Long-range electron transfer

Abstract

Recent investigations have shed much light on the nuclear and electronic factors that control the rates of long-range electron tunneling through molecules in aqueous and organic glasses as well as through bonds in donor-bridge-acceptor complexes. Couplings through covalent and hydrogen bonds are much stronger than those across van der Waals gaps, and these differences in coupling between bonded and nonbonded atoms account for the dependence of tunneling rates on the structure of the media between redox sites in Ru-modified proteins and protein-protein complexes.

Fig. 1.

Timetable for activationless electron tunneling through various media: vacuum (black, β = 2.9–4.0 Å^-1), MTHF glass (violet, β = 1.57–1.67 Å^-1), aqueous glass (cyan, β = 1.55–1.65 Å^-1), and toluene glass (green, β = 1.18–1.28 Å^-1). Investigations of ET rates in D-(bridge)-A complexes have produced exponential distance dependences: xylyl bridges, β = 0.76 Å^-1 (red) (12); alkane bridges, β = 1.0 Å^-1 (orange) (10); and β-strand bridges in ruthenium-modified azurin, β = 1.1 Å^-1 (yellow).

Fig. 2.

Tunneling distances and backbone structure models showing locations of the Cu active site (blue) and the Ru(bpy)₂(im)(HisX)²⁺ label (orange) in Ru-azurins: Ru-Cu (Å), HisX (X = 122, 15.9; 83, 16.9; 109, 17.9; 124, 20.6; 107, 25.7; 126, 26.0).

Fig. 3.

Tunneling timetable for intraprotein ET in Ru-modified azurin (blue circles), cyt c (red circles), myoglobin (yellow triangles), cyt b₅₆₂ (green squares), HiPIP (orange diamonds), and for interprotein ET Fe:Zn-cyt c crystals (fuchsia triangles). The solid lines illustrate the tunneling-pathway predictions for coupling along β-strands (β = 1.0 Å^-1) and α-helices (β = 1.3 Å^-1); the dashed line illustrates a 1.1-Å^-1 distance decay. Distance decay for electron tunneling through water is shown as a cyan wedge. Estimated distance dependence for tunneling through vacuum is shown as the black wedge.

Fig. 4.

Tunneling-time (1/k_obs) contours as functions of donor-acceptor distance (β = 1.1 Å^-1) and driving force [in units of λ; k_BT/λ = k_B(295 K)/(0.8 eV) = 0.318].

Fig. 5.

Distance dependences of the rates of single-step and two-step electron tunneling reactions. Solid line indicates theoretical distance dependence for a single-step, ergoneutral (ΔG_RP = 0) tunneling process (β = 1.1 Å^-1). Dashed lines indicate distance dependence calculated for two-step ergoneutral tunneling (R;HP) with the indicated free-energy changes for the RH step.