1730
F. Nemoto and K. lshizu
teraction of the metal ion with the binding sites of the ligand exists. Certain aspects of the dynamics of metal-ligand interaction can be studied using these techniques.
References and Notes (1) This research was supported by the Italian National Council of Research (C.N.R.). (2) (a) A. I. Lehninger, Phys. Rev., 30, 393 (1950); (b) M. J. Johnson and J. Berger, Adv. Enzymol., 2, 69 (1942). (3) E. L. Smith in "Enzymes and Enzyme Systems", J. T. Edsall, Ed., Harvard University Press, Cambridge, Mass, 1951, p 47. (4) J. Eisinger, R. G. Shulman, and W. E. Blumberg. Nature (London), 192, 963 (1961); M. Cohn, Biochemistry, 2, 623 (1963); G. Navon, R. G. Shulman, B. J. Wyluda, and T. Yamane, Proc. Natl. Acad. Sci. U.S.A., 60, 86 (1968); G. H. Reed, H. Diefenbach, and M. Cohn, J. Biol. Chem., 247.3066 (1972), and references therein. (5)C. Zimmer and G. Luck, Eur. Biophys. Congr., Proc., Ist, 1, 397 (1971). (6) A. Albert, Blochem. J., 47, 531 (1950). (7) A. Albert, Biochem. J., 50, 690 (1952). (8)H. C. Ailen, M. L. Mandrioii, and J. W. Becker, J. Chem. Phys., 56, 997 (1972); M. Cohn and J. Townsend, Nature(London),173, 1090 (1954). (9) C. C. Mc Donald and W. D. Phillips, J. Am. Chem. SOC., 85, 3736 (1963); A. M. Bowles, W. A. Szarek, and M. C. Baird, lnorg. Nucl. Chem. Lett., 7, 25 (1971); M. K. Kim and A. E. Martell, J. Am. Chem. Soc., 91,
872 (1969); R. Mathur and R. 6. Martin, J. Phys. Chem., 69, 668 (1965). (10) R. H. Carlson and T. L. Brown, horg. Chem., 5, 268 (1966); M. K. Kim and A. E. Martell, J. Am. Chem. SOC., 88, 914 (1966). (11) R. A. Haines and M. Reimer, lnorg. Chem., 12, 1482 (1973). (12) D. R. Williams, J. Chem. SOC.A, 9, 1550 (1970); C. W. Childs and D. D. Perrin, ibid., 8, 1039 (1969); M. K. Kim and A. E. Martell, J. Am. Chem. SOC.,89, 5138 (1967). (13) D. R. Eaton, Adv. Chem. Ser., No. 100, 174 (1971). (14) D. R. Williams, horg. Chim. Acta Rev., 123 (1972). (15) E. E. Bittar, "Cell pH", Butterworths, Washington, D.C., 1964. (16) M. Eiden, B. Haines, and H. Kahler, J. Natl. Cancer lnst., 16, 541 (1955). (17) L. Burlamacchi. G. Martini, and E. Tiezzi, J. Phys. Chem., 74, 3980 (1970). (18) L. Burlamacchi, 0.Martini, and M. Romanelli, J. Chem. Phys., 59, 3008 (1973). (19) B. R. Mc Garvey, J. Phys. Chem., 61, 1232 (1957). (20) N. Bloembergen and L. 0. Morgan, J. Chem. Phys., 34, 842 (1961). (21) A. Hudson and G. R. Luckhurst, Mol. Phys., 16, 395 (1969). (22) L. Burlamacchi and E. Tiezzi, J. Mol. Struct., 2, 261 (1968). (23) M. Eigen, Pure Appl. Chem., 6, 105 (1963). (24) M. Romanelll and L. Burlamacchi. to be submitted for publication. (25) L. Burlamacchi and E. Tiezzi, J. Phys. Chem., 73, 1588 (1969). (26) L. Burlamacchi, G. Martini, and E. Tiezzi, J. Phys. Chem., 74, 1809 (1970). (27) L. Burlamacchi, J. Chem. Phys., 55, 1205 (1971). (28) G. Martini, M. Romanelli, and L. Burlamacchi In "Molecular Motions in Liquids", J. Lascombe, Ed., 1974, p 371.
