2110
J . Phys. Chem. 1991,95, 2110-2112
feel that the conclusion of Eberstein that ClOOCl will not dissociate to C102and a free chlorine atom at wavelengths above 220 nm is probably not correct. Finally, we have carried out calculations of the dipole and quadrupole moments of the chlorine peroxide isomer at the MBPT(2) level, using a 118-GTO basis set derived from basis B by deleting the outermost d and f orbitals on chlorine. These calculationswere carried out analytically, using the relaxed density formalism of Salter, Trucks, and Bartlett.27 Since ClOOCl is relatively well descrihed by a single reference determinant, the values presented in Table IV should be quite accurate, with the dipole moment likely to fall within a few tenths of a debye of the exact value. Since we believe that ClOOCl is the most stable form of CI2O2,we present these results in the hope that they will assist experimentalists in further verification of the existence of C1OOCl.
for the ClOClO form, while the MBPT(2) force field for ClOOCl is probably fairly accurate. Similarly, the oscillator strengths present4 by Jensen and Oddershede" may also have large uncertainties since the RPA method is only reliable for single-reference cases. The strong state mixing observed in our MRCC studies suggests that the RPA method may not provide a good description of the excitation process. It is unlikely, however, that the oscillator strength for the ClOOCl excitation near 250 nm is larger than that for CIClO, since the RPA values differ by 3 orders of magnitude and are probably not qualitatively in error. Calculation of the oscillator strength using more sophisticated models is an important area for further calculations and will be carried out with the FSMRCC method after this capability has been impiemented.
Conclusions Perhaps the most important conclusion to be drawn from the present study is that the C1202isomers,particularly the hypervalent straightchain ClOClO form and chloryl chloride, are extremely difficult to study theoretically. In fact, the strong infiniteorder effects obwwed in the study of the relative stabilitiesof these forms suggest that any results obtained with finite-order MBPT (also known as Moller-Plewt or MP perturbation theory) models for these isomers should not be regarded as quantitative by experimentalists who seek stabilities to better than 1 kcal/mol. Meaningful properties and relative energies for these systems must be determined with models including infiniteorder effects, such as the coupled-cluster approximation, or even multireference correlated treatments. For example, the multireference nature of CICIOz is comparable to that of ozone. Consequently, the MBPT(2) harmonic frequencies and infrared intensities for this molecule presented by McGrath et a1.6 may be no more reliable than are those for ozone. The harmonic force field of ozone has recently become a popular benchmark for quantum chemical method^.^^*^* It has been shown by this group and others that finitesrder MBPT models do an extremely poor job of predicting the harmonic frequencies of ozone, with the widely used MBPT(2) model overestimating the frequency of the antisymmetric stretching mode by more than lo00 cm-'. Therefore, in the absence of higher level calculations or definitive experimental observations, one must be ready to assume that the MBPT(2) force field of CIC102is no better than that for ozone. The same is true
Although the calculations of excitation energies and relative stabilities of CI2O2isomers presented here are by far the most extensive yet carried out on this system, they are still not conclusive. Quantum chemical calculations alone are still a long way from solving the problem of the Antarcticozone hole. The difficult nature of the C1202systems necessarily demands high-level infinitesrder treatment of electron correlation and very large basis sets. We have succeeded only in showing that the peroxide is mmr likely the lowest energy structure with a predicted dissociation energy in good agreement with accurate experimental values. Furthermore, we have demonstrated that the ClOOCl and CIC102 isomers can absorb UV radiation near 250 nm and that the upper state in each case involves the population of a CI-O antibonding orbital. This latter finding contradicts the assumption of Eberstein12regarding the photodissociation of ClOOCl and therefore vitiates his argument regarding the photodissociation products in the near-UV region. Consequently, high-level quantum chemical calculations do not rule out the importance of the role of C10 in polar omne depletion. Perhaps most important, our studies agree well with the laboratory studies which show that ClOOCl is the major (if not the sole) product of C10 recombination at temperatures and pressures characteristic of the polar stratosphere.' In addition, they provide added confidence to studies which find chlorine atoms (and C100, which subsequently decomposes to C1 and 0,)to be the major products of CI2O2photolysis1° and to in situ observations of C10 which indicate that ClOOCl is the nighttime reservoir of C10 in the wintertime polar stratosphere.29
(27) Salter, E. A.; Truclrs, G.W.; Bartlett, R.J. J. Chem. Phys. 1989,90, 1752. (28) Scumria, G. E.; Lee, T. J.; Scheiner, A. J.; Schaefer, H. F. J. Chem. Phys. 1989,90,5635. Raghavachari, K.;Trucks, G. W.; Poplc, J. A.; Replogk, E. Chem. Phys. L r r f . 1989, 158,207. Lee,T. J.; Scuseria. G. E.J . Chem. Phys. 1990,93,489.
