J. Phys. Chem. 1982, 86, 2059-2062
2059
Electrostatic Model for the Heats of Formation and Dipole Moments of Chlorine- and Fluorine-Substituted Methanes G. S. Buckley and A. S. Rodgers' Department of Chemistry, Texas A d M University, Co//ege Station, Texas 77843 (Received: June 15, 198 1; In Final Form: January 18, 1982)
Heats of formation and dipole moments of chlorofluoromethanes are shown to be accounted for quantitatively with an electrostatic model. Initial point charges are placed at infinite distance, and the atoms are moved to molecular dimensions and allowed to polarize. If the heat of formation of the compound is considered to be composed of bond contributions, electrostatic work, and polarization work, a good fit of the experimental data is obtained. The model shows potential for extension to the halogenated ethanes.
Introduction Two major additivity schemes have developed over the years to account for the molecular properties of chemical compounds. The first, bond additivity,lP2 evaluates a property of a molecule as the sum of contributions from its chemical bonds. The second, group a d d i t i ~ i t ycon,~~~ siders a molecule to be composed of chemical groups, i.e., polyvalent atoms with their bonded neighbors, each of which contributes a transferable quantity to the property being calculated. Corrections to both include easily identifiable allowances for steric and strain interactions in the molecule. Of the two methods, group additivity is the more reliable in determining heats of formation for molecules with low polarity. As the polarity of the molecule increases, neither method reproduces experimental values with the deeired accuracy. Deviations of the AHH;s have been attributed to polar interactions"' within the molecules and rationalized with electrostatic models.* Several corrective schemes have been applied to the simple bond additivity method to account for deviations of the calculated heats of formation from experimental values. Two categories of these schemes may be identified. One category includes the empirical methods"" which involve the introduction of parameters identified as contributions from interactions, either atomic or bond, taken two or three at a time. Zahng proposed such a method in which, in addition to normal bond contributions, adjacent bond interactions were taken two at a time. For each pair of bonds attached to a common atom, L, a term r X L Y is included in the heat of formation expression if X and Y are different. However, the bond terms in the Zahn method do not appear readily transferable from one type of compound to another, for example, from linear or simply (1) S. W. Benson and J. H. Buss, J. Chem. Phys., 29, 546 (1958). (2)J. D.Cox and G. Pilcher, "Thermochemistry of Organic and Organometallic Compounds", Academic Press, New York, 1970,Chapter 7. (3)S. W. Benson, 'Thermochemical Kinetics", 2nd ed, Wiley, New York, 1976,Chapter 2. (4)S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. ONeal, A. S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69,279
Chart I E2 E3-
\ E 5 -E
/ €4
1
'5
2 - E3 - € 4
branched hydrocarbons to the multiply branched compounds.12 The second category of corrective scheme for bond additivity is composed of corrections based on physical models of the molecular system. An example of this type of correction is Benson and Luria's electrostatic model for the heats of formation of saturated and unsaturated hydrocarbons and free radicals.13-15 In this model, each type of hydrogen and carbon is assigned a charge, transferable from compound to compound, and the electrostatic energy generated from the placement of these charges at molecular dimensions is added to the bond contributions to give the AHH,.Most hydrocarbons can be fitted to better than 1 kcal/mol with this model, but systems with atoms with lone-pair electrons will not give this good agreement. An electrostatic model is proposed here as an extension to bond additivity for the prediction of the heats of formation of the chlorofluoromethanes. It is found that the inclusion of a term for work of polarization with the bond and electrostatic energy terms gives good agreement with experimental heats of formation and dipole moment data. The model shows potential for extension to the fluorineand chlorine-substituted ethanes.
Description of Model Suppose the molecule in Chart I is assembled from infinitely separated initial charges, Yi,brought to molecular dimensions and polarized to final charges ci. The final charge, ci, is taken to be the initial charge, Yi, plus the charge induced by the field generated at the midpoint of the bond by each atom. The total field at the midpoint of the 5-j bond, for example, is given by
IlM9\.
