Modern Spectroscopic Techniques and Applications


energies for the same organosilicon compounds using semiempirical (AM1) and

C3H7SiCl (cis-cyclopropylchlorosilane) 55.47 55.80 53.87 55.03 54.00 [79]

Based on these results, the values calculated at the DFT(B3LYP/6-31G\*

closer to the experimental data than those obtained at the semiempirical (AM1) level. The mean error is 2.50 (5.45%) for AM1, compared to 1.08 (1.86%) for DFT

those calculated by using AM1 and DFT methods are represented, respectively, in Figure 4a and b. Examination of this correlations shows that these methods are able to calculate accurately the zero-point vibration energies of the organosilicon compounds with a small advantage for the DFT method. For the adjustment of calculated ZPEs, the use of the regression line of the form ZPEexp = aZPEtheor (Table 3) permits to reduce the mean error of 2.5–1.83 kcal/mol for AM1 and from 1.08 to

culated ZPEs, the scaling factors of Scott and Radom [80] are used.

Compound ZPE (kcal/mol)

Vibrational Zero-Point Energy of Organosilicon Compounds

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

H3SiOSiH3 32.90 35.38 30.93 33.16 32.91 \*\* Si(OH)3-O-Si(OH)3 55.86 52.36 51.11 56.39 53.31 \*\* C2Si2H8O (1-oxa-2,5-disilacyclopentane) 56.90 56.93 55.41 57.43 54.91 \*\* (H2SiO)3 (cyclotrisiloxane) 41.40 40.72 38.12 41.43 36.20 \*\* (H2SiO)4 (cyclotetrasiloxane) 54.91 54.99 51.19 55.05 50.33 \*\* (C2H5O)4Si 171.18 174.09 170.16 172.95 177.34 \*\* CH3SiH2SiH2CH3 63.83 65.90 62.65 65.31 65.75 \*\* H3SiSiH2SiH3 39.94 41.41 36.92 40.19 40.24 \*\* (Me3Si)2SiH2 143.61 145.34 141.84 145.47 148.96 \*\* ((CH3)3Si)3SiH 205.33 207.45 204.16 208.86 214.05 \*\* CH3OSi(CH3)3 91.48 94.07 90.79 92.94 94.66 \*\* Et3SiOH 126.18 127.66 125.19 128.10 130.90 \*\* Ph3SiOH 172.20 176.01<sup>e</sup> 174.18 173.66 177.46 \*\* nbutyl3SiOH 228.34 231.16 228.10 231.39 239.62 \*\* (CH3)3SiOSi(CH3)3 134.88 139.31 133.95 137.52 141.63 \*\* (CH3)3SiOCOCH3 97.34 97.38 97.00 98.80 101.94 \*\*

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

6-31G\*c

134.19 137.23 134.29 135.98 142.06 \*\*

84.22 85.17 84.27 84.87 90.39 \*\*

, empirical Eq. (4)) zero-point energy

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

) methods. Results are summarized in Table 2. To correct cal-

). The correlations obtained between the experimental values and

). When the intercept is different from zero,

) level are

DFT(B3LYP/6-31G\*

with experimental values.

one)

a

b

c

d

e

Table 2.

(CH3)3SiOCOCF3

(trimethylsilyltrifluoroacetate)

Values determined by our model.

Values scaled by 0.95 [80].

Values scaled by 0.96 [80].

Values adjusted by Eq. (6).

(B3LYP/6-31G\*

47

1.06 kcal/mol for DFT(B3LYP/6-31G\*

C8H16SiO2 (4-trimethylsiloxy-3-penten-2-

Values computed by Schulman-Disch extended empirical formula.

Comparison of computed (empirical Eq. (5), AM1, B3LYP/6-31G\*

\*\*Values calculated with HF/6-31G\* and scaled by 0.89 [80].


## Vibrational Zero-Point Energy of Organosilicon Compounds DOI: http://dx.doi.org/10.5772/intechopen.87021

a Values determined by our model.

b Values scaled by 0.95 [80].

c Values scaled by 0.96 [80].

d Values computed by Schulman-Disch extended empirical formula.

e Values adjusted by Eq. (6).

