Chemistry 126 Molecular Spectra & Molecular Structure Week # 7 Electron Spin Resonance Spectroscopy, Supplement Like the hydrogen nucleus, an unpaired electron in a sample has a spin of I=1/2. The magnetic dipole moment of this unpaired electron, µ B, is thus equal to µ B = g e e 2m e c I, (7.1) where g e is the electron g-factor and m e is the electron mass. The absolute magnitude of the electron magnetic moment is e µ B = g e 2m e c [I(I +1)]1/2 h = g e β B I(I +1), (7.2) where the Bohr (electron magneton) β B is defined as β B e h 2m e c = 9.274 10 21 erg/gauss. (7.3) The two components of the spin along a single axis, which we take as the z axis, are m S = ±1/2, and so the application of an external magnetic field along this axis results in Ĥ m S > = g e β B m S B m S >, m S = 1/2,1/2 (7.4) These evenly spaced energy levels diverge as the magnetic field is increased, and with the m S = ±1 selection rule the Electron Spin Resonance (ESR) frequency is hν ESR = g e β B B. The electron g-value is typically near 2, and so for magnetic fields of approximately 0.3 Tesla the ESR transition frequency is near 10 10 Hz, or 10 GHz. ESR is thus a microwave technique. ThelayoutofatypicalESRspectrometerisshowninFigure7.1. Inthepast, klystrons served as the microwave source, but much more efficient and solid state sources such as YIG or Gunn oscillators can now be used. The sample is located in a cavity that resides within a homogeneous magnetic field. In the most straightforward implementation of ESR, the microwave absorption at a fixed frequency is monitored as the magnitude of the DC magnetic field is swept. A typical spectrum, in this case that of the benzene radical-anion (C 6 H 6 ), is shown in Figure 7.2. The first derivative appearance of the spectrum is due to the modulation technique employed, as is also illustrated in Figure 7.2. Clearly, for ESR to work there must be unpaired electrons in the sample, and in this sense it is less generally applicable than is NMR. Still, low concentrations of radicals are readily detected with ESR (concentrations as low as 10 10 mol L 1 can be detected with an optimized spectrometer) since the bulk of the sample is invisible, and so a variety of species produced by chemical reactions or radiation, molecules in triplet states, and a range of d-metal complexes can be studied. ESR also has a number of biological applications, 1
Figure 7.1 (Left) ESR field splittings from the spin 1/2 of an unpaired electron (note that due to the charge, the level are switched relative to proton NMR). (Right) The layout of an ESR spectrometer in which the magnetic field is swept, and absorption at a fixed microwave frequency is measured with a lock-in amplifier. include metalloenzymes that contain paramagentic metals, free radicals and biradicals (enyzme oxidation, radiation damage), electron transfer reactions (photosynthesis), etc. Just as for NMR, local fields produced by the molecule alter the magnetic field strength experienced by the unpaired electron, and so the ESR frequency is hν ESR = g e µ B (1 σ)b. (7.5) In ESR, it is conventional to write g = g e (1 σ), where g is the overall g-factor of the complex. This is useful since there is typically only one or at most a small number of unpaired electron types in typical samples. Truly free electrons have g e = 2.0023, and the deviation from this value in actual samples is related to the alteration of the applied field by local electron currents in the molecule. Thus, the change in the g-factors contains information about the electron structure of the material, in particular the site of the unpaired electron. Most organic radicals have g-factors that are close to the free electron value, inorganic radicals often have g-factors that range from 1.9-2.1. d-metal complexes have a much wider range of g-factors, with values between 0-4 observed. In general, however, the change in g-factors is not nearly as useful as chemical shifts in NMR. Hyperfine Structure Fortunately, there is additional interaction that makes ESR much more useful; namely the interaction of the electron magnetic moment with nuclear magnetic moments in the sample. This leads to the formation of hyperfine structure, that is the breaking up of the single ESR frequency into multiple components. Consider, for example, the effect on the 2
Figure 7.2 (Left) The ESR spectrum of the benzene radical-anion in solution. a is the hyperfine splitting that arises from the interaction of the unpaired electron with the nuclear spins of the protons. (Right) For phase sensitive detection at the frequency of small modulations of the magnetic field, a first derivative line shape is produced. 3
