J . Phys. Chem. 1988, 92, 5255-5257 mobile molecules with multiple HBA sites (e.g., arylalkyl compounds, biphenyls) separate solvent clusters would hydrogen bond to each site and undergo separate nonspecific dielectric interactions a t each site; hence we use Eo,,, and ET* for the compounds of Table V and the biphenyl derivatives. For compounds that are not conformationally mobile, such as the polycyclic aromatic hydrocarbons, the same solvent cluster may hydrogen bond at multiple sites; hence we use increments to K* and 0, rather than summations. The use of 6 = 2.0 for the biphenyl derivatives was for similar reasons and for c o n ~ i s t e n c y . ~ ~ The most important class of compounds for which we have not
5255
yet constructed parameter estimation rules are those wherein there is resonance delocalization of electron density, Le., those with an electron-donor substituent para to a mesomeric electron-acceptor substituent. Since the submission of this paper we have determined solvatochromic parameters for a number of such compounds from back-calculations of HPLC data. Their experimental log KO, values compare with values calculated through eq 5 as in Table XIII. We have also not constructed parameter estimation rules for compounds where there is intramolecular hydrogen bonding. Registry No. Octanol, 111-87-5
New Electronegativity Scale for the Correlation of Heats of Formation. 1. Alkyl Derivatives Yu-Ran Luo and Sidney W. Benson* Donald P. and Katherine B. Loker Hydrocarbon Research Institute, University of Southern California. University Park, Los Angeles, California 90089- 1661 (Received: February 12, 1988)
We report a quantitative linear relation between the differences in standard heats of formation [AfHo(RX)- AfHo(CH3X)] AAfHo(RX/CH3X) and V,, the unshielded core potential of X: AAfHo(RX/CH3X) = I,,, + S,V, (eq 4). Here R is CH3-,,,(CH3),,,, which are taken to be ethyl, isopropyl, and tert-butyl when m = 1, 2, and 3, respectively. X is a halogen atom, OH, SH, NH,, H, or CH3, and V, = nx/rx,where n, is the number of valence electrons in the bonding atom in X and rx (angstroms) is its covalent radius. V, was first proposed by Yuan as a measure of electronegativity of the elements. The slope S,and intercept ICin this relation can be related to m; I,,, (kcal/mol) = 0.9 - 1.5m(m - 1) (eq 6); S, (kcal A/mol) = -rn/(0.67 i 0.21m) (eq 7). For the 23 compounds available average deviations are 0.3 kcal/rnol with one maximum deviation of 1.9 kcal/mol. In all cases the experimental uncertainties exceed the deviations. The relation can be used to estimate values of AfHofor other elements and groups where data on AfHo(MeX) are known. With AfHO(MeF) = 55.9 f 0.5 kcal/mol, values are estimated for AfHoof EtF, i-PrF, and t-BuF.
Introduction which has been so surprisingly The law of group successful in estimating the heats of formation, AfHo, of homologous families of compounds, provides direct evidence that chemical forces are short range. However, it has been clear for some time that there are important exceptions to group additivity in compounds such as the fluorocarbons and chlorocarbons with many, very polar bonds. Benson and Shaw4 showed that on comparing AfHo(RX) for alkyl derivatives RX, there were systematic changes in the differences of [AfHo(RX)- AfHo(R'X)] = AAfHo(RX/R'X), where R CH3 and R' Et, i-Pr, or t-Bu, with the polarity of the C-X bond. AAfHO(MeX/t-BuX) changed monotonically from a maximum of 27 kcal for CH30H/t-BuOH to a minimum of 14 kcal for CH4/i-C4HI0. Efforts to find a quantitative correlation of AAfHo with dipole moments or other measures of the polarity of the C-X bond were unsucce~sful.~ A recent study of the thermochemistry of metal organic compounds6 has shown that AAfHo(MH,/MMe,,,) and AAfHO(MMe,,,/MEt,,,) show semiquantitative correlation (f2 kcal) with the electronegativities of M by using Pauling's scale for'electronegativity.' In the present paper we shall make use of a different (1) Buss, J. H.; Benson, S. W. J . Chem. Phys. 1958, 29, 546. (2) Cruikshank, F. R.; Golden, D. M.; Haugen, G. R.; O'Neal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R.; Benson, S. W. Chem. Rev. 1969, 69, 279. (3) Eigenmann, H. K.; Golden, D. M.; Benson, S. W. J . Phys. Chem. 1973, 77, 1687. (4) Shaw, R.; Benson, S. W. Adu. Chem. Series, 1968, No. 75, 288. (5) Benson, S. W. Angew. Chem., Int. Ed. Engl. 1978, 17, 812. (6) Benson, S. W.; Tsotsis, T. T.; Francis, J. T., submitted for publication. (7) Pauling, L. J . Am. Chem. SOC.1947, 69, 542.
