10912
J. Phys. Chem. 1996, 100, 10912-10918
Through-Bond and Through-Space Coupling in Photoinduced Electron and Energy Transfer: An ab Initio and Semiempirical Study Andrew H. A. Clayton, Gregory D. Scholes,† and Kenneth P. Ghiggino* Photophysics Laboratory, School of Chemistry, The UniVersity of Melbourne, ParkVille 3052, Australia
Michael N. Paddon-Row School of Chemistry, The UniVersity of New South Wales, Sydney 2052, Australia ReceiVed: NoVember 29, 1995; In Final Form: March 20, 1996X
Ab initio and semiempirical calculations of transfer integrals for electron transfer and energy transfer have been carried out on rigidly linked norbornane-bridged naphthalene dimers to gain insight into the relative importance of through-bond and through-space interactions on photoinduced energy and electron transfer processes. In the absence of direct through-space orbital overlap between the naphthalene moieties, throughbond interaction involving the linking polynorbornane bridge is found to significantly enhance the transfer integrals for electron transfer and triplet-triplet energy transfer. For singlet-singlet energy transfer direct through-space Coulombic interaction between the naphthalene moieties is non-negligible at the separations considered and acts to reinforce the through-bond interaction. The relationship between electron and energy transfer processes and the application of these results to the interpretation of recent experimental data are discussed.
1. Introduction There are two photophysical processes which involve interchromophore interactions of fundamental importance in spectroscopy and photochemistry: photoinduced electron transfer1 (PET) and electronic energy (or excitation) transfer2 (EET). It is these two phenomena that act concertedly in the highly efficient photosynthetic energy conversion system and also play central roles in the development of a usable synthetic light harvesting system. In both examples EET vectorially funnels light energy to a reaction center where, in many systems, a PET reaction is employed to harness the energy as chemical potential. In synthetic supramolecular systems the various “active” chromophores are connected by some kind of molecular framework.3 This framework may actually play a key role in the EET or PET process by providing an indirect electronic coupling pathway between the donor and acceptor chromophores.4,5 This indirect interaction or superexchange, as first suggested by McConnell,6 is well-known to promote efficient long-range electron transfer.7 Closs et al.8 have proposed a nexus between superexchange-mediated triplet-triplet energy transfer (T-T EET) and electron transfer. More recently, evidence for superexchange through σ bonds has been obtained by examining the distance dependence of rates of singlet-singlet energy transfer (S-S EET) between π-π* excited states in conformationally rigid systems.9,10 The observed rate of S-S EET in one study10 was found to be larger by over 1 order of magnitude than that expected from the Fo¨rster-Dexter dipoledipole11 mechanism. A crucial quantity in characterizing these interactions is the electronic transfer matrix element (ETME), or transfer integral, T.12,13 Under conditions of weak coupling (and where the Condon approximation is valid) T can be related directly to the rate of PET or EET through Fermi’s golden rule. Theoretical evaluation of T can thus be used to predict rates or to enable
trends between related systems to be examined.14 In the present work, the role of superexchange in effecting S-S EET, T-T EET, and electron transfer (ET) is examined in a series of rigidly linked norbornane-bridged naphthalene dimers, Figure 1. These molecules were chosen because of our ongoing experimental studies and interest in such rigidly-linked bichromophores where interchromophore separation and orientation can be controlled.10,15 Experimental data presented previously15a were interpreted as indicating a major contribution from a throughbond mechanism to exciton interactions in this series of molecules. Theoretical calculations of T for T-T EET, S-S EET, and ET are undertaken here using ab initio and semiempirical methods. Specifically, we investigate the role of the connecting bridge and the distance dependence of the interaction with and without the bridge in order to elucidate further the contribution of the through-bond mechanism. 2. Theoretical Background (a) Dynamic Perspective. It has been shown16 that the rate of singlet-singlet EET can be written in the form of the general quantum mechanical rate expression of eq 1,
kEET )
Present address: Department of Chemistry, Imperial College of Science, Technology and Medicine, London SW7 2AY, U.K. X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(95)03532-5 CCC: $12.00
(1)
in which TRP is the electronic transfer matrix element (ETME) connecting reactant and product states (denoted R and P), and the tilde indicates that vibrational overlap factors are included. The reactant state is that where excitation is localized on the donor, whereas for the product state, excitation is localized on the acceptor. The Dirac delta term ensures energy conservation between reactant and product states. A similar expression is used to account for rates of PET, eq 2,
kPET ) †
2π |T˜ |2 δ(EP - ER) p RP
2π (PET) 2 | (FCWD) |T p RP
(2)
where FCWD is a Franck-Condon weighted density of states © 1996 American Chemical Society
Through-Bond and Through-Space Coupling in PET and EET
J. Phys. Chem., Vol. 100, No. 26, 1996 10913 bilayer, or an aromatic “host” crystal that contains small concentrations of donor/acceptor guest molecules. The McConnell formula6,17 has been derived to describe such indirect electronic coupling between identical donor and acceptor chromophores mediated by intervening bridging units. Then, for m bridge units, the through-bond-mediated electronic coupling, TRP, is given by eq 5.
