J. Phys. Chem. 1994, 98, 11918-11923
11918
Solvent Effects on the Oxygen-Organic Molecule Charge-Transfer Absorption Yasunao Kuriyama and Peter R. Ogilby* Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131
Kurt V. Mikkelsen” Department of Chemistry, Aarhus University, DK-8000 Aarhus C, Denmark Received: February 18, 1994; In Final Form: May 24, 1994@
Molecular oxygen and 1-methylnaphthalene form a ground-state “contact complex”, which can absorb light to populate a charge-transfer (CT) state. The effect of solvent on this transition has been examined. The onset of this cooperative absorption linearly shifts to a longer wavelength with an increase in the parameter (n2 - 1)/(2n2 l ) , where n is the solvent refractive index at optical frequencies. The data do not correlate with functions in which the static dielectric constant of the solvent is used. These results are consistent with (a) a ground-state complex that does not have substantial charge separation, and (b) a solute-solvent interaction in the Franck-Condon CT state that is most likely dominated by dipolar coupling terms. Recent studies indicate that the CT state lifetime is approximately the same as the time required for solvent orientational relaxation. As a consequence, envisioning the CT state principally as a Franck-Condon state is likely to be accurate for many common organic solvents. From this perspective, the spectroscopic data reported herein should be useful in attempts to estimate the relative energy of the CT state in a given solvent.
+
Introduction Ground-state molecular oxygen (X3Zg-) can interact with a variety of organic molecules M, giving rise to a distinct absorption. This phenomenon was first reported by Evans’ 40 years ago and has since been studied e x t e n s i v e l ~ . ~When - ~ the organic component is in high concentration, such as in neat liquids or solid polymers, this feature usually appears as a red shift in the absorption Under dilute conditions, however, either in the gas phase or in an “inert” solvent, it is possible to discern a unique oxygen-dependent absorption band upon subtraction of the absorption profile due to M.5-7 In a seminal 1960 paper, Tsubomura and Mulliken4 assigned this absorption to a transition from a ground-state M-02(X3Zg-) complex to the M-02 charge-transfer (CT) state. A great deal of evidence indicates that the ground-state complex is weakly bound at best and is perhaps better characterized as a “contact” complex in which there is only fleeting overlap between the M and 0 2 orbital^.^^^^^.'^^^^ The CT state is often represented as an excited-state complex with radical cation and radical anion character (M’+O2*-). As such, it can exist as either a singlet or triplet spin state. Because the ground-state complex has triplet spin multiplicity, the allowed transition forms the triplet CT state (Scheme 1). Theoretical and experimental studies indicate that the M-02 CT state plays an important role in the oxygen-organic molecule p h o t o s y ~ t e m . ~ . ~ The , ~ , ~extent ~ - ~ ~ to which the CT state participates in a given process, either directly or indirectly, depends in part on the CT state energy. The quenching of an organic molecule triplet state (3M1) by oxygen provides an important example. As depicted in Figure 1, when the CT state is substantially higher in energy than the 1.3,5[3M1-02(X3Zg-11 states, the quenching process does not directly populate the CT state. However, coupling between the CT and 1,3.5[3M1* O2(X3Cg-)] states imparts CT character into the latter, which would otherwise not have a lot of charge separation. The extent to
* Authors to whom correspondence should be addressed. @Abstractpublished in Advance ACS Abstracts, October 15, 1994.
0022-365419412098-11918$04.5010
Isolated Molecule
Complex States
Isolated Molecule
Figure 1. Diagram showing several states of the oxygen-organic
molecule complex.
SCHEME 1
which the 1,3,5[3M1--02(X3&-)] states acquire CT character influences the efficiency of 02(a1Ag)production and, thus, can have important photochemical consequences. The CT state energy depends in part on (a) the ionization potential (IP) of M, (b) the electron affinity (EA) of oxygen, and (c) interactions with the solvent that not only influence the stability of the respective ions M’+ and 02’- but also mitigate Coulombic forces between M’+ and 0 2 ’ - .
