J. Phys. Chem. 1991, 95, 1976-1979
1976
structure contributed by both the Fe and the S atoms will be obtained at small negative bias and all positive bias voltages. One might also expect to observe electronic heterogeneity of the surface on a large scale as clearly demonstrated in Figure I .
Conclusions We have demonstrated the usefulness of the STM in conjunction with related spectroscopic techniques for studying semiconductor surfaces. The TS technique yields information about the energy-band structure of the semiconductor and about impurity states. STS should also reveal spatial variation of electronic structure over the surface and perhaps various states associated
with chemical contamination. We have suggested some problems associated with these measurements and some precautions one has to take in the interpretation of the experimental results. Finally, we should emphasize that the present study and our previous study on n-Ti02 (001) surface are exploratory ones. We are now investigating the applicability of these techniques to the in situ study of the electrode/electrolyte interface.
Acknowledgment. The support of this research by the Texas Advanced Research Program and NSF (CHE 8805685) is gratefully acknowledged. We are indebted to Dr. Helmut Tributsch for his contribution of the samples of FeS,.
Electron Donor-Acceptor Orbital Correlations. 8. Selection Rules for Vibrational Enhancement of Intermolecular Electron Transfer William A. Glauser, Douglas J. Raber, and Brian Stevens* Department of Chemistry, University of South Florida, Tampa, Florida 33620 (Received: June 18, 1990)
Transient intermolecular vibrational modes of the intermediate 1 :I donor-acceptor complex not only permit energy conservation along the reaction coordinate but by virtue of their transformation properties also modify the symmetry of the reaction surfaces involved in intermolecular electron transfer. Symmetry species are assigned to these transient modes for complexes belonging to C,,C,, and C,, point groups in order to identify those modes that provide an adiabatic channel for the electronicallydiabatic process. Sirice each symmetry species of these point groups is represented by at least one transient mode, it is concluded that geminate charge recombination via unconstrained 1: I EDA complexes should be efficient.
Introduction In common with other chemical and photochemical processes, intermolecular electron transfer is usually defined in exclusive electronic terms, and its reaction coordinate is described with reference to Born-Oppenheimer (nuclear potential energy) surfaces. In this context the transfer of an electron from electronically excited donor D* to acceptor A in sequence 1 may be classified D*
+A
- - (D*A)
(D+A-)
D+ + A-
(I)
as adiabatic if zeroth-order locally excited (LE) and chargetransfer (CT) configurations ID*A) and )D+A-) belong to the same symmetry species of the point group describing the intermediate complex, or as diabatic if it involves a nonradiative transition (D*A) (D'A-) between surfaces of different symmetry' (and/or spin angular momentum). In the former case the rate constant increases (within limits) with the free energy separation of LE and CT ~ t a t e s , ~whereas J the rate constant of a diabatic process increase^^,^ as this energy gap is reduced; accordingly the efficient production of radical ion pairs of high redox potential (and minimum energy loss) is promoted by diabatic electron transfer.6 If r, denotes the totally symmetric representation of the D/A complex point group, the adiabatic requirement is expressed by condition 2a, which, in terms of symmetry species of donor (C$-2
-
I'(lD*A)) 8 I'(lD+A-)) =
r,
(2a)
C C$-, C dq* C &*) and acceptor C e-, C el* < B2*) frontier orbitals (subjuced to the same point group) reduces6 to condition ( I ) Forster, Th. Pure Appl. Chem. 1970, 24, 443. (2) Marcus, R. A. Ann. Reo. Phys. Chem. 1964, I S , 155. (3) Rehm. D.; Weller, A. Isr. J . Chem. 1970, 8, 259. (4) Robinson. G. W.; Frosch, R. P. J . Chem. Phys. 1963, 38, 1187. (5) Siebrand, W. J. Chem. Phys. 1967, 46, 440. (6) Stevens, B. Chem. Phys. 1988, 122, 347.