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TABLE I: AfHo(RX) of a Number of Alkyl Derivatives'
CHq F OH C1 2"
Br
SH I CH3 H
-55.96 -48.2 f 0.1 -19.6 f 0.1 -5.5 f 0.1 -8.5 f 0.3 -5.5 f 0.2 3.5 f 0.3 -20.0 f 0.1 -17.8 f 0.1
CpH, -56.3 -26.8 -11.3 -14.8 -11.1 -1.8 -25.0 -20.0
f 0.1 f 0.3 f 0.2 f 0.4 f 0.2 f 0.4 f 0.1 f 0.1
i-C,H, -70.1' -65.1 -34.6 -20.0 -23.8 -18.2 -9.6 -32.1 -25.0
f 0.1 f 0.3 f 0.2 f 0.6 f 0.2 f 0.9 f 0.2 f 0.1
t-CaHs -74.7 f 0.2 -43.6 f 0.5 -28.9 f 0.2 -3 1.6 f 0.4 -26.2 f 0.2 -17.2 f 0.8 -40.2 f 0.2 -32.1 f 0.2
All values are in kcal/mol. Uncertainties listed are experimental precision, not accuracy. We estimate that in general AfHo of carbon compounds are not known to better than fO.ln kcal/mol, where n = number of carbon atoms. bReference11. CThevalue may be incorrect (see text).
electronegativity scale first proposed by Yuan* and show that it yields a quantitative correlation of AAfHo(RX/R'X) with the unshielded core potential, V,. There have been a number of reviews of the data on AfHoof organic compounds in the last 2 decades, and some of the experimental values have undergone "analytical" revision by small We shall adopt amounts, generally less than 0.5 kcal/m01.*~~J~ (8) Yuan, H. C. Acta Chim. Sin. 1964, 30, 341. (9) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. (10) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and MetalsOrganic Compounds; Academic: London, 1970. (1 1) Kudchader, S. A,; Kudchader, A. P. J. Phys. Chem. ReJ Data 1978, 7, 1285.
0 1988 American Chemical Society
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Luo and Benson
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
TABLE II: AtH" (kcal/mol) in Some Series XCH+,(CH3), X -AfHo -AAiHo H CH4 17.8 f 0.1 2.2 f 0.2 CH,(CHI) 20.0 f 0.1 5.0 f 0.2 CH2(CH,)2 25.0 f 0.1 CH(CHd9 32.1 f 0.2 7.1 f 0.3 CHI CH3CHS 20.0 f 0.1 5.0 f 0.2 CHICH2(CH,) 25.0 f 0.1 7.1 f 0.3 CH,CH(CH,)2 32.1 f 0.2 8.1 f 0.3 CH,C(CH3)3 40.2 f 0.2 CI CCIH, 19.6 f 0.1 7.2 f 0.4 CCIH2(CHI) 28.6 f 0.3 CCIH(CH,), 34.6 f 0.3 7.8 f 0.5 CCKCH,), 43.6 f 0.5 9.0 f 0.6 OH C(OH)H, 48.2 f 0.1 8.1 f 0.2 C(OH)H,(CH,) 56.3 f 0.1 8.8 f 0.2 C(OH)H(CH,)z 65.1 f 0.1 9.6 f 0.3 C(OH)(CH,), 74.7 f 0.2
-
E
Y
h X
2
-16-t8-
> -20I
ill
r -22
TABLE 111: Relations between A A P " and V , A AfH" AAiH" AAfH" X r x / k V, (EtX/MeX) (i-PrXIMeX) (t-BuX/MeX) F 0.706 9.915 -26.5f0.3 -8.1f0.2 -16.9f0.2 O ( 0 H ) 0.74 8.11 -24.0 f 0.6 -7.2 f 0.4 -15.0 f 0.4 c1 0.994 7.04 -14.5 f 0.3 -23.4 f 0.3 -5.8 f 0.3 N(NH2) 0.75 6.67 -6.3f0.5 -15.3f0.7 -23.1f0.5 Br 1.141 6.13 -5.6 f 0.3 -12.7 f 0.3 -20.7 f 0.3 S(SH) 1.04 5.77 -13.1 f 1.0 -20.7 f 0.9 I 1.333 5.25 -5.3 f 0.5 -5.0 f 0.2 -12.1 f 0.3 -20.2 f 0.3 C(CH3) 0.771 5.19 -7.2 f 0.2 -14.3 f 0.2 -2.2 f 0.2 H 0.371 2.70
OThe bond lengths of diatomic molecules are taken from ref 15 and other values from ref 7 and 16. TABLE I V Values of the Intercepts (I,,,) and Slopes (S,,,)for Linear Eq 4 S,,,,kcal .fi/mol I,,,, kcal mol-' R exptl est (eq 5) exptl est (eq 5) Et 0.9 f 0.3 0.9 -1.14 f 0.04 -1.14 i-Pr -2.2 f 0.3 -2.1 -1.84 f 0.04 -1.83 t-Bu -8.1 f 0.3 -8.1 -2.30 f 0.04 -2.31
