3.2 Estimation based on simple atom additivity

In order to be able to compare the results obtained by the application of the empirical formula based on bond contribution additivity (Eq. (5)) to those obtained by the approach based on atomic contribution additivity, we have grouped in Table 2 the values of vibrational zero-point energies computed with the extended rule of Schulman and Disch (Eq. (4)). The increment of the silicon atom was calculated by AbdulHussain and Fleifel [28]. The value of this increment is shown in Table 4, with those previously published [25–29] for the atoms H, C, O, N, Cl, F, Br, S, and P. Note that the formula of Schulman and Disch was established on the basis that the structural isomers of organic compounds have almost the same value of ZPE. However, the difference can reach 4 kcal/mol [9]. The results obtained by the method based on the additivity of the atomic contributions show, for the 91 silicon compounds, an average error of 2.53 (6.9%). The correlation between the experimental and calculated values by the Schulman-Disch extended formula is shown in Figure 3. The statistical parameters obtained in this case are a correlation coefficient of 0.9972, a slope of 0.95, and a standard deviation of 2.45. Using the regression curves (Table 3) for adjusting the calculated values permits to reduce the


Compound ZPE (kcal/mol)

Vibrational Zero-Point Energy of Organosilicon Compounds

DOI: http://dx.doi.org/10.5772/intechopen.87021

CH2Br(CH3)2SiH (bromomethyl dimethyl

C12H18Si (1-methyl-1-phenyl-1-

C11H16SiS (3-methyl-3-phenyl-1,3-

C2H6SiCl2 (2-chloroethylsilyl chloride

C2H6SiCl2 (2-chloroethylsilyl chloride

C-gauche-Si-trans (Gt))

C-trans-Si-trans (Tt))

45

silacyclohexane)

thiasilacyclohexane)

silane)

SiHCl3 9.29 9.02 7.26 8.54 4.08 [50] SiH3Cl 17.01 17.08 14.50 15.88 13.88 [51] SiH2Cl2 13.31 13.05 11.00 12.42 8.98 [51] SiH4 19.90 21.11 17.71 18.87 18.78 [52] C4H12Si (diethylsilane) 90.68 90.26 87.36 89.65 91.26 [52] C6H16Si (triethylsilane) 125.98 124.83 121.78 124.68 127.50 [52] C8H20Si (tetraethylsilane) 161.23 159.40 156.08 159.52 163.74 [52] CH4SiCl2 (dichloromethylsilane) 27.09 27.67 25.27 26.67 27.10 [53] CH5SiCl (chloromethylsilane) 32.48 34.40 30.62 33.60 32.00 [53] CH6Si (methyl silane) 37.21 38.44 35.51 36.99 36.90 [54] C3H6Si (1-silylpropyne) 43.96 42.85 42.71 43.64 44.66 [55]

H3SiSiH3 30.08 31.26 27.27 29.69 29.51 [57] C11H16Si (1-phenyl-1-silacyclohexane) 151.56 151.30<sup>e</sup> 144.93 145.51 146.90 [58] C10H14SiS (3-phenyl-1,3-thiasilacyclohexane) 134.31 133.54<sup>e</sup> 127.60 137.91 130.65 [58]

H2ClSiSiH3 27.48 27.23 23.89 26.34 24.61 [59] HCl2SiSiH3 23.63 23.20 20.29 22.63 19.71 [59] H2ClSiSiH2Cl 23.94 23.20 20.64 22.93 19.71 [59] Cl3SiSiH3 19.47 19.17 16.53 18.62 14.81 [59] HCl2SiSiHCl2 16.09 15.13 13.29 15.43 9.91 [59] Cl3SiSiH2Cl 15.90 15.13 13.14 15.18 9.91 [59] Cl3SiSiHCl2 11.95 11.10 9.56 11.37 5.01 [59] Cl3SiSiCl3 7.77 7.07 5.85 7.31 0.11 [59] Si4H10 (n-butasilane) 50.50 51.56 46.54 50.82 50.97 [60] Si5H12 (n-pentasilane) 60.93 61.70 56.14 61.23 61.70 [60] Si6H14 (n-hexasilane) 71.39 71.85 65.80 71.85 72.43 [60] Si7H16 (n-heptasilane) 81.85 82.00 81.57 82.43 83.16 [60] Si8H18 (n-octasilane) 92.54 92.15 85.11 92.90 93.89 [60] Si9H20 (n-nonasilane) 102.75 102.29 94.71 103.47 104.62 [60] Si10H22 (n-decasilane) 113.33 112.44 104.26 114.00 115.35 [60] C2H5SiCl (gauche vinyl silyl chloride) 37.31 37.05 35.75 37.14 35.88 [61] C2H5SiCl (cis vinyl silyl chloride) 37.31 35.70 34.19 37.14 35.88 [61]

Exp. Eq. (5)<sup>a</sup> AM1<sup>b</sup> B3LYP/

6-31G\*c

66.33 67.47 64.75 66.89 67.62 [56]

169.58 170.00<sup>e</sup> 161.97 162.84 165.02 [58]

152.32 152.24e 144.66 146.27 148.77 [58]

46.71 46.27 43.99 46.00 45.22 [62]

46.62 46.27 44.01 46.03 45.22 [62]

Eq. (4)<sup>d</sup> Ref.

Table 1.

Bond contributions to ZPE (in kcal/mol).

mean error to 1.68 (4.0%) if the intercept is different from 0 (b 6¼ 0) to 2.28 (7.0%) if b = 0. These results are slightly less good than those obtained by our approach.