\____,_
(5)R. H.Boyd, J. Chem. Phys., 38, 2529 (1963). (6)J. R. Lacher and H. A. Skinner, J. Chem. SOC.A, 1034 (1968). (7)J. D.Cox, H. A. Gundry, and A. J. Head, Trans. Faraday SOC.,60, 653 (1964). (8)G. S.Buckley, W. G. F. Ford, and A. S. Rodgers, Thermochim. Acta, 42,349 (1980). (9)C. T. Zahn,J. Chem. Phys., 2,671 (1934). (IO) T. L. Allen, J. Chem. Phys., 31, 1039 (1959). (11)G.R. Somayajulu and B. J. Zwolinski, J. Chem. Soc., Faraday Trans. 2, 70,973 (1974).
where diis the vector from the ith atom to the midpoint of the 5-j bond, and D is the dielectric constant, hereafter taken as unity. Since the largest effect in a chemical (12)A. S. Rodgers, J. Phys. Chem., 71,1996 (1967). (13)S.W. Benson and M. Luria, J.Am. Chem. Soc., 97,704 (1975). (14)S.W. Benson and M. Luria, J. Am. Chem. Soc., 97,3337(1975). (15)M.Luria and S. W. Benson, J.Am. Chem. Soc., 97,3342 (1975).
0022-3654/82/2086-2059$0 1.25/0 0 1982 American
Chemical Society
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The Journal of phvsical Chemistty, Vol. 86, No. 7 1, 1982
Buckley and Rodgers
TABLE I: Properties Used in Parameterization and Results compd
expt
bond add.
CF,Cl,
17.9 * O . l a 56.8 ?: 2.OC 108.2 * 0.2c 165.7 i l . O c 223.0 + 0.2‘ 19.59 ? 0.16c 22.8 + 0.2c 24.6 i 0.2c 22.9 + 0.14‘ 117.9 0.6d
13.2 63.9 114.5 165.2 215.9 15.8 18.4 21.1 23.7 119.8
CH, F CH, F, CHF, CH, C1 CH,Cl, CHC1, CF,Cl,
1.85e 1.97= 1.65e 1.8ge 1.57f 1.04e 0.51g
CH,a CH, F~ CH,F
CHF, b
CF,a CH, C P CH,C1 a CHC1,
cc1,a
*
Zahn
SE
model Ih
model 11’
18.0 57.0 108.6 165.7 223.4 19.4 22.3 24.1 24.2 116.8
17.9 56.5 108.8 165.5 223.4 20.0 23.2 24.7 23.6 117.2
18.2 56.6 108.5 166.1 223.1 18.6 22.5 24.9 22.7 117.3
1.87 1.94 1.52 1.76 1.71 1.20 0.56
1.87 1.95 1.52
1.81 2.00 1.68 1.68 1.68 1.26 0.54
- A H f , kcal/mol
16.0 59.3 108.4 163.4 224.3 20.4 23.0 23.9 23.0 117.8
Dipole Moments, D
1.80 1.66 1.18 0.56
a Geometry from Dan Stull, Ed.. JANAF Thermochemical Tables, US Department of Commerce, PB 168370 and SuppleGeometry from L. E. Sutton, Spec. PubL-Chem. Soc., No. 11 (1958); No. 1 8 (1965) Supplement. ments. A. S. Rodgers, J. Chao, R. C. Wilhoit, and B. J. Zwolinski, J. Phys. Chem. Ref. Data, 3 , 117 (1974). S. S. Chen, R. C. Wilhoit, and B. J. Zwolinski, J. Phys. Chem. Ref. Data, 5, 5 7 1 (1976). e A. L. McClellan, “Tables of Experimental Dipole ’Moments”, Voi. 2, Rahara Enterprises, El Cerrito, CA, 1974. f G. A. Barclay and R. J. W. LeVevre, J. Chem. SOC.,556 (1950). C. P. Smyth and K. B. McAlpine, J. Chem. Phys., 1, 190 (1933). Equation 5. Equation 6.