Figure 7.3 The hyperfine interaction between an electron and a spin 1/2 nucleus results in a total of four energy levels. Due to the symmetry of the interactions, the splittings result in a doublet of equal intensity. ESR spectrum of a single H nucleus. The proton spin provides a magnetic field whose strength in the direction of the externally aligned field depends on the orientation of the nuclear spin. The local field is thus B local = B +am I m I = ±1/2, whereaisthehyperfine coupling constant. Halftheradicalsinthesamplehavem I = +1/2, the other half contain m I = 1/2. The resonance frequencies in this situation become hν ESR = gµ B (B +a/2) or B = hν gµ B a 2 hν ESR = gµ B (B a/2) or B = hν gµ B + a 2 (7.6) for the two populations. Thus, the single resonance transition is split into two components separated by a and centered on the field determined by the g-factor of the radical, as is illustrated in Figure 7.3. For radicals with a single 14 N nucleus (which has I = 1), the ESR spectrum is split intoatripletofequalintensitiesduetothethreeem I components(onethirdofthenitrogen nuclei are in each of the spin sub-components). In general, a spin-i nucleus will split the ESR line into 2I +1 hyperfine lines of equal intensity. 4
In most molecules, there will be several magnetic nuclei present. If the nuclei are equivalent (say the two methylene protons in the ethyl radical), some of the hyperfine lines will be coincident and will not be resolvable. If the perturbing nuclear spins arise from protons, then for N equivalent protons there will be N +1 hyperfine lines with a binomial intensity distribution that is, the intensity distribution is given by Pascal s triangle much as it is in NMR. Schematic examples of hyperfine structures for a combination of N and H nuclei are shown in Figure 7.4. This hyperfine structure provides a fingerprint that can serve to identify the types of radicals present in a sample. More importantly for chemists, the magnitude of the splitting depends on the distribution of the unpaired electron near the magnetic nuclei present. In C 6 H 6, for example, the unpaired electron is spread uniformly around the ring, and the hyperfine splitting is 0.375 mt. Since one proton is near a C atom which has 1/6 th of the electron spin density, the hyperfine splitting caused by a an electron in a single C H bond would be closer to 2.25 mt. In other radicals, the so-called McConnell equation can be used to predict the hyperfine splitting pattern, which states: a = Qρ Q = 2.25 mt, (7.7) where ρ is the unpaired electron spin density on a C atom and a is the hyperfine splitting observed for the H atom to which it is attached. In napthalene, for example, there are two types of protons, where the α protons are positioned at the four interior positions and the β protons occupy the four positions on the outside of the two aromatic rings. The four α protons alone would give rise to a five-line spectrum; and each of these lines would be further split into a quintet by the four β protons; resulting in the 25 line spectrum shown in Figure 7.5. The observed splittings yield a(α) = 0.490 mt and a(β) = 0.183 mt. Using the McConnell equation results in a predicted electron spin density of 0.22 and 0.08 for the two positions. What drives these hyperfine interactions? For molecules whose orientation is fixed, there is a dipole-dipole interaction term that treats the nuclear spins as point sources(these were the NMR terms from the previous lecture). The resulting interaction is anisotropic; that is, the magntiude and sign of the interaction depend on the relative orientation of the sample and the applied magnetic field. For electrons in p orbitals, the point magnetic dipole approximation is relatively good, but for electrons in an s orbital the correct treatment is analogous to that of the Fermi contact term that is important in nuclear hyperfine structure in atoms and in the rotational spectra of molecules. In fluid samples where the orientation is not fixed, such as those spectra presented in these lecture notes, another mechanism must be considered since the dipole-dipole interaction averages to zero in isotropic systems. The explanation, and one that holds in NMR as well, is called a polarization interaction. In π-electron radicals there are two possible interactions of the proton spin, and the C H bond is typically characterized by a σ orbital. There is a magnetic interaction between a proton and the σ electrons such that one of the electrons tends to have a greater probability of being near the H atom. Classically speaking, the other σ bonding electrons should be closer to the C atom, and by Hund s rule the overall energy should be lower if these electron spins are aligned. Thus, the unpaired electron can indirectly sense the spin of the proton. Theoretical calculations lead to predicted hyperfine interactions of 2.8 mt, close to that observed. 5
Figure 7.4 The ESR hyperfine structures of radicals containing (a) one 14 N and two equivalent protons and (b) three equivalent 14 N nuclei. 6