ECT FZ IP, - EAoxygen - solvent interaction terms (1) For a CT state in equilibrium with the surrounding solvent, these
0 1994 American Chemical Society
Oxygen-Organic Molecule Charge-Transfer Absorption TABLE 1: Solvent Effects on the Onset of the 1MN-Oxygen Cooperative Absorption
~~
2,2,2-trifluoroethanol acetonitrile diethyl ether ethanol tetrahydrofuran cyclohexane 1,2-dichloroethane carbon tetrachloride toluene benzene chlorobenzene benzonitrile bromobenzene
1.290 1.342 1.351 1.359 1.405 1.424 1.444 1.458 1.494 1.498 1.522 1.526 1.557
26.7 37.5 4.2 24.3 7.4 2.0 10.4 2.2 2.4 2.3 5.6 25.7 5.4
12.0' 7.54 12.2 8.22 8.29 9.53 6.17 10.3 8.19 7.51 7.28 8.10' 5.88
336.1 344.8 335.0 342.0 352.5 345.5 350.0 349.5 359.0 355.5 359.5 360.0 358.5
Refractive index at the sodium D line, 25 "C. * Static dielectric constant. Oxygen concentration in an oxygen-saturated solution at 630 Torr. Units are M. Calculated from data in ref 30. Wavelength at which the quantity absorbance/[Oz] = 2.0. Data are from the spectrum obtained when the deoxygenated 1MN spectrum is subtracted from the oxygenated 1MN spectrum for a given solvent. e Estimated by using data from ref 30.
interaction terms vary with the static dielectric constant cst of the medium.26 [When using SI units, the latter is equal to the product of the relative (E*) and vacuum ( E O ) permittivities. In atomic units, est= E,.] Under these equilibrium conditions, the CT state is expected to be more stable in acetonitrile (est = 37.3, for example, than in cyclohexane (Est = 2.0). From this perspective, experiments designed to ascertain whether or not the CT state participates in a given process often involve a comparison of data recorded in solvents such as these, where the difference between Est values is large.18 Upon consideration of quantum mechanical as well as electrostatic terms, we can expand our perspective and draw potential surfaces for both the ground and CT states of the M-02 complex. In so doing, we assume that dispersion forces and perhaps some configuration interaction with the CT statelZb impart a slight binding energy to the ground-state complex (dissociation energy < 1 k c a l / m ~ l ) . ~ .Nevertheless, ~J~ the latter is still best characterized as a Mulliken contact complex that does not have significant charge separation. The CT state, however, is significantly more bound than the ground state due principally to the Coulombic forces arising from photoinduced charge separation.lZb We thus expect that a change in solvent will influence the CT state more than the M-02 ground state. Specifically, for a given solute M, solvent-dependent changes in the M-02 cooperative absorption band should principally reflect interactions between 3(M'+02*-)and the surrounding medium. To our knowledge, experiments that probe these interactions have heretofore not been reported. Thus, we set out to examine the effect of solvent on the M-02 CT absorption band and ascertain whether or not the data conform to established theoretical models. Furthermore, we set out to determine if the spectroscopic transitions that form the FrunckCondon CT state could be used to better understand phenomena that ultimately influence the extent to which other states of the M-02 complex acquire CT character. Experimental Section All solvents (Table 1) were obtained from Aldrich (HPLC or spectroscopic grade) and used as received. Solute molecules whose M-02 CT absorption was studied, 1-methylnaphthalene [ lMN] and 1-methoxynaphthalene [lMON] (Aldrich), were purified by chromatography on silica gel prior to use. Solutions
330
339
348
357
366
375
wavelength (nm)
Figure 2. Absorption onset for 0.3 M I-methylnaphthalene dissolved in deoxygenated (- - -) and oxygenated (-) benzene.
were deoxygenated by gentle bubbling with nitrogen gas for 30 min. Oxygen-saturated solutions were prepared by bubbling with oxygen gas for 30 min. Absorption spectra were recorded on a Beckman model DU40 spectrophotometerusing 1-cm path length cells. Background data were obtained by recording the spectrum of each solvent saturated with nitrogen gas. The background spectrum for each solvent was subtracted from the corresponding spectrum of the dissolved solute. In some cases, the difference between the solvent refractive index (see Table 1) and the refractive index of the solute [nD(lMN) = 1.6159, n ~ ( l M 0 N )= 1.6211 is sufficiently large that light scattering could potentially mask the onset of absorption. All spectra (e.g., Figure 2), however, were obtained from solutions 0.3 M in solute, which is in a domain where the quantity measured as absorbance depends linearly on the solute concentration in accordance with the Beer-Lambert law. Thus, errors due to light scattering are not likely to influence the data. Results 1-Methylnaphthalene (1MN) is an appropriate molecule for this study for several reasons: (1) It readily dissolves in a variety of solvents. (2) The 1MN-02 CT absorption is red-shifted relative to the solvent-02 CT absorption in many common organic solvents. (3) Because the 1MN triplet-state energy is low (59.6 kcal/mo1),18 oxygen-induced 'Mo 3M1transitions in 1MN appear in a spectral region (-400-500 sufficiently red-shifted relative to the 1MN-02 CT transition (Figure 2). [The ambient pressure used in the present study (-630 Torr), however, is low enough to preclude observation of the induced absorption to the triplet state.] Given the nature of the M-02 cooperative transition in liquid solvents, it is necessary to examine changes in the absorption onset instead of the band maximum. Thus, this approach must also be used in control experiments where the spectra of deoxygenated 1MN are examined. In nitrogen-saturated solutions, the onset of 1MN absorption is solvent dependent. This absorption arises from the allowed transition that populates the *(n,n*) state of 1MN. In working with data such as those shown in Figure 2, it is necessary to define a parameter characteristic of each spectrum that can be used for analysis. We choose to use the wavelength (in nanometers) at which the absorbance is 0.02, denoted by A ( A = 0.02).28 On the basis of the discussion presented in the next section, A (A = 0.02) can be examined as a function of the solvent parameter (n2 - 1)/(2n2 f l), where n is the solvent refractive index at optical frequencies. Values of ;1 ( A = 0.02) obtained from the 1MN data in nitrogen-
-
,
11920 J. Phys. Chem., Vol. 98, No. 46, 1994
370 360
Kuriyama et al.