TRP ≈
( )( ) T2 t -A -A
m-1
(5)
where T is the chromophore-bridge coupling, t the bridgebridge coupling, and A the energy gap between chromophore and bridge configurations. For long bridges, such a model predicts an exponential attenuation of the magnitude of electronic coupling with increasing bridge length (eq 6), Figure 1. Structures of the molecules investigated.
TRP ≈ T0 exp[-β(m-m0)]
(incorporating temperature, isotope, and activation energy effects), and now the product state is the charge-separated configuration. In general both T and FCWD will be different for EET compared to ET, although relationships between ETMEs are established below. Effects of donor-acceptor distance and orientation on rate are commonly attributed to corresponding changes in the transfer integral.14 (b) Donor-Acceptor Transfer Integrals for ET and EET. The present work aims to compare the magnitudes and distance dependence of the ETMEs, TRP, for EET and ET. Recent work has established the form and nature of such ETMEs in considerable detail.13 For electron transfer the ETME is considered to have a distance dependence governed by the interchromophore overlap integral between reactant and product states (SRP) and is given by (ET) TRP ) HRP - SRPHRR ≈ KSRP
(3)
where HRP is the Hamiltonian interaction matrix element between (normalized) reactant and product wave functions, HRR is the energy of the reactant state, and K is a constant. In this case SRP is approximately the overlap integral between LUMO orbitals of donor and acceptor, Sd*a*. Recently, an analogous theory for electronic factors in EET has been developed.13 The resultant ETME contains contributions from a Coulombic interaction (uCoul, e.g. dipole-dipole) for S-S EET only, as well as interchromophore orbital overlap dependent terms for both S-S EET and T-T EET and is given by eq 4. (EET) ≈ uCoul + K′SRP TRP
(4)
where SRP is the product of two interchromophore molecular orbital overlap integrals (≈SdaSd*a*) and K′ is a constant (different from that of eq 3). The above discussion refers explicitly to a simple donoracceptor system where overlap occurs directly between the chromophores of interest; however, as we will now discuss, such interactions may be promoted over large through-space separations by suitable intermediates. (c) Superexchange-Mediated Coupling in Donor-BridgeAcceptor Systems. As introduced in Section 1, electronic coupling may be mediated by additional components present in the system which couple to the donor and acceptor via the interaction Hamiltonian. Typical relay units include σ bond “spacer” groups, intervening chromophoric substituents, a lipid
(6)
with
β ≈ -ln(|t/A|) and
T0 ≈ T2/t where T0 is the through-bond electronic coupling for m0 bridge units (or bonds) and β is the decay constant (per bond) which describes the attenuation of the coupling with distance. A detailed analysis of the application and validity of the McConnell model has been given by Jordan and Paddon-Row,5 who emphasize the approximations inherent in the McConnell formalism. Some simple, approximate relationships for the distance dependence of (orbital overlap dependent) transfer integrals for through-bond ET and EET can be derived. The through-bond attenuation exponents are related by eq (7) and the preexponential factors via eq 8. The abbreviations ET and HT refer to electron transfer and hole transfer, and E is the energy gap between the locally excited state and the charge-separated configurations.
