Investigation of through-bond coupling dependence on spacer structure

Article abstract of DOI:10.1021/ja952852i

Intramolecular electron transfer rate constants in solution are measured for radical anions and cations of molecules having biphenyl and naphthalene groups as donor and acceptor. The molecules have one or more five-bond hydrocarbon chains between the dono

Full text of DOI:10.1021/ja952852i

378
J. Am. Chem. Soc. 1996, 118, 378-387
Investigation of Through-Bond Coupling Dependence on
Spacer Structure
Basil P. Paulson,† Larry A. Curtiss,*,† B. Bal,‡,§ Gerhard L. Closs,‡,§ and
John R. Miller*,†
Contribution from Argonne National Laboratory, Argonne, Illinois 60439, and Department of
Chemistry, UniVersity of Chicago, Chicago, Illinois
ReceiVed August 18, 1995X
Abstract: Intramolecular electron transfer rate constants in solution are measured for radical anions and cations of
molecules having biphenyl and naphthalene groups as donor and acceptor. The molecules have one or more five-
bond hydrocarbon chains between the donor and acceptor groups in trans, gauche, and cis conformations. The rates
suggest that one trans chain is as effective as two gauche chains or three cis chains, consistent with Hoffmann’s
prediction of more effective coupling through trans hydrocarbon chains. Ab initio calculations of the couplings are
in reasonable agreement with the experiments. Calculations of electronic coupling pathways provide insight into
the reason for the superiority of the trans conformation, which gives constructive interference between the two
largest pathways. The calculations also show that “cross talk” can enhance couplings in cyclic spacers in contrast
to its deleterious effect in norbornyl spacers. Comparisons of couplings through these spacers with simple hydrocarbon
chains require that large nonbonded interactions be taken into account.
1. Introduction
shown above, and measured electron transfer rates in related
compounds having larger π groups.8-13 The first compound
pictured has all-trans chains between the two ethylenic π groups,
whereas the other two include one and two cisoid linkages
shown in bold. The cisoid linkages (dihedral angles ) 46° from
MM2 calculations14 ) were found to reduce the couplings
substantially.12 The reduction per cisoid link varied depending
on the number of links, their relative positions, and whether
the rates or photoelectron splittings were measured.12 Many
other experimental results demonstrate the importance of
through-bond interactions.15-31
The electronic coupling interaction between a donor and
acceptor is one of the least understood aspects of charge transfer
reactions. In intramolecular charge transfer reactions where the
donor (D) and acceptor (A) are tethered by a rigid spacer (S) in
the form DSA, the coupling between the donor and acceptor
has been found to occur primarily through the bonds of the
spacer. This is true even when the spacer is an insulator, such
as a saturated hydrocarbon. Though there are many important
aspects about this interaction, the focus of the present study is
to determine how this through-bond (TB) interaction depends
on the structure of the spacer.
In the present study, the charge transfer rates of a new series
of compounds are used to investigate the structural dependence
In 1968, Hoffmann and co-workers1,2 proposed that through-
bond interactions were relatively large in magnitude and strongly
dependent upon the orientation of the intervening bonds.
Evidence leading to Hoffmann’s study had been growing from
a variety of areas, including structural effects on chemical
properties3 and UV spectra.3-5 Hoffmann concluded that a fully
extended, all-trans configuration of the bonds yielded the best
through-bond interaction, and deviation from this configuration
reduced the magnitude of this interaction. The first clear
example came in the late 1970s from Pasman and co-workers6,7
in a study of the UV spectra of dicyanovinyl thioether isomers.
Further confirmation came from the elegant compounds of
Paddon-Row
(3) Grob, C. A. Angew. Chem., Int. Ed. Engl. 1969, 8, 535-622.
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Am. Chem. Soc. 1981, 103, 5575-7.
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G. F. Tetrahedron 1980, 36, 3241-8.
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Patney, H. K. J. Am. Chem. Soc. 1982, 104, 6849-51.
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105, 670-1.
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and co-workers who measured and computed splittings in
photoelectron spectra for several compounds, including those
† Argonne National Laboratory.
‡ University of Chicago.
§ Deceased.
X Abstract published in AdVance ACS Abstracts, December 15, 1995.
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0002-7863/96/1518-0378$12.00/0 © 1996 American Chemical Society

InVestigation of Through-Bond Coupling Dependence
J. Am. Chem. Soc., Vol. 118, No. 2, 1996 379
the specific interactions that produce them.1,2,6-8,13,15,17,21,34-40
These efforts evolved further to compute the “pathways” of
interaction through the spacer to give an intuitive picture of
what the important coupling interactions are.13,41-47 The general
conclusions are consistent with those from Hoffmann and
othersslonger range, vicinal interactions strongly affect the
coupling. In this paper the term “chain” is used to refer to
connected atoms or bonds and is distinguished from the terms
“path” or “pathway”, which refers to a series of electronic
interactions between bonds in such a chain.
This paper presents measurements by pulse radiolysis of rates
of electron transfer in anions and hole transfer in cations of the
molecules shown in Figure 1. The results are compared with
calculations of electronic couplings between simple CH2
π
donor/acceptor groups through the same spacers and through
simple alkyl chains having trans, gauche, and cis conformations.
Figure 1. Compounds used for experimental investigation of the
dependence of coupling on structure of the spacer. B ) biphenyl, N )
naphthyl; 1,4C ) 1,4-cyclohexane, bcO ) 1,4-bicyclo[2.2.2]octane,
1,5tD ) 1,5-trans-decalin, and 1,5cD ) 1,5-cis-decalin. At the bottom
of the figure are five-bond hydrocarbon chains having the same
conformations as those in the molecules.
2. Experimental Methods
1,2-Dichloroethane (DCE) was purchased from Burdick and Jackson,
distilled from P2O5 under an argon atmosphere, and then placed in an
evacuated bulb over a mixture of 4 and 3 Å molecular sieves.
Tetrahydrofuran (THF) was dried over sodium metal with benzophe-
none as a redox carrier and indicator, distilled under nitrogen, placed
in a dry evacuated bulb with a sodium/potassium alloy, and sonicated
for several minutes until the aqua blue color from solvated electrons
appeared, indicating the solution was dry and oxygen-free. The samples
were prepared by vacuum distilling the solvents into the silica cells
containing the compounds. After the solvent was transferred to the
sample cell, the solutions were cooled to temperatures just above the
solvent freezing point and sealed while pumping at pressures of <10-4
mbar.
of through-bond coupling (Figure 1). All the compounds have
chains of four saturated carbon atoms (five saturated carbon-
carbon bonds) separating the donor and acceptor. The dihedral
angles about the central C-C bonds vary from 0° to 180°. For
the two 1,5-decalin spacers, the dihedral angle in the central
five-bond, four-carbon chain is nearly 180°, to give that central
chain the ideal trans conformation favored by Hoffmann and
shown in the lower left of Figure 1. The 1,4-substituted
cyclohexane (1,4C) spacer has two identical five-bond chains
connecting the donor and acceptor. In each of these chains the
dihedral angle about the central C-C bond is ca. 60°. Thus,
the 1,4C spacer can be viewed as containing two five-bond
chains, each having a gauche conformation, as shown in the
bottom center of Figure 1. Similarly, the 1,4-substituted
bicyclooctane has three five-bond cis chains with central dihedral
angles of 0° (lower right in Figure 1). In the 1,5-decalins, in
addition to the central five-bond chain, two seven-bond chains
are present to hold the five-bond chain in the desired conforma-
tion. The expectation that the seven-bond chains contribute little
to the coupling is supported in section 4.C.2. The intramo-
lecular electron transfer (ET) and hole transfer (HT) rates were
measured for the radical anions and radical cations of these
molecules. The experimental results are presented along with
the calculated results on model systems using ab initio molecular
theory.32,33
The radical anions were generated by irradiating solutions of the
DSA compounds in THF with 30 ps, 20 MeV electron pulses from the
Argonne linac. Irradiation generates solvated electrons (<2 × 10-5
M) that attach to the donor and acceptor groups to form an equal
distribution of D-SA and DSA-. In DCE the linac pulses produce
two oxidizing species, DCE•+ and CH2dCHCl•+
. Electrons are
dissociatively captured to produce Cl- and radicals, neither of which
reacts with the DSA molecules. Both cations react with the DSA
compounds to form an equal distribution of D+SA and DSA+. The
intramolecular charge transfer reactions were then observed photo-
metrically as they proceeded to equilibrium. The HT reactions were
monitored at 730 nm, and the ET reactions were monitored at 650 nm.