likewise linear but have a slope approximately 1.4 times larger than that obtained from the 1MN data (Le., the CT absorption onset shifts further to the red as n is increased).
Discussion
x
350
I
I 0 17
0.14
02
0.23
0.26
From Scheme 1 and the Beer-Lambert law, the absorbance due to the CT transition in a cell of path length I depends on the product of the absorption coefficient ECT and the concentration of the ground-state M-02 complex (eq 2). The latter, in A,
= ZrcT[complex] = k,Keq[ 1MN][02(X3Zg-)] ( 2 )
(n'-~)i(~n'+~)
Figure 3. Wavelength at which the absorbance equals 0.02 vs (n2 1)/(2n2 l), where n is the solvent refractive index. Data marked by
+
filled circles were obtained from oxygenated 1-methylnaphthalene solutions, and data marked by open circles were obtained from deoxygenated 1-methylnaphthalenesolutions. The solid lines are linear least-squares fits to the data.
360
330
i
1
320 0.14
02
0 17
0 23
0 26
(n'-l)i(~n'+I )
Figure 4. Wavelength at which the quantity absorbance/[Oz]equals 2 vs (n2 - 1)/(2n2 l), where n is the solvent refractive index. The data were obtained from the spectrum that results when the deoxygenated 1-methylnaphthalenespectrum for a given solvent was subtracted from the oxygenated 1-methylnaphthalenespectrum in the same solvent. The solid line is a linear least-squares fit to the data.
+
saturated solutions increase slightly with an increase in (n2 1)/(2n2 1) (Figure 3). Upon saturating solutions of 1MN with oxygen, the absorption onset shifts to a wavelength longer than that observed in the corresponding nitrogen-saturated solutions (Figure 2). This is characteristic of the transition to form the M-02 CT state. This absorption onset is likewise solvent dependent, but the magnitude of these latter changes is much larger than those observed in the deoxygenated solutions. Values of 2 (A = 0.02) obtained from the oxygenated solutions show a substantial increase with the increase in (n2 - 1)/(2n2 1) (Figure 3).28 In an attempt to reduce the number of variables that contribute to the observed phenomenon and focus principally on the M-02 CT transition, the spectrum of 1MN recorded in a nitrogensaturated solution was subtracted from the corresponding spectrum of an oxygenated 1MN solution.29 The absorbance obtained from these difference spectra was then normalized by the oxygen concentration in the given solvent (Table 1). The parameter 2 (A/[O2] = 2.0), which denotes the wavelength at which absorbance/[02(X3Zg-)] = 2.0, depends linearly on the parameter (n2 - 1)/(2n2 1) with a correlation coefficient of 0.92 (Figure 4).28 When these same data are plotted against functions of the solvent dielectric constant E,, (vide infra), no correlation is observed. When the parameter il(Al[O2] = 2.0) obtained from solutions of lMON is plotted against (n2 - 1)/(2n2 l), the data are
+
tum, can be expressed in terms of the equilibrium constant for complex formation Kes and the concentrations of ground-state oxygen and 1MN. Although we normalized the absorbance data for solventdependent changes in [02(X3Zg-)], solvent-dependent changes in Kq are difficult to q ~ a n t i f y .However, ~ on the basis of the assumption that the M-02 ground state does not have significant charge separation, we suggest that the solvent dependence of Keq is likely to be small compared to the solvent dependence of both and the energy gap between the M-02 ground and CT states. The effect of solvent on solute radiative transitions has been a subject of experimental and theoretical study for many y e a r ~ . ~ ' -Recent ~j activity in which solvent effects on electrontransfer processes are examined has provided additional insight into this important problem, particularly with reference to transitions that involve a charge-transfer ~ t a t e . ~ ~ - j ~ The perspective used in the present analysis has been described in previous publication^.