0022-3654/91/2095-1976$02.50/0
2b if D* has the electron configuration &4#q91*. Condition 2
r(4'*)8 r(e,*)= TI
(2b)
also describes "strong" exciplex formation insofar as I'(lD+A-)) = I'((D*A) # rl and the CT configuration ID+A-) cannot interact with the rl ground state. In this way selection rules proposed6 for adiabatic intermolecular electron transfer between various (ILa,ILb)donor and acceptor states have been formulated in terms of the intermediate complex description as either a ("strong" or "weak") exciplex or EDA complex. Thus the condition I'(lD*A)) # r(lD+A-)) = I'(1DA)) =
r,
(3)
defines diabatic electron transfer, "strong" EDA complex formation, and (efficient) adiabatic exoergic charge recombination (process 4), and it has been proposed that "weak" EDA complexes
D+ + A--
DA
-
D
+A
(4)
associated with diabatic charge separation and diabatic charge neutralization offer the most efficient photochemical source of separated radical ions of high redox potentiaL6 Insofar as the overall energy E , of a reacting system is conserved, this must undergo a continuous redistribution between nuclear and electronic terms as the reaction proceeds. This is illustrated in Figure 1 for activated (Figure la) and activationless (Figure 1 b) processes where nuclear kinetic energy curves T,(q) appear as mirror images of potential (Born-Oppenheimer) energy curves EBo(q)= (V, + T, + Ve)(q)about E,; here the nuclear kinetic energy of reactants supplies the activation energy where necessary (Figure I a) whereas that of the products accommodates both the activation energy and the internal energy change AEBo. Since the translational and rotational contributions to nuclear kinetic energy have no potential energy component, the partitioning of E, between T, and EBOalong the reaction coordinate must be described in terms of nuclear displacements that transform as 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 5, 1991 1977
Electron Donor-Acceptor Orbital Correlations 1,
--.,.
‘\
/’ /
I
/
/.--. .’\---.
T,,
...(s&s ..-..-..;=. I
reactlon coordinate Figure 1. Nuclear kinetic (T,) and potential (Em) energy curves for (a) activated and (b) activationless bimolecular processes. E, denotes total energy of reaction system. TABLE 1: Origin of Intermolecular (van der Waals) Vibration Modes of Donor/Acceptor Complex“
p2,-
...
..i-..
,
*--.
x
...
-..
!
x-shear (h,)
.?-stretch (SJ
..--..
Y
._- -..
..+-
-c.x,-;.
..-..,..- .... --.. I
z-torsion (tz)
y-torsion (t,)
x-torsion (tx)
Figure 2. The six generalized intermolecular (van der Waals) vibrational
modes illustrated for the benzene-ethylene Ch cofacial complex. Ty-
Tz-
h, shear s, stretch
TY-
TzFor example, R,+ denotes relative in-phase x component of molecular rotation and T; refers to out-of-phase relative molecular translation along intermolecular z axis. transient (van der Waals) intermolecular vibrational modes of the complex, and consequently modify the vibronic symmetry of the reacting system. We examine here the conditions under which the formation of a transient intermolecular normal mode of the complex can provide an adiabatic channel for an electronically diabatic process with particular reference to the activationless coupling of LE, CT, and ground states involved in charge separation (sequence l ) and charge recombination (process 4). State correlations including nuclear terms originated with the recognition by Chiu’ and Metropo~los*-~ that the symmetry of the total wave function provides a more general basis for reactant and product correlation subject to the conservation of (ro)vibronic symmetry. In this contribution we develop a theoretical analysis of the consequences of symmetry-specific vibrational excitation on the outcome of the intermolecular electron transfer which may contribute to the rational design of molecular systems used in the conversion of radiant to chemical energy.
Intermolecular Vibration Modes The dynamics of bimolecular complex formation may be simplified by reducing the two-body problem to a one-body internal and one-body external (center of mass) problem.I0 The isolated fragments have six translational (T) and six rotational (R) degrees of freedom which, with reference to the center of mass, will have in-phase (Tx+, T,,+, T ,: Rx+,R,+, R,’) and out-of-phase (T;, Ty-,T;, R;, R,-, R;) components along x , y , and z axes. The former survive as external degrees of freedom of the complex, while the latter describe six periodic motions of the coupled system corresponding to intermolecular vibrations. Since the intermolecular normal modes originate in restricted (out-of-phase) translational and rotational motions of the molecular components, they will transform as translational and rotational representations of the point group of the complex. This allows the assignment of intermolecular vibrations in terms of their molecular rotational and translational origin as summarized in Table I and illustrated in Figure 2 for the cofacial benzeneethylene complex in C,, symmetry with intermolecular z axis. Specifically three van der Waals (vdW) torsional modes (t,, tu, tz) transform as relative molecular rotations (R;, R;, R;) about the respective axes, two vdW shearing modes (hx, h,) transform ~
~
(7) Chiu, Y. N. J . Chem. Phys. 1976, 64, 2991. (8) Metropoulos, A.; Chiu, Y . N. J . Chem. Phys. 1978,68,5607; 69, 1336. (9) Metropoulos, A . Chem. Phys. Lett. 1981, 83, 357; 1982. 85, 199. (IO) Menapace, J . A.; Bernstein, E. R. J . Phys. Chem. 1987, 91, 2533.
