molecular theory

2
Theory When a molecule or compound with an unpaired electron is placed in a strong magnetic field, the spin of the unpaired electron can align in two different ways creating two spin states, ms = ± ½. The alignment can either be along the direction (parelle) to the magnetic filed which corresponds to the lower energy state ms = - ½ or opposite (antiparallel) to the direction of the applied magnetic field ms = + ½ . The two allignments have different energies and this difference in energy lifts the degeneracy of the electron spin states. The energy difference is given by: ∆ E = E+ - E- = hv = gmßB h = Planck’s constant (6.626 x 10-34 J s-1), v = the frequency of radiation, ß = Bohr magneton (9.274 x 10-24 J T-1), B = strength of the magnetic field in Tesla, g = the g-factor (more explanation on g factor) During the experiement the values of h, v, and ß does not change and g value decrease as B increases. The g-factor is a unitless measurement of the intrinsic magnetic moment of the electron, and its value for a free electron is 2.0023. The concept of g can be roughly equated to that of chemical shift in NMR. EPR spectrum is the absorption of microwave frequency radiation ploted against the magnetic field intensity 3.1. Working principles of EPR: In an EPR experiment the field of the spectrometer magnet is swept linearly to excite some of the electrons in the lower energy level to the upper energy level while the sample is exposed to fixed microwave irradiation. The free or the upaired electrons have a small magnetic field and orient themselves parallel to the larger field produced by the spectrometer’s magnet. At a particular magnetic field strength the microwave irradiation will cause some of the free electrons to “flip” and orient against the spectrometer’s magnetic field. This separation between the lower and the higher energy level is exactly matched by our microwave frequency. The condition where the magnetic field and the microwave frequency are “just right” to produce an EPR resonance (or absorption) is known as the resonance condition

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Molecular Theory

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Theory When a molecule or compound with an unpaired electron is placed in a strong magnetic field, the spin of the unpaired electron can align in two different ways creating two spin states, ms = . The alignment can either be along the direction (parelle) to the magnetic filed which corresponds to the lower energy state ms = - or opposite (antiparallel) to the direction of the applied magnetic field ms = + . The two allignments have different energies and this difference in energy lifts the degeneracy of the electron spin states. The energy difference is given by: E = E+ - E- = hv = gmB

h = Plancks constant (6.626 x 10-34 J s-1),v = the frequency of radiation, = Bohr magneton (9.274 x 10-24 J T-1),B = strength of the magnetic field in Tesla,g = the g-factor (more explanation on g factor) During the experiement the values of h, v, and does not change and g value decrease as B increases. The g-factor is a unitless measurement of the intrinsic magnetic moment of the electron, and its value for a free electron is 2.0023. The concept of g can be roughly equated to that of chemical shift in NMR. EPR spectrum is the absorption of microwave frequency radiation ploted against the magnetic field intensity 3.1. Working principles of EPR:In an EPR experiment the field of the spectrometer magnet is swept linearly to excite some of the electrons in the lower energy level to the upper energy level while the sample is exposed to fixed microwave irradiation. The free or the upaired electrons have a small magnetic field and orient themselves parallel to the larger field produced by the spectrometers magnet. At a particular magnetic field strength the microwave irradiation will cause some of the free electrons to flip and orient against the spectrometers magnetic field. This separation between the lower and the higher energy level is exactly matched by our microwave frequency. The condition where the magnetic field and the microwave frequency are just right to produce an EPR resonance (or absorption) is known as the resonance condition is detected by the spectrometer., EPR spectroscopy can be carried out by eithervarying the magnetic field and holding the frequency constant orvarying the frequency and holding the magnetic field constant (as is the case for NMR spectroscopy).Typically in a comericial spectrometer works by varying the magnetic field and holding the frequency constant. EPR spectrometers working at frequencies ranging from several hundred MHz to several hundred Ghz are in use. 1-2 GHz (L-band) and 2-4 GHz (S-band), 8-10 GHZ (X-Band), 35 Ghz (Q-band) and 95 GHz (W-band). The most commonly used EPR spectrometer is in the range of 9-10 GHz (X-band).