Nick

Tunneling occurs when a molecule penetrates through a potential energy barrier rather than over it. Cite error: A <ref> tag is missing the closing </ref> (see the help page). Although not allowed by the laws of classical dynamics, particles can pass through classically forbidden regions of space in quantum mechanics based on wave-particle duality.^[1]

Analysis of tunneling can be made using Bell’s modification of the Arrhenius equation which includes the addition of a tunneling factor, Q:

$k=QAe^{-E/RT}$

where A is is the Arrhenius parameter, E is the barrier height and

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/wiki.riteme.site/v1/":): {\displaystyle Q=\frac{e^α}/{β-α}(βe^{-α}-αe^{-β})}
$Q={\frac {1}{2}}$
where $a={\frac {E}{RT}}$
and Failed to parse (syntax error): {\displaystyle b=\frac{2ap^2(2mE)^{1/2}{h}}

Examination of the β term shows exponential dependency on the mass of the particle. As a result, tunneling is much more likely for a lighter particle such as hydrogen. Simply doubling the mass of a tunneling proton by replacing it with its deuterium isotope drastically reduces the rate of such reactions. As a result, very large kinetic isotope effects are observed that can not be accounted for by differences in zero point energies.Cite error: A <ref> tag is missing the closing </ref> (see the help page).

Also for reactions where isotopes include H, D and T, a criterion of tunneling is the Swain-Schaad relations which compare the rate constants of the reactions when H,D or T are the protons: k_H/k_T=(k_D/k_T)^X and k_H/k_T=(k_H/k_D)^Y
Experimental values of X exceeding 3.26 and Y exceeding 1.44 are evidence of a certain amount of contribution from tunneling. ^[2]

(From original Wiki page) In organic reactions, this proton tunneling effect has been observed in such reactions as the deprotonation and iodination of nitropropane with hindered pyridine base^[3] with a reported KIE of 25 at 25 °C:

and in a 1,5-sigmatropic hydrogen shift^[4] although it is observed that it is difficult to extrapolate experimental values obtained at elevated temperatures to lower temperatures:^[5]^[6]

(End of original Wiki page)

There has long been speculation that high efficiency of enzyme catalysis in proton or hydride ion transfer reactions could be due partly to the quantum mechanical tunneling effect. Environment at the active site of an enzyme positions the donor and acceptor atom close to the optimal tunneling distance. It is also possible that the enzyme provides tunneling-promoting vibration. ^[7]
Studies on ketosteroid isomerase have provided experimental evidence that the enzyme actually enhances the coupled motion/hydrogen tunneling by comparing primary and secondary kinetic isotope effects of the reaction under enzyme catalyzed and non-enzyme catalyzed conditions.^[8]
There are many examples of proton tunneling in enzyme catalyzed reactions that were discovered by KIE. Some well studied examples are alcohol dehydrogenase and glucose oxidase. (Truhlar et al, Acc Chem. Res. 2002, 35, 341-349; Kohen et al, Acc. Chem. Res. 1998, 37, 397-404).

References

^ R.J. Silbey, R.A. alberty, M.G. Bawendi (2005). Physical Chemistry 4th Edition. John Wiley and Sons, Inc. pp. 326–338. ISBN 0-471215-04-X.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Lev I. Krishtalik (2000). "The mechanism of the proton transfer: An outline". Biochimica et Biopysica Acta. 1458 (1): 6–27. doi:10.1016/S0005-2728(00)00057-8. PMID 10812022.
^ Edward Sheldon Lewis and Lance Funderburk (1967). "Rates and isotope effects in the proton transfers from 2-nitropropane to pyridine bases". J. Am. Chem. Soc. 89 (10): 2322–2327. doi:10.1021/ja00986a013.
^ Michael J. S. Dewar, Eamonn F. Healy, and James M. Ruiz (1988). "Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene". J. Am. Chem. Soc. 110 (8): 2666–2667. doi:10.1021/ja00216a060.{{cite journal}}: CS1 maint: multiple names: authors list (link)
^ William von E. Doering and Xin Zhao (2006). "Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicyclo[4.4.0]dec-1-ene: Evidence for Tunneling?". J. Am. Chem. Soc. 128 (28): 9080–9085. doi:10.1021/ja057377v. PMID 16834382.
^ In this study the KIE is measured by sensitive proton NMR. The extrapolated KIE at 25 °C is 16.6 but the margin of error is high
^ Amnon Kohen; Judith P Klinman (1999). "Hydrogen tunneling in biology". Chem.Biol. 6 (7): R191-198. doi:10.1016/S1074-5521(99)80058-1. PMID 10381408.
^ Thomas C. Wilde; Grzegorz Blotny; Ralph M. Pollack (2008). "Experimental Evidence for Enzyme-Enhanced Coupled Motion/Quantum Mechanical Hydrogen Tunneling by Ketosteroid Isomerase". J. Am. Chem. Soc. . 130 (20): 6577–6585. doi:10.1021/ja0732330. PMID 18426205.

[silbey-1] R.J. Silbey, R.A. alberty, M.G. Bawendi (2005). Physical Chemistry 4th Edition. John Wiley and Sons, Inc. pp. 326–338. ISBN 0-471215-04-X.{{cite book}}: CS1 maint: multiple names: authors list (link)

[Krishtalik-2] Lev I. Krishtalik (2000). "The mechanism of the proton transfer: An outline". Biochimica et Biopysica Acta. 1458 (1): 6–27. doi:10.1016/S0005-2728(00)00057-8. PMID 10812022.

[3] Edward Sheldon Lewis and Lance Funderburk (1967). "Rates and isotope effects in the proton transfers from 2-nitropropane to pyridine bases". J. Am. Chem. Soc. 89 (10): 2322–2327. doi:10.1021/ja00986a013.

[4] Michael J. S. Dewar, Eamonn F. Healy, and James M. Ruiz (1988). "Mechanism of the 1,5-sigmatropic hydrogen shift in 1,3-pentadiene". J. Am. Chem. Soc. 110 (8): 2666–2667. doi:10.1021/ja00216a060.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[5] William von E. Doering and Xin Zhao (2006). "Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicyclo[4.4.0]dec-1-ene: Evidence for Tunneling?". J. Am. Chem. Soc. 128 (28): 9080–9085. doi:10.1021/ja057377v. PMID 16834382.

[6] In this study the KIE is measured by sensitive proton NMR. The extrapolated KIE at 25 °C is 16.6 but the margin of error is high

[Kohen-7] Amnon Kohen; Judith P Klinman (1999). "Hydrogen tunneling in biology". Chem.Biol. 6 (7): R191-198. doi:10.1016/S1074-5521(99)80058-1. PMID 10381408.

[pollack-8] Thomas C. Wilde; Grzegorz Blotny; Ralph M. Pollack (2008). "Experimental Evidence for Enzyme-Enhanced Coupled Motion/Quantum Mechanical Hydrogen Tunneling by Ketosteroid Isomerase". J. Am. Chem. Soc. . 130 (20): 6577–6585. doi:10.1021/ja0732330. PMID 18426205.

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