TABLE 11: Transformation Properties of van der Waals Vibrational Mode or Complexes of C, Cm and CJ,Symmetry
shear
stretch
torsion
cs
,If
a’
a’
a”
a’’
C2”
ai
bi
b2
ai
e
b2 e
bi e
G”
e
a’ a2 a2
as relative translations T; and T,; while the vdW stretching mode (s,) transforms as relative molecular translation T; along the intermolecular z axis. Dissociation of the complex into radical ions is accompanied by conversion of these transient modes into out-of-phase translationa! and rotational motion of the products (Table I). The vdW mode symmetry species listed in Table I1 for complexes belonging to C,, C2,, and C3,point groups can also be assigned group theoretically as follows. We deduce the number of times each irreducible representation appeared in the reducible representation by noting the response of the atomic Cartesian displacement vectors to the symmetry operations appropriate to the point group of the complex. First, the six irreducible representations corresponding to the three external translations and three external rotations were subtracted out. Next, the 3n - 12 irreducible representations corresponding to the intramolecular vibrational modes are identified through their assignments in the literature” and subsequently subtracted out. Finally, the remaining six irreducible representations necessarily correspond to the six intermolecular vibrational modes that we seek to evaluate. As expected, they carried the same symmetry labels as the six external translations and rotations. Still another verification of our general assignments can be made with computational normal-mode analyses1° using the standard Wilson G F matrix method10*12 (contained as a subroutine in the AMPAC code’)). The six intermolecular modes are readily identifiable by their characteristic low frequencies; all lie in the range 20-200 cm-I. They are easily distinguished from the six external modes, which have zero or negative harmonic frequencies, and from intramolecular modes, which all lie above 400 cm-I. The vdW stretch and the x- and y-axis torsions involve perpendicular motion of one component relative to the plane of the other and may therefore be involved in dissociative mechanisms. ( I I ) Herzberg. G. lnrared and Raman Specfra;Van Nostrand: Princeton, NJ, 1945. (12) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vihrafions, Theory of Infrared and Raman Vibrational Spectra; McGraw-Hill: New
York,-1955. (13) Stewart, J . J . P. QCPE Program No. 523, 1985.
Glauser et al.
1978 The Journal of Physical Chemisrry, Vol. 95, No. 5, I991
TABLE IV: Vibrational Selection Rules for Adiabatic Forward Intermolecular Electron Transfer for Complexes of CL Symmetry sym of LE sym of CT electronic state electronic
TABLE 111: Vibrational Selection Rules for Adiabatic Forward Intermolecular Electron Transfer for Complexes of C. Symmetiy sym of CT electronic
state
sym of LE electronic state
A'
A' A"
h,, h,, t, s,, t,, tv
state
A"
A,
A2
B,
B2
t,, t, h,, hy, t, SI,
The vdW shears and the z-axis torsion involve parallel motion of one component relative to the plane of the other. Spectroscopic evidence indicates that these latter motions are active in the vibronic coupling mechanism that results in significant interelectronic mixing.I0
TABLE V: Vibrational Selection Rules for Adiabatic Forward Intermolecular Electron Transfer for Complexes of Cs Symmetry' sym of LE sym of CT electronic state electronic
Vibronically Modified Selection Rules for Intermolecular Electron Transfer Zeroth-order vibronic states may be expressed as a product of electronic and vibrational wave functions where the vibronic-state symmetry is the direct product of irreducible representations of electronic and vibrational terms,I4 i.e. rvb
=
r e @ rvib
(5)
Equation 5 is also valid in the presence of first-order or higher order mixing of electronic and vibrational motion insofar as the interaction operators are totally symmetric in the Herzberg-Teller expansion.I5 In the harmonic oscillator approximation the vibrational wave function is the product of 3n - 6 normal modes,I2 and its symmetry species is the product of 3n - 6 irreducible representations ri where ri = r(HUi)is determined by the Hennite polynomial HUiof the ith mode in quantum level u. Thus r v j b belongs to the totally symmetric representation rlof the molecular (complex) point group when u is even or zero and HUihas even parity, whereas the excitation of a non-totally symmetric vibrational mode to an odd quantum state provides a vibrational wave function of the same symmetry. This can couple electronic (LE and CT) states of different symmetry since the vibronic Hamiltonian is totally symmetric or, in the present context, an odd quantum state of a transient vdW mode of appropriate symmetry can provide an adiabatic channel for electronically diabatic electron transfer process if
The condition for vibronically adiabatic charge recombination (process 4) is expressed as
(7) since the complex ground state transforms as I',.
