126
J. Phys. Chem. 1983, 87,126-130
An Electrostatic Approach to Heats of Formation and Dipole Moments: Chlorine- and Fluorine-Substituted Alkanes G. S. Buckley and A. S. Rodgers’ Department of Chemistry, Texas A & M University, College Station, Texas 77843 (Received: June 25, 1982)
An electrostatic model introduced earlier for predicting the heats of formation and dipole moments of fluorinated
and chlorinated methanes is extended with success to longer straight-chain saturated compounds. The results are compared with the group and trigonal additivity approaches and shown to be an improvement in many cases. Discussion of the incremental methylene contribution to the heat of formation is presented for fluorinated and chlorinated species.
Introduction Recently, a method for predicting the heats of formation and dipole moments of fluorinated and chlorinated methanes was presented.’ In this semiempirical model, atoms are considered as intrinsic point charges at infinite distance. As the charges are moved to molecular dimensions, the electric fields generated induce new charges onto each atom. The heat of formation of the compound is then calculated as the sum of bond contributions, electrostatic work, and polarization work. In the earlier work, initial charges, polarizability parameters, and bond contributions were determined for fluorinated and chlorinated methanes. In this study, the model is extended to straight-chain saturated molecules with the introduction of a bond contribution and polarizability parameter for the carboncarbon bond. The extension of this model is desirable as all of the schemes for the prediction of heats of formation fail when the polarity of the groups in the molecule is significantly different2 For example, both bond and group additivity predict a zero enthalpy change for reaction 1,far from the CF3CF3 + CH3CH3 2 2CF3CH3 (1) observed-15.1 f 1.2 kcal mol-’. The nonzero enthalpy change has been attributed to electrostatic effects,34 and thus an electrostatic model is proposed here. Benson and Luria’ have indicated that their electrostatic model, though very successful with hydrocarbon molecules and free radicals, is not as satisfactory when molecules containing atoms with lone pair electrons are considered. The model developed here takes an electrostatic approach to account for the effect of fluorine and chlorine atom substitution on the heats of formation of alkanes. Although accurate experimental information is scarce for this class of compounds, sufficient data are available to determine the parameters needed for the proposed electrostatic model. Calculations based on this model are then compared with the remaining experimental data as well as with predictions of group additivity and Somayajulu-Zwolinski’s trigonal a d d i t i ~ i t y .In ~ addition, several (1) Buckley, G. S.; Rodgers, A. S. J . Phys. Chem. 1982, 86, 2059. (2) Benson, S. W. J . Phys. Chem. 1981,85, 3375. (3) Boyd, R. H. J . Chem. Phys. 1963, 38, 2529. (4) Lacher, J. R.; Skinner, H. A. J . Chem. SOC.A 1968, 1034. (5) Cox, J. D.; Gundry, H. A.; Head, A. J. Trans. Faraday Soc. 1964, 60, 653. (6) Buckley, G. S.; Ford, W. G. F.; Rodgers, A. S . Thermochim. Acta 1980, 42, 349. (7) (a) Benson, S. W.; Luria, M. J . Am. Chem. SOC.1975, 97, 704. (b) Ibid. 1975, 97, 3337. (c) Luria, M.; Benson, S . W. Ibid. 1975, 97, 3342. (8)(a) Benson, S. W. “Thermochemical Kinetics”; Wiley: New York, 1976; 2nd ed. (b) Benson, S. W.; Cruickshank, F. R.; Golden, D. M.; Haugen, G. R.; O’Neil, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R. Chem. Rev. 1969, 67, 279.
disproportionation reactions similar to (1)are considered in an effort to distinguish between the models and finally, the methylene contribution to the heat of formation is compared in the three models with some interesting conclusions.