Experimental methods for acquisition of transient absorption data and
fitting of the data have been described elsewhere.48
(33) v. Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J.
B.; Schlegel, H. B.; Ragavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez,
C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.;
Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J.
A. Gaussian 90, Revision J; Gaussian Inc.: Pittsburgh, PA.
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9.
Invocation of the concept of localized or partly localized
orbitals has enabled “dissection” the electronic couplings into
(23) 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,
3258-69.
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115-94.
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1988, 1508-10.
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1990, 112, 1710-22.
(26) Oevering, H.; Verhoeven, J. W.; Paddon-Row, M. N.; Warman, J.
M. Tetrahedron 1989, 45, 4751-66.
(27) Lawson, J. M.; Craig, D. C.; Paddon-Row, M. N.; Kroon, J.;
Verhoeven, J. W. Chem. Phys. Lett. 1989, 164, 120-5.
(28) Joachim, C.; Launay, J. P.; Woitellier, S. Chem. Phys. 1990, 147,
131-41.
(41) Naleway, C. A.; Curtiss, L. A.; Miller, J. R. J. Phys. Chem. 1991,
95, 8434-7.
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(43) Beratan, D. N.; Onuchic, J. N.; Winkler, J. R.; Gray, H. B. Science
1992, 258, 1740-1.
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N. J. Am. Chem. Soc. 1990, 112, 579-86.
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107-16.
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176, 387-405.
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N. J. Am. Chem. Soc. 1993, 115, 4345-9.
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Molecular Orbital Theory; John Wiley and Sons: New York, 1986.

380 J. Am. Chem. Soc., Vol. 118, No. 2, 1996
Paulson et al.
Synthesis of 1-((eq)-4-Biphenylyl)-5-((eq)-2-naphthyl)-trans-deca-
lin and 1-((eq)-4-Biphenylyl)-5-((eq)-2-naphthyl)-cis-decalin. The
following procedure is based on a synthetic methodology developed
by Green,49 who prepared similar compounds for electron transfer
research.
was washed with pentane and filtered, yielding 0.73 g of crude product.
The product was then dissolved in 15 mL of acetic anhydride and 1
mL of acetyl chloride and refluxed for 45 min. The acetyl chloride
was distilled off under reduced pressure, and the residue was dissolved
in methylene chloride so the acetic acid could be washed out with water
extractions. The product was purified by column chromatography with
silica gel, and the products were eluted with 5% methylene chloride/
hexane; 0.39 g of mixed olefins was recovered. The proton NMR and
TLC indicated that more than one olefin was present.
1,5-Decalindione. 1,5-Decalindiol was oxidized to 1,5-decalindione
using a procedure by Johnson.50 An oxidizing solution was prepared
containing 35 g of sodium dichromate, 27 mL of acetic acid, and 47
mL of concentrated sulfuric acid in 155 mL of water. Twenty grams
of the diol, suspended in 400 mL of benzene, was chilled in an ice
bath. The oxidizing solution was slowly added to the benzene
suspension over a 2 h period and vigorously stirred overnight with a
mechanical stirrer. Additional water was added to the mixture, and
the organic layer was separated. The aqueous layer was extracted with
three 100 mL portions of benzene. The organic fractions were
combined and washed with 200 mL of water, 200 mL of saturated
sodium bicarbonate solution, and 200 mL of water. The benzene was
evaporated, and the crude product was recrystallized from ethanol
yielding 10.5 g of crystalline product. 1H NMR (CDCl3, 500 MHz):
δ 2.42 (1H, m), 2.34-2.40 (3H, m), 2.27 (2H, doublet of triplets, J )
6, 12 Hz), 2.08-2.16 (4H, m), 1.58-1.74 (4H, m).
1,5-Decalindione Monoethylene Ketal. The 1,5-decalindione mo-
noethylene ketal was prepared by refluxing 10.5 g of 1,5-decalindione,
3.9 g (1 equiv) of ethylene glycol, and 0.1 g of p-toluenesulfonic acid
in 150 mL of benzene overnight with a water separator. The mixture
was washed with 40 mL of saturated aqueous sodium bicarbonate
solution and 40 mL of water. The solvent was evaporated, and the
crude product was purified by silica gel column chromatography. The
1,5-decalindione bis-ethylene ketal was eluted with pure hexane, and
the monoketal was eluted with 10% methylene chloride/hexane. The
crude 1,5-decalindione monoethylene ketal was recrystallized from
hexane, yielding 5.2 g of pure product. 1H NMR (CDCl3, 500 MHz):
δ 3.80 (4H, m), 2.30 (2H, m), 2.05 (1H, s), 1.20-2.0 (11H, m).
5-(4-Biphenylyl)decalin-1-one. 4-Bromobiphenyl (5.0 g, 21 mmol)
was dissolved in 100 mL of dry THF and cooled in a dry ice-acetone
bath; 15.2 mL (24 mmol) of 1.6 M n-butyllithium was slowly added,
and the mixture was stirred at low temperature for 0.5 h; 3 g (14 mmol)
of 1,5-decalindione monoethylene ketal, dissolved in 40 mL of dry
THF, was added, and the solution was stirred for an additional 45 min
at low temperature. The solution was then allowed to warm to room
temperature and stirred for an additional 2 h. Twenty milliliters of
water was added to the solution, and the aqueous phase was extracted
with three 40 mL portions of methylene chloride. The organic fractions
were combined, washed with water, dried over anhydrous magnesium
sulfate, and evaporated. The residue was washed with pentane (to
remove the excess biphenyl) and filtered, yielding 3.4 g of crude
product. This was dissolved in 20 mL of THF and added to 1 pint of
absolute ethanol with 4 mL of perchloric acid and 0.9 g of 10% Pd on
carbon. The flask was evacuated, refilled with hydrogen gas, and stirred
for 2 days. The catalyst was filtered off, and enough solvent was
evaporated to allow the product to crystallize out. Yield: 0.86 g of
5-(4-biphenylyl)decalin-1-one. Mp: 216-7 °C. MS: m/z (M+) 304.
1H NMR (CDCl3, 500 MHz): δ 7.60 (3H, m), 7.45 (2H, d), 7.40 (2H,
m), 7.30 (2H, m), 2.65 (1H, doublet of triplets), 2.35 (2H, m), 2.05
(1H, d), 1.95 (1H, m), 1.20-1.90 (10H, m).
The mixture of olefins was hydrogenated by dissolving the mixture
in 20 mL of THF and 150 mL of absolute ethanol with 0.1 g of 10%
Pd on carbon. The atmosphere was replaced with hydrogen gas, and
the mixture was stirred for 2 days. The catalyst was filtered off and
the solvent evaporated. The proton NMR of the product indicated that
there were several isomers present. The isomers were epimerized by
the procedure used by Green49 for similar compounds. The mixture
was dissolved in 7 mL of DMSO (dried over 4 Å sieves) with 0.22 g
of potassium tert-butoxide. The solution was stirred overnight at 80
°C, the reaction quenched with water, and the mixture acidified with
several drops of dilute hydrochloric acid. The product was extracted
with three 100 mL portions of methylene chloride; the methylene
chloride extracts were combined, washed with water and brine, dried
over anhydrous magnesium sulfate, and evaporated. The proton NMR
indicated that product consisted mostly of two isomers.