\*\*Values calculated with HF/6-31G\* and scaled by 0.89 [80].

#### Table 2.

Compound ZPE (kcal/mol)

C2H7SiCl (1-chloroethylsilane) 49.70 50.30 47.41 49.27 50.12 [63] C2H7SiCl (gauche ethyl chlorosilane) 51.38 51.65 49.18 51.11 50.12 [64] C2H7SiCl (trans ethyl chlorosilane) 51.42 51.65 49.19 51.10 50.12 [65] H3SiOH 24.21 23.94 21.77 23.22 22.18 [66] C3H6Cl2Si (1,1-dichlorosilacyclobutane) 49.65 51.84 51.55 52.36 49.10 [67] C2H8Si (ethylsilane) 54.79 55.69 52.75 54.54 55.02 [68] C3H9SiCl (chlorotrimethylsilane) 68.16 69.05 66.13 67.91 68.24 [69] C3H10Si (trimethylsilane) 71.95 73.08 70.20 71.86 73.14 [69] C4H12OSi (methoxytrimethylsilane) 93.41 94.07 90.81 92.94 94.66 [69] (CH3)3SiOH (trimethylsilanol) 75.35 75.91 73.33 75.47 73.14 [69] C3H10Si (gauche-n-propylsilane) 72.29 72.94 70.00 71.89 73.14 [70] C3H10Si (anti-n-propylsilane) 72.07 72.94 70.00 71.78 73.14 [70] C3H10Si (trans ethylmethylsilane) 72.14 73.01 70.21 72.07 73.14 [71] C3H10Si (gauche ethylmethylsilane) 72.27 73.01 70.30 72.20 73.14 [71] C4H10Si (cis methylsilylcyclopropane) 76.81 77.09 74.07 75.51 77.02 [72] C4H10Si (gauche methylsilylcyclopropane) 76.44 77.09 74.10 75.45 77.02 [72] C3H12Si2 (1,1,1-trimethyldisilane) 82.56 83.23 79.69 82.38 83.87 [73] C5H12Si (cyclopentylsilane) 94.60 94.34 93.21 94.05 95.14 [74]

C6H14Si (cyclohexyl silane (chair-axial)) 112.93 111.59 110.54 112.00 113.26 [75] C3H8Si (allylsilane) 57.75 58.34 56.22 57.51 58.90 [76]

C3H7SiCl (methylvinyl silyl chloride) 54.48 54.38 52.92 54.55 54.00 [78] (H3Si)2CCH2 49.65 51.26 47.92 57.01 51.51 \*\* ((CH3)3Si)2CCH2 152.56 155.19 151.46 155.08 160.23 \*\* C5H12Si (1,1-dimethyl-1-silacyclobutane) 93.33 94.55 93.48 94.57 95.14 \*\* C3H8Si (silacyclobutane) 59.06 59.91 59.25 59.71 58.90 \*\* C4H10Si (1-methyl-silacyclobutane) 76.38 77.23 76.50 77.18 77.02 \*\* Cl3SiCH3 25.44 26.34 24.28 25.83 22.20 \*\* Cl2Si(CH3)2 46.36 47.69 45.17 47.17 45.22 \*\* (CH3)3SiCN 71.85 72.45 70.99 72.59 73.95 \*\* SiH3CN 19.27 20.49 19.36 19.98 19.59 \*\* Si(OH)4 34.56 32.43 32.10 34.64 32.38 \*\* HSi(OH)3 30.79 29.60 28.85 30.88 28.98 \*\*

C2H6SiCl2 (2-chloroethylsilyl chloride

Modern Spectroscopic Techniques and Applications

C6H14Si (cyclohexyl silane (chair-

C3H8SiCl2 (anti dichloromethyldimethyl

C3H8SiCl2 (gauche dichloromethyldimethyl

equatorial))

silane)

silane)

46

C-trans-Si-gauche (Tg))

