Department of Chemistry, **Machine** VP

University of New South Wales

**Co-Investigator** Michael J Shephard

Department of Chemistry,

University of New South Wales

**Theoretical Modelling of Chemical Reactivity and Electron Transfer**

Long-range electron transfer (ET) between two redox centres (chromophores) is characterized by those processes in which the electron transfer takes place over distances substantially larger than the sum of the van der Waals radii of the chromophores. Application of Fermi's Golden Rule leads to the following expression for the rate of nonadiabatic electron transfer:

where FCWD is the Franck-Condon weighted density of states and *V*
is the electronic coupling matrix element. It is *V* that largely
controls the dynamics and distance dependence of long-range ET processes
because, if *V* is zero, then so is the ET rate. Consequently,
considerable effort, experimental and theoretical, is being directed towards
determining the factors that affect the magnitude of *V*.

The simplest and least ambiguous way of investigating experimentally the distance dependence of the dynamics of long-range ET is through the use of rigid, covalently linked donor-bridge-acceptor systems, such as our systems, 1(n), in which the donor and acceptor chromophores are fixed at well defined separations and orientations, through attachment to a rigid bridge of variable length.

Extremely rapid rates of both thermal and photoinduced intramolecular ET
were observed in these systems. ET in these systems is facilitated by
efficient electronic coupling through the saturated bridge bonds, as
illustrated by 2. An important goal of theoretical treatments of ET is to
calculate the electronic coupling element, *V*, through saturated bridges,
and to ascertain how this quantity depends on the nature of the bridge spanning
the chromophores, such as bridge length, bridge configuration, and the chemical
composition of the bridge. In this context, my group, has developed a natural
bond orbital (NBO) and Koopmans' theorem (KT) based approach to calculating and
dissecting the electronic coupling, *V*, for a variety of bridge
systems.

**What are the basic questions addressed?**

This project seeks to extend our preliminary findings by studying a variety of bridges, illustrative of which are 3(n) - 5(n). Bridge 3(n) is particularly interesting in that it serves as a peptide model. Valuable information about coupling in proteins will therefore be obtained from our calculations on 3(n). Systems 4(n) will enable us to explore how the electronic coupling depends on the nature of the chromophore. Systems, such as 5(n) will be studied to ascertain the influence of destructive interference in attenuating the propagation of electronic coupling through parallel bridges, as in 1(n), caused by the presence of cross links that connect the bridges.

**What are the results to date and the future of this work?**

Progress has been satisfactory, and a number of important results have
been published. In particular, using the natural bond orbital (NBO) method, we
have found that the principal cause for the stronger distance dependence of
electronic coupling through a norbornylogous bridge, as in 6, compared to a
simple *n*-alkyl chain, as in 7, is the presence of destructive
interference between the two parallel relays in the former. This interference
occurs largely *via* direct, through-space interactions between pairs of
NBOs located on different relays, as shown by the double-headed arrows in the
polynorbornyl diene structure, 6.

We have just completed a high level *ab* *initio* MO study of
the potential energy surface of the norbornane cation radical, 8. These
results have helped to resolve the experimental esr spectral data for this
compound. These results will also be of use to our studies on the coupling for
hole transfer through polynorbornyl bridges.

We have begun to investigate the possibility that structures such as 9 and 10 should display constructive interference effects through the bridges. If this turns out to be correct then this will represent a useful advance in the rational design of bridges for molecular electronic devices.

**What computational techniques are used and why is a supercomputer
required?**

The NBO/KT calculations and analyses are carried out on a Silicon Graphics workstation at UNSW. Geometry optimizations of large (greater than 30 atoms) and higher level calculations including electron correlation, can only be efficiently carried out on the VP2200. The correlation calculations, in particular are extremely CPU and memory intensive and are only viable using a powerful vector machine such as the VP2200.

**Publications**

*Investigating Long-Range Electron Transfer Processes with Rigid,
Covalently Linked Donor-{Norbornylogous Bridge}-Acceptor Systems*, M N
Paddon-Row, Acc. Chem. Res., **27**, 18 (1994).

*Why is a Simple n-Alkyl Bridge More Efficient than a Polyalkyl Bridge at
Mediating Through-Bond Coupling?,* M J Shephard, M N Paddon-Row, K D
Jordan, J. Am. Chem. Soc. , **116**, 5328 (1994).

*On the Origin of Transannular Interactions in Diketones and
Methylene-Ketones, as Detected by 13C N.M.R. Spectroscopy: An Ab Initio MO
Study*, M N Paddon-Row, Tetrahedron , **50**, 10813 (1994).

*Long-Range Interactions in a Series of Rigid Non-conjugated Dienes: 2. Role
of Electron Correlation in Determining the Distance Dependence of the
[[pi]]+,[[pi]]- and [[pi]]+ ^{*},[[pi]]-^{*} Splittings, *K
Kim, K D Jordan, M N Paddon-Row, J. Phys. Chem. ,