^^-^^ Briefly, the solute is perceived to exist in a spherical cavity defined by the solvent. The latter is approximated as a linear, homogeneous, and isotropic dielectric medium characterized by its macroscopic dielectric constants: (1) The static dielectric constant Est and (2) the optical dielectric constant cop,which is equivalent to the square of the refractive index n obtained at optical frequencies. The solute charge distribution (e) at any given time polarizes the dielectric medium. This induced polarization generates a reaction field that acts back on the solute within the solvent cavity. The dielectric solvation energy (i.e., polarization energy) for the nonequilibrium condition of a solvent-solute system under the influence of a high-frequency perturbation, such as a UV-vis electromagnetic field, is35$42-50
+
+
+
where is the total charge distribution of the solute (electronic and nuclear) at any given time and e' is the equilibrium charge distribution prior to the perturbation such as that found in the ground state in an absorption experiment. The R1, elements characterize the reaction field that interacts with the charge distribution e. For a spherical cavity, these elements are42,53-55
The coupling constants gl are expressed in terms of the radius
Oxygen-Organic Molecule Charge-Transfer Absorption rc of the cavity and the dielectric constants
E.
The magnitude of the dipolar ( 1 = 1) coupling constant differs from that of the quadrupolar ( 1 = 2 ) constant and so forth for larger moments in the multipole expansion. Thus, for example, the dipolar coupling term derived from the optical dielectric constant copis
J. Phys. Chem., Vol. 98, No. 46, 1994 11921 Thus, the transition energy AE(gs -. ex) for this generic solute is the difference between eqs 15 and 14 and depends on both the static and optical dielectric constants of the solvent. When the solute is the M-02 complex, however, the term AE(gs -.ex) thus obtained for the transition 3[1M~-*-02(X3Zgg-)] 3[M'+02'-] is much simpler than that described above. Specifically, when it is assumed that (a) 3[M'+02'-] has comparatively large charge moments and (b) there is almost no charge separation in the M-02 ground state, the difference between eqs 15 and 14 reduces to an expression that depends only on the optical dielectric constant cop of the solvent and the charge distribution Qex of the M-02 CT state (eq 16).
-
hE(gs -ex)
= ITx - Eps =
c, qic+ -
- l n 2-1 gl(Eop)= -rc3 2n2 1
+
where the substitution n2 = copwas made in eq 7b. The (Tlm(g))elements in eqs 4 and 5 are expectation values of the nuclear (n) and electronic (e) solvent operators,
where Z, is the charge and R, the position vector of the nucleus g and where
where t"(r) is a linear combination of conventional spherical polynomials!2 The subscriptsp and q correspond to the orbitals 4p and 4q,and apu+ and up. are the creation and annihilation operators for an electron in orbital q+, with spin 0. The spherical polynomial functions Tlmyield monopole, dipole, quadrupole, etc. terms when integrated over the solute charge distribution. We now consider a vertical electronic transition from the ground state (gs) to a Franck-Condon excited state (ex) of an arbitrary solute. In this transition, only the optical polarization vector of the solvent changes. The solvent inertial or orientational polarization vector does not change and corresponds to that for the charge distribution of the solute ground state. The ground-state energy is given as the sum of the energy in a vacuum E,,, and the solvation energy Esolas expressed in eq 3.
We describe the excited-state energy in a similar fashion.
