experimental or ab initio (HF/6-31G\* ) data are available. However, the ZPEs calculated for 3-phenyl-1,3-thiasilacyclohexane, 1-phenyl-1-silacyclohexane, 3-methyl-3 phenyl-1,3-thiasilacyclohexane, 1-methyl-1-phenyl-1-silacyclohexane, and (C6H5)3SiOH are underestimated.

This is due to the presence of the aromatic ring in these organosilicon compounds [29, 38–40]. Nevertheless, the adjustment of empirical ZPE values by Eq. (6) leads to a decrease of the mean error which becomes 1.02 kcal/mol (i.e., 1.98%).

The curve of correlation between the experimental and empirical values (Figure 2) appears very satisfactory, the slope is close to unity (0.99), the correlation coefficient is equal to 0.9994, and standard deviation is 1.2. The statistical data concerning the regression curves ZPEexp = aZPEtheor + b and ZPEexp = aZPEtheor are summarized in Table 3. The use of this data for the adjustment of the empirical values of vibrational zero-point energies (ZPEs) reduces the mean error to 0.9 kcal/mol.
