2787
NOTES
FIRST CYCLE
-A \
SECOND. CYCLE
oxygen reduction in nonaqueous media.Q Oxygen adsorbed on the platinum electrode accounts for the abnormally high oxygen concentration observed on the first cycle. This suggests that the superoxide ion may be involved in the process. The reactions of aromatic hydrocarbon radical anions with molecular oxygen, superoxide anion, and peroxide are currently under study in hopes of relating the above process with other luminescent systems which have been reported.1° Although aromatic hydrocarbon radicals10Band anionic species’l have been shown to produce luminescence on reaction with oxygen, this constitutes the first evidence for such a reaction of aromatic hydrocarbon radical anions. Acknowledgment. The authors wish to acknowledge the support of the Petroleum Research Fund through Grant No. PRF 2880-A3,5.
-.50
-1.00 -1.50 VOLTS (E. SCE)
-2.00
Figure 2. Cyclic voltammogram with light emission as a function of potential. [Diphenylanthracene] = 3.0 X M in DMF; scan rate = 200 mV/sec. Solution was bubbled for 30 min with nitrogen gas containing 1%02. The first cycle shows t h e irreversible peak due t o adsorbed material on t h e platinum electrode. All subsequent cycles (10) gave traces identical with those shown for cycle 2.
amine t o dimethylacetamide* the luminescence was still observed with approximately the same intensity under identical conditions. These experiments indicate that the chemical reaction is not proton abstraction from the solvent. Also, trace known amounts of water and phenol were added to the system and it was found that in both cases light emission intensity decreased with increasing proton-donor concentration. Attempts were made to remove completely all traces of molecular oxygen from the system by use of a more sophisticated bubbling techniquelsd but as shown previously,sd they were found to be unsuccessful although the oxygen levels were well below the limits of electrochemical detectability. It was found that when bubbling solutions with nitrogen mixtures containing small known amounts of oxygen (1 to 5%), the intensity of the emitted light was enhanced as the oxygen content increased and were considerably greater when compared to those which had been exhaustively deoxygenated by helium. It was also found that in each case the first cycle of a continuous cyclic voltammetry study was accompanied by a more intense emission than any succeeding cycle and usually the electrochemistry showed a very small irreversible peak a t -0.85 V (see Figure 2). This peak corresponds to that observed for
(8) Some controversy exists in the electrochemistry of aromatic hydrocarbons as to whether a proton abstraction reaction can occur to a significant extent in dimethylformamide. See (a) M. Peover, “Electrochemistry of Aromatic Hydrocarbons and Related Substances” in “Electroanalytical Chemistry,” Vol. 11, A. Bard, Ed., Marcel Delrker, Inc., New York, N. Y.,1967, p 28, and references cited therein. For evidence that dimethylformamide is labile in the presence of a strong base and/or electron donor, see (b) H. Brederick, F. Effenberger, and R. Gleiter, Angew. Chem. Int. Ed., 4, 951 (1965), and (c) J. C. Powers, R. Weidner, and T. G. Parsons, Tetrahedron Lett., 1713 (1965). For a more current study of the reactions of aromatic hydrocarbon radical anions with proton donors, see (d) J. Janata and H. B. Mark, Jr., J. Phys. Chem., 72, 3616 (1968). The use of dimethylacetamide negates this possibility. (9) (a) D.L. Maricle and W.G. Hodgson, Anal. Chem., 37, 1562 (1965); (b) A. D.Goolsby and D. T. Sawyer, ibid., 40, 83 (1968). (10) (a) R. E’. Vassil’ev and A. A. Vichutinski, Nature, 194, 1276 (1962); (b) J. Stauff, Photochem. Photobiol., 4, 1199 (1965); (c) J. Stauff, Angew. Chem. Int. Ed., 7, 477 (1968); (d) E.J. Bowen, “Organic Photochemistry,’’ International Symposium, Strasbourg, 1964,Butterworth and Co. Ltd., London, p 473, (11) K. D. Legg and D. M. Hercules, J . Amer. Chem. Soc., 91, 1902 (1969).
Molecular Orbital Theory of Electron DonorAcceptor Complexes. 111. The Relationship
of State Energies and Stabilization Energies to the Charge-Transfer Transition Energy
by R. L. Flurry, Jr., and Peter Politzer Department of Chemistry, Louisiana State University in New Orleans, New Orleans, Louisiana 70122 (Received Febrtkary 17,1969)
I n the earlier papers of this series (parts I and 11),1 there has been presented a linear combination of molecular orbitals approach to the quantum-mechanical description of donor-acceptor complexes. An important feature of this treatment is the explicit inclusion of the (1) Part I: R. L. Flurry, Jr., J . Phys. Chem., 69, 1927 (1965); part 11: R. L. Flurry, Jr., {bid., 73, 2111 (1959). Volume 79,Number 8 August 1960
NOTES
0 0 .
0 0 0
0
e l
-2-
0
00
0
-0
s.---.-
3.2
3. a
316?
314
I
4.0
4.2
I
4,4
.