The isomers were cleanly separated using normal phase column
chromatography. The crude mixture was dissolved in a 10% methylene
chloride/hexane solution and put onto a 30 cm long, 3 cm diameter
column of neutral alumina (activity 1). The product was eluted with
10% methylene chloride in hexane solution, collected in 20 mL
fractions. Each fraction was analyzed with reverse phase HPLC, using
a 10 cm Alltech C18 econosphere column, eluted with 100% acetonitrile
at 1.0 mL/min. The two products were recrystallized with absolute
ethanol.
1-((eq)-4-Biphenylyl)-5-((eq)-2-naphthyl)-trans-decalin. Mp: 225-7
°C. 1H NMR (CDCl3, 500 MHz): δ 7.80 (t, 3H, J ) 7.5 Hz), 7.60 (d,
3H, J ) 8.8 Hz), 7.54 (d, 3H, J ) 7.5 Hz), 7.40 (m, 4H), 7.35 (m,
3H), 2.48 (1H, doublet of triplets, J ) 3, 11 Hz), 2.35 (1H, doublet of
triplets, J ) 3, 11 Hz), 1.88 (t, 2H, J ) 11 Hz), 1.7-1.2 (m).
1-((eq)-4-Biphenylyl)-5-((eq)-2-naphthyl)-cis-decalin. Mp: 200-1
°C. 1H NMR (CDCl3, 500 MHz): δ 7.90 (t, 3H, J ) 7 Hz), 7.60 (d,
3H, J ) 8 Hz), 7.54 (d, 2H, J ) 7 Hz), 7.44-7.38 (m, 6H), 7.35 (t,
1H, J ) 7 Hz), 7.26 (d, 2H, J ) 7 Hz), 3.0 (d, 1H, J ) 13 Hz), 2.9 (d,
1H, J ) 13 Hz), 2.2 (2H, doublet of triplets, J ) 2, 14 Hz), 2.0 (1H,
doublet of quartet, J ) 3, 13 Hz), 1.9 (2H, doublet of triplets, J ) 2,
13 Hz), 1.85 (d, 2H, J ) 13 Hz), 1.75 (d, 2H, J ) 13 Hz), 1.65 (d, 2H,
J ) 13 Hz), 1.6-1.2 (m), 1.15 (d, 1H, J ) 11 Hz), 1.0 (d, 1H, J ) 11
Hz).
3. Theoretical Methods
A. Coupling Calculation. The method used to calculate
the coupling interactions is based on previous studies.41,42,45-47,51,52
The method replaces the donor and acceptor chromophores with
methylene groups. The rational for this substitution is that the
greatest interaction between the donor and acceptor with the
spacer occurs at their point of contact with the spacer. This
minimizes the number of atoms involved in the calculation. In
this model, the methylenes are initially a pair of degenerate p
orbitals (related by symmetry). The coupling interaction
between the two orbitals results in a mixing that splits them
into symmetric and antisymmetric combinations. Koopmans’
theorem53 (KT) provides an approximate way to calculate the
splitting parameter, ∆, from the differences in the eigenvalues,
ꢀ, of the molecular orbitals corresponding to the symmetric (φ+)
and antisymmetric (φ-) combinations of the p orbitals on the
1-(4-Biphenylyl)-5-(2-naphthyl)decalin. 2-Bromonaphthalene (1.2
g, 5.6 mmol) dissolved in 40 mL of dry THF was cooled in a dry
ice-acetone bath, and 3.9 mL (1.1 equiv) of 1.6 M n-butyllithium was
slowly added. This mixture was stirred at low temperature for 1 h
before 0.86 g (2.8 mmol) of 5-(4-biphenylyl)decalin-1-one, dissolved
in 20 mL of dry THF, was added. This was stirred for 2 h at low
temperature, allowed to warm to room temperature, and stirred for an
additional 1 h; 20 mL of water was added to the solution, and the
aqueous phase was extracted with three 40 mL portions of methylene
chloride. The organic fractions were combined, washed with water,
dried over anhydrous magnesium sulfate, and evaporated. The residue
(48) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller,
J. R. J. Phys. Chem. 1986, 90, 3673-83.
(51) Ohta, K.; Closs, G. L.; Morokuma, K.; Green, N. J. Am. Chem.
Soc. 1986, 108, 1319.
(52) Curtiss, L. A.; Naleway, C. A.; Miller, J. R. J. Phys. Chem. 1993,
97, 4050-8.
(53) Koopmans, T. Physica 1934, 1, 104.
(49) Green, N. J. Ph.D. Dissertation Thesis, The University of Chicago,
1986.
(50) Johnson, W. S.; Gutscge, C. D.; Banerjee, D. K. J. Am. Chem. Soc.
1951, 73, 5464.

InVestigation of Through-Bond Coupling Dependence
J. Am. Chem. Soc., Vol. 118, No. 2, 1996 381
CH2 donor and acceptor groups:54
∆ ) ꢀ(φ-) - ꢀ(φ+)
(1)
(2)
The ∆ is associated with the electronic coupling VDA by54
∆
V )
2
The validity of the various KT values depends, in part, on
the importance of electronic relaxation. The sign convention
used for the KT couplings is similar to that used by Newton.54
The interaction is defined as positive when energy of the
symmetric orbital φ+ from the many electron wave function is
lower than the energy of the antisymmetric orbital φ-. The
∆SCF (self-consistent field) method was also used to calculate
couplings. This method uses the unrestricted Hartree-Fock
(UHF) energies of the ground (Eg) and first excited (Ee) states,
V ) ((Eg - Ee)/2. The ∆SCF method includes electronic
relaxation effects of the excitation that are not included in the
KT method and thus might be expected to be more realistic,
although Kim55 found long-distance KT couplings through
polynorbornyl spacers to be in better agreement with ∆MP2
couplings, which include correlation effects, than with ∆SCF
couplings. The same sign convention is used for the ∆SCF
couplings as was used for the KT couplings. The KT calcula-
tions were carried out on the neutral triplet radicals, whereas
the ∆SCF calculations were done on doublet cations and anions.
Ab initio molecular orbital theory32,33 was used to obtain
couplings for comparison with experiment. All ab initio
calculations were done at the HF/3-21G level. The 3-21G basis
has been found to give reasonable agreement with couplings
calculated using larger basis sets.45,52 The semiempirical
molecular orbital method AM1 was also used to calculate
couplings to assess its reliability for larger systems. The UHF
method was used in calculations on open-shell systems (cation,
anion, neutral triplet). The resulting wave functions had
delocalized donor/acceptor orbitals, that is, an equal electron
distribution on the -CH2 groups for structures with symmetrical
donor/acceptor groups.
B. Structures Used in the Calculations. Optimized
structures of the neutral triplet radicals were used in the
calculations. The structures were initially obtained from mo-
lecular mechanics (MM2 optimization)56-58 and then refined
at the semiempirical AM159 molecular orbital level. The angles
of the methylene groups are constrained to be those preferred
by the aromatic chromophores (based on molecular mechanics
calculations and NMR experiments). The structures of trans-
1,4-dimethylenecyclohexane (1,4C), 1,4-dimethylenebicyclo-
octane (bcO), 1,5-dimethylene-trans-decalin (1,5tD), and 1,5-
dimethylene-cis-decalin (1,5cD) are illustrated in Figure 2.