Equation 16 is thus consistent with (a) the perspective outlined in the introduction and (b) the results of our spectroscopic measurements. Specifically,we expected that solvent-dependent changes in the M-02 cooperative absorption band would principally reflect the interactions between the CT state and the surrounding medium. The lack of a correlation between I (A/ [02] = 2.0) and functions of cst is consistent with an M-02 ground state that has vanishing charge moments. Furthermore, we indeed observe a reasonably good correlation between A (A/ [ 0 2 ] = 2.0) and a function of the optical dielectric constant. In choosing the latter, we used the relationship shown in eq 7b, which derives from the dipolar solute-solvent coupling term. These data are shown in Figure 4. When values of I (A/[02] = 2.0) are plotted against (n2 - 1)/(3n2 2), which is proportional to the quadrupolar coupling term (i.e., 1 = 2 in eq 6), an equally good correlation is observed. However, because the quadrupolar term is a factor of rc2smaller than the dipolar term, we suggest that the dipole contribution to solute-solvent coupling influences the M-02 CT transition most. The 1-methoxynaphthalene (1MON) data are also consistent with eq 16. lMON has a lower ionization potential than does 1MN. In a given solvent, the 1MON-02 CT state should thus be lower in energy than the 1MN-02 CT state. Indeed, the CT absorption onsets for oxygenated lMON solutions are all red-shifted relative to those in 1MN solutions. Furthermore, this difference in ionization potentials also yields a different M-02 solute charge distribution e (specifically, the 1MON0 2 CT state has a larger dipole moment than the 1MN-02 CT state). This in tum results in a different induced solvent reaction field. The latter is manifested as a change in the slope of the I ( A 4 0 2 1 = 2) vs (n2 - 1)/(2n2 1) plot. As an extension of this phenomenon and from eq 16, if the dipole moment of one CT state is known (e.g., lMN'+02'-), then the above-mentioned slopes can be used to determine the dipole moment of the second CT state (e.g., 1MON'+02'-). It should be noted that the observed spectral shifts could also derive from solvent-induced changes in the transition probability (Le., ECT in eq 2). For example, because of solvent-dependent changes in the potential surface of the CT state, a corresponding change in Franck-Condon factors for this transition could be manifested as a spectral shift. With respect to this specific point, however, recall that the M-02 ground state is weakly bound and thus has an extremely shallow potential surface. Thus, we suggest that Franck-Condon factors for this transition will not be particularly sensitive to even large changes in the excited state potential surface. Nevertheless, in the M-02 photosystem, the general phenomenon of solvent-dependent changes in the probability of radiative transitions, and the extent to which such
+
+
Kuriyama et al.
11922 J. Phys. Chem., Vol. 98, No. 46, 1994 changes are reflected in spectral shifts, is a problem that has yet to be fully understood despite having received a great deal of recent a t t e n t i 0 n . 5 ~On ~ ~the ~ basis of the limited data reported herein, the observed spectral shifts are at least consistent with principles embodied in eq 16. Available data indicate that the M-02 CT state has a lifetime ( r 5 10 ps) approximately the same as the time required for solvent reorientation. Rotational correlation times for the solvents listed in Table 1 range from 1 ps for acetonitrile to -20-30 ps for some of the larger molecules that comprise a more viscous medium.52,59-61 Thus, in a solvent such as benzonitrile, it is likely that the M-02 CT state lifetime is short enough to preclude the formation of an excited state surrounded by an equilibrated solvent. Under these conditions, (a) the CT state will principally be stabilized by induced, rather than permanent, charge moments in the solvent (we suggested above that, of these moments, the dipolar terms are likely to be most important), and (b) spectroscopic data such as those in Figure 4 will accurately reflect the CT state energy. On the other hand, in the comparatively nonviscous medium acetonitrile, where rotation of the small solvent molecules is facile, we expect that rapid solvent rotational relaxation will yield a CT state principally stabilized by permanent dipoles in the solvent. Because acetonitrile (a) does not readily yield large induced dipoles (i.e., the solution is characterized by a small optical dielectric constant) and (b) has a comparatively large permanent dipole (i.e., the solution is characterized by a large static dielectric constant), the energy difference between the FranckCondon CT state and the solvent-equilibrated CT state in acetonitrile is large. Thus, for this particular solvent, the spectroscopic data shown in Table 1 and Figure 4 are not representative of the equilibrium CT state energy. The importance of dispersive, as opposed to electrostatic, interactions in stabilizing the M-02 CT Franck-Condon state is clearly illustrated by the 1MN data recorded in acetonitrile and benzonitrile. Both of these solvents have a comparatively large static dielectric constant est. Values of A (A/[02] = 2 ) obtained in these seemingly similar solvents, however, are strikingly different, exhibiting one of the largest spectral shifts observed in this study. The 1MN absorption onset in benzonitrile is red-shifted relative to the absorption onset in acetonitrile. This is consistent with the phenyl group in benzonitrile being more polarizable than the methyl moiety of acetonitrile, as reflected in the respective refractive indexes. Thus, a rapid change in the charge distribution of the 1MN-02 complex upon photon absorption will more effectively induce a corresponding change in benzonitrile than in acetonitrile. These induced dipoles in benzonitrile will consequently better stabilize the CT Franck-Condon state. In the introduction, we indicated that the CT state can play an important role in the M-02 photosystem. In order to ascertain exactly how, and to what extent, the CT state participates in a given system, it is important to quantify the CT state energy. For example, if the CT state is lower in energy than the 1,3*5[3M1** -02(X3Gg-)]states, then it is possible to directly populate the CT state upon oxygen quenching of a triplet-state photosensitizer. On the other hand, the CT state may be sufficiently high in energy that CT character can only be indirectly acquired by lower-lying M-02 states through configuration interaction (i.e., a high activation barrier to electron transfer precludes direct population of the CT state in a thermal reaction). In such analyses, should one consider the FranckCondon (FC) or solvent-equilibrated (SE) CT state? We first address the case in which the CT state is energetically inaccessible and is thus not directly populated. The mixing of
states in the M-02 complex can be represented in a model presented by Mulliken62in which the wavefunction Y for one particular state is expressed as a linear combination of zeroorder wavefunctions q5 for all available M-02 states.