Radical Ion Pair Formation Excited states of the intermediate complex have transformation properties assigned on the basis of donor-acceptor frontier-orbital correlations; of these, the lowest energy LE and CT states are of interest in connection with process 1. Whereas the CT state may belong to any of the four symmetry species in C,, the photochemically relevant locally excited states will generally be nontotally symmetric and restricted to a BIor B2 symmetry label of this point group. Condition 6 provides a basis for assigning those intermolecular (vdW) vibrational modes that provide a vibronically adiabatic channel connecting LE and CT states of different electronic symmetry. These are identified below with reference to Tables Ill-V for complexes belonging to the C,, C2,,and C,, point groups, respectively, in which conrdection the following are noted: (14) Bunker, P. R . Molecular Symmetry and Spectroscopy; Academic Press: New York. 1979. ( 1 5 ) Herzberg, G.;Teller, E. Z . Phys. Chem. 1933, 821, 410.
TABLE VI: Transient van der Waals Modes Effective in Promoting Adiabatic Charge Recombination
point group CTstatesym A' A" promoting modes s, h,
A,
A2 t,
B,
B2
A,
A2
h,
s,
t,
h,
t,
h, t,
ty
t,
tY
s,
tx
E h, h, t, tY
(a) The diagonal elements define adiabatic ion-pair formation which is expected to be inefficient if the corresponding free energy change is small. (b) At least one vdW mode belongs to each symmetry species of the point group (cf. Table 11). The simplest case is presented by C, complexes (Table III), in which there are two identical sets of off-diagonal (Le., diabatic) elements. Regardless of the symmetry of the LE and CT states, the s,, t,, and tu intermolecular vibrations fulfill the adiabatic vibronic criteria. For complexes possessing C. symmetry, the situation is more complex. The first two rows in Table IV can usually be ignored since the lowest lying LE state in aromatic hydrocarbons transforms as either B, or B1. Neglecting the two remaining off-diagonal elements (vide supra), six possible combinations remain. For exciplexes (B,or B2 CT state), only the t, mode will promote the LE-CT transition, whereas for EDA complexes (A, or A2 CT state), either the h,, tu set or h,, t, set of vibrations fulfill the criteria. In C,, symmetry, any LE state of a hydrocarbon donor will transform as the degenerate representation E. Diabatic electronic transitions will be promoted by either set of degenerate vibrations (hx, h,) or (t,, tu) as shown in Table V .
Geminate Charge Neutralization Recombination of radical ions to form the complex ground state (process 4) is highly exoergic and therefore efficient for an electronically adiabatic process. The complex states of interest here are the lowest energy CT state, which correlates with the radical-ion pair, together with the totally symmetric ground state. Condition 7 defines a vibronically adiabatic channel for the electronically diabatic recombination process and permits the identification of appropriate vdW modes (of the ground state) presented in Table VI for complexes of C,, C, and C,, symmetry. Clearly, vibronically adiabatic channels are available for the recombination of radical-ion pairs belonging to any symmetry spccies of the point groups considered with the implication that this process will generally be fast for unconstrained electron donor-acceptor systems. In this case the design of solar energy storage systems based on primary charge separation must provide for rapid secondary redox processes that may involve electron transfer to secondary donors and/or acceptors in a rigid envi-
J. Phys. Chem. 1991, 95, 1979-1987
1979
Conclusions
is kinetically facilitated if the process is electronically diabatic but vibronically adiabatic. We have identified specific van der Waals modes that fulfill these criteria for generalized complexes possessing C,,C,,, and C3, symmetries.
Excitation of intermolecular vibrational modes provides a mechanism for the acceleration of intermolecular electron transfer via an excited intermediate complex. Forward electron transfer
Acknowledgment. This material is based upon work supported by the Division of Chemical Sciences, U.S.Department of Energy, under Award No. DE-FG05-MER-13975.
ronment where intermolecular torsional and shearing motion is restricted.
