An improved semiclassical theory of radical pair recombination reactions

Manolopoulos, David E.; Hore, P. J.

doi:10.1063/1.4821817

Cited by 40 publications

(72 citation statements)

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“…In fact, the initial electronic singlet state of the radical pair is quantum mechanically entangled [although the entanglement, as such, confers no advantage in terms of the general operation of the compass (60), nor is it essential for the existence of the spike]. We recently showed that the spin dynamics of long-lived radical pairs in weak magnetic fields can be described by a semiclassical approximation that becomes increasingly accurate as the number of nuclear spins is increased (61,62). If the behavior of a realistic radical pair magnetoreceptor can be satisfactorily modeled in terms of classical rather than quantum oscillations, then arguably it does not belong under the quantum biological umbrella.…”

Section: Discussionmentioning

confidence: 99%

The quantum needle of the avian magnetic compass

Hiscock

Worster

Kattnig

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Migratory birds have a light-dependent magnetic compass, the mechanism of which is thought to involve radical pairs formed photochemically in cryptochrome proteins in the retina. Theoretical descriptions of this compass have thus far been unable to account for the high precision with which birds are able to detect the direction of the Earth's magnetic field. Here we use coherent spin dynamics simulations to explore the behavior of realistic models of cryptochrome-based radical pairs. We show that when the spin coherence persists for longer than a few microseconds, the output of the sensor contains a sharp feature, referred to as a spike. The spike arises from avoided crossings of the quantum mechanical spin energy-levels of radicals formed in cryptochromes. Such a feature could deliver a heading precision sufficient to explain the navigational behavior of migratory birds in the wild. Our results (i) afford new insights into radical pair magnetoreception, (ii) suggest ways in which the performance of the compass could have been optimized by evolution, (iii) may provide the beginnings of an explanation for the magnetic disorientation of migratory birds exposed to anthropogenic electromagnetic noise, and (iv) suggest that radical pair magnetoreception may be more of a quantum biology phenomenon than previously realized. magnetic compass | magnetoreception | migratory birds | quantum biology | radical pair mechanism M igratory birds have a light-dependent magnetic compass (1-4). The primary sensory receptors are located in the eyes (2, 3, 5-7), and directional information is processed bilaterally in a small part of the forebrain accessed via the thalamofugal visual pathway. The evidence currently points to a chemical sensing mechanism based on photo-induced radical pairs in cryptochrome flavoproteins in the retina (8-18). Anisotropic magnetic interactions within the radicals are thought to give rise to intracellular levels of a cryptochrome signaling state that depend on the orientation of the bird's head in the Earth's magnetic field (8,9,19). In support of this proposal, the photochemistry of isolated cryptochromes in vitro has been found to respond to applied magnetic fields in a manner that is quantitatively consistent with the radical pair mechanism (15). Aspects of the radical pair hypothesis have also been explored in a number of theoretical studies, the majority of which have concentrated on the magnitude of the anisotropic magnetic field effect (9,10,16,17,(19)(20)(21)(22)(23)(24)(25)(26)(27). Very little attention has been devoted to the matter we address here: the precision of the compass bearing available from a radical pair sensor (28).To migrate successfully over large distances, it is not sufficient simply to distinguish north from south (or poleward from equatorward) (29). A bar-tailed godwit (Limosa lapponica baueri), for example, was tracked by satellite flying from Alaska to New Zealand in a single 11,000-km nonstop flight across the Pacific Ocean (30). A directional error of more than a few degre...

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Section: Discussionmentioning

confidence: 99%

The quantum needle of the avian magnetic compass

Hiscock

Worster

Kattnig

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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167

223

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“…17 found that the process in Eq. (19) only occurs at temperatures below 200 K for PTZ-Ph n -PDI wires with n ≥ 2, whereas the experiments of Weiss et al 15 that we have compared with here were performed at room temperature. 16 Finally, the background could be due to a fraction of the radical pairs being formed in the triplet state, rather than the singlet state, during the initial charge separation:…”

