Multidimensional Marcus Theory: An Analysis of Concerted Reactions
Equations permitting the application of Marcus theory to reactions with two, three, or four reaction coordinate dimensions have been derived by analogy with the one-dimensional case. All of these equations are based on the quartic approximation to the reaction coordinate; G x = ax 2 + bx 3 + cx 4. T...
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| Published in | Journal of the American Chemical Society Vol. 118; no. 51; pp. 12878 - 12885 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
American Chemical Society
25.12.1996
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| Abstract | Equations permitting the application of Marcus theory to reactions with two, three, or four reaction coordinate dimensions have been derived by analogy with the one-dimensional case. All of these equations are based on the quartic approximation to the reaction coordinate; G x = ax 2 + bx 3 + cx 4. The final equations require as input only the energies of each corner intermediate and intrinsic barriers for each dimension. Computer programs have been written to allow finding of the transition state, by numerical search of the high dimensional hyperspace. These programs allow examination of potentially concerted reactions involving multiple processes. Numerical exploration shows that the conditions which must be met for a transition state to involve more than one reaction coordinate become increasingly stringent as the number increases, to the point that it is essentially impossible to have four coordinates changing at once. |
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| AbstractList | Equations permitting the application of Marcus theory to reactions with two, three, or four reaction coordinate dimensions have been derived by analogy with the one-dimensional case. All of these equations are based on the quartic approximation to the reaction coordinate; G x = ax 2 + bx 3 + cx 4. The final equations require as input only the energies of each corner intermediate and intrinsic barriers for each dimension. Computer programs have been written to allow finding of the transition state, by numerical search of the high dimensional hyperspace. These programs allow examination of potentially concerted reactions involving multiple processes. Numerical exploration shows that the conditions which must be met for a transition state to involve more than one reaction coordinate become increasingly stringent as the number increases, to the point that it is essentially impossible to have four coordinates changing at once. |
| Author | Guthrie, J. Peter |
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| Cites_doi | 10.1146/annurev.pc.31.100180.001303 10.1146/annurev.pc.15.100164.001103 10.1021/ja01054a003 10.1016/0009-2614(78)80443-6 10.1016/S0040-4039(00)94731-2 10.1021/ja00161a038 10.1038/221340a0 10.1002/hlca.19670500232 10.1021/jo00301a005 10.1021/ja00179a040 10.1039/DF9602900021 10.1002/anie.196400011 10.1021/ja00019a025 10.1021/ja00340a023 10.1021/ja00313a043 10.1021/ja00302a019 10.1021/jo00289a049 10.1021/j100849a019 10.1021/ar50059a003 10.1021/ja00486a048 10.1021/ar50033a001 |
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| Notes | ark:/67375/TPS-Z4ZGZNT5-C istex:1FE7E446C1E91DACBCC2272EB446FB9FD57AC516 Abstract published in Advance ACS Abstracts, December 15, 1996. |
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| Title | Multidimensional Marcus Theory: An Analysis of Concerted Reactions |
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