16323,24
These zero-order wavefunctions are expressed in terms of electronic and nuclear coordinates of both the solute (i.e., the M-02 complex) and the surrounding solvent. With the exception of the CT state, zero-order states of the M-02 complex are not expected to have much charge separation (vide supra). As a consequence, solvent nuclear position vectors for these predominantly neutral states should (a) all be somewhat similar, (b) differ substantially from those in the solventequilibrated CT state, and (c) be the same as those in the Franck-Condon CT state. From this perspective, it appears likely that the overlap of nuclear wavefunctions will favor mixing with the Franck-Condon CT state rather than the solvent-equilibrated CT state [i.e., in eq 17, e 2 f f o r Y that represents a lower-lying state such as 'M0.e *02(b1C,+)]. From perturbation theory, one might expect the extent of this state mixing to be inversely dependent on the energy gap between the CT and pertinent valence M-02 states. Thus, the spectroscopic data presented in Table 1 and Figure 4 should be useful in attempts to ascertain whether or not configuration interaction with the CT state plays an important role in a given solvent system. When the CT state is energetically accessible in a thermal reaction from a valence M-02 state (e.g., the 1,3,5[3M1* * Q(X3Cg-)] states), the electron-transfer theory of Marcus, and modifications thereof, can be applied.63@ Under these conditions, the activation barrier to electron transfer depends in part on a solvent reorganizational term that reflects the difference between the Franck-Condon and solventequilibrated CT states. Thus, even when the CT state is energetically accessible in a thermal reaction, the spectroscopic data reported herein should be useful in attempts to characterize the extent of CT state participation. The relevance of the preceding discussion is embodied in a recent paper by Wilkinson et al.65 For a series of substituted naphthalenes, these authors examined the influence of CT interactions on (a) the photosensitized yield of 02(a1A,) and (b) the rate constant for quenching of the naphthalene triplet state by 02(X3Z,-). Wilkinson finds that when the solventequilibrated CT state is lower in energy than the 3M1..-02(X3Cg-) states, the rate constant for oxygen-induced 3M1 deactivation 3k behaves according to a model in which there is an activation barrier AG* for electron transfer (eq 18).
3k = exp(-AG*lRT)
(18)
From Marcus theory, AG* was expressed as a function of a solvent reorganization term (A) and the energy of the solventequilibrated CT state. When the energy of the solventequilibrated CT state is greater than that of the 3M1. * -02(X3&-) states, however, Wilkinson's 3k data are substantially larger than what is predicted by eq 18. It thus appears that when the CT state is thermally less accessible, key features of the mechanism for 3M1 deactivation indeed change. We propose that under these latter conditions, the 3M1.* -02(X3C,-) complex acquires CT character via state mixing. Thus, 3k should not only have a different functional dependence on the energy of the solvent-
Oxygen-Organic Molecule Charge-Transfer Absorption equilibrated CT state but should also depend on the energy of the Franck-Condon CT state as already described. In summary, the CT state lifetime in some solvents may indeed be somewhat shorter than the solvent rotational con-elation time. For these systems, (a) it is thus reasonable to envision the CT state as a Franck-Condon state stabilized principally by induced, rather than permanent, dipoles in the solvent, and (b) the spectroscopic data reported herein should be useful in an attempt to determine the energy of the CT state. In many common solvents, however, it is likely that the CT FranckCondon state will relax somewhat to yield a CT state stabilized by both induced and permanent moments in the solvent. Under these circumstances, care must be exercised in using spectroscopic data to quantify the CT state energy.
