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EPR Spectroscopy

1.1 Outline of EPR Spectroscopy

Hiroyuki Mino

Division of Material Science, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, Japan

1.1.1 Overview

Our most familiar interaction in this world is electromagnetism. Almost all phenomena in material physics arise fromelectromagnetic interactions between light and matter. Our world is a stage for the electron as the main actor. Biosystems are also standing on the stage.

Electromagnetism is mediated by electromagnetic waves, called photons, which are the particles of the force field (the bosons, or force carriers). The electromagnetic waves are classified by frequency: ?-rays, X-rays, ultraviolet light, visible light, infrared light, microwave, and radio wave, in order of decreasing energy. Optical absorption spectroscopy using visible light is the most basic spectroscopic tool. Electron paramagnetic resonance (EPR) is also a spectroscopic tool [1-3]. Optical absorption detects the transition of the electron dipole moment, while EPR detects the transition of spin angular momentum. Spin (S) is classically modeled by the behavior of a small bar magnet. In quantum mechanics the bar magnet is allowed to be only in two states, parallel or antiparallel to the external magnetic field. In the simple case of S = 1/2, only the transition between two states, the up-spin state, |a> (mI = -1/2), and down-spin state, |ß> (mI = 1/2), are allowed. Under an external magnetic field, energy levels are separated, called Zeeman interaction (Figure 1.1.1). The transition between two states is performed by microwave irradiation. Since the two transitions, |a> to |ß> and |ß> to |a>, have the same probabilities, the periodic transitions between the |a> and |ß> states continue during microwave irradiation and is called "Rabi oscillation" (Figure 1.1.2). This oscillation is not unique for magnetic resonance but general for all spectroscopies. If we can detect very fast measurements, the oscillation should be observed in optical light spectroscopy.

Figure 1.1.1 Energy levels for S = 1/2 spin in the magnetic field B0.

Figure 1.1.2 Illustration for the transitions in two levels |a> and |ß>. Microwave irradiation gives oscillation between two levels (Rabi oscillation).

The energy for the spin transition might be smaller than that for the other electronic transitions. However, the electron spin is coupled with the orbital symmetry in the molecules. Therefore, the spin states determined by the EPR method are an indispensable tool to determine the quantum properties of the molecular orbits.

EPR and nuclear magnetic resonance (NMR) are categorized as magnetic resonance techniques. The differences between EPR and NMR are mainly ascribed to the spin size. Considering spin interaction between the spins, the effective interacting distance for a nuclear spin is around 10 Å, while that for electron spin is around 100 Å. Therefore, the EPR spectrum includes many magnetic interactions, such as the nuclei and electron spins within these distances (Figure 1.1.3). The difference in magnitude of the spins is also reflected in the spectral linewidth. NMR is generally estimated as several kilohertz, while the EPR spectral width is estimated as 1 THz (0.3 nm). In the case of the visible light spectrum, it reaches about 300 THz (~100 nm). The differences directly reflect the pulsed technique. In pulse spectroscopy (Figure 1.1.4), the object is irradiated with a strong electromagnetic wave in a short period. The detectable spectral linewidth depends on the pulse width and intensity. For example, the pulse with a length of 10 µs covers a 100 kHz width in the spectrum. Therefore, the short pulse covers the whole NMR spectrum, while only a small region in the spectrum is detected in EPR and visible optical spectroscopy. In the case of EPR, the limitation of a strong microwave pulse is around 20 ns, indicating a linewidth of 50 MHz, about 20 G, in the spectrum. Therefore, EPR may be an intermediate methodology between NMR and visible light spectroscopy (Figure 1.1.5). The pulsed EPR technique has two options, whether to detect a wide range in the spectrum or conversely to detect frequency selective beaching in a spectrum (a hole), denoted as "Hole burning."

Figure 1.1.3 Scale for the interaction of the nucleus and electron spins relative to protein size.

Figure 1.1.4 Coverage area for NMR pulse and EPR pulse relative to spectral width.

Figure 1.1.5 Comparison of EPR spectrum linewidth with NMR and optical spectral linewidth. Gray marker shows the detectable area for a single-pulse excitation.

The application to protein structure studies contributes to the advancement and popularity of the NMR technique. Protein studies are also an important application for EPR. The slow spin relaxation in the protein is suitable for EPR measurements, where the protein works as a kind of solvent virtually. As the electron spin interaction covers proteins, a lot of information in the spectrum disturbs the extraction of the necessary information. Therefore, many EPR techniques have been proposed.

In the external magnetic field B0 along the z-axis, the energy for a bar magnet with a magnetic moment µ is described as:

where ? is the angle between the B0 and µ vectors. The angle ? is arbitrarily selected in classical mechanics. But in quantum mechanics, only two states, parallel or antiparallel to the external magnetic field, are allowed. Using quantum mechanics (), the formula is rewritten as:

where ge and ße are the g-factor and Bohr magneton for the electron, respectively, and Sz = 1/2 or -1/2 (Figure 1.1.2). Considering the magnetic resonance in the two levels, the transition probabilities from the down spin to the up spin and from the up spin to the down spin are the same. As the number of lower levels (ß) is larger than the number of upper levels (a) in the Boltzmann distribution, irradiated microwave energy is absorbed in the spin system. When the microwave energy is continuously supplied, the numbers of spin in both levels become equal, resulting in the loss of absorption. Therefore, the absorption signal is observed in the balance of suppling energy and spin relaxation. The evaluation of the spin relaxation gives the magnetic interaction between spins (Figure 1.1.2).

In the pulse EPR method, microwaves are irradiated only for a short time. Therefore, spin relaxation can be suppressed and evaluated. The electron-nucleus spin interaction can be directly observed by the ENDOR (electron nuclear double resonance) and ESEEM (electron spin echo envelope modulation) methods, and the electron-electron spin interaction is observed by the PELDOR (pulsed electron-electron double resonance) / DEER (double electron-electron resonance) [4] hole burning [5, 6], RIDME (relaxation-induced dipolar modulation enhancement) [7], etc.

When an external magnetic field is applied to the electron spin in the z-direction, the electron spin is quantized in the z-direction (Figure 1.1.6a). The electron spin inverts to the opposite direction by irradiating a microwave pulse with an appropriate length (Figure 1.1.6a). The inverted spin recovers with the thermal divergence to the outside. The recovery time is called spin-lattice relaxation time (T1). T1 is influenced by several different processes, such as the direct process, Raman process, and Orbach process, where the spin-spin interaction is also included. The T1 measurement is one of the traditional distance measurement techniques.

Figure 1.1.6 (a) Recovery of the magnetization to the z-direction in the rotation xyz-frame. After a single inversion pulse (p), the magnetization inverted to the -z-axis and recovered to the z-axis after T1. (b) The two-pulse sequence with p/2 and p and magnetization irradiated along the x-axis. First, the magnetization is oriented from the y-axis to the x-axis after the p pulse. After the period of t, the magnetization is dephasing on the xy-plane. Second, the magnetizations are refocused on the -x-axis after a period of t.

Another relaxation time is the spin-spin relaxation time (T2). The mechanism is classically expressed as spin relaxation on the xy-plane. As the spin is quantized along the z-axis direction in the external magnetic field, there is no energy dissipation in the xy-plane in the first order. The spin-spin relaxation is mainly described as the perturbation from the local magnetic field to the electron spin. When we consider the interaction between electron and nucleus spins, the local magnetic field from a nucleus spin is not always along to the z-axis. Therefore,...