ABSTRACT
I. Introduction....................................................................................................................... 521
II. Theoretical Methods ......................................................................................................... 523
A. Transition State Theory ........................................................................................... 523
B. Tunneling Preliminaries ........................................................................................... 524
C. Approximate Instanton Method ............................................................................... 526
D. Isotope Effects.......................................................................................................... 528
E. Comparison of AIM with Other Methods ............................................................... 528
III. Stepwise Transfer ............................................................................................................. 529
A. Example: Porphine ................................................................................................... 529
B. Isotope Effects.......................................................................................................... 530
C. Temperature Effects ................................................................................................. 532
D. Applications ............................................................................................................. 533
IV. Concerted Transfer ........................................................................................................... 535
A. Example: Acetic Acid-Methanol Complex............................................................ 535
B. Hydrogen Bonded Dimers and Complexes ............................................................. 537
C. Water Wires ............................................................................................................. 537
D. The Proton Inventory Problem ................................................................................ 542
V. Conclusions....................................................................................................................... 543
Acknowledgments ........................................................................................................................ 544
References..................................................................................................................................... 544
Protons, like electrons, are light enough to tunnel through potential-energy barriers, an ability that
provides them with a high mobility. However, while electrons can jump over distances of 10 A
˚
or
more, proton jumps are typically limited to 1 to 1.5 A
˚
. Nevertheless, protons manage to travel over
much larger distances, e.g., across cell membranes. For a long-time the mechanism of this long-
range proton transport was controversial, but in recent years the idea that water molecules
embedded in proteins can serve as proton conduits (water “wires”) has found wide acceptance.
Such transport amounts to a relay process: While the first proton jumps from atom (or group) one to
atom two, the second proton jumps from atom two to atom three, etc. This may be a cyclic process
where the final proton upon reaching atom N jumps back to atom one, or a linear process in which
atom one donates and atom N accepts a proton. Such processes can follow either a classical
mechanism in which energy is conserved throughout or a tunneling path in which energy is
conserved only at the start and finish of the jump.
