Hencsei, P.

Nagy, J.

Réffy, J.

English

Periodica Polytechnica (Budapest University of Technology and Economics)

QUANTUMCHEMICAL CALCULATIONS ON (C6H 5)Si(CH3)3 BY VARIOUS METHODS By J. REFFY, P. HENeSEI and J. NAGY Department of Inorganic Chemistry, Technical University Budapest Received slay 16, 1976. Introduction Quantumchemical calculations on organosilicon compounds involve many problems. Appropriate parameters for silicon atom and various Si-X bonds are inexistent in most quantumchcmical methods. A great many of the methods cannot take the participation of Si 3d orhitals in chemical bonds into consideration. Similarly, in applying all valence electron methods, problems are caused by the high number of centres and orbitals. For this reason a computer "with proper capacity and considerahle running time is necessary for the calculations. In our work various methods were applied for trimethylphenylsilane (C6HsSi(CH3)3) and the results were interpreted in terms of experimental data. The applied quantum chemical methods; input parameters Del Re method For the calculation of (j bond system Del Re method was used, modified and extended for organosilicon compounds [1]. Hiickel method and Hiickel method improved by w-technique The Hiickel method [2] is a simple, approximate, one-electron LCAO-MO method for calculations on JT, systems. Rather than assuming arbitrarily the coulomh and resonance integrals required for our calculations they -were taken from integral tables [3] in the knowledge of bond lengths and ionization energies. For the calculation of these integrals Slater atomic orbital eigenfunc-tions were chosen, then the coulomb Cl.i and resonance {3ij integrals were expressed in parametric form: (f.i = Cl. + h i{3 {3ij = kij{3 • 280 J. REFFY et al. An iterative version of the Hiickel method is the m-technique [4, 5] accounting for the change of the atomic coulomb integral as a function of electron density q; on the atom as follows: (nj - q;)wfJ . PPP method The PPP method is one of the most wide-spread and most efficient :7 electron methods [6, 7]. In this method, the valence state ionization energies I; and the one-centre electronic repulsion integrals yu required for calculating the diagonal elements of the Fock matrix were taken from the ·work by HINZE and JAFFE [8], and by LEVISON and PERKINS [9], respectively. For the estimation of the two-centre electronic repulsion integrals the follo-wing empirical equations were used: MATAGA and NISHIl'.10TO [10]: OHNO [H]: CHOJNACKI [12]: Y9.H - 0 4 ,tlMN ...L 0 6 y9.H I] - • I I] I • I] DORR and al. [13]: D 0 ~( R-1 YU = . . ;j, where Rij is the bond distance. The resonance integral of the carbon-carbon bond was chosen to he -2.39 cV [6], that of the silicon-carbon bond was detennined by the WOLFSBERG-HELMHOLZ formula [14]: fJ~;c = 1/2 k (Is; + le) Ss;c . cos ~, where k is a proportionality coefficient (0.6426), Ss;c is an overlap integral, its value being calculated [3] on the basis of the bond distance and the Burns' effective nuclear charges [15], cos ~ resulted from the consideration of the partial overlapping between p and d orbitals due to the tetrahedral orientation of silicon atom (~ = 190 28') [16]. The parameters of the calculations taking into accoun t the hyper-conjugative effect of methyl groups (lcI' IH 3 , Yc'c', j'HaHa' (Js;c', fJc'Ha) were assumed according to NAGY [16]. 281 IPPP method In the IPPP method [17, 18] the parameters are not constants, but vary in the process of calculation depending on the charges. In our calculations the ionization energies Ii were altered as a function of the effective nuclear charges Zr, using the follo"\Ving equation: The constants ai and bi were determined by means of isoelectronic series [16]. Dependence of the effective nuclear charges on the partial charges can be expressed as follows: z~ = Z~o + 0.35 (o~ oc) where Z~o, Z!