Radical pairs electron-spin states

Consider a geminate radical pair, its component radicals in close proximity and therefore having correlated electron spins reflecting the electronic spin state of the precursor. Three different situations can be envisaged. 

OIDEP usually results from Tq-S mixing in radical pairs, although T i-S mixing has also been considered (Atkins et al., 1971, 1973). The time development of electron-spin state populations is a function of the electron Zeeman interaction, the electron-nuclear hyperfine interaction, the electron-electron exchange interaction, together with spin-rotational and orientation dependent terms (Pedersen and Freed, 1972). Electron spin lattice relaxation Ti = 10 to 10 sec) is normally slower than the polarizing process. 

The quantitative theory of CIDNP " is developed to a state where the intensity ratios of CIDNP spectra can be computed on the basis of reaction and relaxation rates and the characteristic parameters of the radical pair (initial spin multiplicity, T) the individual radicals (electron g factors, hfcs, a) and the products (spin-spin coupling constants, J). On the other hand, the patterns of signal directions and intensities observed for different nuclei of a reaction product can be interpreted in terms of hfcs of the same nuclei in the radical cation intermediate. 

CIDEP (Chemically Induced Dynamic Electron Polarization) Non-Boltzmann electron spin state population produced in thermal or photochemical reactions, either from a combination of radical pairs (called radical-pair mechanism), or directly from the triplet state (called triplet mechanism), and detected by ESR spectroscope... 

Generation of a radical pair in a well-defined electron spin state... 

In 1963, Fessenden and Schuler [1] found during irradiation of liquid methane (CFLt and CD4) at 98 K with 2.8 MeV electron that the low-field line for both hydrogen and deuterium atoms appeared inverted (emissive signals) and that the central deuterium atom line was very weak. Although the cause of such anomalous ESR spectra was not clear at that time, similar anomalous signals have been observed in many reactions and have been called " Chemically Induced Dynamic Electron Polarization (CIDEP). CIDEP should be due to non-equilibrium electron spin state population in radicals and could also be explained later by the radical pair mechanism as CIDNP. 

A much more important technique is electron spin resonance (esr), also called electron paramagnetic resonance (epr). ° The principle of esr is similar to that of nmr, except that electron spin is involved rather than nuclear spin. The two electron spin states (m = and m = are ordinarily of equal energy, but in a magnetic field the energies are different. As in NMR, a strong external field is apphed and electrons are caused to flip from the lower state to the higher by the application of an appropriate radio-frequency (rf) signal. Inasmuch as two electrons paired in one orbital must have opposite spins which cancel, an esr spectrum arises only from species that have one or more unpaired electrons (i.e., free radicals). 

R463 T. Moriya and K. Ueda, Spin Fluctuations and High Temperature Superconductivity , Adv. Phys., 2000,49, 555 R464 B. A. Morrow and I. D. Gay, Infrared and NMR Characterization of the Silica Surface , Surfactant Set Ser., 2000,90, 9 R465 B. Mulloy and M. J. Forster, Conformation and Dynamics of Heparin and Heparin Sulfate , Glycobiology, 2000,10, 1147 R466 H. Murai, S. Tero-Kubota and S. Yamauchi, Pulsed and Time-Resolved EPR Studies of Transient Radicals, Radical Pairs and Excited States in Photochemical Systems , Electron Paramagn. Reson., 2000,17, 130... 

Most radicals in solution react with each other at about the diffusion limit, but because of a quantum mechanical restriction only one of the four possible electron spin states of radical pair ( f t, t J, J, "f and J, J.) is productive. For most solvents, the recombination rate at room temperature is 5 x 10 M s , ... 

CIDNP is based on the following principle 431,432 Initially, the radical pair is born in a spin-correlated state. To form a product in the singlet ground state, the electronic spin state of the radical pair must be a singlet state. Importantly, the electron spins interact with the nuclear spin states. ISC from a triplet to a singlet radical pair is favoured, when... 

The radical-pair mechanism is displayed in Chart 1. Its main ingredients are that spin is conserved during chemical processes that radical pairs are formed, diffuse apart and reencounter and that the eigenstates of their electron spins are different when the radicals are in contact or when they are far apart, leading to an evolution of the electron-spin state under the spin Hamiltonian during a diffusive excursion. The mechanism can be broken dovm into three steps ... 

Generation of a radical pair or biradical in a definite electron spin state. This has already been expounded on in Section II.A, item 1. 

The Radical Pair Mechanism (RPM), first presented in 1969 [26-29] has undergone intense investigation to help explain experimental observations. According to the RPM, a radical pair is created in a non-stationary electronic spin state which in the... 

Decipher whether it is possible that the non-equilibrium Boltzmann population of electron spin states is formed by the radical pair mechanism rather than the triplet mechanism as postulated by Das and co-workers [1]. 

An atom or a molecule with the total spin of the electrons S = 1 is said to be in a triplet state. The multiplicity of such a state is (2.S +1)=3. Triplet systems occur in both excited and ground state molecules, in some compounds containing transition metal ions, in radical pair systems, and in some defects in solids. 

The origin of postulate (iii) lies in the electron-nuclear hyperfine interaction. If the energy separation between the T and S states of the radical pair is of the same order of magnitude as then the hyperfine interaction can represent a driving force for T-S mixing and this depends on the nuclear spin state. Only a relatively small preference for one spin-state compared with the other is necessary in the T-S mixing process in order to overcome the Boltzmann polarization (1 in 10 ). The effect is to make n.m.r. spectroscopy a much more sensitive technique in systems displaying CIDNP than in systems where only Boltzmann distributions of nuclear spin states obtain. More detailed consideration of postulate (iii) is deferred until Section II,D. 

Fig. (3. Precession of electron spins in S, To and T i states of a radical pair.

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

---