the values given in the latest of theseg without commenting on the changes made. In Table I we present values of AfHoon a series of compounds MeX, EtX, i-PrX, and t-BuX from Pedley et aL9 In Table I1 we compare values of AfHo(RX) for a number of sequences in which R is CH3-,(CH3),. The last column in Table I1 presents the successive differencs in AfHo(RX) with C H 3 for H substitution. As can be seen, these differences are not constant nor are the third-order differences constant. This has been discussed in detail earlier4*5,12-14 without being resolved. The lack of constancy of AAfHo(RX)with H/Me substitution is a measure of the failure of the first-order law of bond additivity as applied to AfH0(RX).' Linear Relations between AAfHo(RX) and V,. As defined by Yuan,8 the unshielded core potential V, = n x / r x where , n, is the number of valence electrons of X and rx is its covalent radius. These are listed in Table I11 along with values for the following differences in AfHo(RX): AAfHo(EtX/MeX) = AfHo(EtX) - AfHo(MeX)
-141
(1)
AAfHo(i-PrX/MeX) = AfHo(i-PrX) - AfHo(MeX) (2) AAfHo(t-BuX/MeX) = AfHo(t-BuX)- AfHo(MeX) (3) (12) Benson, S. W.; Luria, M . J . Am. Chem. SOC.1975, 97, 704. (13) Benson, S.W. Chem.-Tech. (Heidelberg) 1980, 10, 121. (14) Benson, S . W. J . Phys. Chem. 1981, 85, 3375. (15) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure, IV, Constants of Diatomic Molecules; VNR: New York, 1979. (16) Little, E. J., Jr.; Jones, M. M. J . Chem. Educ. 1960, 37, 231.
'\
Figure 1. Linear relationships between AAfH" and V,.
We have found three linear relations between AAfHo and V, as shown in Figure 1. The values of the intercepts, I,, and slopes, S,, for these straight lines are listed in Table IV: AAfHo(RX/MeX) = I , + S,V, (4) These three straight lines can be further described with six parameters ( I , and S,) by one empirical relation with only four parameters: rn AAfHo(RX/MeX) = 10.9 - 1.5m(m - I ) ] 0.67 + 0.21mvx (5)
where R represents Et, i-Pr, and t-Bu. As shown in Table IV, the estimated and observed values of intercepts and slopes derived from eq 5 are in excellent agreement with each other. Note that I, = 0.9 - 1.5m(m - 1 ) S, = -m/(0.67
+ 0.21m)
(6)
(7)
As can be seen from Figure 1, only four points, AfHo(C2H5NH2), AfHo(i-C3H7Br), AfHo(i-C3H71), and AfHo(t-BuBr), deviate from the straight lines. The deviations are all within the experimental uncertainty of about f l - 2 kcal. For elements or groups X where AfHo(MeX) is known, we can estimate from eq 4 AfHo for EtX, i-PrX, and t-BuX, the differences in AfHoof the alkyl group. Values estimated for the alkyl fluorides are
AfHo(C2H,F) = -66.3 f 0.5 kcal mol-' AfHo(i-C3H7F)= -76.2 f 0.5 kcal mol-' AfHo(t-C4H9F)= -86.9 & 0.5 kcal mol-'
We feel that the values given in ref 9 for i-PrF (see Table I) may be in error. Discussion In his article, Yuans showed that V, was proportional to the effective nuclear potential using G o r d y ' ~ 'assumption ~ that the other valence electrons exerted a shielding of one-half the electronic charge. For our present purposes it does not matter whether this is correct or whether some other factor of proportionality should be used. (It is more than likely that a proportionality factor would (17) Gordy, W.; Smith, W. V.; Trambulo, R. F. Microwaue Spectroscopy; Wiley: New York, 1953.