system would be expected to be along the chemical bond, the field is truncated to include only that part which is parallel to bond 5-i; thus where Fj is the bond vector for the 5-j bond. The dipole moment induced in the 5-j bond by this parallel component of the field is given as (3) where aj is the longitudinal polarizability of the 5-j bond. The induced dipole, pj, is related to the difference in charge between the final calculated charge, t j , and the initial charge, Yj,characteristic of each type of atom. (4) € j - Yj = /Lj/l?jl = ajl&,,,j/lFjl The polarizabilities OIHC, aFC, and a c 1 c and the initial charges on the atoms YH, YF, and Ycl are parameters to be determined in this work, thus allowing the final charges on the atoms cH, tF, and tC1 to be determined by eq 4. Two methods for the evaluation of the AHFof molecules are considered. Both methods treat the heat as being composed of a bond contribution from each chemical bond plus the electrostatic work of assembling the ej charges to molecular dimensions from infinity.
Here B(5-j)’s are the bond contributions, also treated as parameters, and Rij is the distance from atom i to atom j in the molecule. In the first method, no polarization work is considered, so the complete expression for the heat of formation is given by eq 5. In the second method, polarization work is included, so the expression for the heat of formation becomes eq 6.16 Here ri is the bond length
of the 5-j bond. Dipole moments are calculated in the (16)C. J. F. BBttcher, “Theory of Electric Polarization”, Elsevier, Amsterdam, 1962.
usual manner for a system of point charges.
Calculations Five different predictive schemes have been tested here using a least-squares procedure applied to the heats of formation and dipole moments for the weighted compounds in Table I. Each property was given a weighting of one. The predicted properties in Table I1 were calculated from the parameters determined in the minimization process but were not themselves included in the weighting. The minimization was achieved by using the Marquardt procedure1’ programmed to run on a Cromemco 2-2 microcomputer system. Geometries used are referenced in Table I. As the complexity of the calculations increases, it is found that the number of local minima also increase. Both the bond additivity and Zahn schemes exhibit strong single minima, due to the small number of parameters. For example, both the bond additivity and Zahn schemes require only one parameter to fit a CX, molecule, while the other procedures require three. These other models tend to display multiple local minima in the region of physical interest. In order to investigate the least-squares surface in the vicinity of a true solution, we constructed a test case with calculated heats and dipoles for a set of predetermined parameters. It was found that the minimization process did indeed find some local minima in the region of the true solution, but a systematic search resulted in finding the true solution. The parameterization for each of the last three methods was deemed the best possible fit after a thorough search in the regions of physical interest. Results and Discussion Tables I and I1 give the results for all five predictive schemes based on the optimization procedure used here. Table I11 gives the parameters determined in each case to give the best fit. Bond additivity with three parameters (17) (a) D. W. Marquardt, J . SOC.I d . Appl. Math., 11,431(1963);(b) J. C.Nash, “CompactNumerical Methods for Computers: Linear Algebra and Function Minimization”, Adam Hilger Ltd., Bristol, 1979, Chapter
17.
The Journal of Physical Chemistty, Vol. 86, No. 11, 7982 2081
Chlorine- and Fluorine-Substituted Methanes
TABLE 11: Predicted Properties compd
expt
bond add.