Calculation of the Barrier to Internal Rotation of the Alkyl Group in the 4,4'-Diethylbiphenyl Anion Radical from Electron Spin Resonance Data Fujito Nemoto' and Kazuhiko lshizu Department of Chemistry, Faculty of Sclence, Ehime University, Bunkyo-cho, Matsuyama 790, Japan (Received June 25, 1974: Revised Manuscript Received May 5, 1975)
+
Based on the Heller-McConnell relationship for hyperconjugation, A46 = (Eo E2 cos2 8 ) p p n , the positive temperature dependence of the ethyl P-proton splitting was adequately interpreted in terms of restricted rotation of the ethyl group in a twofold sinusoidal potential, and the rotational potential barrier of the ethyl obtained by the statistical treatment of cos2 0 was about I kcal/mol. The energy of the nonbonding interatomic interaction was calculated using the Lennard-Jones 6-12 potential. Excellent agreement is found between the experimentally determined value of the potential barrier and that theoretically calculated.
Introduction In terms of hindered internal rotation, the equilibrium conformation of the alkyl group has been extensively studied by ESR measurement of @-protonsplittings. According to previous investigations,1,2alkyl groups have been treated as a rotator rocking in the simple sinusoidal potential and the energy barriers of the hindered rotation have been estimated from an analysis of the positive temperature dependence based on Boltzmann statistics. The rotational potential function employed, however, was more or less tentative and no detailed explanation of the potential function has been given. In this work, analysis of the rotational potential function of ethyl groups was performed in detail, based on the temperature dependence of the ethyl P-proton splittings of the 4,4'-diethylbiphenyl anion. Equilibrium dihedral angles of the ethyl group were calThe Journal of Physical Chemistry, Vol. 79, No. .16, 1975
culated using a Mathieu type potential function and the rotational wave function expanded in a Fourier series. The maximum height of the potential barrier was estimated from comparison of the observed and calculated temperature dependence. On the other hand, the energy of the nonbonding interaction between the alkyl group and the neighboring aromatic protons was calculated on the basis of a LennardJones 6-12 potential. The maximum repulsion energy between the ethyl and the ring protons thus calculated justified the value of the potential barrier which was experimentally determined.
Experimental Section 4,4'-Ditolyl and 4,4'-diethylbiphenyl were synthesized in the same manner as is reported in the previous w0rks.3,~ The anion radicals were prepared in solution of dimethoxy-
1731
ESR of the 4,4'-Diethyibiphenyl Anion Radical
TABLE I: Hyperfine Coupling Constants ( G )for Protons Temp, A,'
A2H
AsH
"C
+ i ( e ) . The
@-protonsplitting at any temperature was calculated based on eq 1and 2, using Boltzmann statistics.
e = a + eo
A ~ @Bp4*(COS2 = e) m
4,4'-Ditolyl 4,4'-Diethylbiphenyl
5.63 3.77
ESR ESR
2.73 2.73
0.49 0.49
-90 -90
(cos2 e ) =
i=O
( + i ( a )(cos2(a
+
(3)
+i(a))e-EJkT
m
C e-EiIkT
(4)
1=0
where the contribution of Bo was neglected in eq 2 and the value of Bp,* was estimated as 2(5.63) (G) based on the methyl proton splitting of ditolyl a n i ~ n In . ~addition, ~~ we made the assumption that the motion of the ethyl group is a restricted rotation in a twofold potential, V(a), and, at the most stable conformation, it will take a position parallel with the axis of 2pr ring carbon atom; that is, the dihedral angle of ethyl protons at the minimum potential, 00, is equal to ~ 1 3 The . wave function, +1, and the energy of eigenvalue, EL, are obtained by solving the following equation:
1 t
5.0
4.0
Figure 1. Temperature dependence of the hyperfine coupling constants measured by ESR: (-0-0) 4,4'ditolyl, (-0-0) 4,4'-diethylbiphenyl.
------
-----
ethane (DME) by reduction with potassium everywhere. The ESR spectra were measured in the temperature range from +2O to -110O using a Japan Elecron Optics (JEOL) JES-ME-3X type spectrometer equipped with 100-kHz magnetic field modulation.