J . Phys. Chem. 1988, 92. 5257-5261 systematically vary with the group in the periodic table.) Any proportional correction would maintain the linear relation between AAfHo and V, found here. Pauling's electronegativity scale7 was derived from the heats of formation of diatomic molecules and was based on a qualitative argument concerning ionic character in the bonds. While it was of great utility in organizing the data on heats of formation on diatomic molecules, it could never be extended quantitatively to polyatomic molecules. Yuan did not attempt to use V, for estimation. He simply observed that there was a nearly linear relation between V, and Pauling's values of electronegativity X,.This was not a proper comparison since energies of bonds are proportional to the square of differences in X , for the two elements forming a bond. In fact a comparison of V, with XX2 gives a better linear relation, but it is far from quantitative. However, the biggest discrepancy between X, and V, is in the value assigned to hydrogen. It is very close to the value of carbon in the Pauling scale and almost all other scales but very different from the V, for carbon. Intuitively V, or something proportional to V, seems a quite reasonable measure of the strength of the covalent bond, and so it is perhaps not too surprising that it affords such an excellent correlation. The relation that we have found for AfHo(RX/MeX) permits us to estimate AfHo(RX) for alkyl derivatives when AfHo(MeX) is known. It also allows us to estimate in turn group contributions
5257
for C-X(H)m-3(C)m. This in turn with other groups that are known18 permit us to estimate AfHo(RX) for any single R of almost any complexity. Conversely, if AfHo(RX) are available for any one more complex molecule, eq 5 together with other group values permits us to estimate AfHo(RX) for all other molecules, including CH3X. In subsequent papers we will discuss the extension of this approach to molecules in which X is a group such as Et, i-Pr, t-Bu, C2H3, C3H5, C6H5, C6HsCH2, RCO, HOCO, NC, RO, O2N0, ONO, RCOO, ON, OzN, CN, RS, R S 0 2 , etc.
Acknowledgment. This work has been supported by grants from the National Science Foundation (CHE-84-0376 1) and the US. Army Research Office (DAAG29-85-K-0019). Registry No. CH3F, 593-53-3; CH,OH, 67-56-1; C H Q , 74-87-3; CH3NH2,74-89-5; CH3Br, 74-83-9; CH3SH, 74-93-1; CHJ, 74-88-4; CH3CH3, 74-84-0; CH4,74-82-8; CZHSOH, 64-1 7-5; CZHSCI, 75-00-3; C2HSNH2,75-04-7; C2H5Br,74-96-4; CzHSSH,75-08-1; C2H51,75-03-6; CH3CHzCH3, 74-98-6; i-C3H7F, 420-26-8; i-C3H70H, 67-63-0; iC3H7C1,75-29-6; i-C3H7NHz,75-31-0; i-C3H7Br,75-26-3; i-C3H7SH, 75-33-2; i-C3H71, 75-30-9; CH(CH&, 75-28-5; t-C4HgOH, 75-65-0; t-C4H,C1, 507-20-0; t-C4H9NH2, 75-64-9; t-C4HgBr, 507-19-7; tC4HgSH, 75-66-1; t-C.+HJ, 558-17-8; CH,C(CH,)j, 463-82-1. (18) Benson, S. W. Thermochemical Kinetics, 2nd ed.;Wiley: New York, 1976.
