ROTATORY D IS PERSION CURVES 443

dichroism curve with greater accuracy. This is allsubject to the other assumptions already mentioned,and these do place a limit on the extent to which thepresent method could thereby be improved.

ACKNOWLEDGMENTS

The major portion of this work was done in col-laboration with the late Professor William E. Moffittat Harvard University, where the author was holderof a National Research Council-American Chemical

Society Petroleum Research Fund Postdoctoral Fel-lowship.

The numerical work was carried out on the IBM 704computer at the Bell Telephone Laboratories in MurrayHill, New Jersey. It is a pleasure to acknowledge thegenerous hospitality of the Bell Laboratories madeavailable through the kind courtesy of Dr. S. O. Morganand Dr. W. P. Slichter. The author also would like toexpress his appreciation to Dr. M. E. Terry and MissShirley Reed for their competent help and advice inconnection with the computational procedures.

REVIEWS OF MODERN PH YSICS VOLUME 32, NUM BER 2 A P R IL, 1960

. .'. xeory o)': t~e Optica. . Activity oI ..~imesity. .

.DerivativesEDEL KASSKRMAN

Bell Telephone Laboratories, Inc. , MNrroy Hill, Peto Jersey

'N the previous paper, Dr. Moscowitz mentions the~ - importance of the rotational strength in determiningthe contribution of an electronic state to the opticalactivity of a molecule. From Rosenfeld's equation wemay represent the observed rotation, employing lightof frequency v, as

LM] ~ Qg v'Rg/(vg' —v'),

where LM] is proportional to the optical activity permolecule. The rotational strength EI, is given by p, pexcept for a phase factor. Here, p, and p are the electricand magnetic moments associated with the ground tok state transition of frequency vI, .

For optically inactive systems, p, and p may beperpendicular, so that E~ vanishes. With an activemolecule, a natural approach for theory has been toconsider the interaction of individually inactive por-tions, the electric moment of one group having a com-ponent parallel to the magnetic moment of another.This is the approach used in the coupled oscillatorsmodel of Born, ' ' Kuhn, ' ' and Kirkwood. ' A recentexample is found in MofBtt's treatment of polypeptides. '

Although the decomposition into groups is frequentlyarbitrary, one system in which it is particularly at-tractive is the active biphenyls. The ortho substituentsprevent coplanarity and extensive conjugation between

*Presented at the William E. Moffitt Memorial Session.' M. Born, Optik (Verlag Julius Springer, Berlin, 1933).2 T. M. Lowry, Optica/ Rotatory I'ower (Longman's Green and

Company, Inc. , ¹wYork, 1935).'W. Kuhn in Stereochemie, edited by K. Freudenberg (Franz

Deuticke, Leipzig and Vienna, 1933).4 J. Kirkwood, J. Chem. Phys. 5, 479 (1937).' W. E. MoKtt, J. Chem. Phys. 25, 467 (1956).

the rings. Except for the dipolar interactions the pielectrons of the two rings may be considered separately.

An attractive series for the study of the opticalactivity of biphenyls is the substituted bimesityls(Fig. 1). The four ortho methyl groups should preventextensive motion about the interring bond. Theoreticalcomputations can therefore be restricted to a singleconformation. The symmetry of the three methylgroups in each ring permits the 3,3-disubstitutedbimesityl to be considered as two interacting monosub-stituted benzene rings. The axis of rotation greatlysimplified the computations. Finally, Adam andMoyer's preparation and resolution of the diaminobi-mesityl' and the synthetic versatility of the aromaticamino group allowed the preparation of other sym-metrical, optically active, bimesityl derivatives.

Assuming that the optical activity in the visible andnear ultraviolet is adequately described by the lowest

&Hge'

/ ~ iVY 4~rrrr

/~'CHg.

FIG. 1. 3,3'-disubstituted bimesityl. Arrow designatesaxis of rotational symmetry.

6W. W. Moyer and R. Adams, J. Am. Chem. Soc. 51, 630(1929l.

