J . Phys. Chem. 1989, 93, 1674-1675
1674
New Electronegativity Scale for the Correlation of Heats of Formation. 5. Simple Sillcon-Containing Compounds Yu-Ran Luo and Sidney W. Benson* Donald P. and Katherine B. Loker Hydrocarbon Research Institute, Department of Chemistry, University of Southern California, University Park, Los Angeles, California 90089- 1661 (Received: July 11, 1988)
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A new linear equation on AfHo(SiH3X)has been found: AAfHo(SiH3X/HX)/p = a bVx, where AAfHo(SiH,X/HX) E AfHo(SiH3X)- AfHo(HX),p is the number of hyrogen atoms in the HX molecule, Vx is the unshielded core potential of the atom in X attached to H, and a and b are constants dependent on the properties of Si. The linear relation between AfHo(SiH3X)and AfHo(CH3X) is discussed.
Introduction A few simple, accurate, linear relations between AAfHoand Vx,the unshielded core potentials of the atom in X attached to C or to H (in HX), have been described in the previous papers.'-3 The relations have been also used to determine the values of group parameters for C-centered groups, AfHo[C-(X)(C)m(H)3-m]. They have been expressed as ( RX/CH3X), AAfHo(CH3X/HX),or ADHo(X-R/X-CHJ
+ b(C,m) + Vx A A f H o ( C H 3 X / H X ) / p = a ( C ) + b(C)Vx
AAfHo(RX/CH3X) = a(C,m)
(1)
(2)
where R = CH3-m(CH3)m,which are ethyl, 2-propy1, and tert-butyl groups when m = 1, 2 , and 3, respectively: X = F, CI, Br, I, H , O H , S H , NH2, and CH,. a(C,m) and a(C) or b(C,m) and b(C) are constants dependent on m and the properties of carbon. We will begin to discuss the thermochemistry of non-carboncentered groups, such as Si, Ge, and some metallic elements in this work. A relation similar to eq 2 is reported here. The equation will be used to relate the thermochemistry on Si-centered groups and C-centered ones.
6L
I_
E -
4-
0 U
2a
-20I \ X
I "-2-
-0
C
r
a -6
'2j
New Linear Relation for AfHo(SiH3X/HX)
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Recently, new data on the heats of formation of compounds SiH,X, where X = F, C1, Br, I, and H , have been recommended. These data are listed in Table I. Following ref 2, we find a linear relation between AAfHo(SiH3X/HX)and Vx,as shown in Figure I . It is given by A A f H o ( S i H 3 X / H X ) / p = 13.0 - 3.28Vx
(3)
very similar to eq 2. The mean deviation of the eq 3 from experimental data for X = F, CI, Br and H is very small, 0.2 kcal/mol. The data for iodine are markedly off the line by 2.5 kcal/mol. The experimental uncertainty for SiH31 is reported as f 2 kcal/mol, and on the basis of the agreement found for the other halides we propose that the value for AfHo(SiH31,g)be changed to 2.1 kcal/mol (see Table I). The linear relation between AAfHo(CH3X/HX)/p and Vx has also been shown in Figure 1 to compare the two straight lines. It is interesting that the slopes for the lines have different signs. ( 1 ) Luo, Y.-R.; Benson, S . W . J . Phys. Chem. 1988, 92, 5255. (2) Luo, Y.-R.; Benson, S. W. J . A m . Chem. SOC.in press. (3) Luo, Y.-R.; Benson, S . W. J . A m . Chem. Soc., in press. (4) Luo, Y.-R.; Benson, S. W. J . A m . Chem. SOC.,in press. (5) Schlegel, H.B. J . Phys. Chem. 1984, 88, 6254. (6) Walsh, R. J . Chem. Soc., Faraday Trans. I 1983, 79, 2233. ( 7 ) Walsh, R . The Chemistry of Organosilicon Compounds; Patai, S.. Rapport, Z., Eds.; Wiley: New York, Chapter 5, in press. (8) Pedley, J. B.; Naylor, R. D.;Kirby, S. P. Thermochemical Data of' Organic Compounds. 2nd ed.; Chapman and Hall: London, 1986
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Figure 1. Linear relations between AAfHo(SiH3X/HX) or AAfHo(CH,X/HX) and V,: (1) carbon-centered, -15.8 2.S8Vx; (2) silicon-centered, 13.0 - 3.28Vx.
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The slope for the carbon-centered group is positive, but that for the silicon-centered group is negative. This is a consequence of the fact that silicon is less electronegative than carbon and hence forms a stronger bond with more electronegative elements such as CI and F than does H. The converse is true for carbon. Note that the overall ordinate ranges are about the same for the two elements, about 22 kcal/mol.
Discussion Combining eq 3 with eq 2 , we have a new equation: AAfHo(SiH3X/CH3X)/p = 28.8 - 5.86Vx
(4)
where X = F, C1, Br, I, and H. We can also derive another dependent relation: AAfHo(SiH3X/HX)/p = -7.1 - 1.27AAfHo(CH3X/HX)/p (5)
0 1989 American Chemical Society
J . Phys. Chem. 1989, 93, 1675-1676 TABLE I: Values of AAfHo(SiH3X/HX) ( k ~ a l / m o l ) ~ X VX AfH'(SiH,X) F 9.915 -84.8 f 0.5" CI 7.04 -32.4 f 2.5' Br 6.13 -15.3 f 2.1' I 5.25 -0.5 f 2.0b (2.1) 8 . 2 f 0.5' H 2.70
AfH' (HX)' -65.3 f 0.2 -22.06 f 0.03 -8.67 f 0.04 -6.33 f 0.03 0
AAfHo(SiH3X/HX) -19.5 f 0.6 -10.34 f 2.5 -6.63 f 2.2 -6.68 f 2.1 (-4.2) 8.2 f 0.5
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p 1
1 1 1
2
AAfHo(SiH3X/HX)/p -19.5 f 0.6 -10.34 f 2.5 -6.63 f 2.2 -6.68 f 2.1 (-4.2) 4.1 f 0.3
'Reference 5 . 'References 6 and 7. CReference8. dNote: Values in parentheses are derived here; see text. In general, these two equations can be written as
A A f H ~( s ~ H ~ x / c H ~ = ~ )a ( ~ i , ~+ ) pi,^) vx AAfHo(SiH,X/HX) = a'(Si,C)
+ b'(Si,C)AAfHo(CH3X/HX)
(6) (7)
where a(Si,C), a'(Si,C), b(Si,C), and b'(Si,C) are all constants dependent on the properties of carbon and silicon.