Results and Discussion The proton hyperfine coupling constants of 4,4'-ditolyl and 4,4'-diethylbiphenyl anions5 remeasured under the identical experimental conditions are summarized in Table I. The @-protonhyperfine splitting of each alkylbiphenyl was precisely measured as a function of temperature over the temperature range from +10 to ~ - 9 0 ~As. we already reported in previous work^,^,^ the positive temperature dependence of A46 of ethyl was reconfirmed, in addition, the fact that both AzH or A3H remain constant, or show only a minor change, was clearly demonstrated, as shown in Figure 1. Free rotation of the methyl group can be assumed everywhere, since A46 of ditolyl anions showed no detectable changes throughout the entire temperature range. It has been well known that the magnitude of the @-proton splitting can be calculated using the following equationd -446
=
( Q ( e ))p4r
Q ( e ) = Bo
+ B2 COS'
(1) 0
(2) where Bo and Bz are empirical parameters, p4* is the spin density at the para position, and 0 is the angle between the axis of the 2pr orbital and aliphatic C-H bond of the ethyl group, both projected on the plane perpendicular to the bond between the methylene carbon of the ethyl and the aromatic carbon. ( Q ( 0 )) is the quantum mechanical average of cos2 0 over the appropriate rotational wave functions
where the moment of inertia of the molecular fragment Ph-C2H5 can be calculated as I = 0.50 X g cm2 taking into account the fact that a preferred rotation of the residual group occurs about the longer axis of the molecule of 4,4'-dialkylbiphenyls. With reference to previous works, the potential barrier, V ( a ) ,was approximated as V(a) = V0/2(1
- cos 2 4
(6)
The hamiltonian matrix j ) was diagonalized by expanding the wave function into a Fourier series: m
+;(a)
C (C, sin ja + D,,COS ja)
,=o
(7)
The temperature dependence of ( cos2 e ) was calculated for various V Ovalues as shown in Figure 2. The calculated value of (cos2 0) and its temperature dependence gave the best agreement with the experimental results when VOwas estimated to be 1kcallmol. Calculation of Repulsive Potential Energies between the Ethyl and the Aromatic Protons. The calculations of nonbonded interaction energies between the rotating ethyl and the aromatic protons were carried out using the following approximations. (1)The methyl group in the ethyl is treated as a rare gas atom, Kr, since the methyl group has been thought to be rapidly rotating in comparison with the motion of the ethyl, and not only its spherical radius but also van der Waals radius are almost comparable with those of the Kr atom. (2) Two kinds of interatomic interaction were considered in the present calculations. The first is the interaction between the ring-meta protons and the alkyl @ protons, @ H ~ - H ~The . second is the interaction between the ring-meta protons 'and the methyl group, @H,-cH? All other interactions were neglected. The total interatomic potential was calculated by the summation of every pairs of interactions, and each interatomic interaction was estimated based on the LennardJones 6-12 potential function.
@H,-H&R~I) = A H - H I R ~ ~-' B ~H-HIR,,~
(8)
@H,-CH&R~) = AH-dR112 - BH-KJRL'
(9)
where R , is the interatomic distance between the ringThe Journal of Physical Chemistry, Vol. 79, No. 16, 1975
F. Nemoto and K. lshizu
1732
-
-90
-50
t("C)
Figure 2. Temperature dependence of (cos2 0 ) calculated for various VOvalues.