Molecules having CH2 donor and acceptor groups will be
abbreviated using only the name of the spacer (e.g., 1,4C will
be used for 1,4-dimethylenecyclohexane). The orientations of
the donor/acceptor orbitals, which mimic those of the aromatic
donor and acceptor groups, are also shown in the figure. The
five-bond backbone chains in 1,5cD and 1,5tD have all-trans
configurations (dihedral angle of 180°). The methylene groups
in 1,5cD have a (0,0) conformation as illustrated in Figure 3
Figure 2. Illustrations of conformers of bcO, 1,5cD, 1,5tD, and 1,4C
with CH2 donor/acceptor groups and five-bond chains. Also illustrated
are 1,3C, 2,6tD, and 2,7tD.
Figure 3. Illustration of five bond-chain of 1,5cD.
for the five-bond backbone chain. The methylene groups in
1,5tD are twisted by 30° in opposite directions about the C-C
bond. The five-bond chains in bcO and 1,4C have dihedral
angles of 0° and about 60°, respectively. In addition to these
molecules, we also considered systems with three-, four-, and
seven-bond chains as the shortest link between the donor and
acceptor, including cis-1,3-dimethylenecyclohexane (1,3C), 2,7-
dimethylene-trans-decalin (2,7tD), and 2,6-dimethylene-trans-
decalin (2,6tD). The structures and orientations of the meth-
ylenes are illustrated in Figure 2. These three donor/acceptor
systems were studied previously47 using slightly different
structures. Experimental measurements have also been reported
previously for compounds containing the 1,3C, 2,7D, and 2,6tD
spacers.48,60 The results are presented here for comparison with
the five-bond compounds. All of the methylene-substituted
donor/acceptor systems have symmetry and are listed in Figure
2.
C. Superexchange Analysis. We use the superexchange
pathways method to provide information about how electronic
coupling is transmitted through the bonds of the spacer. The
pathways method is based on the idea of superexchange61-64
(SE), the indirect coupling of donor (D) to acceptor (A) wave
functions through a chain (path) of high-energy intermediate
(54) Newton, M. D. Chem. ReV. 1991, 91, 767-92.
(55) Kim, K.; Jordan, K. D.; Paddon-Row, M. N. J. Phys. Chem. 1994,
98, 11053-8.
(56) Allinger, N. L. AdV. Phys. Org. Chem. 1976, 13.
(57) PCMODEL for the MacIntosh, v. 4.41, Serena Software, Bloom-
ington, IN.
(58) Spartan Molecular Modeling Program, v. 3.1, Wavefunction Inc.,
V. K. A., Irvine, CA.
(59) Dewar, M. J. S.; et al. J. Am. Chem. Soc. 1985, 107, 3902-9.
(60) Johnson, M. D.; Miller, J. R.; Green, N. S.; Closs, G. L. J. Phys.
Chem. 1989, 93, 1173-6.
(61) Anderson, P. W. Phys. ReV. 1950, 79, 350-356.
(62) Anderson, P. W. Magnetism; Academic Press: New York, 1963;
Vol. I, p 25.
(63) Halpern, J.; Orgel, L. Discuss. Faraday Soc. 1960, 29, 32.
(64) McConnell, H. M. J. Chem. Phys. 1961, 35, 508-15.

382 J. Am. Chem. Soc., Vol. 118, No. 2, 1996
Paulson et al.
Table 2. Comparison of Experimental Hole Transfer Coupling
Table 1. Intramolecular Charge Transfer Rates, Bond Coupling
Ratios, and Center-to-Center Distances
Elements to ab initio Calculations
electron transfer
coupling
hole transfer
experimental
UHF/3-21Gd
b
approximate
RB-N
coupling
compda (Å)
kETc (s-1
)
per chaind kHTc (s-1 per chaind
)
RD-A
coupling
KT
∆SCF
compda (Å)b kHT (s-1
)
ratioc
(mH) ratioe (mH) ratioe
1,5tBDN 12.0 3.0 × 109 ( 20%
1,5cBDN 12.0 2.1 × 109
1,4BCN 11.7 2.0 × 109
BbcON 11.6 2.0 × 109
1.2
1.0
0.49
0.33
0.99 × 109
1.0
1.0
0.50
0.25
1,5cBDN 12.0 0.99 × 109
1,5tBDN 12.0 0.97 × 109
1,4BCN 11.7 1.0 × 109 f
BbcON 11.6 5.6 × 108
1,3BCN 10.0 3.5 × 109 f
2,7tBDN 12.5 2.9 × 108 f
2,6tBDN 14.0 5.0 × 107 f
1
-13.78
1
-13.3
1
0.97 × 109
1.0 × 109 e
5.6 × 109
1.0
1.0
0.75
1.9
0.78
0.24
-13.57 0.98 -12.0 0.91
-3.70 0.27 -6.27 0.47
-1.65 0.12 -0.51 0.04
a Abbreviations: BbcON, 1-(4-biphenyl)-4-(2-naphthyl)bicyclo[2.2.2]-
octane; 1,4-BCN, 1-(4-biphenyl)-4-(2-naphthyl)cyclohexane; 1,5tBDN,
1-(4-biphenyl)-5-(2-naphthyl)-trans-decalin; 1,5cBDN, 1-(4-biphenyl)-
5-(2-naphthyl)-cis-decalin. Stereochemistry of aromatics on six-
member rings is equatorial. b The biphenyl to naphthalene center-to-
center separation was calculated by MM2 molecular mechanics using
PCMODEL.57 c Estimated uncertainties are (15% unless otherwise
stated. d Relative to 1,5cD. Calculated by |V/chain| ) (ket)1/2/(no. of
equivalent chains). e Rate constant from ref 60.
10.87 0.79
8.78 0.64
14.2 1.1
8.14 0.61
-1.46 0.11 -2.14 0.16
a Abbreviations: B, biphenyl; N, naphthalene; cD, cis-decalin; tD,
trans-decalin; C, cyclohexane. The numbers preceding the abbreviated
spacer indicate donor/acceptor attachment position. Stereochemistry
is equatorial in all cases. b The biphenyl to naphthalene center-to-center
separation was calculated by MM2 molecular mechanics using PC-
MODEL.57 c Determined from the square root of the ratio of the HT
rate of the compound relative to the rate of 1,5cD. d Calculations were
performed on molecules in which the biphenyl and naphthalene groups
are replaced by CH2 groups (see Figure 2). AM1-minimized structures
of the triplet biradical were used in the calculations. e Ratio of the HT
coupling of the molecule relative to the coupling of 1,5cD. f Rate
constant from ref 60.
states. From perturbation theory,64,65 the coupling of the donor
and acceptor by one such chain (the kth) is given by
V ) - (-â )/ (B )
(3)
∏
∏
k
ij
i
n+1
n
The âij are the couplings between the ith and jth states. The Bi
is the energy difference between the ith state and states D and
A. In a molecular electron transfer reaction, there will be many
such chains. The total coupling is the algebraic sum over all
chains
are roughly constant throughout these compounds (for donor-
acceptor separations of five bonds), their Franck-Condon
factors are expected to differ little. With this simplification,
the relative coupling between the spacers can be directly deduced
from the charge transfer rates by the relation |V| (ket)1/2
.
Though the spacers vary substantially in structure, the charge
transfer rates do not. With the assumption that each sym-
metrically identical path of carbon-carbon bonds connecting
the donor and acceptor will contribute equally to the total
electronic coupling, it is possible to infer the coupling efficiency
as a function of the conformation of the hydrocarbon chains in
the bridges. The column entitled “coupling per chain” is the
coupling efficiency for each five-bond chain relative to 1,5cD
which has the trans planar geometry that is expected to yield
the largest through-bond coupling. The results for this set of
donor/acceptor compounds indicate that the cis five-bond chain
(in bcO) has a coupling of about one-fourth to one-third that of
the trans chain (in 1,5cD and 1,5tD), whereas the gauche chain
(dihedral of 57° in 1,4C) has a coupling of about one-half that
of the trans chain. Remarkably this relationship is the same
for electron transfer in anions and hole transfer in cations.