~ are effective nuclear charges calculated according to the Burns rules, !Jc, !JSi are (J partial charges obtained by Del Re calculations, !Jc, !JSi are Jr partial charges. The ionization energies were varied in an iterative process on the basis of Jr partial charges until self-consistency. EHT method The Extended Hiickel method [19, 20] is an all valence electron method. The ionization energies necessary for the calculations were chosen on the basis of data published by HINZE [21] (for sand p orbitals) and by LEVISON and PERKINS [9] (for silicon 3d orbitals). The CNDO/2 method [22, 23, 24] is the most correct all valence electron method as compared to those developed earlier. The calculations were carried out with original parametrization (on spd basis). The input parameters of the various calculations on CsH5Si(CH3)3 molecule are summarized in Table 1. The geometrical data used were as follows: Rcc = 1.397 A, R SiC = 1.853 A, R SiC' = 1.888 A, RCH = 1.0864 A, RC'H = 1.093 A [25]. (The atom marked C' is the carbon atom of methyl groups attached to silicon atom.) 282 Del Re Huckel .r. REFIT et al. Table 1 Input parameters of quantumchemical calculations for CsHsSi(CH3):] Method o~ = 0.07 (sp") 0.12 (5p~) o'it = 0 o~i = -0.10 Parameters ;·CC = 0.1 '1CH = -0.2 YHC = 0.4 '1SiC = 0.2 '1CSi = 0.'1 . w = 1.0 "cc = 1.00 "CH = 1.00 I'SiC= 0.90 Huckel w-techn. h Si = -1.8152 kSiC = 0.3374 PPP IPPP EHT i lc = -11.16 eY IS! = -1.10 eV le = -11.19 eV I(H) = -10.26 eV ;.CC = 11.13 eV YSiSi = 3.762 eV ;.'ee = 9.71 eV YH,H, = 9.33 eV IC = -0.6133 exp (1.0362 Zc) ISi = -0.2066 exp (0.9555 ZSi) Is(C) = 21.01 eV Ip(C) = 11.27 eV IiH) = 13.60 eV Is(Si) = 17.31 eV I/Si) = 9.19 eV Id(Si) = LlO eV ;CS<C) = 1.575 ;Cp(C) = 1.400 ;CiH) = 1.000 qiSi) = 1.616 ~p(Si) = 1.133 ~d(Si) = 0.583 Results, discussion fJ~c = -2.39 eV f3~iC = 1.3151 eV f3~iC' = -1.5521 eY f3~'H3 - -7.4013 eY The experimental data for trimethylphenylsilane are presented in Table 2. The results of the calculations bv various methods are described in the following part. Fig. 1 illustrates the partial charges obtained hy Del Re method, Hiickel method and Hiickel method 'with cv-technique, respectively. The effect of the variation of parameter cv was investigated for several compounds, and it was concluded that the best agreement ",ith the exper-imental data was achieved for organosilicon compounds with cv values ranging from 0.8 to 1.0 [30]. The charges presented in Fig. lib and Fig. lie indicate lJltraviolet spectrum Dipole moment Ionization potential lac chelnical shifts QUANTUJ[CHEMICAL CALCULATIONS Table 2 Experimental data for CsH.Si(CHa)a i.max = 188, 211, 264 nm ! (LIE = 6.59, 5.88, 4.70 eV) ! f.l= 0.248 D I ,,_ 'I 1=8.79 e, Cl: +11.3 ppm C· + 4.7 ppm 11 C:; - 0.8 ppm C4 : + 0.2 ppm ethanol solution by Onsager's method reference material: benzenel 283 [26] [27] [28] [29] that the (CH3)3Si group cannot be strongly ortho and para orienting (as it would result from the + I effect of the silicon, neglecting the -lVI effect of the silicon atom), since in these positions there are small positive charges unfavourable to electrophylic attack. At the same time the free valences of carhon atoms (F(C i )) are larger in ortho and para position than in met a positions (Table 3), this result is in accordance "\vith the weak ortho and para orienting behaviour of the (CH3)3Si group [31]. The orienting effect of a trimethylsilyl group is correctly reflected by the trend in partial charges hy both kinds of Hiickel calculations. The resulting an dipole moment calcu-lated hy m-technique shows better agreement with the experimental value. The bond hetween the silicon and aromatic carhon atom has a (p-d)n character of 11%. The electronic transition energy (Llm) is lower than in benzene, the calculations are in accordance "\vith the hathochromic shift H H H+O.Ol~l i -OJ)5G7 H-C-H I +0.2408 H3C-Si-CH3 -o.UUOO a -O.153fl H +0.04.(17 H+o.u·!.O~ .;. 0.0430 b ."':i ,l"I!:";I. I +- 0.0249 c Fig. 1. Charge distribution of CsH.Si(CHah: (a) a distribution, (b) ;z; charge distribution by H iickel method, (c) n charge distribution by co-technique (co = 1,0) 6 Periodica Polytechnica OH 20/3 284 Llm fLcm p(SiC) P(C1C2) p(C2CS) p(CSC4) F(C1) F(C2) F(Cs) F(C4) J. REFFY et al. Table 3 Results of Hiickel calculations Buckel W=O 1.8438 fJ 0.74 D 0.1167 0.6560 0.6690 0.6652 .11_Biickel w-techn. . w= 1.0 _ 1.8767 fJ 0.53 D 0.1137 0.6588 0.6683 0.6656 0.3007 0.4049 0.3981 0.4008 indicated by the ultraviolet spectra. The most important results of the HiickeJ calculations are recapitulated in Table 3. Concerning the results of the PPP calculations, the :n: charge distribution is shown in Fig. 2, the electronic transition energies lEC], the ionization energies I, the a:n: resulting dipole moments fl,,7! and the :n: bond orders pij are presented in Table 4. According