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

6-31G\*c

46.46 46.27 44.30 46.07 45.22 [61]

112.15 111.59 110.54 111.83 113.26 [75]

62.42 62.31 59.76 61.78 63.34 [77]

61.73 62.31 59.78 61.75 63.34 [77]

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

Comparison of computed (empirical Eq. (5), AM1, B3LYP/6-31G\* , empirical Eq. (4)) zero-point energy with experimental values.

energies for the same organosilicon compounds using semiempirical (AM1) and DFT(B3LYP/6-31G\* ) methods. Results are summarized in Table 2. To correct calculated ZPEs, the scaling factors of Scott and Radom [80] are used.

Based on these results, the values calculated at the DFT(B3LYP/6-31G\* ) level are closer to the experimental data than those obtained at the semiempirical (AM1) level. The mean error is 2.50 (5.45%) for AM1, compared to 1.08 (1.86%) for DFT (B3LYP/6-31G\* ). The correlations obtained between the experimental values and those calculated by using AM1 and DFT methods are represented, respectively, in Figure 4a and b. Examination of this correlations shows that these methods are able to calculate accurately the zero-point vibration energies of the organosilicon compounds with a small advantage for the DFT method. For the adjustment of calculated ZPEs, the use of the regression line of the form ZPEexp = aZPEtheor (Table 3) permits to reduce the mean error of 2.5–1.83 kcal/mol for AM1 and from 1.08 to 1.06 kcal/mol for DFT(B3LYP/6-31G\* ). When the intercept is different from zero,

#### Figure 2.

Correlation between experimental ZPEs and empirical values calculated using Eq. (5).


#### Table 3.

Coefficients a, b, and R<sup>2</sup> in equations ZPEexp = b + aZPEtheor in both cases b = 0 and b 6¼ 0.


the function isomers. Furthermore, the adjustment of calculated values, empirically or using quantum methods, with the ZPEexp = b + aZPEtheor model makes the four

(a) Correlation between experimental and theoretical (AM1) ZPE and (b) correlation between experimental

Correlation between experimental ZPEs and empirical values calculated using Eq. (4).

Vibrational Zero-Point Energy of Organosilicon Compounds

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

In this chapter, we reported the extension of our empirical relationship established in 2011 for the computation of zero-point vibrational energies (ZPE) of organosilicon compounds. The bond contributions of Si—H, Si—C, Si—Cl, Si—O, and Si—Si were determined. The application of the proposed empirical model to more than 90 organosilicon shows the reliability of this model. The results derived from this model are compared with those obtained by quantum chemistry methods

obtained by similar empirical approach on the other hand. As a result, the empirical

)) on the one hand and to those

estimates comparable.

and theoretical (B3LYP/6-31G\*

Figure 3.

Figure 4.

49

4. Conclusions and outlook

(semiempirical (AM1) and DFT (B3LYP/6-31G\*

) ZPE.

#### Table 4.

Atom contributions to ZPE (in kcal/mol).

the average error decreases from 2.5 to 1.37 kcal/mol for AM1 and from 1.08 to 1.00 for DFT(B3LYP/6-31G\* ).

As a result, the four estimates of vibrational zero-point energy of the organosilicon compounds (our empirical model, Schulman-Disch extended empirical formula, AM1, and DFT) are correct. But the empirical approaches have the advantage of simplicity and speed. In addition, the approach based on bond contributions additivity has also the advantage of providing different values of ZPE for

Vibrational Zero-Point Energy of Organosilicon Compounds DOI: http://dx.doi.org/10.5772/intechopen.87021

Figure 3. Correlation between experimental ZPEs and empirical values calculated using Eq. (4).

#### Figure 4.

(a) Correlation between experimental and theoretical (AM1) ZPE and (b) correlation between experimental and theoretical (B3LYP/6-31G\* ) ZPE.

the function isomers. Furthermore, the adjustment of calculated values, empirically or using quantum methods, with the ZPEexp = b + aZPEtheor model makes the four estimates comparable.