These conclusions are in accord with Hoffmann’s predic-
tions1,2 about coupling through hydrocarbon chains. These
conclusions rely on the assumptions that direct interactions are
unimportant and that the two chains in cyclohexane and the
three in bcO contribute approximately additively to the total
coupling. These assumptions can be examined, and the nature
of the coupling can be elucidated by comparison of the
experimental results with calculations of the electronic coupling.
B. Comparison of Experimental and Theoretical Cou-
plings. The measured HT and ET couplings are compared with
the 3-21G KT and ∆SCF couplings in Tables 2 and 3. The
AM1 couplings are given in Table 4. The couplings normalized
to that of 1,5cD are included to simplify the comparison of the
experimentally determined values with the calculated couplings.
For the HT data, the actual couplings are unknown, so it is
especially useful to normalize the data. Differences in the
donor-acceptor separation can also alter the Franck-Condon
factors because a shorter donor-acceptor separation will reduce
the solvent reorganization energy. In the compounds where the
donor and acceptor are separated by five bonds, the distances
are nearly constant (Table 1), so no correction has been made.
V ) ΣkVk
(4)
This superexchange picture can be effectively implemented
if the ratio âij/Bi of the coupling elements to the energy
denominators is small. Unfortunately, âij/Bi is large if the
representation is made up of atomic orbitals. A more useful
representation is one in which the intermediate states of the
saturated hydrocarbon are localized σ and σ* bond orbitals. We
have used Fock matrix elements from Weinhold’s natural bond
orbitals (NBOs),66,67 which are localized orbitals. These local-
ized orbitals are obtained by transforming the canonical (i.e.,
delocalized) SCF molecular orbitals (MOs) into a set of
orthonormal bond orbitals. The NBOs can be divided into
“occupied” and “unoccupied” orbitals. The former include core
orbitals, lone pairs, and σ or π bonds, and the latter include σ*
or π* antibonds and extra-valence-shell orbitals (Rydbergs).
These NBOs are used in the calculation of the electronic
coupling interactions in eq 3. The coupling elements, âij, and
the energy denominators, Bi, used in eq 3 are obtained from
off-diagonal and diagonal elements of the Fock matrix in the
NBO representation of the UHF wave function. Paths involving
hops (forward or backward) between occupied orbitals, un-
occupied orbitals, and both occupied and unoccupied orbitals
(referred to as mixed paths) are included in the SE results. In
this study the SE pathways analysis of coupling was carried
out using the â orbitals of the neutral triplet biradical to estimate
couplings for the anion. The signs for the SE couplings are
taken from the KT couplings.
4. Results and Discussion
A. Comparison of Experimental Couplings for Different
Spacers. Electron transfer and hole transfer rate data are
presented in Table 1. Because the donor-acceptor separations
(65) Ratner, M. A. J. Phys. Chem. 1990, 94, 4877.
(66) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211-8.
(67) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985,
83, 735-46.

InVestigation of Through-Bond Coupling Dependence
J. Am. Chem. Soc., Vol. 118, No. 2, 1996 383
Table 3. Comparison of Experimental Electron Transfer Coupling
Elements with ab initio Calculations
experimentala
couplings, UHF/3-21Gb
V
Koopmans
(mH)
∆SCF
compdc
(cm-1
)
ratiod
ratiod
(mH)
ratiod
1
1,5cBDN
1,5tBDN
1,4BCN
BbcON
1,3BCN
2,7tBDN
2,6tBDN
140
170
140
140
160
58
1
-9.17
-9.41
-12.43
-5.77
13.66
5.61
-2.49
1
-10.1
-9.54 0.95
-11.4
-5.25 0.52
14.5 1.4
5.65 0.56
-2.26 0.22
1.2
1.0
1.0
1.1
0.41
0.19
1.0
1.4
0.63
1.5
0.61
0.27
1.1
27
a Electronic couplings were obtained from the ET rates by reference
to the known coupling for a steroid spacer72 and correcting73 for distance
dependence of solvent reorganization energy by use of an approximate
dielectric continuum model. b Calculations were performed on mol-
ecules in which the biphenyl and naphthalene groups were replaced
by CH2 groups. AM1-minimized structures of the triplet biradical were
used in the calculations. c For abbreviations, see Table 2. d Ratio of
the ET rate of the compound relative to the rate of 1,5cD.
Table 4. Comparison of AM1-Calculated Coupling Elements with
Experimenta
Figure 4. Most important paths of the trans, gauche, and cis five-
bond fragments from 1,5cD, 1,4C, and bcO (90,90), respectively, based
on neutral triplet â orbitals. The symmetries of the fragments are C2h,
C2, and C2v, respectively. The total couplings from KT [V(KT)] and
SE analysis [V(SE), convergence to 10-6 hartree] are also given. The
structure of the fragment has the AM1-optimized geometry of the spacer
from which it is derived. (Use of bond lengths and angles from the
trans conformer in a calculation on the cis conformer changes the KT
value from -0.39 to 0.11 mH.) All results are from 3-21G calculations.
Underlined numbers are diagonal matrix elements; other numbers are
off-diagonal matrix elements.
electron transfer
AM1b
hole transfer
AM1b
experimentala KT relative experimentala KT relative
compd coupling ratio (mH) ratio coupling ratio (mH) ratioc
1,5cD
1,5tD
1,4C
bcO
1,3C
2,7tD
2,6tD
1.0
1.2
1.0
1.0
1.1
0.41
0.19
3.79 1.0
1.0
1.0
1.0
0.75
1.9
0.78
0.24
5.68 1.0
5.17 0.91
0.09 0.02
2.40 0.42
4.02 0.71
2.93 0.52
0.12 0.02
2.96 0.78
1.54 0.41
0.64 0.17
5.23 1.4
1.79 0.47
0.30 0.080
ecules having only one chain of carbon atoms and SE pathways
analysis of the chains and complete spacer molecules. In the
first part of this section, we present calculations of the couplings
through isolated trans, gauche, and cis five-bond fragments of
the full spacer. These fragments are created by removing the
other carbon atoms and associated hydrogens and tying off the
dangling bonds with hydrogens. We refer to them as fragments
because they contain only one chain, although they are complete
donor-spacer-acceptor molecules. In the second part, the
couplings in the five-bond fragments are compared to those from
the five-bond chains within the full spacers, and in the third
part, additivity of the couplings is examined. This study is done
for anion coupling because it is less sensitive to the molecular
structure, but the conclusions are expected to be similar for the
cations.
a See previous tables for a description of experimental couplings and
abbreviations. b Electronic couplings were calculated with the AM1
semiempirical Hamiltonian59 for molecules having CH2 donor and
acceptor groups. Koopmans’ theorem was used on the neutral triplet
biradical. c Ratio to coupling calculated with the 1,5cD spacer.
The Koopmans’ theorem approach gives results that are
usually within 20% of the ∆SCF method (Tables 2 and 3) but
are occasionally off by up to a factor of 2, consistent with the
findings of previous studies.42,52
The agreement between the experimental ratios and theory
(∆SCF) is often within 20%, but there are important exceptions,
particularly the calculated ET coupling for bcO and the HT
couplings for 1,4C, 1,3C, and bcO. In these worst cases the
discrepancy in the calculated coupling ratios is less than a factor
of 2, except for the spectacular failure to calculate HT couplings
for bcO. The differences of a factor of 2 between experiment
and theory are probably due to uncertainty of the theoretical
couplings because of dependence on the choice of geometry,
level of theory, and use of the CH2 groups in place of the larger
chromophores. In the case of bcO, the HT coupling is especially
sensitive to the geometry. The use of the optimized structure
of the cation instead of the neutral triplet structure gives a
coupling that is in reasonable agreement with experiment. The
dependence of coupling on the choice of structure used in the
calculation will be presented in a future publication. In this
paper we have used AM1-optimized structures for the neutral
triplet radical in all coupling calculations. When the semi-
empirical AM1 method is used to calculate couplings, the results
are in greater disagreement with the experimental results (see
Table 4).