Acknowledgment. This work was supported by the Army Research Office in a grant to P. R. Ogilby and the Statens Naturvidenskabelige Forskningsraad (Denmark) in a grant to K. V. Mikkelsen. The authors thank D. J. Keller, M. R. Ondrias, and J. V. Ortiz for helpful discussions. References and Notes (1) Evans, D. F. J . Chem. Soc. 1953,345-347. (2) Tames, M.; Strong, R. L. In Molecular Association; Foster, R., Ed.; Academic Press: London, 1979;Vol. 2,pp 331-456 and references cited therein. (3) Munck, A. U.;Scott, J. F. Nature 1956,177,587. (4) Tsuhomura, H.; Mulliken, R. S. J . Am. Chem. Soc. 1960,82,59665974. (5)Lim, E. C.; Kowalski, V. L. J . Chem. Phys. 1962,36,1729-1732. (6) Birks, J. B.; Pantos, E.; Hamilton, T. D. S. Chem. Phys. Lett. 1973, 20.544-546. (7) Gooding, E. A.; Serak, K. R.; Ogilby, P. R. J . Phys. Chem. 1991, 95,7868-7871. (8) Scurlock, R. D.; Ogilby, P. R. J. Phys. Chem. 1989,93,54935500. (9) Ogilby, P. R.; Kristiansen, M.; Clough, R. L. Macromolecules 1990, 23,2698-2704. (10)Orgel, L. E.; Mulliken, R. S. J . Am. Chem. Soc. 1957, 79,48394846. (1 1) Grover, J. R.; Hagenow, G.; Walters, E. A. J . Chem. Phys. 1992, 97,628-642. (12) (a) Kawaoka, K.; Khan, A. U.; Kearns, D. R. J . Chem. Phys. 1967, 46,1842-1853 (Erratum: J . Chem. Phys. 1%7,47,1883-1884). (b)Khan, A. U.; Kearns, D. R. J . Chem. Phys. 1968,48,3272-3275. (13) Murrell, J. N. Mol. Phys. 1960,3, 319-329. (14) Garner, A.; Wilkinson, F. Chem. Phys. Lett. 1977,45, 432-435. (15) McGarvey, D. J.; Szekeres, P. G.;Wilkinson, F. Chem. Phys. Lett. 1992,199,314-319. (16) McGarvey, D. J.; Wilkinson, F.; Worrall, D. R.; Hobley, J.; Shaikh, W. Chem. Phys. Lett. 1993,202,528-534. (17) Redmond, R. W.; Braslavsky, S. E. Chem. Phys. Len. 1988,148, 523-529. (18) Kristiansen, M.; Scurlock, R. D.; Iu, K.-K.; Ogilby, P. R. J . Phys. Chem. 1991,95,5190-5197. (19) Ogilby, P. R.; Sanetra, J. J . Phys. Chem. 1993,97,4689-4694. (20)Wang, B.; Ogilby, P. R. J. Phys. Chem. 1993,97,9593-9598. (21) Onodera, K.;Furusawa, G.; Kojima, M.; Tsuchiya, M.; Aihara, S.; Akaba, R.; Sakuragi, H.; Tokumaru, K. Tetrahedron 1985,41,2215-2220. (22) Darmanyan, A. P.; Foote, C. S. J . Phys. Chem. 1992,96,63176321. (23) Logunov, S.L.; Rodgers, M. A. J. J . Phys. Chem. 1992,96,29152917. (24)Logunov, S. L.; Rodgers, M. A. J. J . Phys. Chem. 1993,97,56435648. (25) Ogilby, P.R. Singlet Oxygen Photophysics; Wiley: New York, in preparation.
