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Magnetoreception in Plants

 

FIGURE 5.1 Vector representation of radical pair spin triplet states T+, T−, T0, and singlet state S. (Adapted from

Steiner and Ulrich (1989).)

Te individual electron spins are confned to cones oriented along the axis of quantization, either

upward (α-spin) or downward (β-spin). Te resultant of the two electron spins is either 1, and oriented

parallel (T ), perpendicular (T0), or antiparallel (T−) to the axis of quantization, or 0 (S). Te correspond­

1

1

+

ing spin eigenfunctions are α1α2 for T+, β1β2 for T−,

(˜ ° + ° ˜

1

2 ^{for T}0^{, and}

(˜ °

1

2

^{−° ˜} ) ^{for S.}

2

1

2

)

2

1

2

Figure 5.1 suggests that there is some phase relation between the spins of diferent electrons. However,

the phase relation distinguishing S and T0 operates between the spin function products α1β2 and β2α1,

and not between the spins of single electrons (Steiner and Ulrich, 1989).

Te main driving force for electronic spin motion is isotropic hyperfne coupling, and the quantum-

mechanical determination of accurate isotropic hyperfne coupling constants essentially relies on the

precise calculation of the electron density at each nucleus with a nonzero magnetic moment (Fermi

contact frst-order interaction (Chipman and Rassolov, 1997)). Te active magnetic feld B is made up as

a vector sum of the external magnetic feld B0 and an efective magnetic feld resulting from the sum of

the hyperfne couplings of the various nuclear spins in the corresponding radical.

B

B

Bhfc

=

0 ⁺

In the absence of an MF, the total spin angular momentum of electrons and nuclei must be conserved,

so that a change in electron spin must be compensated by a change of nuclear spin. In the condition of

zero external feld, any transition between the spin substates of the RP is possible. As the external feld

strength increases, the resultant feld B is more and more determined by B0 so that the directions of the

precession axes of the two spins coincide, precluding transitions between T+, T and S, T0 (so-called spin­

−

fip transitions). However, the precession frequency diference due to the Bhfc component parallel to B0 is

retained, and S-T0 transitions (so-called rephasing transitions) are not suppressed by the external MFs

(Steiner and Ulrich, 1989).

Considering the MF dependence (MFD) of chemical reaction yields caused by the RPM we can con­

sider three cases or combinations of them, as suggested by Sakaguchi et al. (1980). Figure 5.2 depicts

some phenomenological cases of MFD of reaction yields. In the frst case, the suppression of the hyper­

fne coupling-induced S ↔ T+,− transitions by the MF shows a clear saturation behavior of the product

yield (RS). Here, the parameters to be specifed are B1/2, the feld where half of the saturation efect is

obtained, and Bs, the region of beginning saturation, although the latter is not very exactly defned. Te

yield increases suddenly at a low feld and remains almost constant above B . In the second case, a rather

s

monotonously rising MFD curve requires very high MFs for obtaining a saturation. Te yield decreases

with increasing MF by the S-T0 conversion through the electronic Zeeman term. In the combination of

case 1 and case 2 (case 1,2), the yield frst increases with the increasing MF. Such curves may be charac­

terized by the feld values B of the maximum and B of the zero-line crossing. In the last case (case 3),

m

c

RPs are subjected to a moderate but constant exchange interaction and may be characterized by the feld

values Bm, corresponding to the maximum, and ΔB corresponding to the width of the resonance.