1. Five-Bond Fragments. The effect of rotation about the
C3-C4 bond in the trans alkyl C6H12 is investigated in
conformers having C2-C3-C4-C5 dihedral angles of 180°
(trans), 57° (gauche), and 0° (cis). The molecular structures
(bond lengths and bond angles) of these three conformers are
taken from the five-bond (C6) chains of the AM1-optimized
structures of 1,5cD, 1,4C, and bcO, respectively. The cut C-C
bonds are replaced with hydrogens (i.e., C-H bonds), whereas
the orientation of the terminal (D and A) CH2 groups are the
same as in the full systems. The trans form is about 9 kcal/
mol more stable than the cis form at the 3-21G level. The five-
bond fragments are illustrated in Figure 4.
C. Calculations on Isolated Chains and SE Pathways
Analysis. We now discuss the dependence of the calculated
couplings on geometry using HF/3-21G calculations on mol-
At the HF/3-21G level (KT results), the magnitude (absolute
value) of the coupling in the five-bond anion fragment is reduced

384 J. Am. Chem. Soc., Vol. 118, No. 2, 1996
Paulson et al.
Figure 5. Effect of CH2 rotation on the most important paths and total
coupling of trans and cis five-bond fragments (geometry is the same
as in Figure 4). Most important pathways are shown. The donor/acceptor
p orbitals are out of the plane containing the carbon atoms of the bridge.
The pathway calculations are based on neutral triplet â orbitals with
convergence to 10-6 hartrees. All results are from 3-21G calculations.
from 9.28 mH in the trans structure to 0.39 mH in the cis
structure and 0.18 mH in the gauche structure. Similar results
have been reported by Liang and Newton,42,46 and Broo and
Larsson68 for C6H12. Seeing that these calculations are in accord
with the predictions of Hoffmann,1,2 we now apply the pathway
method to seek insight into the superior coupling through trans
chains. Figure 4 shows the two most important pathways for
anion coupling from SE analysis in the cis, gauche, and trans
structures. The contribution from the first and most important
pathway, which passes through only the central C-C antibond,
remains almost constant in the trans, gauche, and cis conform-
ers. But the NBO Fock matrix elements listed in Figure 4
indicate that the matrix element between the C2-C3* and C4-
C5* antibonds is very sensitive to rotation. Even though the
magnitude of this matrix element increases in the cis and gauche
structures, the change in sign causes the contributions from the
first and second paths to reinforce in the trans but to cancel in
the cis and gauche conformers (see Figure 4). Thus the pathway
method identifies the angle dependence of the interactions
between the next-to-central antibonds as a principal origin of
Hoffman’s trans rule. The picture developed here has features
in common with early, qualitative pictures of Hoffman1,2 and
Paddon-Row.8,13
A dramatic change also occurs in the coupling with 90°
rotation of the terminal CH2 groups. The results are shown in
Figure 5. The CH2 groups are oriented to place the donor/
acceptor p orbitals out of the plane containing the carbon atoms
of the bridge. Rotation from in-plane (Figure 4) to out-of-plane
(Figure 5) orientation reduces the magnitude (absolute value)
of the coupling (KT) from 9.28 to 0.49 mH for the trans
structure and increases the coupling from 0.38 to 14.63 mH for
the cis structure. When the donor/acceptor p orbitals are out-
of-plane, they do not interact with the C-C bonds or antibonds
of the spacer, thus eliminating the principal pathways. However
in the out-of-plane orientation, pathways through C-H bonds
of the spacer become important, although their magnitudes are
smaller. In this case the coupling in the cis form is much larger
than the trans form because of better interaction between the
CHs (see Figure 5) and the contribution of many paths. This
illustrates how important C-H bonds can be in determining
the coupling. The energy for rotation of the terminal CH2
groups for both the cis and trans forms is small (<1 kcal/mol).
Figure 6. Illustration of decomposition of coupling in full spacers into
three types: (1) chain, (2) nonchain, and (3) cross talk.
This type of effect has also been noted by Liang and Newton35
for C6H12 and Paddon-Row and Jordan69 for dienes, where they
refer to it as laticyclic hyperconjugation.
2. Comparison of Couplings for Five-Bond Fragments
and Full Spacers. The couplings (KT) in the cis and gauche
fragments are much less (-0.39 and 0.18 mH, respectively,
compared to -9.28 mH for the trans fragment) than expected
on the basis of the experimental results for the full spacers,
which suggest cis = 1/2gauche = 1/4trans. In order to investigate
the reason for this difference and to compare with couplings
through the five-bond chains of the full spacers, the couplings
for the full spacers and fragments have been separated into three
parts as illustrated in Figures 6 and 7. For the full spacers, the
three parts are (1) “nonchain”, (2) “chain”, and (3) “cross talk.”
The nonchain part includes contributions from direct interactions
between the lone pairs, Rydbergs located on the donor/acceptor
carbons, and any other paths that do not pass through the central
three-bond part of the five-bond chain as illustrated in Figure
6. Cross talk70,71 includes paths that hop between the chains in
1,4C or bcO spacers. The chain part includes all other paths
that pass through the central three-bond portion as illustrated
in Figure 6. (The Rydbergs on the bridgehead carbons are
considered to be nonchain.) The decomposition is similar for
the five-bond fragments, except that cross talk is absent and
instead there is a contribution from paths through CHs used to
tie off the dangling bonds. This part is denoted “CH”. The
nonchain and chain parts for the fragment are defined in the
same way as for the full spacer and are illustrated in Figure 7.
The separation is computed using two methods: (1) SE and
(2) Koopmans’ theorem via diagonalization (DIAG) of the Fock
matrix with selected off-diagonal matrix elements deleted. In
(69) 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; Vol. 6, pp 115-94.
(70) Onuchic, J. N.; Beratan, D. N. J. Am. Chem. Soc. 1987, 109, 6771-
8.
(71) Shephard, M. J.; Paddon-Row, M. N.; Jordan, K. D. J. Am. Chem.
Soc. 1994, 116, 5328-33.
(68) Broo, A.; Larsson, S. Chem. Phys. 1990, 148, 103-15.

InVestigation of Through-Bond Coupling Dependence
J. Am. Chem. Soc., Vol. 118, No. 2, 1996 385
Table 5. Contributions (in mH) to Anion Coupling between CH2
D/A Groups in Five-Bond Chain Fragments (with Geometries from
Full Spacers)a
contribution
CHb
type of analysis
1,5cD
1,4C
bcO
SE
diag
SE
diag
SE
diag
-0.15
0.14
1.02 -0.08
0.57 0.30
-12.06 -5.58 -2.63
-9.99 -5.07 -3.94
5.05
4.95
2.12
2.09
0.99
1.46
nonchainc
chain (three-bond)d
totale
SE
diag
-11.26 -0.60
0.38
-9.28 0.18 -0.39
a 3-21G calculations based on SE analysis (10-4 hartree convergence)
and diagonalization (Koopmans’ theorem) with deleted matrix elements.
The column labels (e.g., 1,4C) indicate the spacer from which the five-
bond fragment was obtained. b Contributions from paths passing through
C-H bonds used to tie off dangling C-C bonds. See Figure 7 for
illustration of these paths. c Includes direct interactions and contributions
from paths not passing through the three-bond part of the chain as
illustrated in Figure 7 or from paths passing through C-H bonds used
to tie off dangling C-C bonds. d Contribution from paths passing
through central three-bond chain as illustrated in Figure 7. (Does not
include paths passing through C-H bonds used to tie off dangling C-C
bonds.) For SE analysis, gauche ) 0.45trans and cis ) 0.22trans.
For diagonalization, gauche ) 0.58trans and cis ) 0.44trans. e Total
coupling = nonchain + CH + chain.