Hypernetted Chain Closure Reference Interaction Site Method Theory of Structure and Thermodynamics for Alkanes in Water Toshiko Ichiye and David Chandler* Department of Chemistry, University of California, Berkeley, California 94720 (Received: March 3, 1988)
The solvation structure and thermodynamics of hydrophobic molecules in aqueous solution are studied by the extended reference interaction site method using the hypernetted chain closure (HNC-RISM) and by molecular dynamics simulations. The solvation structure predicted by HNC-RISM agrees only moderately with simulation results. In addition, thermodynamic data from the theory are in poor agreement with experiment, although this may be due at least partially to the potential functions used. These results indicate that HNC-RISM is not a quantitatively accurate theory for nonpolar solutes in aqueous solution. Since problems have already been noted for ionic solutions, this reinforces the need for an improved closure for realistic continuous potential models. A method for obtaining potentials for reduced models is also presented, and the use of HNC-RISM to implement this method is discussed.
I. Introduction The solvation of hydrophobic molecules in water is of great importance in many problems of biological and chemical interest. Consequently, a large number of computer simulations' and more analytic theoretical studies2 have been made on this problem. In this article we study integral equation predictions and molecular dynamics results for the structure and thermodynamics of molecules in aqueous solution. Although a study of hydrophobic solvation using the reference interaction site method has been made by Pratt and Chandler," many new developments since then make a new study of interest. First, an extension of the RISM integral equation using the H N C closure by Rossky and co(1) See, for example: (a) Pangali, C.; Rao, M.; Berne, B. J. J. Chem. Phys. 1979, 71,2975; 1979, 71, 2982. (b) Swope, W. C.; Andersen, H. C. J. Phys. Chem. 1984.88.6548. (c) Joreensen. W. L.: Gao. J.: Ravimohan. C. J. Chem. Phys. 1985,'89,'3470. id) StLatsma, T. P.'; Berendsen, H. J. C.; Postma, J. P. M. J. Chem. Phys. 1986,85, 6720. (2) See, for example: (a) Pratt, L. R.; Chandler, D. J . Chem. Phys. 1977, 67, 3683. (b) Pratt, L. R.; Chandler, D. J . Solution Chem. 1980, 9, 1. (c) Tanaka, H. J . Chem. Phys. 1987,86, 1512. (3) See, for example: (a) Chandler, D.; Andersen, H. C. J . Chem. Phys. 1972, 57, 1930. (b) Lowden, L. J.; Chandler, D. J . Chem. Phys. 1974, 61, c**o
J'LLO.
(4) Pratt, L. R.; Chandler, D. J . Chem. Phys. 1980, 73, 3430, 3434. (5) Hirata, F.; Rossky, P. J. Chem. Phys. Lett. 1981, 83, 329.
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workers, referred to here as HNC-RISM, appears applicable to physically realistic models of molecules having strong polar interactions. Indeed, it has been used with varied success in the study of liquid water structure6 and ionic solutions.' Second, energy parameters for hydrocarbonss and waterg have been developed that give good structural and thermodynamic properties in computer simulations. These developments have motivated us to make several new applications of the HNC-RISM theory. We have three main objectives: First, we compare experimental thermodynamic data for hydrophobic solvation with our HNCRISM results. This is important in light of a study that has been made attempting to predict the conformational equilibria of butane in aqueous solution by using HNC-RISM.'O Also a limited (6) Pettitt, B. M.; Rossky, P. J. J . Chem. Phys. 1982, 77, 1451.
(7) (a) Pettitt, B. M.; Rossky, P. J. J . Chem. Phys. 1986, 84, 5836. (b) Hirata, F.; Rossky, P. J.; Pettitt, B. M. J. Chem. Phys. 1983, 78, 4133. (c) Chiles, R. A,; Rossky, P. J. J . Am. Chem. SOC.1984, 106,6867. (d) Kuharski, R. A,; Chandler, D. J. Am. Chem. SOC.1987, 91, 2978. (8) Jorgensen, W. L.; Madura, J. D.; Swensen, C. J. J . Am. Chem. SOC. 1984, 106, 6638. (9) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J . Chem. Phys. 1983, 79, 926. (10) Zichi, D. A.; Rossky, P. J. J . Chem. Phys. 1986, 84, 1712. (11) The calculations were performed on the Berkeley CRAY XMP by adapting a code written by R. W. Impey.
0 1988 American Chemical Society