Section: Background Contribution To the Triplet Yieldmentioning

confidence: 73%

“…It would be interesting if further experiments could be done to shed more light on the processes in Eqs. (17), (18), (19) and (22) in an attempt to resolve this issue. Especially since the need for a background correction to explain the high field behaviour of the triplet yield does not seem to be confined to these particular PTZ •+ -Ph n -PDI •− molecular wires: relative triplet yields Φ T (B)/Φ T (0) that are significantly larger than 1/3 in the high field limit have also been observed by Wasielewski and co-workers for a variety of other molecular wires.…”

Section: Background Contribution To the Triplet Yieldmentioning

confidence: 99%

“…This new method is routinely applicable to radical pairs with as many as 20 or so hyperfine-coupled nuclear spins, which is the typical size of radical pair encountered in experimental studies of molecular wires. 1,2,[12][13][14][15][16][17] It has also been shown to be more reliable than the various semiclassical approximations [18][19][20][21] that can be applied to the problem. 11 In this paper, we shall exploit our new method by applying it to the PTZ •+ -Ph n -PDI •− molecular wires studied by Weiss et al, 15 which consist of a phenothiazine (PTZ) donor, a perylene-3,4:9,10-bis(dicarboximide) (PDI) acceptor, and a bridge of n para-phenylene rings.…”

Section: Introductionmentioning

confidence: 99%

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Spin-dependent charge recombination along para-phenylene molecular wires

Fay

Lewis

Manolopoulos

2017

The Journal of Chemical Physics

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We have used an efficient new quantum mechanical method for radical pair recombination reactions to study the spin-dependent charge recombination along PTZ •+ -Phn-PDI •− molecular wires. By comparing our results to the experimental data of E. Weiss et al. [J. Am. Chem. Soc. 126, 5577 (2004)], we are able to extract the spin-dependent (singlet and triplet) charge recombination rate constants for wires with n = 2 − 5. These spin-dependent rate constants have not been extracted previously from the experimental data because they require fitting its magnetic field-dependence to the results of quantum spin dynamics simulations. We find that the triplet recombination rate constant decreases exponentially with the length of the wire, consistent with the superexchange mechanism of charge recombination. However, the singlet recombination rate constant is nearly independent of the length of the wire, suggesting that the singlet pathway is dominated by an incoherent hopping mechanism. A simple qualitative explanation for the different behaviours of the two spin-selective charge recombination pathways is provided in terms of Marcus theory. We also find evidence for a magnetic field-independent background contribution to the triplet yield of the charge recombination reaction, and suggest several possible explanations for it. Since none of these explanations is especially compelling given the available experimental evidence, and since the result appears to apply more generally to other molecular wires, we hope that this aspect of our study will stimulate further experimental work.

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“…Although successful in some circumstances, 15 this approach conflicts with Newton's third law of motion, because the torque exerted on the electron spin by the nuclear spins is not balanced by an equal and opposite torque on the nuclear spins from the electron. Our recent extension to the SW theory 16 …”

Section: -14mentioning

confidence: 99%

Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions

Lewis

Manolopoulos

Hore

2014

The Journal of Chemical Physics

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We describe how the semiclassical theory of radical pair recombination reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore, J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different singlet and triplet recombination rates. This is a non-trivial generalisation because when the recombination rates are different the recombination process is dynamically coupled to the coherent electron spin dynamics of the radical pair. Furthermore, because the recombination operator is a two-electron operator, it is no longer sufficient simply to consider the two electrons as classical vectors: one has to consider the complete set of 16 two-electron spin operators as independent classical variables. The resulting semiclassical theory is first validated by comparison with exact quantum mechanical results for a model radical pair containing 12 nuclear spins. It is then used to shed light on the spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing considerably more nuclear spins which has recently been used to establish a 'proof of principle' for the operation of a chemical compass [K. Maeda et al., Nature 453, 387 (2008)]. We find in particular that the intriguing biphasic behaviour that has been observed in the effect of an Earth-strength magnetic field on the time-dependent survival probability of the photo-excited C ·+ PF ·− radical pair arises from a delicate balance between its asymmetric recombination and the relaxation of the electron spin in the carotenoid radical.

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An improved semiclassical theory of radical pair recombination reactions

Cited by 40 publications

References 40 publications

The quantum needle of the avian magnetic compass

The quantum needle of the avian magnetic compass

Spin-dependent charge recombination along para-phenylene molecular wires

Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions

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