Table 6. Contributions (in mH) to Total Coupling in D/A Full
Spacer Anion Systems with Five-Bond Chains from SE Analysis
(10-4 Hartree Convergence) and Diagonalization with Deletion of
Matrix Elements (3-21G Basis)
Figure 7. Illustration of decomposition of coupling in five-bond chain
fragments into three types: (1) chain, (2) nonchain, and (3) CH.
bcO
type of
both methods the neutral triplet â Fock matrix was used to
compute couplings for anions. In the SE method, paths of
different types (1, 2, or 3) at 10-4 hartree convergence were
computed and added together. This is straightforward in the
pathway method because all paths are assumed to be additive.
In the diagonalization method, some explanation is required.
We first discuss the procedure for the full spacer. To obtain
the nonchain coupling, Vnonchain, all off-diagonal matrix elements
associated with the central three-bond chain NBOs (C-C bonds
and antibonds, C Rydbergs, C-H bonds and antibonds, H
Rydbergs) were set to zero and the Fock matrix was diagonal-
ized. The cross talk part, Vcross talk is obtained by deleting (setting
to zero) all elements connecting the NBOs of one chain to those
of the second (and third in the case of bcO) and subtracting the
resulting coupling from the total coupling. The chain coupling
was then computed as Vchain ) Vtotal - Vnonchain - Vcross talk. The
total coupling is Vtotal ) Vnonchain + Vcross talk + Vchain. This is
approximately true in the KT method.
contribution
direct (LP)
analysis 1,5cD 1,5tD 1,4C (90,90) (0,0)
SE -0.23 -0.11 -0.45 -0.37 -0.40
direct (LP Rydberg)a SE
0.22
-3.48 -2.18
-1.38
0.42
1.11
0.59
0.42
1.68
1.19
0.68
1.40
1.00
0.62
nonchainb
SE
diag
SE
diag
SE
SE
SE
SE
diag
SE
diag
SE
cross talk (xt)c
-4.30 -2.65 -5.23
-2.64 -2.98 -2.97
chaind A
-9.93 -9.15 -6.01 -5.10
0.24
B
C
-6.01 -0.73 -3.54
-0.73 -3.54
chain total (no xt)e
-9.93 -9.15 -12.02 -6.56 -6.84
-7.78
-9.93 -9.15 -6.01 -2.18 -2.84
-7.78 -5.40 -1.13 -1.16
-13.41 -11.33 -15.73 -8.02 -11.07
-9.16 -12.42 -5.69 -5.77
-10.20 -3.39 -3.48
chain av (no xt)f
totalg
diag
a Includes interactions through Rydberg orbitals on the donor/acceptor
(LP) carbons. b Includes direct interactions and other contributions from
other paths not passing through the three-bond part of the chain as
illustrated in Figure 6. c Includes contributions from paths that involve
jumps from one chain to another as illustrated in Figure 7. This quantity
is not determined for 1,5cD and 1,5tD as they have only one three-
bond chain. d Contributions from paths passing through individual
chains as illustrated in Figure 6. e Total contribution from paths passing
through all three-bond chains. f Average contribution per chain in full
spacer. For SE analysis, gauche ) 0.60trans and cis ) 0.22(or
0.28)trans. For diagonalization, gauche ) 0.69trans and cis )
0.15trans. g Total coupling = nonchain + cross talk + chain.
The decomposition by diagonalization for the case of the five-
bond fragments proceeds as follows: The contribution, VCH
,
from the C-H bonds used to tie off the dangling C-C bonds
is calculated by deleting the off-diagonal NBO elements of these
CH groups and subtracting the resulting coupling from the total
coupling. The nonchain part, Vnonchain, is calculated by deleting
the chain NBOs and the CH NBOs and diagonalizing the Fock
matrix. Finally, the chain coupling was computed as Vchain
Vtotal - Vnonchain - VCH
)
in bcO) was removed. The SE analysis shows that on the basis
of the chain contributions in the C6H12 fragments, the gauche
fragment yields about one-half and the cis fragment about one-
third of the coupling from the trans fragment. The results from
the fragments are consistent with the conclusions drawn from
the experimental results for the full spacers in section 4. A.
While experimental results are similar for hole transfer, a similar
analysis was not done there because the calculations do not agree
well with experiment for the cis (bcO) case.
.
The decomposition results for the fragments are given in
Table 5. They indicate that for the trans conformer the chain
contribution is dominant [SE: -12.06 mH (chain) vs 1.02
(nonchain)], whereas in the cis and gauche fragments the chain
contributions are nearly canceled by those from nonchain and
CH parts, which are of opposite sign from the chain part. This
cancellation results in the surprisingly small couplings reported
in Table 5. This cancellation in the cis and gauche fragments
is largely due to the importance (positive contribution) of paths
between the C-H bonds added when the second chain (or chains
In Table 6, the couplings for anions of 1,5cD, 1,4cD, 1,4C,
bcO (90,90), and bcO (0,0) are separated into chain, nonchain,
and cross talk contributions as illustrated in Figure 6. In

386 J. Am. Chem. Soc., Vol. 118, No. 2, 1996
Paulson et al.
addition, the chain part is further separated into contributions
from the individual three-bond chains, for example, A, B, and
C in bcO (see Figure 6), by the SE analysis. The cross talk
makes significant contributions (2-5 mH) to the coupling, as
has been found in calculations by Onuchic and Beratan70 for
edge-fused cyclobutanes and by Shephard and co-workers in
norbornyl systems.71 Both Onuchic and Shephard found that
cross talk reduced the coupling through two parallel chains with
cross connections relative to separate chains. An interesting
aspect is that, by contrast, for both 1,4C and bcO, cross talk
increases the coupling. This opposite effect of cross talk may
be the reason that couplings through cyclohexane-based spacers
have almost the same distance dependence as that through
norbornyl spacers, despite the significant all-trans advantage
of the norbornyl systems. The norbornyl systems do give much
larger couplings, but this may be attributed mainly to distance-
independent factors, larger coefficients, and double attachments
of the donor and acceptor groups.22 Although cross talk is
significant, the major contributions come from the five-bond
chains. The coupling from the five-bond gauche chain of 1,4C
(-6.0 mH) is ca. one-half that of the five-bond chain of 1,5cD
(-9.9 mH). This is similar to the results on the fragments and
is consistent with the deduction from experiment that gauche
= 1/2trans. The results for 1,5tD in Table 6 are also consistent
with this conclusion.
In 1,5cD and 1,5tD the contributions from paths passing
through the peripheral seven-bond chains are included in the
nonchain entry in Table 6. They can be estimated to be about
-3 mH for 1,5cD and -2 mH for 1,5tD by subtraction of the
direct and LP Rydberg contributions (rows 1-2) from the
nonchain total. Thus, as expected, the contributions from those
two longer chains are much smaller than those from the central,
trans five-bond chains.
The results in Table 6 indicate that for bcO the three cis five-
bond chains do not contribute equally to the coupling because
of dependence on orientation. For bcO (90,90), the upper chain
(A) contributes -5.54 mH, whereas the lower chains (B and
C) each contribute -0.75 mH. For the bcO (0,0) conformer,
the two lower bridges (B and C in Figure 7) make contributions
of -3.54 mH each (see Table 5), whereas the upper bridge
contribution is near zero (0.24 mH) because of symmetry. The
3.54 mH coupling for each lower bridge in bcO (0,0) is
consistent with the bcO (90,90) result on the basis of a cosine
relation, that is, (5.10 mH) × [cos(30°)]2 ) 3.82 mH. The
average of the contributions from the paths through the three
cis five-bond chains in bcO (90,90) and bcO (0,0) is 2.50 mH
based on SE analysis. Thus, cis = 1/4trans, consistent with the
experimental conclusions. From diagonalization, the average
contribution is smaller, -1.14 mH, but may be a reflection of
the smaller KT coupling compared to the SE coupling. Also,
note that the KT coupling in bcO is about one-half of the
coupling in 1,4C.