Figure 7.5 The ESR spectrum of the napthalene radical-anion. The structural inset presents the caclulation of the unpaired electron spin density on the two types of carbon atoms in the radical. Spin Labelling If groups with unpaired electrons are chemically attached to other molecules, the hyperfine splittings induced in this group can provide information on the changes in local structure. This so-called spin labelling technique has found widespread use in biochemistry as a sensitive detector of changes in protein and membrane structures. In such studies, the spin label is almost always a nitroxide radical, or R 1 (NO)R 2, since it is easy to synthesize (by using molecular oxygen oxidation at room temperature), because it is stable (the nitroxide free radical lifetime is months to years at a range of temperatures near 25 C), and because it is soluble in water and most organic solvents. The dominant hyperfine interaction is caused by the nearby nitrogen nucleus, and since it has a spin of 1 the ESR spectrum of the nitroxide radical is that of a triplet with equal intensities, ignoring any small splittings induced by the H atoms on R 1 and R 2, which is typically a good approximation if there are no protons on the α carbon (and so groups like R 1 = R 2 = t-butyl are by far the most common). For a small nitroxide radical in solution, the tumbling is sufficiently rapid to produce isotropy and three sharp lines are produced, with an average g-factor given by g = (g xx +g yy +g zz )/3. If for some reason the tumbling time scale is reduced (by increasing the viscosity, for example), the individual lines in the triplet begin to broaden and will eventually separate. For nitroxide radicals that have truly fixed orientations, the spectrum is said to be characteristic of strong immobilized nitroxide, and the separation between the two outer lines is equal to 2a zz (the hyperfine tensor component along the applied field direction). For example, if the nitroxide spin label is firmly bound to a large protein, a strongly immobilized spectrum results. With weaker interactions, if some rotational motion occur and the distance between the label and target become variable, the ratio of the outer splitting to the maximum possible splitting (2a zz ) is a measure of the binding. 7
Figure 7.6 (Left) The spin labelled ESR spectrum of BSA with 14% sucrose at 23 C (top). Spectrum b presents a simulation including rapid anisotropic motion, while spectrum c presents the case for slow isotropic motion. (Right) Typical spectrum for a random spin labelled bilayer phospholipid membrane. For di-t-butylnitroxide, the principle g-values are g xx = 2.0088, g yy = 2.0062, and g zz = 2.0027. The largest splittings occur with the magnetic field parallel to the nitrogen pp orbital, while in terms of crystallographic planes, if the magnetic field is parallel to the c crystal axis the field is in the plane of the nitroxide molecule. The principle hyperfine splittings are a xx = 7.6, a yy = 6.0, and a zz = 31.8 Gauss. Note that the values are nearly axially symmetric, and so if we define a zz = A and a xx a yy = A, then the principle hyperfine splittings for intermediate orientations are A 2 = A 2 cos2 q + A 2 sin 2 q, where q is the angle between the applied magnetic field and the parallel component of the g-factor/hyperfine splitting tensors. Examples of nitroxide spin labels on isolated proteins in solution and inserted in lipid bilayer membranes are shown in Figure 7.7. In the former case, the observed spectra are consistent with rapid anisotropic motion of the spin label, while for the membrane case both the parallel and perdendicular components may be measured. The molecules used to construct membranes are typically long and anisotropic, with a hydrocarbon tail that orients parallel to the phospholipid acyl chains. Charge polar groups typically anchor the membrane at the aqueous interface. Typically, the membranes will either have highly ordered bilayers(extended membranes on a planar support structure) or randomly oriented bilayers (as in the case of micelles in solution). 8
Figure 7.7 (Top) Schematic illustration of an ordered bilayer phospholipid membrane with a spin labelled fatty acid that undergoes a restricted precession about a cone angle β. (Bottom) Structures of some commonly used spin labelled fatty acids. 9
In the ordered system, outlined in Figure 7.7, the spin labelled fatty acid will align parallel to the acyl chains of the phospholipids in a membrane bilayer with its carbonyl end at the water interface. Thus, the nitrogen pp orbital will be aligned perpendicular to the membrane surface. Because of the liquid crystal nature of a bilayer the spin labelled fatty acid will undergo anisotropic motion about its long axis (the so-called director axis) and undergo excursions from this axis about the individual C C bonds in the chain. The ESR spectrum permits the characterization of the A and A values for the spin labelled fatty acid. For a randomly oriented bilayer with respect to the magnetic field, the hyperfine values are calculated from the outer and inner maxima/minima in the first derivative spectrum (see Figure 7.6). The order parameter of the membrane is defined as, S = A A A zz (A xx +A yy )/2. Depending on the packing of the phospholipid chains the excursion angle β will be S = 3 < cos2 β > 1 2, and so the average cone swept out by the spin label can be estimated experimentally. When two spin labels are incorporated into polymers or macromolecules, the dipolar coupling between the spin labels varies as r 3 ; and spin echo techniques such as that outlined in Section #23 can be used to provide distance estimates and thus structural information without the need to produce crystals for X-ray analysis. Details of such approaches may be found in the supplemental notes for this section, on what is called DEER ESR. 10