H. J. BERNSTEIN
1550
Bond and Interaction Contributions for Calculating the Heat of Formation, Diamagnetic Susceptibility, Molar Refraction and Volume, and Thermodynamic Properties of Some Substituted Methanes
by H. J. Bernstein N R C No. 8445, Division of Pure Chemistry, National Research Council, Ottawa, Canada (Received October 21, 1964)
The interaction scheme which recognizes bond contributions and interactions between atoms or bonds taken two and three at a time has been shown to be nuinerically equivalent to schemes in which bonds change with substitution. The interaction scheme has been applied to the correlation of such molecular properties as heat of formation, diamagnetic susceptibility, molar refraction and volume, heat capacity, zero-point energy, entropy, and free energy. Substituted methyl group contributions have also been evaluated which permit calculation of the properties of substituted ethanes (considered to have free internal rotation). The agreement between observed and calculated results and the application of the scheme is limited by the amount and accuracy of the experimental data. Notwithstanding, many useful estimates have been made of properties not yet measured. In general, correlations of properties and structure cannot give information about bond properties since all such correlations can be formulated in terms of molecular properties.
time account for the effect of branching on the value An interaction scheme' for correlating molecular of the heat of formation. It has been suggested' that properties has been constructed in terms of constant interactions taken three a t a time might also be sigbond contributions and interactions between nonnificant in evaluating the energy of atomization. In bonded atoms or bonds. I t was first applied to corall of these treatments the CH and CC bonds are conrelating the diamagnetic susceptibility of substituted methanes,2then heat capacities3 and zero-point energies4 sidered unaltered by substitution. It is known, how(one-half the sum of the vibrational frequencies), and ever, that in halogenated methanes the bond distances then the heat of formation of the c h l o r o m e t h a n e ~ ~ ~change as one proceeds from CH, to CXI so that it is to and fluoromethane~.~Physical and thermodynamic data have accumulated to the point where it seems (1) H. J. Bernstein. J . Chem. Phys., 20, 263, 1328 (1952). profitable to reformulate the interaction scheme in (2) J. W. R. Lacher, J . A m . Chem. Sac., 69, 2067 (1947). terms of simpler bookeeping and investigate whether (3) H. J. Bernstein, J . Chem. Phys., 24, 910 (1956). (4) (a) H. J. Bernstein, ibid., 24, 911 (1956); (b) H. J. Bernstein or not even higher order schemes are required. Indeed, and A. D. Pullin, ibid., 21, 2188 (1953); (c) J. C. Evans and H. J. the interaction scheme previously used which recognizes Bernstein, Can. J . Chem., 33, 1171 (1955); (d) H. J. Bernstein, ihid., 34, 617 (1956). contributions from nonbonded atoms or adjacent bonds ( 5 ) S. M. Skuratov and V. P. Koleslav, Z h . F i z . Khim.. 35, 1156 taken two at a time' has been extended to include in(1961). teractions three and four a t a There is some (6) See Yu. G. Papulov, Dokl. Akad. Nauk SSSR. 143, 1395 (1962). theoretical justification for this empirical approach (7) R. D. Brown, J . Chem. Sac., 533 (1953). since molecular orbital theory applied to saturated (8) M. J. S. Dewar and R. Pettit, ibid.. 1625 (1954). hydrocarbon^^-'^ shows that interactions between (9) C. Sandorfy, Can. J . Chem., 33, 1337 (1955). nonbonded atoms or adjacent bonds taken two a t a (10) J. A. Pople and D. P. Santry, Mol. Phys., 7 , 269 (1964). The Jourlzal of Phyeical Chemistry
BONDA N D INTERACTIOK CONTRIBUTIONS FOR CALCULATING METHANEPROPERTIES
be expected that the bond properties are affected by substitution. We shall show here that schemes involving changths in bond properties are numerically equivalent to schemes employing constant bonds plus interacbtioris. I n other words, additivity schemes, i n principle, correlate only niolecular properties and rannot give rigorous information about individual bond properties. In particular cases one niight expect the change of bond property to be the predoniinant factor. itnd interactions might be neglected. However, in principle, the paranieters of an additivity scheme are linear conibiriations of bond properties, their changes with substitution, and interactions between the bonds or nonbonded atonis. I t is not fruitful to employ the most complete interaction scheme including two, three, and four interactions a t a tinie since all five molecules of the series CX,P4-,, for example, are required to establish the parameters. FVe shall consider, therefore, the scheme eniploying only two and three interactions at a time only. The bond-type scheme in which bonds are changing with substitution will then be compared with this scheme.
The Interaction Scheme for Methanes of General Formula CXnYmZpQc-n-m-p The contributions required are best seen from the following exaniple. I n the molecule CXsY there are three C X bond contributions, one CY bond contribution, three vontributions froni interaction of a C X bond with another CX bond and/or an X atom with an X atom which m-e shall call 3 X X ; also, there are three contributions froni interaction of C X with CY and/or a nonbonded X atom with a nonbonded Y atom, which we call 3XY, as well as interactions taken three at a time which are XXX and 3YXX. I t is apparent that the number of interactions of X atoms taken two a t B time is n!/2!, and three a t a time is n ! / 3 ! The number of YXX interactions is siniply the number of Y times the number of XX interactions, i e . , mn!/2!, and so on. Thus, the property of a niolecule of this general series is given by CXnYmZpQ4-n--m-p
nmXY
=
nCX
+ WLCY+
+ mpXZ + n(4 - n - m - p)XQ +
(4 - n
-
1551
m - p)(3 - n _-_ ~m_ _- p) 2
n(n - l ) ( n - 2) 6 n(n - l ) P X X Z 2
+
n(n xxx+---_ 2
-
QQ
1)m --XXY+
+
n(n - 1)(4 - n m - p) -~ XXQ 2
nm(m - I) - ~ _ _ _ _ _ XYY 2
+ nmpXk-Z + +
np(4 - n - m p)XZQ 4 4 - n - m - p)(3 2
-
m(m - l ) ( m - 2) YYY 6
n - wz - p) ~
XQQ
+
- 1)P YYZ + m(m - _ _ _ ~ 2
m(m - 1)(4 - n - m - p ) YYQ 2 nzp(p - '1 YZZ 2
+
+ mp(4 - n
-
+
+ +
nz - p)YZQ
m(4 - n - m - p)(3 - n - m - p ) -YQQ 2
P(P - 1)(4 - n - m - p) ZZQ 2
+
+
p(4 - n - m - p)(3 - n - m - p) 2 ZQQ
+
(4-n-m-p)(3-n-m-p)(2-n-m-p) 6
QQQ
(1)
+ + + cn2 + + + + + inm2 + j p + kp2 + lnp + qmp + m 2 p + sm2p + tnp2 + ump2 + vmnp + tup3
(2)
Collecting terms CXnYmZpQl-n--m--p= CQ4 an bvn dm2 + emn f n 3 gm3 hn2m
where U =
xx + 4XQ - 72- Q Q + xxx 3 -
C x - CQ - __ 2
~
Volume 69, .\'umber
5
May 1965
H. ,J. BERKSTEIN
13.2
j =CZ-