Figure 8. Most important paths and total coupling for electron transfer
in species having five-bond paths from SE calculation using neutral
triplet â orbitals with convergence to 10-6 hartrees. All results are from
3-21G calculations. Underlined numbers are diagonal matrix elements;
other numbers are off-diagonal matrix elements.
The most important pathways between the donor and acceptor
in bcO, 1,5tD, 1,5cD, and 1,4C are shown for anion coupling
in Figure 8. In the case of bcO, results for three orientations
of the CH2 groups are shown: (0,0), (90,90), and (30,-30).
The coupling contributions shown in Figure 8 for the first two
paths in 1,5cD are similar to those of the trans C6H12 fragment
in Figure 4 derived from it, in that they are large and of the
same sign as well as being through the trans chain. The
coupling contributions for the first two paths in 1,4C are also
similar to those of the gauche C6H12 fragment derived from it
in that they are large and of opposite signs as well as being
through a single gauche five-bond chain. The most important
paths in bcO (90,90) are through the top bridge (A in Figure
8). This is expected because of the favorable interaction with
the D/A orbitals. The contributions for the first two paths in
the A branch of bcO (90,90) are similar to those of the cis C6H12
fragment derived from it, although they are larger (absolute
value) and the ordering is reversed, that is, the most important
path is the two-step path instead of the one-step path. The NBO
matrix elements in Figures 4 and 8 indicate that this is due to
larger off-diagonal interaction elements as well as smaller
denominators (Bi, i.e., the difference in diagonal elements).
3. Additivity of Couplings. The 1,4-cyclohexane spacer
can be viewed as two partly overlapping five-bond chains, each
of which contributes a through-bond coupling. Can such a
spacer be considered as the additive sum of two hydrocarbon

InVestigation of Through-Bond Coupling Dependence
J. Am. Chem. Soc., Vol. 118, No. 2, 1996 387
The measured electron and hole transfer rates of the four
compounds with five-bond chains are all approximately the same
despite the different conformations of the chain. Because bcO
has three five-bond chains, 1,4C has two, and 1,5tD and 1,5cD
have one, the results follow the approximate additive relation-
ship: 1 trans chain = 2 gauche chains = 3 (or 4) cis chains,
that is, gauche = 1/2trans, cis = 1/3(or 1/4)trans. This relation-
ship holds for both electron transfer in anions and hole transfer
in cations. Thus, these compounds appear to obey the trans
rule set forth by Hoffmann and are qualitatively con-
sistent with observations and calculations of Paddon-Row and
co-workers.12
Figure 9. Decomposition of coupling in 1,4C and the gauche five-
bond fragment from the SE calculation using 3-21G, neutral triplet â
orbitals with SE analysis convergence to 10-4 hartrees. See text for a
description of the nonchain, chain, cross talk, and CH contributions.
The superiority of trans chains in transmission of electronic
coupling is due to constructive (in trans) and destructive (in
cis and gauche) interference between two principal pathways,
one of which has little angle dependence and one of which has
strong angle dependence. This picture is from ab initio pathway
calculations on anions of five-bond hydrocarbon chains.
chains? The coupling between two CH2 groups attached at
angles (0,0) to 1,4C is -15.73 mH as calculated by the SE
pathway method (or -12.42 mH from Koopmans’ theorem)
using neutral triplet â orbitals and 3-21G basis (see Table 5). If
a “one-armed” cyclohexane is created by removal of two carbons
(Figure 9) so the two CH2 groups are attached to a four-carbon
chain having the same conformation as in cyclohexane, the
coupling is -0.60 mH (0.18 from KT). Given the known
dominance of through-bond interactions, we might expect that
1,4C with two chains might produce twice as much coupling
as the single (CH2)4 chain, but instead the 1,4C produces 26
times (-69 times from KT) as much! This result indicates that
the coupling through two (CH2)4 chains is not twice that through
one. Such nonadditivity can also be seen in calculations of
Liang and Newton.42 Why? The pathway method will be
employed to delineate the reasons for this apparent failure of
additivity and to show that the concept of additivity is valid,
but that TB couplings can behave in unexpected ways due to
important effects of nonbonded interactions.
The decomposition of the coupling for 1,4C by the ab initio
pathways method is illustrated in Figure 9. The SE pathways
analysis on the complete structure (Table 5) indicates that the
paths through each bridge contribute -6.0 mH (-12.0 mH total)
to the total coupling of -15.73 mH. Pathways that include hops
between the two bridges of the ring (cross talk) add another
-4.3 mH to the coupling. The coupling through a five-bond
gauche chain fragment is only -0.6 mH, but the SE analysis
shows that it is that small because of a 5.0 mH contribution
from the C-H bonds introduced when the dangling bonds were
capped by the hydrogens illustrated on the right in Figure 9.
The coupling through the gauche chain without those C-H
bonds, which are not present in the full 1,4C spacer, is -5.0
mH. Once those C-H bonds are accounted for, it is seen that
the two gauche chains contribute a coupling of about 11.2 mH,
which differs from the total for 1,4C by approximately the -4.3
mH cross talk between the two chains and the 0.6 mH direct
interaction. Those two contributions, particularly the substantial
contribution from cross talk, mean that the total is not just the
sum of contributions from the two gauche chains. Both the
large contributions from the capping C-H bonds and the cross
talk are predominantly nonbonded interactions. These findings
contribute further to the picture developed earlier when the
pathway method showed41,45 that most through-bond interactions
arise from paths that skip bonds. The message is similar here:
Through-bond couplings are ironically developed largely through
nonbonded interactions.
Theoretical calculations of the hole and electron transfer
couplings in model molecules having CH2 donor/acceptor groups
are in fair agreement with the trends found from experimentally
measured rates. They agree to within a factor of 2, with the
exception of hole transfer in bcO. In this case, theory and
experiment are in sharp disagreement. The reason may be due
to the sensitivity of the calculations to the structure.
The SE analysis of the five-bond (cis, gauche, and trans)
fragments and the full spacers reveals that the theoretical
couplings for 1,5cD, 1,4C, and bcO are approximately consistent
1
1
with the relationship, gauche = /2trans, cis = /4trans, found
experimentally. Cross talk between chains and direct interac-
tions are found to be more important in the case of bcO and
1,4C spacers, so that the total coupling is not just the sum of
contributions from the separate chains in these cases.
Cross talk between the gauche chains of 1,4C and the cis
chains of bcO enhances the coupling between the π donor and
acceptor in contrast to its deleterious effect in the case of
cyclobutyl70 and norbornyl-based71 spacers. This opposite effect
of cross talk may account for the fact that the distance
dependence of electronic couplings through cyclohexyl-based
spacers is only slightly steeper than that through all-trans
norbornyl spacers, despite the substantial superiority of all-trans
conformation.
Trans alkyl chains, (CH2)n, have couplings similar to rigid
molecules (cis and trans 1,5D) containing trans chains with the
same conformation. This is not true for gauche and cis alkyls
in which the couplings are strongly influenced by interactions
through the C-H bonds used to tie off dangling bonds left when
other chains were removed from 1,4C or bcO. When coupling
through a carbon chain is poor, as in the cis chain from bcO or
the gauche chain from 1,4C, the nonbonded interactions of CHs
make an important contribution to the total coupling.
Acknowledgment. This work was supported by the U.S.
Department of Energy, Office of Basic Energy Sciences,
Division of Chemical Sciences, under Contract No.
W-31-109-ENG-38.
JA952852I
5. Conclusions
The following conclusions can be drawn from this study of
electron transfer in these compounds containing five-bond chains
with dihedral angles ranging from 0° to 180°.
(72) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem. Soc. 1984,
106, 3047.
(73) Paulson, B. P. Ph.D. Thesis, The University of Chicago, 1993.