Modalidad típica

If n.m.r. spectra are obtained of a solution in which a radical reaction is taking place, then the n.m.r. signals due to the starting materials and the products may show

anomalous intensities (either enhanced absorption or emission). These anomalies arise from the phenomenon of Chemically Induced Dynamic Nuclear Polarisation or C.I.D.N.P.

The phenomenon of C.I.D.N.P. was first observed independently by Bargon, Fischer, and Johnsen^^, and Ward and Lawler.^ Initial attempts to explain the phenomenon in terms of the Overhauser effect or dynamic nuclear polarisation led it to be called C.I.D.N.P., but did not explain all the experimental results.

The radical pair, or C K O , theory was proposed independently by Closs^^, and Kaptein and Oosterhoff.^^ This new theory explained all of the experimental results and from now on all discussion of C.I.D.N.P. will be made in terms of this theory.

2.3.1 Interaction of a Nucleus with One Electron

An electron has spin quantum number, S, of 1/2, and magnetic quantum numbers, mg, o f +1/2 and -1/2. The energy of an electron in an applied magnetic field is given by Equation 2.1 :

E = m g g P B (2.1)

where g is the Lande g factor (2.002319 for a free electron), p is the Bohr magneton, and B is the magnetic field strength. As with the ^^N nucleus the energy of the lowest state corresponds to mg equal to - 1/2.

If the electron's spin is coupled to a nuclear spin then the expression becomes Equation 2.2;

E = mg g P B + a mg mi (2.2)

where 'a' is the hyperfme coupling constant. In other words, coupling to a nuclear spin leads to splitting of the electronic energy states and, hence, of the electron spin resonance lines.

A more important consequence in terms of C.I.D.N.P. is the effect of the coupling on the rate of precession of the electron. According to quantum mechanics, the electron spin is not directly aligned with the field but at an angle to it and processes around this direction. The angular velocity of the precession, ©, is related to the energy of the electron and in the absence of nuclear coupling is given by Equation 2.3:

© = (27c/h) g P B (2 3)

If the electron is coupled to a nuclear spin then the expression becomes Equation 2.4:

(Ù = (27r/h) (g p B + a mi) (2 4)

2.3.2 Systems of Two Electrons

For a system of two coupled electrons (the situation in a radical pair) the total spin quantum, S, equals 0 or 1. If S equals 0 then the system is in a singlet state; if S equals 1 then the system is in the triplet state. In the singlet state the spins are opposed, in the triplet state they can have three relative configurations (Figure 2.1):

B

To T-1

Singlet state (S = 0) Triplet state (S = 1) Figure 2.1

If the electrons are not processing at the same frequency then the S = 0 and Tq states can interconvert. The rate of interconversion, or intersystem crossing, is dependent on the rate of precession of the two electrons. Hence, in the absence of nuclear coupling, the rate of interconversion is given by Equation 2.5;

©1 - ©2 = (27c/h) P B Ag (2.5)

where Ag is the difference in g value (gj - g2).

If one of the electrons, say electron 1, is coupled with a nucleus with a hyperfine coupling constant 'a' then the expression becomes Equation 2.6:

© l~ © 2 = (27r/h) (P B Ag + ami) (2.6)

Hence, depending on the sign of'a', one of the two values of m% will increase (©% - ©2) and one will decrease it. Thus the rate of interconversion of the singlet and triplet states depends on the direction of nuclear spins.

For example, consider a radical pair consisting of a p-nitrobenzyl fluoride radical anion and a ^^N-labelled nitrogen dioxide radical. The g value for the p-nitrobenzyl fluoride radical anion is equal to 2.0 0 2^^, and for the nitrogen dioxide radical the g value is equal to 2.0000.^^ Hence, Ag will be negative. The hyperfine coupling constant, ’a’, for the nucleus will be negative because of the negative magnetogyric ratio of this nucleus.

If the radical pair is initially in a triplet state then it will have to undergo interconversion to the singlet state before the radicals can couple. The value of |©i - ©2I must, therefore, be as large as possible. We therefore need amj to be negative, hence, m% should be positive. So the products will be formed with an excess of nuclei in their upper spin state, and the n.m.r. signals due to the products will appear in emission.

If the radical pair is initially in a singlet state, then interconversion to the triplet state will facilitate the separation of the radicals. The products will, therefore, tend to

have a larger excess of nuclei in their lower spin state than at thermal equilibrium. Hence, the signals due to the products will appear in enhanced absorption.

2.3.3 Kaptein*s Rule

The phase of the net polarisation, F, can be predicted from Kaptein’s rule.'^^ For use with n.m.r. spectroscopy, Kaptein's rule has to be modified^^ to allow for the negative magnetogyric ratio of the nucleus (Equation 2.7):

F = - |i 8 a Ag (2.7)

If F is +, net absorption, A If F is - , net Emission, E

where \x = + for a radical pair formed from a triplet precursor. - for a radical pair formed from a singlet precursor.

8 = + for products arising from singlet radical pairs. - for products arising from triplet radical pairs.

a = the sign ofthe hyperfine coupling constant for the nucleus.

Ag = the sign of the difference in g value (gi - g2), where gj is the g value of the radical containing the nucleus.