For the first time, well-founded new kinetic equations for the density matrix of an ensemble of non-interacting radical pairs (RPs) are derived considering their spin-dependent recombination. Recombination of RP is considered as a quasi-unimolecular process. Similar to Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular reactions it is suggested that there is stochastic Poisson process which provides randomly chances for recombination. Those chances appear independent of a spin state of RPs. Whether the chance to recombine will be realized or not depends on the state of the spins of the unpaired electrons of the RPs. For this model the spin density matrix r(t) can be represented as the product of the RP density matrix (hypothetical pair) r0(t), in which the recombination of radicals is not included, and the probability f(t) that the RP in the time interval (0, t) survived, i.e. did not recombine: r(t)=f(t) r0(t). In this work, new kinetic equations for f(t) and r(t) are derived. The equation for f(t) gives in fact kinetic equations for the concentration of RPs. The basic equations are obtained for the situation when all RPs of the ensemble start in the same pure quantum state. The obtained kinetic equations are generalized to the case when the initial state of the system is mixed. For some set of parameters of RPs, results of new kinetic equations presented in this work were compared with results of existing phenomenological kinetic equations. While they correspond qualitatively, there is significant quantitative difference.
| Published in | American Journal of Physical Chemistry (Volume 11, Issue 3) |
| DOI | 10.11648/j.ajpc.20221103.13 |
| Page(s) | 67-74 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Spin Chemistry, New Kinetic Equations, Kinetics of Radical Pairs Recombination, Spin-Dependent Recombination, Radical Pairs
| [1] | Salikhov, K. M.; Molin, Yu. N.; Sagdeev, R. Z.; Buchachenko, A. L. Spin Polarization and Magnetic Effects in Radical Reactions. Academic Kiado Budapest, Elsevier Amsterdam (1984). |
| [2] | Johnson, R. C.; Merrifield, R. E.; Avakian, P. and Flippen, R. B. Effects of Magnetic Fields on the Mutual Annihilation of Triplet Excitons in Molecular Crystals. Phys. Rev. Letters 19, 285 (1967). |
| [3] | Salikhov, K. M. Mechanism of the Excited Triplet States Electron Spin Polarization caused by the mutual annihilation of triplet states. Appl. Magn. Reson. 26, 135-144 (2004). |
| [4] | Corvaja, C.; Franco, L.; Salikhov, K. M.; Voronkova, V. K. The first observation of electron spin polarization in the excited triplet states caused by the triplet-triplet annihilation. Appl. Magn. Reson. 28, 181-194 (2005). |
| [5] | Johnson, R. C.; Merrifield, R. E. Effects of Magnetic Field on the Mutual Annihilation of Triplet Excitons in Anthracene Crystals. Phys. Rev. B, 1, 896-902 (1970). |
| [6] | Evans, G. T.; Fleming, P. D.; Lawler, R. G. Hydrodynamic theory of CIDEP and CIDNP. J. Chem. Phys. 58, 2071-2078 (1973). |
| [7] | Haberkorn, R. Density matrix description of spin-selective radical pair reactions. Mol. Phys. 32, 1491-1493 (1976). |
| [8] | Tomkiewicz, M.; Groen, A.; Cocivera, M. Nuclear Spin Polarization During the Photolysis of Di-t-butyl Ketone. J. Chem. Phys. 56, 5850-5857 (1972). |
| [9] | Pedersen, J. B.; Freed, J. H. Theory of chemically induced dynamic electron polarization. J. Chem. Phys. 59, 2869-2885 (1973). |
| [10] | Pedersen, J. B; Freed, J. H. Theory of chemically induced dynamic electron polarization. Initial triplet polarizations. J. Chem. Phys. 62, 1706-1711 (1975). |
| [11] | Jones, J. A.; Maeda, K.; Hore, P. J. Reaction operators for spin-selective chemical reactions of radical pairs. Chem. Phys. Lett. 507, 269-273 (2011). |
| [12] | Jones, J. A.; Maeda, K.; Steiner, U. E.; Hore, P. J. Reply to Comment on “Spin-selective reactions of radical pairs act as quantum measurement”. Chem. Phys. Lett. 508, 184-185 (2011). |
| [13] | Salikhov, K. M.; Sarvarov, F. S.; Sagdeev, R. Z.; Molin, Yu. N. Diffusion theory of radical pairs recombination considering singlet-triplet transitions. Kinetics and Catalysis 16, 279-287 (1975) (in Russian). |
| [14] | Sarvarov, F. S.; Salikhov, K. M. Theory of spin-dependent recombination of radicals in homogeneous solution. React. Kinet. Catal. Lett. 4, 33-41 (1976). |
| [15] | Shushin, A. I. Effect of state-selective reactive decay on the evolution of quantum systems. J. Chem. Phys. 133, 044505 (2010). |
| [16] | Di Giacomo, F. A Short Account of RRKM Theory of Unimolecular Reactions and of Marcus Theory of Electron Transfer in a Historical Perspective J. of chem. education. 92, 476-481 (2015). |
APA Style