CH, ClF" CHF, Cl" CHFCl, " CF, C1" CFClg C,F,
c,c1,
63.2 f 2' 115.6 k 1.4' 68.1 * 2.1' 169.2 i 0.9' 68.1 f 0.4 320.9 * 1.5d 33.2 i. l.Oe
66.5 117.2 69.1 167.8 71.7 324.2 36.0
CH, C1F CHF, C1 CHFCl, CF, C1 CFC1,
1.82f 1.43g 1.41f O.5lg 0.46g
Zahn
SE
model Ih
model 11'
63.4 114.1 67.3 168.0 69.3
63.9 114.0 67.2 167.6 68.5 278.0 11.9
64.0 115.5 68.7 167.7 68.3 321.0 33.0
1.83 1.50 1.39 0.64 0.45
1.83 1.52 1.39 0.69 0.46
1.84 1.62 1.47 0.60 0.45
-AHf, kcal/mol 64.3 114.0 67.5 169.6 68.9
Dipole Moments, D
a Geometry from Dan Stull, Ed., JANAF Thermochemical Tables, US Department of Commerce, PB 168370 and Supplements. b Geometry from L. E. Sutton, S p e c . P u b k - C h e m . SOC.,No. 11 ( 1 9 5 8 ) ; No. 18 (1965) Supplements. ' s. s. Chen, R. C. Wilhoit, and B. J. Zwolinski, J. Phys. C h e m . R e f . Data, 5 , 571 (1976). S. S. Chen, A. S. Rodgers, J. Chao, R. C. Wilhoit, and B. J. Zwolinski, J. P h y s . C h e m . R e f . Data, 4, 4 4 1 (1975). e J. Chao, A. S. Rodgers, R. C. Wilhoit, and B. J. Zwolinski,J. Phys. C h e m . R e f . Data, 3 , 1 4 1 (1974). R. Boca, P. Pelikgn, and L. Valko, J. Mol. S t r u c t . , 50, 1 6 1 (1978). g A. L. McClellan, "Tables of Experimental Dipole Moments", Vol. 2, Rahara Enterprises, El Cerrito, CA, 1974. Equation 5. l Equation 6.
TABLE 111: Parameters for t h e Models model bond Zahna
SEb model IC model 11'
B(C-H), kcal/mol -3.30 -3.99 -4.07 -4.19 -1.47
B(C-F), kcal/mol -53.97 -56.07 -15.18 -16.14 -49.29
B(C-Cl), kcal/mol -5.93 -5.75 7.87 6.79 -12.55
B(4)
B(5)
B(6)
B(7)
B ( 81
B(9)
2.92 0 0 0.0040
-0.88 0.12 0 079 0.031
1.46 0.20 0.46 0.20
-0.10 -0.084 0.32
-1.65 -1.79 -1.12
-1.32 -1.84 -0.84
" B ( 4 ) = r H c F ; B ( 5 ) = r ~ c c l ; B ( 6 ) r=F C C I . All in kcal/mol. B ( 4 ) = PHc;B(5) = PFC ; B ( 6 )= Pee; B ( 7 ) = Y ~ c i B ( 8=) y F c ; B ( g ) = y c c . Allunltless. ' B ( 4 ) = c l H c ; B ( 5 ) = c u ~ ~ ; B ( 6 ) = a c 1All c . in 10-24Cms. B ( 7 ) = Y H ; B ( ~ ) Y = F;B(g)= Ycl. All in lo-'' esu. gives poor agreement with experimental values with a maximum deviation of 7.1 kcal/mol in the weighted heats and an average deviation of 4 kcal/mol. The additional three parameters of the Zahn method improve the fit markedly but still show large deviations. The last three procedures, each with nine parameters, give much better agreement and similar fits. Smith, Ree, Magee, and Eyring (SE),ls in the interest of examining inductive effects in chemical systems, have developed a semiclassical model for calculating charge distributions in molecules. In this method, a field due only to the bonding atoms is generated at the ucovalentnbond center of a particular bond. Allingerlg has modified the SE procedure to include the fields generated by atoms at least one bond removed from the bonding atoms. SE optimized their parameters to fit experimental dipole moments. Here we have optimized the parameters of the SE procedure to fit both the heats of formation and dipole moments. The concepts of the SE procedure and of our model without polarization are similar, the main difference lying in the significance and values of the parameters. There is no evident extension of the SE procedure to a model which includes polarization work, since no initial charge is apparent in the SE method. The results obtained by using the method of SE are very similar to those that we obtained using eq 5, hereafter referred to as model I. Consequently, we shall compare the results of model I with those that we obtained using eq 6, hereafter referred to as model 11, to show the advantages of including the term for polarization work. (18)R. P.Smith, T. Ree, J. L. Magee, and H. Eyring, J. Am. Chem. Soe., 73,2263 (1951).