Model Description Consider the staight chain saturated molecule depicted in I. In the model to be developed here, each univalent
I
atom, Xi, is assigned an initial intrinsic charge, Yi, dependent only on the chemical element and transferrable from compound to compound. Each carbon of the chain is assigned the initial charge necesssary to neutralize the Y;s of the attached univalent atoms. As an example, Ycl = -Y1 - Y2- Y3 in I. As the initial charges are brought together from infinite distance, polarization occurs due to the electric fields generated by all of the charges in the molecule. The field to be considered here is that generated at the midpoint of each bond. For example, the field located at the center of the C1-X1 bond is given by
in which Ri is the vector from atom i to the midpoint of the C1-Xl bond and D is the dielectric constant, hereafter taken as unity. The symbol ci denotes the final charge residing on atom i, that is, the intrinsic charge on i plus any induced charge. Charge may be transferred to the initial point charges only through the chemical bond, so the field is truncated to include only the component parallel to the bond:
-
Ec,-xl * %l-xl
.+
IEI,C1-X1l
=
I~C1-X1l
where Fcl-xl is the bond vector for the C1-Xl bond. The dipole moment induced in the C1-X1 bond, wcl-xl, is given as k - X 1 = ~C1-XIIEIIC1-X1l (4)
-
(9) (a) Somayajulu, G. R.; Zwolinski, B. J. Trans. Faraday SOC.1966, 62, 2327. (b) J . Chem. SOC.,Faraday Trans. 2 1972, 68, 1971. ( c ) Ibid. 1974, 70, 967. (d) Ibid. 1974, 70, 973.
0022-3654/83/2087-0 126$01.50/0 0 1983 American Chemical Society
The Journal of Physical Chemistry, Vol. 87, No. 1, 1983
Electrostatic Approach to -AH, and k
TABLE 11: Predicted Properties
TABLE I: Properties Used in t h e Determination of Parameters and Results
compd CH4 CH.F CH~F, CHF, CF4 CH,C1 CH,Cl, CHC1, CCI, CF,Cl, CH,CH, C3H8
geemetry ref
a Q Q Q
a a a Q
a a a b C
CA, C6HM C,HM CH,CH,F CH,CHF, CH,CF, CF,HCF, CF,CF,
d d d e f g
h g
- A f f f / ( kcal mol-’ )
expt
PiD
calcd exptm calcd
17.9 * O : l a 56.8 i 2‘ 108.2 t 0,2’ 165.7 2 1‘ 223.0 t 0.2’ 19.59 t 0.16’ 22.8 t 0.2’ 24.6 t 0.2’ 22.9 i 0.14: 117.90 t 0.6t 20.2 * O . l U 24.83 t O . l a 30.06 t O . l a 35.1 i O . l a 39.92 i O . l a 44.85 t O , l a 62.9 ?: 0.4h 119.7 ?: 1.5k 178.2 t 0.4k 263 t 1’ 320.9 i 1 . 5 k
17.2 56.2 107.8 165.4 223.2 18.8 22.9 25.1 22.9 117.1 20.8 25.3 30.2 35.0 39.9 44.5 64.5 118.8 177.8 265.3 319.7
1.85 1.97 1.65
1.87 2.08 1.75
1.89 1.57 1.04
1.71 1.71 1.30
0.51
0.56
1.95 2.3 2.32 1.54
1.86 2.19 2.08 1.77
a Stull, D.R.; Prophet, H. Natl. Stand. R e f . Data Ser., Lide, D. R . J. Chem. Natl. Bur. Stand. 1971, No. 37. Chen, S. S.; Wilhoit, R . C.; Phys. 1960, 33, 1514. Zwolinski, B. J. J. Phys. Chem. R e f . Data 1975, 4 , 859. Bonham, R. A.; Bartell, L. S.; Kohl, D. A. J. A m . Chem. SOC.1959, 81, 4765. e Nygaard, L. Spectrochim. A c t a 1966, 22, 1261. f Beagley, B.; Jones, M. Q.; Hooldsworth, N. J. Mol. Struct. 1980, 62, 105. g Beagley, B.; Jones, M. 0.;Zanjanchi, M. A. I b i d . 1979, 56, 215. Al-Ajdah, G. N. D.; Beagley, B.; Jones, M . 0. Ibid. 1980, 65, 271. I Rodgers, A. S.; Chao, J . ; Wilhoit, R . C.; Zwolinski, B. J. J. Phys. C h e m . R e f . Data 1974, 3 , 1 1 7 . I Chen, S. S.; Wilhoit, R. C . ; Zwolinski, B. J. Ibid. 1976, 5, 571. Chen, S. S.; Rodgers, A. S.; Chao, J.; Wilhoit, R. C.; Zwolinski, B. J. Ibid. 1975, 4 , 441. Buckley, G . S.; Ford, W. G. F.; Rodgers, A . S. Thermochim. A c t a 1981, 49, 199. McClellan, A. L. “Tables of Experimental Dipole Moments”; Rahara Enterprises: El Cerrito, CA, 1974; Vol. 2.