4.6
I
1
4.8
5.0
1
5.2
5.4
Figure 1. Relationship between heats of formation and charge-transfer energies for various iodine complexes: 0, methylbenzenes as donors; 0, simple amines as donors.
potential energy of the electrostatic interaction between the two components of the complex which would result if there were a complete transfer of one electron. I n parts I and 11,it is shown how the energies of the ground state, of the excited state, and of the charge-transfer transition between these two states can be calculated. The equations to be used will differ depending on whether the original donor and acceptor are charged or neutral species, and each of the four possible combinations of a neutral or negative donor with a neutral or positive acceptor must therefore be handled separately. I n these equations, there appear several quantities which cannot be readily evaluated either experimentally or theoretically. Two of these are the coefficients a and b which appear in the expressions for the wave functions of the complex in its ground state QN
=
a$D
+
b$D
-
b$A
and in its excited state 9~ =
a $ ~
Here, $D and $A are the wave functions of the molecular orbitals which serve as donor and acceptor, respectively, of the electron which is transferred between the two interacting entities. A third quantity which is difficult to evaluate is the resonance integral, PDA = S$D*H$AdT, which reflects the extent of interaction The Journal of Physical Chemistry
between the donor and the acceptor. The coefficients PDA can often be estimated or approximated in some manner,' but their presence generally constitutes a problem and often a limitation upon the applicability and usefulness of the whole theoretical procedure. It is the purpose of this paper to point out some simple substitutions which will permit all three of these quantities to be eliminated from the equations and thereby remove the necessity of assigning them values. This can be done without introducing any new approximations. Of the four possible combinations involving variously charged donors and acceptors, one shall be treated in detail; the others can be handled in exactly the same manner. Consider the case of a negatively charged donor and a positive acceptor. On the basis of the discussion given in part 11, the energies of the ground and excited states of the complex are a and b and the integral
EN = a2D f b2A f
-
~ U ~ P D Aa2vee
(1)
while the transition energy is
AECT= EE - EN (b2 - a z ) ( D - A - V,J
- 4abPDA
(3)
Noms
2789
In these equations, D is interpreted as the negative of the ionization potential of the donor, A as the negative of the electron affinity of the acceptor, and V,, is the electrostatic interaction term which was mentioned previously. All of these quantities are discussed in detail in the earlier papers of this series.l Taking !PN, $E, $A, and $D to be normalized and the overlap integral $$D*$AdT to be zero, as is done throughout this treatment, it follows that u2 b2 = 1. Using this to substitute for a in eq 1-3 gives
+
EN = ( 1 - b2)D
+ b2A + 2b(1 - b2)l”’~DA- (1 - bz)Ven (4)
EE = b2D
+ ( 1 - b2)A 2b(1 -
b2)1’2pDA
AECT = (2b2 -- 1)(D - A - Ves)4b(l
- b 2 v e ~ (5)
- b 2 ) 1 / 2 P ~(6)~
Eliminating PDA between eq 4 and 6 and between eq 5 and 6, and simplifying, leaves
+ A - V,, - AEcT) EE = 0.5(0 + A - V,, + AEcT)
EN = 0.5(D
(7) (8)
Exactly the same equations are obtained for the three other types of donor-acceptor interactions, except that when a negative donor and a neutral acceptor are involved, the term Ve,does not appear; it was suggested in part I1 that this term may be neglected in such a situation. I n each case, the quantities a, b, and ,&A are eliminated; the ground- and excited-state energies are now given as functions of parameters which can, for the most part, either be determined experimentally or calculated theoretically with fairly good accuracy. The electrostatic interaction terms, V,,, which differ for each charge combination, may present greater problems, although it should be possible to make reasonable estimates of these in many instances. I n any case, three troublesome quantities are removed from the equations. Equations 7 and 8 can readily be transformed into relations between the stability constants of the complexes
and the observed charge-transfer bands. This has recently been done for the oxygen and carbon monoxide complexes of various hemoglobins.2 The stabilization energy of the complex, AESt,is, to a first approximation
AE,t = EN - D = 0.5(A
- D - V,, - AEcT)
(9) Thus, for a series of closely related complexes, where V,, is constant or varies linearly within the series and where the acceptor remains the same, a plot of AESt (or log K , J 3vs. AECTshould yield a straight line (in view of the linear relationship between D and AEcT).’ On the other hand, if the complexes are dissimilar, no such linear relationship would be expected, because of the probably irregular variation of the term V,,. Briegleb has compared the heats of formation of a number of complexes with their charge-transfer e n e r g i e ~ . ~For a random group of donors with a given acceptor, there is no linear correlation. If, however, series of closely related complexes are considered separately (for example, the methylbenzenes or the simple amines, as donors, with iodine as the acceptor), good linear relationships are observed within these series (Figure 1). The discussion and derivations presented in this paper have been based upon the one-electron treatment of donor-acceptor complexes which was given in parts I and 1I.l In the Appendix to part 11, however, it is shown that the one-electron equations are formally correct for a polyelectron approach as well. The results which have been obtained here should therefore also be valid in the more general treatment. Aclcnowledgmen,t. The authors wish to thank the Petroleum Research Fund of the American Chemical Society for financial support of this work (Grant No. 2796-A5). (2) P. Polhzer, Biochim. Biophys. Acta, 153, 799 (1968). (3) In those cases where the energy of stabilization can be set equal
to the standard free energy of stabilization, then AEBt = AFo.t -2.303RT log Kut A more complete discussion of this point is given in ref 2. (4) Gr. Briegleb, “Elektronen-Donator-Acceptor-Komplexe,” Springer-Verlag, Berlin, 1961, p 130 ff.
Volume 73, Number 8 August 1969