to the results obtained by using various methods for the calculation of i'ij, the MN calculations approximated most closely the experimen-tal values of electronic transition energies. The calculated dipole moments hardly show a change (the greatest difference being 0.031 D), the closest agreement is again achieved by IHN calculation. Also the change of :n: bond orders is very slight. As concerns the :n: charge distribution, the D calculation provides the most polarized charges, and the charges obtained by MN calculation are polarized in the slightest degree. The MN method gives the best result for the ionization energy of the molecule, though the calculated value is by 1.6 eV higher as the experimental one. All the results mentioned match well the results of similar calculations for vinyl and phenoxysilanes [32]. The consideration of the hyperconjugative effect of the methyl groups resulted in a slight change of the electronic transition energies and ionization energy and impaired the calculated dipole moment values. From this experience it was concluded that for the :n: system of larger molecules (e.g. containing a phenyl group) the hyperconjugation of CH3 groups is not reasonable to Q U .:LYTUJfCBEMICAL CALCULATIONS 285 8i-0.0377 8i-0.0418 Si-O.0400 -0.0096 -0.0157 -0.0122 -0.00U3 o +0.0233 o +0.0186 o +0.0285 -0.0008 -0.0047 +0.0117 +0.0191 +0.0150 MN OH CH (H3) +0.0577 / C-O.0426 / 8i-0.0413 Si-0.0816 8i-0.0422 -0.0188 -0.0050 +0.0089 o o +0.Oli4 +0.0024 -0.0153 o +0.0107 -O.OOli +0.0249 +OiJ099 +0.0071 D 11']>P Fig. 2. 7l charge distribution of CsH;Si(CHa)a calculated by PPP method be taken into account. The iterative PPP method gave somewhat worse results for electronic transition energies and better results for ionization energy and dipole moment. The calculation indicated positive :re partial Table 4 Results of PPP calculations ppp ppp ppp ppp ppp IPPP !d.N OH CH D hyperconj. lECl (eV) 4.781 4.828 4.809 4.812 4.775 4.764 5.748 5.010 5.343 4.968 5.684 5.626 6.529 6.411 6.469 6.577 6.416 6.393 I (cV) 10.446 11.403 11.020 11.106 10.401 10.303 Pcm (D) 0.298 0.329 0.316 0.312 0.075 0.288 SiC 0.193 0.204 0.199 0.203 0.188 0.202 C1Cz 0.654 0.653 0.653 0.653 0.654 0.653 PijczCa 0.669 0.670 0.669 0.670 0.669 0.669 CaC4 0.665 0.665 0.665 0.665 0.665 0.665 6* 286 J. BEFFY et al. charges for the carbon atoms of the phenyl group and considerable negative charge on the silicon atom. The (f7C partial charges obtained by Del Re and PPP calculations showed the best correlation with the l3C chemical shifts if hyperconjugation was considered, but even in this case the correlation was worse than for the CNDOj2 calculation. Compared with the result of Huckel method, the PPP calculation provided a higher value for the 7C bond order (0.19 to 0.20) of the silicon - aromatic carbon bond. The EHT method gave the worst results. This method indicates baseless charges in compounds containing heteroatom and is not suitable for calculating the dipole moment. The partial charge of aromatic carbon atoms does not show correlation 'with the J3C chemical shifts. For the electronic transition energy (L1m) 4.033 eV, for the ionization energy (I) 10.427 eV was obtained. Considering the results of calculations by the CNDO/2 method it was found that the calculated dipole moment 0.33 D was in a good agreement with the experimental value. The bond order between the silicon and aromatic carbon atom is 1.087, which is very near to the value calculated by the Huckel method improved by co-technique. On the basis of the CNDOj2 method, the bond orders were calculated by two different 'ways: cither as the sum of squares of the corresponding density matrix elements (A) [33], or as the sum of the products of the corresponding density matrix and overlap integral matrix elements (B). The values of bond orders are presented in Table 5. The bond orders by both methods are seen to show the same trend, but method B results in unfoundedly low bond orders. Even the data obtained by method A can only be applied to estahlish tendencies, since these values appear to be somewhat low. On the basis of the Buckel method, the aromatic carbon-carbon bond orders are expected in the range 1.6 to 1.7, and the carbon-hydrogen bond orders are likely to approach unity. Table 5 CNDOj2 bond orders Bond orders Bond A B Si-Cl 1.0866 0.9770 Cl-C2 1.3487 0.9256 