Abstract
The quintessential quantum process in biology and chemistry involves electrons switching between two states. Two examples are electron transfer reactions in proteins when an electron moves from an orbital on the donor moiety D to an orbital on the acceptor moiety A and bond formation or bond breaking in an enzyme when electrons shift from a non-bonding state to a bonding state or vice versa. The energy expectation values of the two states E 1(t) and E 2(t)vary in time due to motions along a reaction coordinate, but also due to thermal fluctuations of the remaining degrees of freedom of the combined reaction—protein system. Often the interaction energies which couple the two electronic states involved in the reaction are weak, i.e., are small compared to the temporal variations of E 1(t) and E 2(t). In this rather typical case the actual reaction process is confined to moments when the two electronic states become energetically degenerate [E 1(t) = E 2(t)] or, to use a widely accepted phrase, when the curves E l and E 2 cross.
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References
Schulten K. and Tesch M., Chem. Phys. 158 (1991) 421–446.
Xu D. and Schulten K., Chem. Phys. 182 (1994) 91–117.
Xu D. and Schulten K., The Photosynthetic Bacterial Reaction Center: II. Structure, Spectroscopy and Dynamics,Plenum Press, New York, 301–312, (1992).
Kubo R., Adv. Chem. Phys. 15 (1969) 101.
Berendsen H.J.C. and Mavri J., J. Phys. Chem. 97 (1993) 13464–13468.
Treutlein H., Schulten K., Deisenhofer J., Michel H., Brünger A. and Karplus M., The Photosynthetic Bacterial Reaction Center: Structure and Dynamics, Plenum, New York, 149, (1988) 139–150.
Treutlein H., Schulten K., Niedermeier C., Deisenhofer J., Michel H. and Devault D., The Photosynthetic Bacterial Reaction Center: Structure and Dynamics, Plenum, New York, 149, (1988), 369–377.
Marcus R.A., J. Chem. Phys. 24 (1956) 966–978.
Marcus R.A., J. Chem. Phys. 24 (1956) 979–989.
Treutlein H., Schulten K., Deisenhofer J., Michel H., Brünger A. and Karplus M., Proc. Natl. Acad. Sci. USA 89 (1991) 75–79.
Uhlenbeck G.E. and Ohrnstein L.S., Phys. Rev. 36 (1930) 823.
Chandrasekhar S., Rev. Mod. Phys. 15 (1943) 1.
Bittl R. and Schulten K., Chem. Phys. Lett. 146 (1988) 58–62.
Nonella M. and Schulten K., J. Phys. Chem. 95 (1991) 2059–2067.
Schulten K. and Bittl R., J. Chem. Phys. 84 (1986) 5155–5161.
Bittl R. and Schulten K., J. Chem. Phys. 90 (1989) 1794–1803.
Pütz B., Barsky D. and Schulten K., Chem. Phys. Lett. 183(5) (1991) 391–396.
Pütz B., Barsky D. and Schulten K., J. Magn. Res. 97 (1992) 27–53.
Nadler W. and Schulten K., J. Chem. Phys. 82 (1985) 151–160.
Barsky D., Pütz B., Schulten K., Schoeniger J., Hsu E.W. and Blackband S., Chem. Phys. Lett. 200 (1992) 88–96.
Markham J. J., Rev. Mod. Phys. 31 (1959) 956.
Jortner J., J. Chem. Phys. 64(1976) 4860–4867.
DeVault D., Quantum-mechanical tunneling in biological systems, Cambridge University press, 1984.
Cardeira A.O. and Leggett A.J., J. Ann. Phys. (N.Y) 149 (1983) 374–456.
Cardeira A.O. and Leggett A.J., Physica A 121 (1983) 587–616.
Leggett A.J., Chakravarty S., Dorsey A.T., Fisher M.P.A. Garg A. and Zwerger W., Rev. Mod. Phys. 59 (1987) 2–86.
Lord Rayleigh, The Theory of Sound, Vol. I, 2nd ed., Mac Millan and Company Ltd., London, 1894.
Lord Rayleigh, Scientific Papers,vol. I, p. 491 and vol. IV, p. 370, Cambridge University Press, 1899–1920.
Rips I. and Jortner J., J. Chem. Phys. 87 (1987) 2090–2104.
Bader J.S., Kuharski R.A. and Chandler D., J. Chem. Phys. 93 (1990) 230–236.
Thankappan V.K., Quantum Mechanics, John Wiley and Sons, New York, (1985).
Garg A., Onuchic J.N. and Ambegaokar V., J. Chem. Phys. 83 (1985) 4491–4503.
Onuchic J. N., Beratan D. N. and Hopfield J. J., J. Chem. Phys. 90 (1986) 3707–3721.
Fleming G. R., Martin J. L. and Breton J., Nature 333 (1988) 190.
Nagarajan V., Parson W. W., Gaul D. and Schenck C., Proc. Natl. Acad. Sci. USA 87 (1990) 7888–7892.
Gunner M. R. and Dutton P. L., J. Am. Chem. Soc. 111 (1989) 3400–3412.
Marcus R. A. and Sutin N., Biochem. Biophys. Acta 811 (1985) 265–322.
Sumi H. and Marcus R. A., J. Chem. Phys. 84 (1986) 4894–4914.
Hopfield J.J., Proc. Natl. Acad. Sci. USA 71 (1974) 3640–3644.
Bixon M. and Jortner J., J. Phys. Chem. 90 (1986) 3795–3800.
Martin J. L., Breton J., Lambry J. C. and Fleming G., The Photosynthetic Bacterial Reaction Center: Structure and Dynamics, J. Breton and A. Vermeglio, Plenum Press, New York and London, (1988) 195–203.
Kirmaier C. and Holten D., The Photosynthetic Bacterial Reaction Center: Structure and Dynamics, J. Breton and A. Vermeglio, Plenum Press, New York and London, (1988) 219–228.
Warshel A. and Hwang J.K., J. Chem. Phys. 84 (1986) 4938–4957.
Warshel A., Chu Z. T. and Parson W. W., Science 246 (1989) 112–116.
Wolynes P.G., J. Chem. Phys. 86 (1987) 1957–1966.
Zheng C., McCammon J. A. and Wolynes P. G., Proc. Natl. Acad. Sci. USA 86 (1989) 6441.
Abramowitz M. and Stegun I.A., Handbook of Mathematical Functions, Dover, New York, (1972).
Press W.H., Flannery B.P., Teukolsky S.A. and Vetterling W.T., Numerical Recipes in C, Cambridge University Press, Melbourne, (1988).
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Schulten, K. (1996). Curve Crossing in a Protein: Coupling of the Elementary Quantum Process to Motions of the Protein. In: Bicout, D., Field, M. (eds) Quantum Mechanical Simulation Methods for Studying Biological Systems. Centre de Physique des Houches, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09638-3_4
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