SUmlMry
Acknowledgment. This work was made possible by grants from the Florida State SupercomputingCenter and the United States Air Force Office of Scientific Research (Contract no. 90-0207). (29) Toohey, D. W.; Anderson, J. G.; Brunc, W. H.; Chan, K.R.Science, submitted for publication.
Slgn of Circular Dkhrolsm Induced by &Cyclodextrin Masato Kodrka National Chemical Laboratory for Industry, Tsukuba, Ibaraki 305, Japan (Received: November 2, 1990) On the basis of the coupled oscillator theory, the circular dichroism induced by j3-cyclodextrin (8-CDx) is calculated. It is revealed from the calculation that outside the cavity of j3-CDx the sign of the induced circular dichroism (ICD) becomes opposite to that inside it; namely, outside the cavity of j3-CDx an electric transition polarized along the axis of the cavity gives negative ICD while a transition polarized normal to it affords positive ICD. The present rule is supported qualitatively in view of the dipole-dipole interaction between a transition moment of a chromophore and an individual bond in j3-CDx.
Introduction I n d u d circular dichroism (ICD) has been frequently utilized to obtain the orientation of an aromatic molecules involved in cyclodextrin (CDx)'* or to determine the direction of a transition
moment of a Using the Kirkwood-Tinow expression based on the coupled oscillator theory,12Harata et al.' (1) Harata, K.;Uedaira, H.Bull. Chem. Soc. Jpn. 1975. 48, 375.
0022-3654/91/2095-21 lOS02.50/0 0 1991 American Chemical Society
Letters
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2111 -ol
*,"
-1 0
-20
0
10
20
(A, Figure 2. Dependence of the calculated rotational strength (&/h2) on the position of a chromophore (I): (a) 4 = OD, (b) 4 = 90°. 2
(C)
Figure 1. Schematic figures of a chromophoreand cyclodextrin (CDx). (a) An example of a chromophore located inside CDx. (b) An example of a chromophorelocated outside CDx. (c) Relation between the position of a transition moment and the structure of &CDx.
and Shimizu et al." derived a rule that inside the cavity of &CDx (Figure 1a) a transition with an electric transition moment parallel to the axis of 8-CDx cavity gives positive ICD while that perpendicular to it brings about negative ICD. Recently many researchers modified BCDx into functional host molecules such as artificial enzymes, in which anchored functional groups are situated either inside or outside the Although the rule between the direction of a transition and a sign of ICD inside the cavity is already presented, no principles have been offered so far (2)Shimizu, H.;Kaito, A.; Hatano, M. Bull. Chem. Soc. Jpn. 1979,52, 2678. (3) Shimizu, H.; Kaito, A.; Hatano, M. Bull. Chem. Soc. Jpn. 1981,54, 513. (4)Shimizu, H.; Kaito, A.; Hatano, M. J. Am. Chem. Soc. 1982,104, 7059. (5) Kobayashi, N.;Saito, R.; Hino, H.;Hino, Y.; Ueno, A.; Osa, T. J . Chem. Soc., Perkin Trans. 2 1983,1031. (6)Ueno, A.; Moriwaki, F.; Osa, T.; Hamada, F.; Murai, K. J. Am. Chem. Soc. 1988,110,4323. (7) Ueno, A.; Suzuki, I.; Osa, T. J. Am. Chem. Soc. 1989,1 1 1 , 6391. (8) Kobayashi, N.J. Chem. Soc., Chem. Commun. 1988,918. (9)Komiyama, M.; Takeshige, Y. J. Org. Chem. 1989,54,4936. (10)Yamaguchi, H.;Higashi, M.; Oda, M. Spectmchim. A d a 1988,I I A , 547. (11) Kobayashi, N.; Minato, S.;Osa, T.Makromol. Chem. 1983,184, 2123. (12)Tinoco, 1. Jr. Ado. Chem. Phys. 1962, 4, 113. (13) Tabushi, 1.; Kuroda, Y.; Shimokawa, K. J. Am. Chem. Soc. 1979, 101,4759. (14)Tabushi, I.; Yuan, L. C. J . Am. Chem. Soc. 1981,103, 3574. (15) Fujita, K.; Ueda,T.; Imoto, T.; Tabushi, I.; Toh, N.; Koga, T. Eimrg. Chem. 1982,11, 108. (16)Fujita, K.; Ueda, T.; Imoto, T.;Tabushi, I.; Toh, N.; Koga,T. Eioorg. Chem. 1982,11, 72. (17)Yoon, C.-J.; Ikeda, H.; Kojin, R.; Ikeda, T.; Toda, F. J. Inclusion Phemm. 1987,5,85. (18) Ikeda, T.; Kojin, R.; Yoon, C.-J.; Ikeda, H.; Iijima, M.; Toda, F. J. Inclusion Pheom. 1987,5,93. (19)Nakamura. A.; Saitoh, K.; Toda, F. Chem. Lett. 1989,2209. (20)Ueno, A.; Minato, S.;Suzuki, I.; Fukushima, M.;Okubo, M.; h, T.;Hamada. F.; Murai, K. Chem. Lett. 1990.605. (21)Pamt-Lopez,H.; Djedaini, F.; Perly, B.;Coleman, A. W.;Galons, H.; Miocque, M. Tetrahedron Lett. 1990, 31, 1999.