J. Phys. Chem., Vol. 98, No. 46, 1994 11923 (26) Gilbert, A.;Baggott, J. Essentials of Molecular Photochemistry; CRC Press: Boca Raton, E,1991;pp 159-160. (27) Evans, D. F. J. Chem. Soc. 1957,1351-1357. (28) The data were also analyzed by using the wavelength at other absorbance values. The results thus obtained were consistent with those shown in Figures 3 and 4. (29) (a) Because the nitrogen- and oxygen-saturated spectra of a given solution were recorded sequentially, this treatment also reduces errors that arise from spectrometer baseline drift and gratindfilter changes that contribute, in part, to the scatter in Figure 3. (b) For reasons not apparent to us, the unsubtracted 1,2-dichloroethane data did not follow the trends shown in Figure 3. Thus, these data were not included in the plot. The subtracted 1,2-dichloroethane data are included in Figure 4,however, and follow the trend exhibited by the other solvents. (30)(a) Murov, S. L.; Carmichael, I.; Hug, G. L. Handbook OJ Photochemistry, 2nd ed.; Marcel Dekker: New York, 1993. (b) Achord, J. M.; Hussey, C. L. Anal. Chem. 1980,52,601-602. (c) Sawyer, D.T.; Chiericato, G.; Angelis, C. T.; Nanni, E. J.; Tsuchiya, T. Anal. Chem. 1982, 54, 1720-1724. (31) Mataga, N.; Kubota, T. Molecular Interactions and Electronic Spectra; Marcel Dekker: New York, 1970. (32) Bayliss, N. S.;McRae, E. G. J . Phys. Chem. 1954,58, 10021006. (33) McRae, E. G. J . Phys. Chem. 1957,61,562-572. (34) Amos, A. T.; Burrows, B. L. Adv. Quantum Chem. 1973,7,289313. (35)Karelson, M. M.; Zemer, M. C. J . Phys. Chem. 1992,96,69496957. (36)Marcus, R. A. J. Chem. Phys. 1965,43,1261-1274. (37)Marcus, R. A. J . Phys. Chem. 1989,93,3078-3086. (38) Hush, N. S. Electrochim. Acta 1968,13, 1005-1023. (39)Li, B.; Peters, K. S. J . Phys. Chem. 1993,97, 13145-13148. (40)Niwa, T.; Kikuchi, K.; Matsusita, N.; Hayashi, M.; Katagiri, T.; Takahashi, Y.; Miyashi, T. J . Phys. Chem. 1993,97,11960- 11964. (41) Gould, I. R.; Noukakis, D.; Goodman, J. L.; Young, R. H.; Farid, S. J . Am. Chem. Soc. 1993,115, 3830-3831. (42) Mikkelsen, K. V.; Agren, H.; Jensen, H. J. A.; Helgaker, T. J . Chem. Phys. 1988,89, 3086-3095. (43) Mikkelsen, K. V.; Dalgaard, E.; Swanstrom, P. J . Phys. Chem. 1987, 91,3081-3092. (44) Mikkelsen, K. V.; Agren, H. J . Phys. Chem. 1990,94,6220-6227. (45) Mikkelsen, K.V.; Jorgensen, P.; Jensen, H. J. Aa. J . Chem. Phys. 1994,100,6597-6607. (46) Gehlen, J. N.; Chandler, D.; Kim, H. J.; Hynes, J. T. J . Phys. Chem. 1992,96,1748-1753. (47)Kim, H. J.; Hynes, J. T. J. Phys. Chem. 1990,94,2736-2740. (48)Kim, H. J.; Hynes, J. T. J , Chem. Phys. 1990,93,5194-5210. (49)Kim, H. J.; Hynes, J. T. J . Chem. Phys. 1990,93,5211-5223. (50)Kim, H. J.; Hynes, J. T. J . Chem. Phys. 1992,96,5088-5110. (51) Asahi, T.; Ohkohchi, M.; Mataga, N. J. Phys. Chem. 1993,97, 13132-13137. (52) Barbara, P. F.; Jarzeba, W. Adv. Photochem. 1990,15, 1-68. (53) Kirkwood, J. G. J . Chem. Phys. 1934,2, 351-361. (54) Wong, M. W.; Frisch, M. J.; Wiberg, K. B. J. Am. Chem. Soc. 1991,113,4176-4782. (55) Wong, M. W.; Wiberg, K. B.; Frisch, M. J. J . Chem. Phys. 1991, 95,8991-8998. (56) Scurlock, R. D.; Ogilby, P. R. J . Phys. Chem. 1987,91,45994602. (57) Schmidt, R.; Afshari, E. J . Phys. Chem. 1990,94,4377-4378. (58) Bromberg, A.; Foote, C. S. J . Phys. Chem. 1989,93,3968-3969. (59)Fleming, G. R. Chemical Applications of Ultrafast Spectroscopy; Oxford University Press: New York, 1986. (60)Rosenthal, S. J.; Xie, X.; Du, M.; Fleming, G. R. J. Chem. Phys. 1991,95,4715-4718. (61) Simon, J. D. Arc. Chem. Res. 1988,21, 128-134. (62) Mulliken, R. S.;Person, W. B. Molecular Complexes;Wiley: New York, 1969. (63) Marcus, R. A. Angew. Chem., Int. Ed. Engl. 1993,32,1111-1121. (64)Rehm, D.; Weller, A. Isr. J . Chem. 1970.8- 259-271. (65) Wilkinson, F.; McGarvey, D. J.; Olea, A. F. J . Phys. Chem. 1994, 98,3762-3769.