Kev Minullinovich Salikhov. (2022). New Kinetic Equations for Spin-Dependent Recombination of Radical Pairs and Their Comparison with Existing Phenomenological Equations. American Journal of Physical Chemistry, 11(3), 67-74. https://doi.org/10.11648/j.ajpc.20221103.13
ACS Style
Kev Minullinovich Salikhov. New Kinetic Equations for Spin-Dependent Recombination of Radical Pairs and Their Comparison with Existing Phenomenological Equations. Am. J. Phys. Chem. 2022, 11(3), 67-74. doi: 10.11648/j.ajpc.20221103.13
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajpc.20221103.13,
author = {Kev Minullinovich Salikhov},
title = {New Kinetic Equations for Spin-Dependent Recombination of Radical Pairs and Their Comparison with Existing Phenomenological Equations},
journal = {American Journal of Physical Chemistry},
volume = {11},
number = {3},
pages = {67-74},
doi = {10.11648/j.ajpc.20221103.13},
url = {https://doi.org/10.11648/j.ajpc.20221103.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpc.20221103.13},
abstract = {For the first time, well-founded new kinetic equations for the density matrix of an ensemble of non-interacting radical pairs (RPs) are derived considering their spin-dependent recombination. Recombination of RP is considered as a quasi-unimolecular process. Similar to Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular reactions it is suggested that there is stochastic Poisson process which provides randomly chances for recombination. Those chances appear independent of a spin state of RPs. Whether the chance to recombine will be realized or not depends on the state of the spins of the unpaired electrons of the RPs. For this model the spin density matrix r(t) can be represented as the product of the RP density matrix (hypothetical pair) r0(t), in which the recombination of radicals is not included, and the probability f(t) that the RP in the time interval (0, t) survived, i.e. did not recombine: r(t)=f(t) r0(t). In this work, new kinetic equations for f(t) and r(t) are derived. The equation for f(t) gives in fact kinetic equations for the concentration of RPs. The basic equations are obtained for the situation when all RPs of the ensemble start in the same pure quantum state. The obtained kinetic equations are generalized to the case when the initial state of the system is mixed. For some set of parameters of RPs, results of new kinetic equations presented in this work were compared with results of existing phenomenological kinetic equations. While they correspond qualitatively, there is significant quantitative difference.},
year = {2022}
}
TY - JOUR T1 - New Kinetic Equations for Spin-Dependent Recombination of Radical Pairs and Their Comparison with Existing Phenomenological Equations AU - Kev Minullinovich Salikhov Y1 - 2022/09/08 PY - 2022 N1 - https://doi.org/10.11648/j.ajpc.20221103.13 DO - 10.11648/j.ajpc.20221103.13 T2 - American Journal of Physical Chemistry JF - American Journal of Physical Chemistry JO - American Journal of Physical Chemistry SP - 67 EP - 74 PB - Science Publishing Group SN - 2327-2449 UR - https://doi.org/10.11648/j.ajpc.20221103.13 AB - For the first time, well-founded new kinetic equations for the density matrix of an ensemble of non-interacting radical pairs (RPs) are derived considering their spin-dependent recombination. Recombination of RP is considered as a quasi-unimolecular process. Similar to Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular reactions it is suggested that there is stochastic Poisson process which provides randomly chances for recombination. Those chances appear independent of a spin state of RPs. Whether the chance to recombine will be realized or not depends on the state of the spins of the unpaired electrons of the RPs. For this model the spin density matrix r(t) can be represented as the product of the RP density matrix (hypothetical pair) r0(t), in which the recombination of radicals is not included, and the probability f(t) that the RP in the time interval (0, t) survived, i.e. did not recombine: r(t)=f(t) r0(t). In this work, new kinetic equations for f(t) and r(t) are derived. The equation for f(t) gives in fact kinetic equations for the concentration of RPs. The basic equations are obtained for the situation when all RPs of the ensemble start in the same pure quantum state. The obtained kinetic equations are generalized to the case when the initial state of the system is mixed. For some set of parameters of RPs, results of new kinetic equations presented in this work were compared with results of existing phenomenological kinetic equations. While they correspond qualitatively, there is significant quantitative difference. VL - 11 IS - 3 ER -
Email: