J. Phys. Chem. 1993,97, 1743-1745
1743
Predicted Weak Distance Dependence of Through-Bond Mediated Electronic Coupling in BAlkane Bridges. An ab Initio Molecular Orbital Study Michael N. Paddon-Row,*J Michael J. Shephard,? and Kenneth D. Jordan'** School of Chemistry, University of New South Wales, P.O.Box 1, Kensington, N S K Australia 2033, and the Department of Chemistry. University of Pittsburgh, Pittsburgh, Pennsylvania I5260 Received: November 17, 1992; I n Final Form: January 20, 1993
r+,r-and r+*,r-* splittings for a series of divinylalkanes, CHZ=CH(CHZ),CH=CHZ, and diethynylalkanes, HC=C(CH2),C=CH,wereobtained in the Koopmans' theorem approximation using the 3-21G basis set. The r+,r-splittings for the divinyl molecules follow approximately an exponential decay with increasing number (n) of C-C bonds: M ( r )= A exp(-@n), with @ = 0.26 per bond. In contrast, the @ value between successive members in the diethynyl series steadily diminishes with increasing chain length, down to a value of only 0.1 1 per bond for the longest members studied (p = 22,23). These results suggest that all-trans alkyl chains should be extremely effective mediators of rapid hole transfer over large distances (>21 A). Long-range intramolecular electron transfer (ET) continues to generate considerable activity,' and a variety of rigid, donor(saturated hydrocarbon bridgej-acceptor molecules has been synthesized and used to explore experimentally the distance dependence and other factors on ET dynamics. Hydrocarbon bridges that have been employed in these molecules include cyclohexane, Decalin,and steroid-basedsystems,2J bicyclo[2.2.2]octane? triptycene,s polyspirocyclobutanes,6and polynorbornyltype bridges.7 Such studies have demonstrated that very rapid ET rates (> 1O9 s-I) can occur over interchromophoreseparations as great as 13 A7 and that this is due to a through-bond (TB)g coupling mechanism involving mutual interactions of the chromophore orbitals with the bridge orbitals. Furthermore, the ET rates, k,,,for the various donor-(saturated hydrocarbon bridgejacceptor systems follow an approximate exponential distance dependence, from which it can be deduced, within the context of nonadiabatic ET theory, that the corresponding electroniccoupling matrix element, He,, also falls off approximately exponentially with increasing number, n, of bridge C-C bonds:
He, = Hoe, exp(-@n) (1) The fl values lie within the range 0.4 Ifl I0.6 for a variety s y s t e m ~ . l ~ +These ~ * ~ +experimental ~-~ observations have created widespread theoretical interest in determining how bridge characteristics affect the magnitude and distance dependence of Ha.Recent theoreticalstudieshave provided considerableinsight into the distance dependence of the electronic coupling through linearly fused norborny1,g bicyclo[ 1.1. l]pentyl,lOJ1and bicyclo[2.2.2]octyll and cyclohexyl and Decalinrz bridges. This has led to the somewhat surprising state of affairs that the nature of the coupling through hydrocarbon ring systems is better understood than that through simple n-alkane bridges. It is well-knownsasd that bonds arranged in a trans orientation are much moreeffective at conveying electronic interactions than are those oriented in a cis manner. Moreover, it has been known for some time that n-alkanes, in an all-trans conformation, are very effective at relaying electronic interactions over large distances. For example, MO calculations by one of us (M.N.P.R.) on a model ethene...(CI~H2s)**~thene complex, with the methyl groups in van der Waals contact with the ethenes, give a splitting between the r orbitals of 0.02 eV even though the double bonds are separated by 23 A!l3 More recent studies of coupling between the nitrogen lone pairs in the NH2(CH&NH2 species by Broo and Larsson14and between the terminal methylene groups of the
' University of N e w South Wales. f
University of Pittsburgh.
0022-36S4/93/2097-1743$04.00/0
polymethylene CH2(CH2),CH2 systems by Liang and Newton15 and by Curtiss et a1.16 have shown that the distance dependences of the electronic coupling through the polymethylene bridges in these systems are similar to those reported for the polynorbornyl bridges.gJ0 In this work we examine the electronic coupling in the a,wdivinylalkanes, l(a), n = 4 2 0 , and the a,w-diethynylalkanes, 2(a), n = 4 2 4 , for even values of n, where n is the number of alkane C-C bonds spanning the chromophores. A fundamental differencebetween the l(a)and 2(n) series and previously studied polymethylene bridge systems is the smaller energy gaps between the u (P) orbitals of the chromophores and the C-C u ( u * ) orbitals of the bridges in the former.I7 A Koopmans' theoremis (KT) approach is adopted to estimate the co~p1ings.l~This approach, in which the r+,r-and r+*,r-* splitting energies are taken as measures of the electronic couplings relevant for hole and electron transfer, respectively, has been shown to be quite successful at predicting couplings through saturated bridge~.~-20 (The and - refer to the in-phase and out-of-phasecombinations of the 7r (and t*)orbitals localized on the left- and right-hand vinyl or ethynyl groups. In the case of the diethynyl compounds only the componentsof the r and r* orbitals that lie in the plane of the carbon atoms are considered.) The orbital splittings for l(a) and 2(a) were obtained from HF/3-21G calculations.21.22Prior studies have shown that the 3-21G basis set is adequate for describingTB couplingin saturated hydrocarbon bridge~.~c.dJO Geometries were optimized under the constraintof Czand Cbsymmetryfor l(0) and 2(a), respectively.23 For the divinyl systems, l(a), the dihedral angle between the plane of each double bond and its respective allylic C-C bridge bond was fixed at 90° in order to maximize the u-r overlap. This arrangement is clarified by (a) in Scheme I. In a simple McConnell model?4 the magnitudes of the r+,rand r+*,u-*splittings between two chromophores, connected by a saturated bridge, follow an exponential dependence on the number, n of C-C u bonds in the bridge:
+
AE(r*)= A, exp(-fl,n) U ( r )= A, exp(-@,n) where the subscripts hand e refer to hole and electron, respectively. The HartrebFock splittings need not show a strictly exponential dependence on the number of bonds, and comparison of the /3 values obtained from the splittings in successive members in a series of molecules provides a measure of the departures from exponential behavior. Table I summarizes the splittings and fl values for the divinyl alkanes, l(4)-l(20). The r+,w- splittings fall off slowly with Q 1993 American Chemical Society
Letters
1744 The Journal of Physical Chemistry, Vol. 97,No.9, 1993
TABLE IE
and T+*,*-* Splitting Energlea (eV), B b ( e 2 ) .ad Be(+2) V d w ~(per Bond) Determined from tbe spllttittg~ for Dktbpyldkuw, 2(a) .ad 2(a+t)’
SCHEMEI’
hE(*), md
l(n)
3(n) a
n-2m + 2
2(n)
4(n)
n-2mt2
n=3m
t
n
= 2m + 2
5(n)
1
n=3m+ 1
n = number of C-C u bonds in the bridge spanning thechromophorcs.
‘I+,*- and *+*,‘I-* Splitting Energies (ev), AE(r), and All(%*) md Corre~p~ndiag Br(+2) md B e ( W 2 ) Vahm (WM) htc“id from spllttingcp for DiviaywLows, l(a) and l(H2)’ TABLE I:
molecule
1(4) 1(8) l(10) l(12) l(14) l(16) l(18) l(20)
hE(r)
0.58 0.29 0.16 0.094
0.055 0.032 0.019 0.011 0.0067
@h(na+2) 0.35 0.30 0.27 0.27 0.27 0.27 0.26 0.26
hE(r*) 0.74 0.20 0.077 0.036 0.014 0.0052 0.0021 0.00082 0.00032
A(n,n+2) 0.65 0.48
0.38 0.49 0.48 0.45 0.47 0.48
a Values are from HF/3-21G calculations at HF/3-21G optimized gcometries.
increasing bridge length, ranging from 0.58 eV, in 1(4),to 0.007 eV, in 1(20), in which the ethylenic groups are separated by 25 A. Starting with the shortest chains, and progressing to longer chains, the successive B h values (per bond) decrease from 0.35 to 0.30, to 0.27, and reach a limiting value of 0.26 per bond for still longer bridges. The limiting Oh value of 0.26 per bond for l(a) is smaller than those calculated for the polynorbomyldienes, 3(a)(0.34per bond)? thedivinyhtaffanes, S(D) (0.30per and the CH2(CH2)pCH2 species (0.31 per b0nd)15.26.2~but larger than that for thediethynylstaffanes, 4(a) (0.20 per bond).IO (The limiting @h and Be values for I(D)-!!(D) species are summarized in Table 111.) For the polynorbornyldienes,3(a),and the diethynylstaffanes, 4(a),it has been found that the *+*,‘I-* splittings fall off more rapidly with increasing bridge length than do the r+,r-splittings.9JO This is also true for the l(a) series and for the 2(a) series, discussed below. The 8, values for the l(a) series average to 0.49 per bond, with the values determined from the splittings for the first few membersin theseriaundergoingsizabledeviations from the average. The limiting Be value for the l(a)series is also 0.48 per bond, which is smaller than those found for the polynorbornyldienes(0.54 per bond), essentially identical to that for the CH2(CH2),CH2 species (0.49 per bo11d),~5326+2~ but larger than that for the diethynylstaffanes (0.37 per bond).IO Table I1 summarizesthesplittingsandBvaluaforthediethynyl alkanes, 2(4)-2(24). The r+,x- splittings in the 2(a) series drop off much more slowly with increasing bridge length than in the divinyl alkanes. The u+,r-splitting in 2(24) is 0.023 eV, slightly larger than that in 1(16), in which the chromophores are ca. 10 A closer. TheBhvaluesdecreasemonotonically with bridge length, fromavalueof 0.27 per bond (determined from the r+,r-splittings for the first two members in the series) to the astonishingly small value of 0.1 1 for the last two members considered. This is by far the smallest 3 I value yet reported for electronic coupling through a saturated hydrocarbon bridge. The 8, values for the 2(a) series average to 0.45 but range from 0.73 to 0.14, with the largest deviations from the average occurring early in the series. The limiting Be value in this case is ca. 0.38 which is appreciably
molecule
2(4) 2(6) 2(8) 2(10) 2(12) 2~4) 2(W 2(W 2(W 2(22) 2(W
I+ ‘ ,*-
m(‘I*), 4a hE(r)
0.50 0.29 0.19 0.13 0.097 0.073 0.057 0.044 0.035 0.028 0.023
@h(n,n+2) 0.27 0.22 0.17 0.15 0.14 0.13 0.12 0.12 0.1 1 0.11
a(**) Be(n,n+2) 1.37 0.32 0,089 0.067 0.028 0.0093 0.0047 0.0022 0.00088 0.00038 0.00018
0.73 0.64 0.14 0.43 0.56 0.34 0.37 0.47 0.42 0.38
Values are from HF/3-21G calculations at HF/STO-3G optimized geometries.
TABLE Ilk Lid-
Bond) for ~(D)-S(D)’ molecule
hE(r)*
0.01 1 0.0067 0.028 0.023 0.085 0.043 0.068 0.038 0.038 0.015
&(+2)
dB e ( e 2 ) V d u e ~(per
fih(n,n+2) 0.26 0.11 0.34 0.20 0.30
hE(r*)b 0.00082 0.00032 0.00038 0.00018 0.032 0.01 1 0.035 0.01 1 0.013 0.0035
be(n,n+2) 0.48 0.38 0.54 0.37
0.44
Values are from HF/3-21G calculations. In electronvolts. Reference 10. Paddon-Row, M.N.,unpublished.
smaller than that found for the l(a) series and comparable to that in the 4(a) series. The most important finding of this study is that the r+,’~splittings in the l(a) and 2(a) series fall off very slowly with increasing bridge length, with the limiting B h values being 0.26 and 0.11, respqtively. The limiting Bh value for the 2(a) series is about 3 times smaller than those calculated for the coupling of the p orbitals for the NH2 or CH2 “chromophores” through trans-polymethylenebridges.”I6 The much slower attenuation of the r+,r-splittings in the diethynyl compounds is most likely due to the fact that the r / C - C u energy gaps in these compounds are smaller than the CH2 p/C-C u (or NHI p/C-C a) energy gaps. Energy gap considerations also explain the more effective r+,r-TB couplingin 2(a) compared to l(a), and in 4(a)compared to 5(a) (see Table 111); at the HF/3-21G level of theory, the ‘I orbital of acetylene is about 0.7 eV more stable than that of ethylene. Although the present results indicate that alkane bridges adopting the all-trans conformation should be more effective at promoting hole transfer than electron transfer, they should, nevertheless, still be extremely efficient electron-transfer mediators, with 8, values of 0.48 and 0.40 per bond for the l(a) and 2(a) series, respectively. Our prediction that alkyl chains should be very effective mediators of long-range electron-transfer processes is consistent with various experimentalelectron-transfer studies on monolayer assemblies, which reported B values ranging from 0.25 to 0.9 per bond for the coupling through alkyl chains.28-”J Intriguingly, the results of the present study indicate that such films should, in fact, be considerably more efficient at mediating hole transfer than electron transfer. Acknowledgmeint. We are grateful to the Australian Research Council (M.N.P.-R.) and the National Science Foundation (K.D.J.) for supportof this research. M.J.S.acknowledgesreceipt of a Commonwealth Postgraduate Research Award.
Letters
References a d Notes (1) (a) Wasielewski, M. R. Photoinduced Electron Transfer, Parr D Fox, M. A., Chanon, M., Eds.; Elstvier: Amsterdam, 1988; Chapter 1.4. (b) Closs, G. L.; Miller, J. R. Science 1988,240,440. (c) Paddon-Row, M. N.; Verhoeven, J. W. New.J. Chem. 1991, I S , 107. (d) Winklcr, J. R.; Gray, H. B. Chem. Reo. 1992, 92, 369. (e) Wasielewski, M. R. Chem. Reo. 1992, 92,435. (f) hied, S.S.;Ogawa, M. Y.; Wishart, J. F. Chem. Reo. 1992, 92, 381. (2) (a) Calcaterra. L. T.; Closs, G. L.; Miller, J. R. J. Am. Chem. Soc. 1983,105,670. (b) Miller, J. R.;Calcaterra, L.T.; Closs,G. L. J . Am. Chem. Soc. 1984. 106. 3047. (3) Pasman, P.; Mes, G. F.; Koper, N. W.; Verhoeven, J. W. J . Am. Chem. Soc. 1985,107, 5839. (4) Joran, A. D.; Leland, B. A.; Felker, P. M.; Zewail, A. H.; Leland, B. A.; Joran. A. D.; Felker, P. M.; Zewail. A. H.; Hopfield, J. J.; Dervan, P. 8. J. Phys. Chem. 1985, 89, 557. (5) Wasielewski, M. R.; Niemczyk, M. P.; Johnson, D. G.;Svec, W. A,; Minsck, D. W. Tetrahedron 1989,45,4785. (6) Stein, C. A,; Lewis, N. A.; Seitz, G. J. Am. Chem. Soc. 1982, 104, 2596. (7) (a) Penfield, K. W.; Miller, J. R.; Paddon-Row, M. N.; Cotsaris, E.; Oliver,A. M.; Hush, N. S . 1.Am. Chem. Soc. 1987,109,5061. (b) Oevering, H.; Paddon-Row, M. N.; Heppener, M.;Oliver, A. M.;Cotsaris, E.; Verhoeven, J. W.; Hush, N. S . J . Am. Chem. Soc. 1987. 109, 3528. (c) Oliver, A. M.; Craig, D. C.; Paddon-Row, M. N.; Kroon, J.; Verhoeven, J. W. Chem. Phys. Lerr. 1988,150,366, (d) Kroon, J.; Verhoeven, J. W.; Paddon-Row, M. N.; Oliver, A. M. Angew. Chem., Int. Ed. Engl. 1991, 30, 1358. (8) (a) Hoffmann. R.; Imamura, A,; Hehre, W. J. J . Am. Chem. Soc. 1968.90. 1499. (b) Hoffmann. R. ACC.Chem. Res. 1971.4. 1. IC) Gleiter. R. Angnu. Chem.;Inr. Ed. Engl: 1974,13.696. (d) Paddon-Row, M.N. Acc: Chem. Res. 1982, 15, 245. (9) (a) Paddon-Row, M. N.; Jordan, K. D. In Modern Models of Bonding and Delocalization; Liebman, J. F., Greenberg, A,, Eds.; VCH Publishers: New York. 1988: D 10. (b) Paddon-Row. M. N.: Wonn. S.S.Chem. Phvs. Lerr. 1990,'167,43'2. (c)'Jordan, K. D.; Paddon-Row, fi:N. J. Phys. Chbm. 1992,96. 1188. (d) Jordan, K. D.; Paddon-Row, M. N. Chem. Reo. 1992, 92, 395. (10) Paddon-Row, M. N.; Jordan, K. D. J. Am. Chem. Soc., in press. (11) Liang, C.; Newton, M.D. J . Phys. Chem. 1992, 96,2855. (12) Naleway, C. A.; Curtiss, L. A,; Miller, J. R. J . Phys. Chem. 1991, 95, 8434. (13) Paddon-Row, M. N.; Shephard, M. J., unpublished. Other calculations on the ethene...(C,,H2~)...ethenecomplex are described in refs IC and 9a. Even earlier work describing coupling in ethene.-(CH&.-ethene models
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1745 isdescribed in: (a) Paddon-Row, M.N. J . Chem. Soc.,Perkin Trans. 2 1985, 257. (b) Craig, D. C.; Paddon-Row, M. N.; Patney, H. K. Ausr. J . Chem. 1986,39,1587. (c) Paddon-Row, M. N.; Englehardt, L. M.; Skelton, B. W.; White, A. H.; Jsrgensen, F. S.;Patney, H. K. J . Chem. Soc., Perkin Trans, 2 1987, 1835. (14) Broo, A.; Larsson, S. Chem. Phys. 1990, 148, 103. (15) Liang, C.; Newton, M. D. J. Phys. Chem., submitted. (16) Curtiss, L. A.;Naleway,C. A.; Miller, J. R. J . Phys. Chem..submitted. ( 1 7) In the case of the CHI and NH2 'chromophores" employed by other researchers, the relevant chromophore orbitals are actually p type rather than or T * . (18) Koopmans, T. Physica 1934,1, 104.
(19) It has been shown that with the lowest I* orbitals obtained from HF/3-21G calculations correspond to anion states in a Koopmans' theorem sense rather than approximations to continuum functions. See ref 9 and Falcetta. M. F.; Jordan, K. D. J. Am. Chem. Soc. 1991, 113,2903. (20) Newton, M. D. Chem. Reo. 1991, 91. 767. (21) The Hartree-Fock (HF) calculations were performed with the Gaussian 90 program: Frisch, M. J.; Head-Gordon, M.;Trucks, G. W.; Foresman, J. B.;Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Mclius,
C.F.;Baker,J.;Martin,R.L.;Kahn,L.R.;Stewart,J.J.P.;Topiol,S.;Pople,
J. A. Gaussian, Inc.: Pittsburgh, PA, 1990. (22) For a discussion of the STO-3G and 3-21G basis sets, as well as citations to the original literature, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (23) Geometries for l(n) and 2(n) were optimizied using the 3-21G and STO-3G basis sets, respectively. (24) McConnell, H. M. J . Chem. Phys. 1961, 35, 508. (25) An HF/3-21G//3-21G study on 5(n), n = 4-16, has recently been completed: Paddon-Row, M.N., unpublished. (26) The @ values given in refs 15 and 16 differ from ours, both because they report the splittings as a function of distance (in angstroms) between the two chromophores, and because their expression for the splitting is: hE = A exp((-@/2)n), which contains a factor of 2 that is absent in our eq 1. (27) The @h and Be values for the CH~(CHZ),CH~ species are determined from the I+,*- and I+*,*-* splittings of the CH~(CHZ),CH~ (p = 5,6,7, and 8) species, deduced from results given in Table 111 of ref 15. (28) (a) Kuhn, H. J. J . Photochem. 1979, IO, 111. (b) Kuhn, H. Pure Appl. Chem. 1979, 51, 341. (29) MBbius, D. Be?. Bunsen-Ges. Phys. Chem. 1978, 82, 848. (30) Finklea,H. O.;Hanshew,D.D.J. Am.Chem.Soc. 1992,114,31733181.
