Organometallics zyxwvu 1986, zyxwvut 5, 375-379 375 Revised MNDO Parameters for Silicon zyxwvutsrqponmlkjihgfedcbaZYXWVUTS Michael J. S. Dewar,* James Friedheim, Gilbert Grady, Eamonn F. Healy, and James J. P. Stewart zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712 Received May 24, 1985 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE MNDO has been reparametrized for silicon. The results for a wide variety of silicon-containing compounds are in much better agreement with experiment. Enthalpies of reaction and activation are compared with results from recent high level ab initio calculations. Introduction While MNDO calculations, using the original' parame- ters for silicon, have given satisfactory results in many cases,2recent extensive calculations, here and el~ewhere,~ have revealed certain inadequacies. In particular, calcu- lations with the previous parameters showed an undue preference for divalent silicon. One manifestation of this was to be seen in reactions involving SiRz species. Reac- tions involving the formation of such silylenes were in- variably predicted to be much too exothermic (see Table 11). The original MNDO version also performed badly for compounds containing multiply bonded silicon, greatly underestimating the strengths of the multiple bonds. For example, silaethylene and silacetylene were predicted to have bond orders of 1 and 2, respectively (Table VII). Large errors also occurred in calculations for compounds of silicon with other heteroatoms, most notably oxygen. We have now reoptimized the parameters for silicon, taking advantage of a new and much more efficient al- gorithm for parametrization. The increased speed of the new procedure allowed far more reference functions to be included in the basis set. In addition the 6, and 6, pa- rameters zyxwvutsr as well as the orbital exponents zyxwvut ls and lp were uncoupled and allowed to optimize independently. Procedure The sum of squares of the differences between the calculated values for the properties and the reference values was used to define the error function SSQ. These properties included heats of formation, ionization energies, dipole moments, and geometries. The first derivatives of the heat of formation and ionization energies with respect to the various parameters were calculated analytically. The derivatives of the dipole moments were evaluated by finite difference, and the derivative of the energy with respect to geometry was used as a measure of the deviation of the calculated geometry from the experimental. A knowledge of these derivatives allowed the calculation of the deriva- tive of the SSQ with respect to the various parameters. If the surface were purely parabolic and the exact Hessian, or second derivative, matrix was known, then the optimum set of parameters (P? could be evaluated in one step from the current set (P) using the relationship p' = p - zyxwv GH-1 (1) Dewar, M. J. S.; Rzepa, H. S.; McKee, M. L. J. Am. Chem. Soc. (2) Dewar, M. J. S.; Healy, E. F. Organometallics 1982, 1, 1705. (3) Verwoerd, W. S. J. Comput. Chem. 1982,3,445. 1978, 100, 3607. Table I. Revised MNDO Parameters for Silicon optimized parame- ters value derived " m e t e r s value UJeV -37.037 5330 Eh,,(298 K)/kcal mol-' 108.39 U,,/eV -27.7696780 Eel/eV -82.839 422 0 ra/au 1.315 9860 Dl/au 1.258034 9 r,/au 1.7099430 D2/au 0.978 582 4 &lev -9.0868040 pJau 0.360896 7 Pp/eV -1.075827 0 pz/au 0.366 424 4 0.450 674 0 ar/A-' 2.205 316 0 p3/au g,/eV 9.8200000 g,,/eV 7.310 000 0 ga,/eV 8.3600000 gp2/eV 6.540 zyxwv OOO 0 h,,/eV 1.3200000 Table 11. Heats of Formation for a Variety of Substituted Silylenes and Silanes Using the Original Silicon Parameters MNDO obsd error SiH 70.30 86.40" -16.10 SiH2 26.31 58.60b -32.29 SiF2 -216.48 -147.90" -68.48 SiC12 -105.63 -39.60" -66.04 SiBr2 -51.64 -12.20c -38.44 SiH3(CH3) -15.53 -7.77d -7.76 SiH2(CH3)2 -41.54 -19.98d -21.56 SiH(CH& -66.46 -37.43d -29.03 Si(CH& -90.10 -57.100 -31.50 SiHK&H& -56.61 -43.62' -12.99 SiH(C2H5)3 -85.49 -48.We -37.69 Si(C2HA -1 11.03 -64.40' -47.60 SiH4 1.20 7.300 -6.10 SizHB 11.5 7.30" 4.20 SisHs 32.5 29.90" 2.60 "Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttall, R. L. J. Phys. Chem. Ref. Data, Suppl. 1982, 11, 2. *Vanderwielen, A. J.; Ring, M. A.; O'Neal, H. E. J. Am. Chem. SOC. 1975, 97, 993. 'Schafer, H.; Braderreck, H.; Morcher, B. 2. Anorg. Allg. Chem. 1967, 352, 122. dPedley, J. B.; Iseard, B. S. 'CATCH Tables for Silicon Compounds"; University of Sussex, 1972. ' Pedley, J. B.; Rylance, J. Sussex-N.P.L. Computer Analysed Thermochemical Data, University of Sussex, 1977. where G is the f i i t derivative matrix and H-' is the inverse Hessian. However, because of the more complex nature of the surface and the advisability of choosing small step sizes, a more conservative approach was adopted. From a knowledge of the derivatives of the SSQ for two slightly different sets of parameters an approximate Hessian was constructed. A line search along the search direction yielded the optimum step size, and this information was 0276-7333/86/2305-0375$01.50/0 0 1986 American Chemical Society