_. - - o (
Figure 4. Conformations of the 4,4'diethylbiphenyl anion and nonbonded interaction energies between the rotating ethyl and ringmeta protons as a function of a . TABLE 11: Averaged Values of Cos2 B for Para-Substituted Ethylbenzenes
_-
Figure 3. Scheme showing the distances Ri and Rii between ringmeta protons and methyl group in the ethyl, and between ring-meta protons and ethyl p protons, respectively. meta proton and the alkyl ,f3 proton, Ri is that between the ring-meta proton and the methyl group, respectively. As shown in Figure 3, Rij and Ri a t any rotation angle of the ethyl ( a ) were calculated by taking the bond angle of the tetrahedral carbons to be 109O 29' and that of ring carbons to be 120O. Bond distance between carbon and hydrogen atoms were estimated to be 1.09 8, everywhere, and the carbon-carbon distance are 1.52 8, for the aliphatic group, 1.45 8, for the alkyl carbon-ring carbon separation, and 1.40 8, for the aromatic ringas The numerical values of parameters A H - H ,BH-H, A H - K ~ , and BH-K~in the Lennard-Jones 6-12 potential were already established by Yasuda and Ohbatake:9J0 AH-H= 4.7 X lo2 kcal 8,12/mol, BH-H= 9.2 kcal A6/mol, A H - K = ~ 3.3 X lo4 kcal 8,12/mol, BH-K~= 1.2 x 102 kcal A6/mol. The interatomic potential energy, *, is given by
Radical
(cos2e)
4,4'-Diethylbiphenyl anion 4-Ethylnitrobenzene anion 4- Ethylphenoxyl 4-Ethylbenzosemiquinone anion
0.37 0.42 0.39
Lit.
0.36 11 12 13
ever, is ne'arly comparable with the thermal activation energy a t 300OK. Therefore, one may expect that thermal activation will effectively contribute to free rotation of the ethyl group. This would be indeed true, because experimental values of ( cos2 0) hitherto reported for para-substituted ethylbenzenes are all close to % as summarized in Table 11. These values are considerably larger than those for 9-ethylanthracene (0.25)14and 9-ethylxanthy12 (0.25) in which the motion of the ethyl group is thought to be strongly restrained and the ethyl /3 proton is almost oriented a t the most stable conformation (Bo = a/3).
Acknowledgment. The numerical calculation was carried out on the FACOM 230-60, a t the Data Processing Center. Kyoto University, Japan. We are indebted to Professor H.H. Dearman for reading the manuscript. References a n d Notes
In Figure 4, we plot of the interatomic potential energy as a function of the rotating angle ( a )of the ethyl group. The maximum repulsion energy thus calculated was 1.3 kcal/mol when the methyl group is fixed on the aromatic ring, on the other hand, repulsion energies between the fl proton and the ring proton are always less than 0.04 kcal/ mol. The potential curve calculated for various sets of parameters indeed has the twofold potential structure, and the potential barrier height shows satisfactory agreement with the value obtained from measurement of the temperature dependence of the @-protonsplittings. In conclusion, the rotation of the ethyl group may be more or less restricted in the twofold potential which has the barrier height of 1 kcal/mol. The potential barrier of restricted rotation, howThe Journal of Physical Chemistry, Vol. 79, No. 16, 1975
(1) (2) (3) (4) (5)
(6) (7) (8) (9) (10) (1 I ) (12) (13) (14)
E. W. Stone and A. H. Maki, J. Chem. Phys., 37, 1326 (1962). N. D. Sevilia and G. Vincow, J. Phys. Chem., 72, 3647 (1968). K. Ishizu, Bull. Chem. SOC.Jpn., 37, 1093 (1964). K. Ishizu, K. Mukai, H. Hasegawa, K. Kubo. H. Nishiguchi, and Y. Deguchi, Bu//. Chem. SOC.Jpn., 42, 2808 (1969). The referee kindly communicated that ENDOR measurements of the hyperfine coupling constants were recently undertaken for 4,4'ditoiyl anion radical. T. C. Christidis and F. W. Heineken, Chem. Phys., 2, 239 (1973). C. Heller and H. M. McConnell, J. Chem. Phys., 32, 1535 (1960). N. L. Bould, J. Am. Chem. Soc., 91, 6666 (1969). L. Pauling, "The Nature of the Chemical Bond", 3rd ed, Cornell University Press, ithaca, N.Y., 1960, p 260. H. Yasuda, Prog. Theor. Phys., 45, 1361 (1971). M. Oobatake and T. Ooi, Prog. Theor. Phys., 48, 2132 (1972). T. M. Mckinney and D.H.Geske, J. Am. Chem. SOC.,89,2806 (1967). T. J. Stone and W. A. Waters, J. Chem. SOC., 213 (1964). J. Pilar, J. Phys. Chem., 74, 4029 (1970). D. Bachmann, 2.Phys. Chem., 43, 198 (1964).