where ac,-xl represents the polarizability along the C1-Xl bond. Here a distinction must be made between bonds to a univalent atom and those between two carbon atoms. In the case of a bond to a univalent atom, the induced dipole is related to the difference between the initial charge and final charge on atom i (the univalent atom) which is given by kC1-X1 ~C1-X1l~IIC1-X11 €xl- Yx, = -(5) lFC1-X1l I~cl-x,l
-.
For a carbon-carbon bond, however, the change in charge on one particular carbon atom is due to polarization across not one, but four bonds. Thus the charge transferred across the C-C bond needs to be isolated from that transferred across the other three bonds. Perhaps the most straightforward way of calculating the charge transferred across a particular C-C bond is to recognize that initially (if one splits the molecule across a C-C bond), each “half” of the molecule will have zero charge. Thus, after polarization, any charge developed in “half” of the molecule, say Aqx, must then have been transferred across that C-C bond. As a result, for C-C bonds ac-clEnc-cl (6) Aqx = 1%-cl note that the Aqx is the sum of final charges on that half
-
127
compd CH,FCl CHF,Cl CF,C1 CHFC1, CF C1, CCl,CCl, CC1,CCl ,H CCl,CH, CCl,HCH, CCIH,CH, CF,ClCF,Cl CHCl,CH,Cl CH,ClCH,Cl gauche CH,FCH,F C F ,ClCH , CFCl,CF,Cl CF,CH,Cl CFCl,CFCl, CF ,CH ,F
geometry ref
a a Q Q
Q
b b b b b c
c c
-AHf/(kcal mol-’) dD expt calcd exptj calcd 63.2 t 2f 115.6 t 1.4f 169.2 t 0.9f 6 8 . 1 t 2,1f 68.1 t 0.4f 33.2+ lb 34.8 t l b 3 4 t 0.33b 31.1 * 0 . 2 b 26.83 t O.l€ib 215.2 t 0.9g 35.5 0.6g 30.7 t 0.4g
63.8 114.9 167.6 68.4 68.1 33.9 36.1 35.9 32.1 25.9 215.7 33.7 30.2 106.6
*
d c
1.82 1.43 0.51 1.41 0.46
1.90 1.68 0.63 1.53 0.47
0.92 1.77 2.07 2.02
1.32 1.49 1.73 1.66 2.23 2.84
128.8 2.21 1.92 169.0 0.49 C 177.3 2.06 c 122.3 e 214 2’ 216.4 Rodgers, A. S.; Wilhoit, R. C.; a Table I, ref a. Zwolinski, B. J. J. Phys. Chem. Ref. Data 1974, 3, 141. Sutton, L. E. “Tables of Interatomic Distances and Configuration in Molecules and Ions”; Chem. SOC.Spec. Fernhold, L.; Kveseth, K. A c t a Publ. 1958, No. 18. Chemica Scandinavica 1980, A34, 163. e Table I, ref h. f Table I , ref j . g Cox, J. D.; Pilcher, G. “Thermochemistry of Organic and Organometallic Compounds”; Academic Press: New York, 1970. Papina, T. S.; Kolesov, V. P. Vestn. Mosk., Univ., Ser. 2: K h i m . 1978, 19, 500. I Table I, ref k . I Table I , ref m . c
126.6 i 1.2h 174 t 48
+_
of the molecule toward which the C-C bond vector points. Equations 5 and 6 and the charge neutrality condition form a linear system of equations in the ti. Thus for a molecule of known or estimated geometry, the ti's are calculated from the values of the intrinsic charges, Yi,and polarizability parameters, ai. The heat of formation of a molecule is then formulated as the sum of four terms:
AHf=
c B ( C - X ) + CIRiE;I + c
bonds
j