(19)N. L. Allinger and M. T. Wuesthoff, Tetrahedron, 33,3 (1977).
The results of model I give a slightly better fit to the experimental data than those of model 11. The deviations in the heats of formation are of similar magnitude in both models, but two of the weighted dipole moments show greater deviations in model 11. This difference in the results is not a sufficient basis for selection. However, model I1 has several advantages over model I. There is some debate over the magnitude and direction of the bond moment of the C-H bond. Several authorssa have suggested a bond moment of about 0.3 D directed C--H+. If one examines the final charges for hydrogen in the two models under consideration (because of the low polarization of the C-H bond in both models, the final hydrogen charges vary little from compound to compound and are close to the initial charge), it is found that model I1 gives a dipole moment of about 0.35 D directed C--H+, while model I gives a C+-H- moment of 0.09 D. Model I1 thus gives a C-H moment in accord with that suggested by others. Benson and Luria13 have achieved reasonable success with an electrostatic model for determining the heats of formation of saturated hydrocarbons in which the charge placed on hydrogen was a constant value of 0.278 X 10-lo esu. Both models here, because of the low aCH,predict an essentially constant H charge through the series of chlorofluoromethanes. Only model 11, though, yields a value of the charge on H (in the range of 0.303 X 10-10-0.346X (20)W. L. G. Gent, Q.Rev., Chem. SOC.,2, 383 (1948). (21)R. Rollefson and R. Havens, Phys. Reu., 57, 710 (1940). (22)A. M. Thorndike, J. Chem. Phys., 15, 868 (1947). (23)C.P.Smyth, J. Phys. Chem., 41, 209 (1937). (24)C.P.Smyth, 'Dielectric Behavior and Structure", McGraw-Hill, New York, 1955,pp 240-3.
2062
J. Phys. Chem. 1982,86,2062-2065
lO-'O esu for this series of compounds) which is in reasonable agreement with the charge found by Benson and required to give agreement with experimental heats of formation of alkanes. The importance of any model proposed lies in its extension to halogenated molecules containing more than one carbon. In order to investigate the potential of the model here for extension to the ethanes, we have calculated the AHF values of CzF6 and CZCl6. In the general case, extension of the model to the ethanes would require the introduction of two new parameters, B(C-C) and acc. However, with a symmetrical ethane, there is no net field at the midpoint of the C-C bond so acc is not required and B(C-C) may be calculated from ethane and transferred to
C2F6and C2C16. Table I1 shows that there is very poor agreement between the experimental and predicted heat in model I, while model I1 gives excellent agreement in the case of C2F6 and C2C16. The electrostatic model with polarization work included (model 11) presented here fits the experimental heats of formation and dipole moments of the chlorine- and fluorine-substituted methanes well and shows potential for application to the substituted ethanes. Ideally, extension of the model to any chlorine- or fluorine-substituted saturated hydrocarbon should introduce but two new parameters, B(C-C) and acc. The extension of the model to unsymmetrically substituted ethanes is currently being pursued.
Gas-Phase Reaction of Daughter Ions from the Decay of Multitrltiated Propane with Benzene and Toluene. Solution of a Longstanding Anomaly Fulvlo Cacace, Romano Clpolllnl, and Plerlulgl Glacomello University of Rome, 00 100 Rome, Itaiy, and University of Camerino, 62032 Camerino, Macerate, Itaiy (Received: Juiy 30, 198 1; In Final Form: December 29, 198 1)
The population of the daughter ions from the decay of multitritiated propane has been sampled by using as a probe their gas-phase reactions with benzene and toluene at pressures up to 400 torr. Tritiated n- and isopropylated arenes account together for 70-75% of the total activity of the decay ions. This observation-and the failure to detect aromatic allylation-removes an early radiochemical anomaly, by showing that decay of tritiated propane yields propyl ions as the most abundant daughter species, following a trend established for all other tritiated hydrocarbons. The abnormally high abundance of allyl ions measured by mass spectrometry is traced to the decomposition C3H7+ C3H6+ + H2allowed by its low activation energy, the lack of collisional stabilization,and the long residence time which characterizes operation of a "charge" mass spectrometer. The excitation energy required for the decomposition is likely to arise from the deformation energy of the propyl cations, born from the sudden nuclear transition in a shape reminiscent of the parent hydrocarbon molecule.