I Figure 3. Definition of geometric parameters for a parallel-polarized transition moment (4 = )'0 and a bond in 8-CDx.
when a chromophore is placed outside CDx (Figure lb). Such principles could be used to estimate the orientations of such anchored chromophores when they are located outside. In a previous paper, the author reported that an opposite rule holds when a chromophore was located outside the cavity of a-CDx.2z The question is raised, in this stage, whether this tendency is observed also in other CDx's. There are three types of CDx (a-, P-, and y-CDx) commonly used, within which 8-CDx is most familiar in the so-called host-guest chemistry because of its pore size, solubility, and other proper physicochemical properties. In the present work, thus, ICD is calculated for 8-CDx by using the coupled oscillator theory. The author tries, furthermore, to interpret the sign of ICD from the viewpoint of the geometric relation between a transition moment and an individual chemical bond of CDx.
Calculation Method The rotational strength corresponding to the transition from a ground state (0) to an excited state (a), &,was calculated in a similar manner as that in the previous studyz2 using the Kirkwood-Tinoco equation (1) based on the coupled oscillator theory.I2 %, = *U&2C
-aIl)p)j c(uo,Z - u.2)
vojYa33
i
Here ej is the unit vector in the direction of the symmetry axis of a bond j in 8-CDx, r, is the vector directed from the center of a chromophore to a bondj, rj is the absolute value of the vector (22)Kodaka,M.; Fukaya, T. Bull. Chem. Soc. Jpn. 1989.62, 1154.
2112 The Journul of Physical Chemistry, Vol. 95, No. 6,1991
Letters Then from eq 1 (GF), and a(GF),/dZ have the following form.
1.o
c
4222 sin a - 3 zu cos a sin 8 - u2 sin a) cos a cos @
A
WF), -=
az
1
-0.5 -1.0
L
-6
-2
-4
0
2
4
[a(-6z3 sin a
+ 12z2ucos a sin b +
9zu2 sin a -
3a3 cos a sin 6) cos a cos 8](zz
+ u2)-7/2(4)
Here (GF), is assumed to have a positive maximum at z = 0; that is,
6
zla
Fiture 4. Dependence of (GF),on the position of a chromophore ( Z / o ) for a parallel-polarized transition (0 = O O ) .
(GF), = -
cos a cos 6 sin a
>O
a2
(5)
and
r,, yo, is the frequency of the electric transition of a bond j , is the unit vector in the direction of the electric transition moment (p ),, in a chromophore with its frequency v,, a33 and allare bond polarizability at zero frequency, parallel and perpendicular to the symmetry axis of each bond, respectively, in B - C D X ,and ~ ~ c is the velocity of light. The geometry of 8-CDx was determined from the X-ray crystalline data of ~CDx-l,ediazabicycl0[2.2.2]octane complex.23 The axes of the coordinates were defined as shown in Figure 1. All the C6-06 and 0-H bonds were neglected due to the flexibility, and all C-H bonds were also neglected since they may have isotropic polari~ability.~~
R d Q and Discussion In Figure 2 is shown the dependenceof the calculated rotational strength, which is represented by R,,,/k2,on the Z coordinate. Inside the cavity of &CDx a transition polarized parallel to the axis of 8-CDx (2axis) brings about positive ICD while that perpendicular to the axis gives negative ICD, which is in good agreement with the rule found by Harata et a1.I Outside the cavity, however, the sign of ICD is found to be entirely inverted, especially prominently on the negative side of z (narrower rim of O-CDX). Although the calculated R,,, value may be the superimposition of the individual rotational strength of the each bond in CDx, in the Kirkwood-Tinoco expression the mcwt dominant factor determining the sign of individual rotational strength is the geometry term, (GF),, It seemed particularly interesting, therefore, to compare the behavior of &, with that of (GF),. In the case where a transition moment is parallel to the axis of P-CDx, the coordinate system (X,Y,Z) and the geometric parameters can be defined as shown in Figure 3 and the following equations hold. e,=k e, = (cos a sin @)i (cos a cos 8)j (sin a)k = ai - zk we, = sin a eol-r, = -z e,-' = u cos a sin 8 - z sin a X e p , = -a cos a cos 6 (2)
+
+
From eqs 5 and 6 sin 8 = 0 cos a cos fl sin a
(7)