EDEL KASSERMAN

excited states of the molecule, the pi-electron approxi-mation is used in formulating the wave functions forthe bimesityl derivatives. The molecular wave functionsare of the form

Qsx= (2) ~(O'arzO'szz+OszO~zz),B

where 0'nrz and Osz represent the ground and s excitedstates of ring I. The A refers to those functions whichare symmetric with respect to the axis of rotation, the8 to those that are antisymmetric. Overlap andexchange between rings are neglected, as are any eGectsof nuclear vibrations.

The individual benzene rings are described by thefour LCAO-ASMO functions of Goeppert-Mayer andSklar. ~ The three methyl groups are considered byassuming that the energies of these states are thoseobserved for the corresponding states of mesitylene.The 3,3' substituents are taken into account by intro-ducing two excited state functions representing transferof charge from the substituent to the ring. These sixOs states may interact by means of one-electron (intra-ring) perturbations. These are the resonance integralbetween the substituent and the adjacent carbon atomand the change in the coulomb integral at the 3,3'carbon atoms.

In addition to the intraring perturbation, the"exciton" (dipole-dipole) interaction between rings wasexamined. This perturbation can split the degeneracyof A and I3 states. But since the intraring and interringperturbations are of A symmetry, neither can mix Aand 8 states. Thus, each compound requires the eigen-values and eigenvectors of two sixth-order energymatrices.

The one-electron perturbations were evaluated fromobserved spectra. The shift of the lowest energy bandof the ortho and meta identically disubstituted deriva-tives from that of the corresponding monosubstitutedbenzene yielded the resonance integral. Similar com-parison of the para with the corresponding ortho andmeta derivatives yielded the change in the Coulombintegral. The dipole-dipole interaction was obtained bydirect computation from the wave functions .

It was found that the deviation of the rings fromperpendicularity was extremely important in deter-mining the magnitude of the optical rotation computed.Only two 08 functions, one of each symmetry, cangive rise to optical activity. These correspond to oneof the degenerate states responsible for the intense E~band of benzene (the 0'r state in MofEtt's notation').

7 M. Goeppert-Mayer and A. L. Sklar, J. Chem. Phys. 6, 645(1938).

W. E. Mof5tt, J, Chem. Phys. 22, 324 (1954).

TABLE I. Rotations of nonperpendicular bimesityls at 5790 A.

Substituent

FQH

NH3+N(CH )

NHgCl0BlI

Calc

30.0

44.436.696.0

93.6334.2

Obs

—1.61353537898

185213432

The other bimesityl states become active only bymixing with them. These Qy functions have allowedelectric and magnetic moments so that their rotationalstrengths are large, but they cancel one another exactly.Their degeneracy is not directly resolved by dipole-dipole interactions when the rings are perpendicular.The splitting which does occur, due to mixing withother states, yields only a small predicted rotation;much less than that observed in most cases.

That the rings do deviate from perpendicularity isindicated by an examination of the Van der Waals'interactions between the groups attached to the benzenerings. By using known potential functions it is foundthat the adjacent ortho methyl groups are displacedby the 3,3' substituents. The 2,2' methyls are closerthan the 6,6' methyls. This leads to a slight rotationabout the interring bond (2'for the largest substituent).The 0& functions are now split directly by the excitoninteraction and much larger rotations are possible.

With all the elements of the energy matrices deter-mined, the eigenvalues and eigenvectors were computedby means of an IBM 650. They were substituted intoRosenfeld's equation to produce the optical activities.The values at 5790 A are given in Table I. Similaragreement between theory and experiment, within afactor of 2.5, is found at other wavelengths. Suitablepotential functions are not available for F, NH3+, and0, but we may utilize evidence of their "size" fromother sources to demonstrate a good correlation betweenthe magnitudes of steric interactions and opticalrotation.

In conclusion, we may note that the absolute con-figuration of Fig. 1 is predicted to be levorotatory inthe visible for all compounds studied except diQuoro-bimesityl.

ACKNOWLEDGMENT

This problem was suggested by the late ProfessorWilliam E. Moist. Much is owed to his inspiring direc-tion of its prosecution both by his conversations withthe author and through his papers in which many of theprocedures employed are discussed.