C2-Ca 1.4494 0.9522 Ca-C4 1.4420 0.9513 C2-H2 0.9467 0.6772 Ca-Ha 0.9579 0.6809 C4- H 4 0.9582 0.6813 QCLYTUMGHEJ[[CAL CHGTL1TlOXS 287 Table 6 Variation of Si-C bond order vs. bond distance Bond di~ta!1ce Bond order (1) A B 1.75 1.1238 1.0649 1.80 1.1076 1.0214 1.853 1.0866 0.9770 1.90 1.0686 0.9374 Investigating the same bond, the correlation between the bond orders calculated by both methods A and B is extremely good. We studied the change in the Si-C (aromatic) bond order of the molecule in dependence of bond distances ranging from 1.75 to 1.90 A. The results have been compiled in Table 6. The correlation coefficient between the A and B bond orders is 0.992. The bond order is considerably affected by the Si-C bond distance; the bond order is expected to increase if the bond distance decreases. The calculated dipole moment is next to the experimental result when the bond distance is about 1.85 A. The calculated dipole moments are in this order: 1.75 A - 0.097 D; 1.853 A - 0.32 D; 1.90 A-0.586 D. The equilibrium silicon - carbon (aromatic) bond distance appears to be 1.886 A, the total energy of the molecule indicates a minimum at this value [34]. The calculations are consistent with the experimental silicon - carbon (aromatic) bond length of 1.87 A determined by X-ray diffraction method for phenylsilanes [35]. The partial charges obtained by CNDO/2 method are presented in Fig. 3. In many respects the same trends can be observed as for the partial charges H H H-r-(U)31J I -0.1633 H-C-H I +o.o:r:G H3C-Si-CH3 H-O.0154 o -n.(ll:~:! Fig. 3. Charge distribution for CsH5Si(CH3)3 calculated by CNDO/2 method 288 J. REFFY et al. Table 7 l3C NMR chemical shifts (reference material: benzene) and electron densities calculated by CNDOj2 method Chemical shift I Electron density I Partial charge Cl +11.3 4.0945 -0.0945 C2 (orto) +4.7 3.9415 +0,0585 C3 (meta) -0.8 4.0132 -0.0132 C4 (para) +0.2 3.9738 +0.0262 calculated by the Del Re and the Hiickel method "with m-technique, for instance, in both cases the greatest negative charges can be located on the carbon atoms, in meta positions from among the ring carbon atoms, and the partial charge becomes increasingly positive in meta-para-ortho order. The l3C NMR chemical shifts of the molecule are comparable to the calculated electron densities as well as the partial charges of carbon atoms. From data in Table 7, a good correlation is seen between the experimental and calculated electron densities for carbon atoms in ortho, meta and para positions; in the case of the carhon atom linked to the silicon the data cannot be compared to characteristics of other carbon atoms because of the different chemical setting. According to the CNDO;2 calculation, the ionization energy of the molecule is 11.52 eV, a value by 2.7 eV higher than the experimental one. l\L-\'IRE and LE\lOUZIN found in photoelectron spectroscopic investigations the OT2 and OT3 molecular orbital levels of trimethylphenylsilane to be degen-erate [36]. The lack of level splitting does not mean, ho·wever, that the role of d orbitals is negligible. It ·was proven by MAIRE based on the photoelectron spectra of compounds p-ClC6H 4M(CH3)3 (where M=C, Si, Ge, 5n) that the splitting of OT2 and ;r3 levels sho·wed a minimum in the case of the silicon derivative, this experimental fact could be explained by the existence of (p-d);r interaction [37]. In the trimethylphenylsilanc the mentioned degen-eration of the levels is a result of the +1 and -?vI effects of silicon acting oppositely. Summary In this work the structure of trimethylphenylsilane (CuH5Si(CH3h) was investigated by various quantumchemical methods. Proper conclusions on the bond structure could be drawn on the basis of Hiickel method with OJ-technique. PPP and CNDO!2 methods. QU~NTUMGHEMIG.d.L G~LGUL~TIONS 289 References 1. NAGY, J.-HENCSEI, P.-RiFFY, J.: Acta Chim. Acad. Sci. Hung. 65, 51 (1970) 2. HtiCKEL, E.: Z. Physik. 70, 204 (1931); 72, 310 (1931); 76, 628 (1932) 3. KRUGLYAK, A.-WmnIA1'l, D. R.: Tablici integralov kvantovoj khimiii. Tom 1., Vichis-litelnij Centr. 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QUANTUMCHEMICAL CALCULATIONS ON (C6H5)Si(CH3)3 BY VARIOUS METHODS

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QUANTUMCHEMICAL CALCULATIONS ON (C6H5)Si(CH3)3 BY VARIOUS METHODS

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