-
Introduction The chemical consequences of the 0 decay of tritium have been the subject of extensive theoretical, massspectrometric, and radiochemical investigation.'Y2 In particular, the decay of suitably tritiated molecules has been largely exploited as a technique for the mechanistic and kinetic studies of ion-molecule reactions in gaseous and condensed The mass-spectrometric data show that the process B GHmT
p
-
+ [C,Hm3He]+
3He + C,H,+
(1)
is the overwhelmingly predominant fragmentation pathway of tritiated hydrocarbons, giving an abundance of daughter C,H,+ ions that exceeds 70% in all cases. Furthermore, in the few comparable cases so far investigated, the position of the radioactive atom within the parent molecule appears, if at all, to affect the decay-induced fragmentation pattern to a minor extent, as shown by the abundance of (1) Wexler, S. 'Action Chimiques et Biochimiques des Radiations"; Haissinsky, Ed.; Maason: Paris, 1965; Vol. VIII. (2) Cacace, F. 'Hot Atom Chemistry Status Report";IAEA Vienna, 1975. (3) Cacace, F.Adu. Phys. Org. Chem. 1970, 8, 79. (4) Cacace, F.'Interactions between Ions and Molecules";Aualm, P., Ed.; Plenum Press: New York, 1975. (5) Cacace, F.'Kinetics of Ion-Molecule Reactions";Ausloos, P., Ed.; Plenum Press: New York, 1979. (6) Cacace, F. Adu. Chem. Ser., in the press. (7) Akulov, G.P. Usp. Khim. 1976,45, 1970.
the C7H7+daughter ions which is the same, i.e., 78 f 1.5%, from the four isomeric monotritiated toluenes.8 A conspicuous exception does exist however, namely, the decay of tritiated propanes, which give remarkably low and different abundances of C3H7+daughter ions: 56% from [l-3H]propaneand 41% from [2-3H]propane. The anomaly, tentatively traced to the abnormally low energetic requirements for the unimolecular fragmentation of excited C3H7+ions into allyl ions,8has not been removed by more recent theoretical"" and mas~-spectrometric~'-'~ studies. This represents a disturbing discrepancy in the current interpretation of the chemical phenomena triggered by the 0 decay. We report an experimental attempt to clarify the situation by sampling the population of the labeled daughter ions from multitritiated propane. As a probe we use a suitable nucleophile (benzene or toluene), whose encounter takes place within a short time subsequent to the formation of the decay ion, in a reaction environment characterized by highly efficient collisionalMabilization processes. (8) Wexler, S.; Anderson, G. R.; Singer, L. A. J . Chem. Phys. 1960,32, 417. (9) Ikuta, S.; Iwata, S.; Imamura, M. J . Chem. Phys. 1977, 66, 4671. (10) Ikuta, S.;Yoshihara, K.; Shiokawa, T. Radiochem. Radioanal. Lett. 1977, 28, 435. (11) Ikuta, S.;Hashimoto, S. Chem. Phys. 1979, 42, 262. (12) Nishizawa, K.; Narisada, K.; Teramatau, H.; Iwami, H.; Shinagawa, M. Mass Spectrosc. (Tokyo) 1973, 21, 199. (13) Omori, T.; Kikuki. T.: Shio Kawa, T. Radiochem. Radioanal. Lett. 1979, 37, 233.
0022-3654/82/2086-2062$01.25/0@ 1982 American Chemical Society