βEET ≈ βET + βHT
(7)
T0ETT0HT ≈ E
(8)
EET
T0
Such a relationship (eq 7) was first proposed by Closs et al.8 for T-T EET. The effect of the through-bond interaction is to effectively increase the range of donor-acceptor orbital overlap; thus by employing the effective two-state model, the theory for the two chromophore system (eqs 3 and 4) is preserved. 3. Computational Methods (a) Molecular Systems. The molecular systems employed in the present study are shown in Figure 1. Two series of dinaphthyl systems are studied: in one series (labeled DN-nB) the naphthalene chromophores are linked by polynorbornane bridges, n bonds in length; the other series (labeled DN-nS) contains no intervening spacer groups, but consist of naphthyl chromophores fixed in an identical geometrical arrangement, as in the DN-nB. The molecules DN-4B, DN-4S, DN-6B, and DN-6S were investigated in order to assess the relative importance of direct through-space and through-bond orbital overlap of the chromophores and for comparison with previous
10914 J. Phys. Chem., Vol. 100, No. 26, 1996
Clayton et al.
TABLE 1: Electron Transfer, T(ET), and Hole Transfer, T(HT), Integrals (Koopmans’ Theorem Orbital Splittings/2) (in cm-1) molecule
CNDO/S CNDO/S STO-3G STO-3G 3-21G 3-21G T(HT) T(ET) T(HT) T(ET) T(HT) T(ET)
DN-4B DN-4S DN-6B DN-6S
351 8 65 0
456 4 145 0
911
512
283
191
1316 48 420 2
600 10 206 1
experimental studies.15a Geometries were optimized at the selfconsistent-field molecular orbital level (SCF-MO), using MNDO with the C2V symmetry constraint.18 The edge-to-edge and center-to-center chromophore separations in DN-4B are 4.9 and 8.5 Å, respectively, while the corresponding separations in DN6B are 7.6 and 11.3 Å.15a For DN-4S and DN-6S the separations between the closest hydrogen atoms on the opposing naphthyl chromophores are approximately 3.4 and 6.2 Å, respectively. (b) Effective Transfer Integrals for Electron and Energy Transfer. Interactions between the two chromophores of the dimer lead to pairs of electronic states corresponding to each state of the isolated chromophore. In the following we refer to energy “splittings” as the difference in energy between the two dimer electronic states corresponding to each monomer state. Effective transfer integrals for hole transfer, T(HT), or electron transfer, T(ET), were obtained as half the Koopmans’ theorem splittings of the π ionization potentials and π* electron affinities, respectively, in the neutral dimer of interest.4,5 Available tests on related polynorbornane-bridged dienes have shown that the Koopmans’ theorem approximation gives a reasonable estimate of both the magnitude and the attenuation with increasing bridge length of the ionization potential in comparison with secondorder Møller-Plesset calculations.19 All ab initio calculations in the present work were performed by the Gaussian-92 program package (Cray UNICOS version).18 Semiempirical calculations utilized the CNDO/S method with Mataga-Nishimoto parametrization for the two-center Coulomb repulsion integrals, as described previously.20 Effective transfer integrals for singlet-singlet and triplettriplet energy transfer were obtained as half the energy exciton splitting in the calculated S0-Si and S0-Ti vertical dimer transition energies, respectively. It should be emphasized that although neither method is expected to describe closely the exact excited state wave function or absolute interchromophore interactions, we are using these methods as a gauge of relatiVe interactions. These ab initio excited state calculations were conducted using the CI-singles method18 with STO-3G and 3-21G basis sets. Such calculations overestimate the excitation energies for naphthalene since they neglect electron correlation effects; however, since we are interested in energy splittingssnot absolute energiessthis method should be useful. Semiempirical calculations using the CNDO/S method, together with configuration interaction, were also carried out to determine the spectroscopic states. In the CI treatment 50 singly substituted Slater determinantal basis function configurations were used for the naphthalene model and 100 configurations for the naphthalene dimers. 4. Results The effective transfer integrals for electron transfer and hole transfer calculated using ab initio and semiempirical methods are collected in Table 1. It is notable that the orbital interactions calculated for the compounds incorporating the linking bonds (DN-nB) are 2 orders of magnitude larger than those mediated through space (i.e. in the DN-nS dinaphthyl systems with no linking bonds).