Long-Distance Charge Recombination within Rigid Molecular Assemblies in Nondlpolar Solvents John M. Warman,* Kenneth J. Smit, Matthijs P. de Haas, Stephan A. Jonker, Radiation Chemistry Department, IRI, Devt University of Technology, Mekelweg 15, 2629 JB Delft, The Netherlands
Michael N. Paddon-Row, Anna M. Oliver, Department of Chemistry, University of New South Wales, P.O. Box I , Kensington, New South Wales 2033, Australia
Jan Kroon, Henk Oevering, and Jan W. Verhoeven Department of Organic Chemistry, University of Amsterdam, Nieuwe Achtergracht 129, 1018 WS Amsterdam, The Netherlands (Received: June 18, 1990; In Final Form: October 8, 1990)
The lifetimes of the charge-separated states formed on photoexcitation of rigid donor-insulator-acceptor molecules with variable edge-to-edge separation from 5 to 15 A have been measured in the nondipolar solvents trunr-decalin,benzene, dioxane, and their admixtures by using the time-resolved microwave conductivity (TRMC) technique. The lifetime is governed by two recombination pathways: direct to the ground state and indirect via the locally excited donor. The latter becomes increasingly important as the separation distance increases and/or the driving force for charge separation decreases. Very large solvent effects are found. Data are presented on the effects of changing the donor and acceptor groups and of modifying the norbornyl type u-bonded bridges.
Introduction In a recent paper] data were presented on the rates of charge separation and recombination following photoexcitation of a series of rigid donor-insulator-acceptor molecules in which the length of the insulating bridge was varied from approximately 5 to 14 A. For both processes the electron-transfer rate was found to decrease exponentially with edge-to-edge separation distance, Re in angstroms, according to the expression k = u exp(-0.88Re) For barrierless conditions toward charge separation the preexponential frequency factor, uCs, was found to be on the order of lOI4 s-I and only very weakly dependent on the nature of the surrounding medium even in going from saturated hydrocarbons to highly polar acetonitrile. The frequency factor for the charge recombination process on the other hand was found to be extremely sensitive to the solvent, increasing by almost 2 orders of magnitude in going from cyclohexane, for which uCR = 8 X lo9PI, to dioxane, This great sensitivity of recombination kinetics to the surrounding medium prompted the experiments on solverit mixtures which are included in the present work. It was found that a deviation from the exponential dependence, given by the above equation, occurs for the longer bridge compounds in saturated hydrocarbon solvents.l** In fact, the rate of decay of the giant dipole state was actually found cvcntually
-
(1) Paddon-Row, M. N.; Oliver, A. M.; Warman. J . M.; Smit, K. J.; de Haas, M. P.; Oevering. H.; Verhoeven,J. W. J . Phys. Chem. 1988, 92,6958. ( 2 ) Smit. K. J.; Warman, J. M.; de Haas, M . P.;Paddon-Row, M. N.;
Oliver, A. M . Chem. Phys. Leff. 1988, 152, 177.
0022-3654/91/2095-1979$02.50/0
to increase with distance for the largest separations. Under these conditions the rate becomes sensitive to the electronic polarizability of the medium so that pronounced differences even between different saturated hydrocarbons are found.* This effect has been attributed to the Occurrence of an additional pathway for charge recombination involving back electron transfer to regenerate the local excited donor state. As expected, the advent of this process is found to be accompanied by delayed donor fluore~cence.~The reason for the effect has been proposed to be the decrease in energy difference between the local excited donor state and the charge-separated state as the latter gradually loses the energy of Coulombic attraction between the charged centers with increasing distance between them. Particular attention will be paid to this “problem”, which limits the maximum attainable lifetime of the charge-separated state, in the present paper. While the rate of charge separation has been found to be relatively insensitive to the dielectric properties of the surrounding medium for the norbornyl-type bridge compounds, it has been shown to be very sensitive to the structure of the bridge i t ~ e l f . ~ . ~ The introduction of only a single “kink” in the all-trans structure is sufficient to produce almost an order of magnitude reduction in the rate of the forward electron-transfer process. This has been taken as evidence for a high through-bond as opposed to (3) Oevering, H. Ph.D. Thesis, University of Amsterdam, 1988. (4) Oliver, A. M.;Craig, D. C.; Paddon-Row, M. N.; Kroon, J.; Verhocven. J . W . Chem. Phys. Left. 1988, 150, 366. (5) Lawson, J . M.; Craig, D. C.; Paddon-Row, M. N.; Kroon. J.; Verhoevcn, J . W . Chem. Phys. Lerr. 1989, 164, 120.
0 1991 American Chemical Society