The equations (3)-(7) are interesting because they relate the relatively sparse thermochemistry of silicon compounds with those for carbon compounds, which are more abundantly available.
Acknowledgment. This work has been supported by a grant from the National Science Foundation (CHE-87- 14647). Registry No. SiH,I, 13598-42-0.
COMMENTS Comment on "Raman Line Shapes of the v, Stretching Mode in Orientationally Disordered N,O Crystals" Sir: In a recent paper! Lemaistre et al. investigated the influence
of orientational disorder on the Raman spectrum of N,O crystals. The model applied is based on resonance dipolar interactions, and the disorder is restricted to 180' rotational flip of the dipoles. The theoretical derivation results in the conclusion that the Raman spectrum depends on the disorder while the I R spectrum is independent of the disorder. This conclusion has also been obtained in ref 2 where the I R and the Raman spectra of solid CO are studied. There the derivation starts with the fact that the flip of a dipole by an angle of K radians leads to a sign inversion of the matrix elements describing the interactions with all other dipole moments. It is shown that eigenvalues and resulting IR transition probabilities are independent of the configuration chosen for the molecular orientations. Therefore the k 0 selection rule of the ordered crystal applies also for the IR spectrum of the disordered system. The situation is different for the Raman spectrum which relies on the molecular polarizability tensors. These are of g symmetry; i.e., a rotation by an angle of H leaves the polarizability tensors invariant. The configurational average for a completely orientationally disordered system leads to scattering strengths and depolarization ratios which are independent of the mode; therefore the Raman spectrum reflects the density of states (DOS). These arguments have been presented in ref 2 and have led to results which are confirmed on a more rigorous basis in ref I . The authors of ref 1 go one step further, distinguishing between completely and partially disordered crystals. By simulation calculations! and also analytically3 they find that the resulting Raman spectrum can be described as a linear combination of the perfectly ordered and of the completely disordered spectrum, Le., a linear combination of the k N 0 spectrum and the DOS. The ~k =0 linear combination coefficients are c, = ( 1 - 2 ~ for) the spectrum and c2 = 4p( 1 - p ) for the DOS, respectively, where ( I ) Lemaistre, J.-P.; Ouillon, R.; Ranson, P. J . Phys. Chem. 1988. 92, 1070. ( 2 ) Zumofen, G. J . Chem. Phys. 1978, 68, 3747. (3) Lemaistre, J.-P. Presented at the Symposium on Dynamical Processes in Condensed Molecular Systems, Jerusalem, 1988.
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p donotes the percentage of the flipped molecule^.^ These coefficients can also easily be obtained from the arguments given above. With values of p between 0.0 and 0.5 the coefficients c I and c, vary between 0 and 1 and can be considered as order parameters. The observation that the inverse depolarization ratio depends on the frequency has led the authors of ref 1 to the conclusion that the N 2 0 crystal is not completely disordered; the parameters cI and c2 obtained from spectral fits suggest that the disorder deviates slightly from completene~s.'!~ In the theoretical analysis in ref 1 several contributions to the molecular interaction have been neglected. First of these is the diagonal part in the intermolecular interaction, Le., the part which results when the molecule is moved from the vacuum into the solid environment and which is reflected by the matrix shift of the transition frequency. The orientational disorder causes fluctuations in the site diagonal matrix elements which lead to a broadening of the transition frequencies. This has been discussed in detail for solid C O in an investigation of line broadening in the IR transitions of C O isotopes present a t natural abundance in C O
crystal^.^ The simultaneous treatment of the diagonal and the off-diagonal disorder is difficult. In a first approximation the diagonal and the off-diagonal disorder can be treated independently and the spectrum can then be computed by folding the spectrum resulting from the off-diagonal disorder with a Gaussian with a width taken from the diagonal-disorder calculation. It is expected, however, that to a good approximation the diagonal disorder cannot give rise to a frequency-dependent depolarization ratio. Also neglected in ref 1 are higher order terms in the resonance intermolecular interactions which may be i m p ~ r t a n t . ~If. ~these are based on molecular properties with u symmetry, they do not alter the conclusions given for the off-diagonal disorder based on transition dipole moments alone. However, if these properties are of g symmetry, the situation changes. To elucidate this, let us assume that the dominant part in the resonance interaction is quadrupole-quadrupolar. Since the molecular quadrupole tensor shhows g symmetry, the intermolecular interaction does not change upon a molecular orientational flip by an angle of H . From this (4) Legay, F.; Legay-Sommaire, N.; Zumofen, G. Chem. Phys. Lett. 1982, 68. 437. ( 5 ) Zumofen, G.; Dressler, K. J . Chem. Phys. 1976, 64, 5198.
0 1989 American Chemical Society