TABLE 2: Calculated S0-Ti Vertical Transition Energies (in cm-1) for DN-4S, DN-4B, and the Model Chromophore N-2 According to CNDO/S/CI DN-4B N-2 DN-4S dimer state excitation excitation monomer state excitation energy energy (C2V symmetry) energy (Cs symmetry) A′′
17 590
A′
25 150
A′′
25 450
A′′
27 550
A2 B1 A2 B1 B2 A1
19 960 19 960 27 120 27 120 27 780 27 780
19 960 19 990 27 120 27 140 27 590 27 650
It is well-known that small basis sets, even split valence sets such as 4-31G and 3-21G, can underestimate through-space orbital interactions.21-23 Consequently, the Koopmans’ thereom transfer integral for hole transfer calculated using the 3-21G basis set may be too small. This was checked using the procedure of the ghost atom method of Curtiss et al.23 for DN4S, where such effects should be most apparent. The ghost orbitals of the bisnorbornane bridge atoms are included in the 3-21G calculation of DN-4S (that is, only the 3-21G orbitals of each bridge atom are added, but not the electrons and nuclear charge). This method increases the spatial extent of the orbitals of the naphthalene groups, thereby greatly improving the through-space interactions. The resulting transfer integral for DN-4S including ghost orbitals is 50 cm-1. While the throughspace interactions are larger (by 40 cm-1) than predicted using the straight DN-4S system without ghost functions, the value is still substantially smaller than the integral for DN-4B (600 cm-1, cf. Table 1). Thus through-bond coupling is by far the dominant interaction in DN-4B. The calculated CNDO/S S0-Ti and S0-Si absorption “spectra” of the model naphthalene monomer N-2, the DN-4S dimer, and the DN-4B dimer are collected in Tables 2 and 3, respectively. The dimer spectra exhibit pairs of electronic states corresponding to each state of the monomer spectrum. The magnitude of the energy splitting between the two dimer electronic states quantifies the direct component of the electronic interaction matrix element for energy transfer and exciton interactions. The DN-4S dimer spectrum exhibits virtually no splitting in the first, second, or third excited triplet states; that is, the calculated interactions in DN-4S indicate virtually zero triplettriplet interchromophore interaction. This is anticipated since the through-space overlap between the two naphthalene moieties must be very small. In contrast, the calculated DN-4B absorption spectrum shows significant splittings in each of these first three excited triplet states. This suggests an influence due to the intervening norbornane bonds. (These observations are in accord with the results obtained using the ab initio method; for example, the splitting between the triplet states in DN-4S was calculated to be less than 0.1 cm -1 using the 3-21G basis set). For the singlet states (Table 3), both bonded and nonbonded dimers show significant splitting of the original monomer S2 singlet excited states, indicating a combination of through-space and through-bond interactions. The presence of the bonds increases the calculated splitting significantly for DN-4B over those calculated for DN-4S. A comparison of the calculated monomer oscillator strengths with those of the bonded DN-4B and DN-4S systems shows significant differences attributable to the presence of the linking polynorbornane bridge. In the DN-4S system the calculated oscillator strengths of each of the lowest excited dimer states are comparable with that calculated for the monomer. In contrast, the DN-4B system displays
Through-Bond and Through-Space Coupling in PET and EET
J. Phys. Chem., Vol. 100, No. 26, 1996 10915
TABLE 3: Calculated S0-Si Vertical Transition Energies (in cm-1) and Oscillator Strengths for DN-4S, DN-4B, and the Model Compound N-2 According to CNDO/S/CI monomer state (Cs symmetry)
N-2 excitation energy
oscillator strength
dimer state (C2V symmetry)
DN-4S excitation energy
oscillator strength
DN-4B excitation energy
oscillator strength
A′′
31 820
0.0027
A′
37 060
0.072
A2 B1 A2 B1
32 610 32 610 37 170 37 220
0.0030 0.0022 0.0000 0.135
32 490 32 560 37 130 37 260
0.0062 0.0029 0.0000 0.129
A′′
42 960
0.220
A′′
43 820
1.78
TABLE 4: Triplet-triplet Electronic Energy Transfer Integrals (in cm-1) molecule DN-4B DN-4S DN-6B DN-6S
CNDO/S CNDO/S CNDO/S 321-G 321-G 321-G (T1) (T2) (T3) (T1) (T2) (T3) 15 0 3 0
10 0 8 0
30 0
