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spins resonate and the random distribution changes into a coherent net Mxy component. Spin systems giving rise to net Mxy components are known to be phase coherent.

Nuclear spins with different electronic environments may be brought into resonance by either one of two techniques. In the frequency-sweep method, the spectrum is recorded by sweeping the applied radiation frequency. In the transient-response method, the transient signal for its component frequencies is sorted/transformed after an induction (by pulse(s) of an applied field in terms of angles, e.g. 90° or 180°) of transient response in the system. The transient signal is changed into a normal spectrum by Fourier transformation in the transient-response method, which is used by most modern NMR spectrometers. There are four parameters that define the NMR spectrum:

7.5.1.1 Intensity or area under resonance peak. The amplitudes of the resonance/transient signals are directly proportional to the number (concentration) of nuclei in an equilibrium system of nuclear spins. Relative concentrations are usually measured from the resonance intensities (peak heights). This provides an indication for the relative quantities of the resonance nuclei with different chemical environments (chemical structures) in the molecule.

7.5.1.2 Chemical shift. The frequency (v) at which any nucleus will resonate in the NMR spectrum is give by v = yH/2rc where y is a constant known as the magnetogyric ratio and H is the local field experienced by the nucleus, which corresponds to the applied magnetic field (Ho) by H = Ho(1 - o) since the nucleus will usually be shielded by the surrounding electrons. The extent of this shielding is represented by a shielding parameter (o). It becomes v = {yH0(1 - o)}/2n indicating that nuclei with different shielding parameters, i.e. different electronic environments may be brought into resonance either by a frequency sweep or by a field sweep of the spectrum. In principle, the NMR spectrum can be recorded either in cycles per second (hertz, frequency units) or milligauss (field units), since the frequency of any given resonance will be proportional to the applied magnetic field. Available spectrometers may employ different field strengths, which have been increased with improved spectrometers. A scale of field-independent, frequency-referenced units, called the chemical shift scale is chosen. The chemical shift (8) is defined as

§ = (Vref - Vs) (Hz)/Vo (MHz) = 106[(8ref - §obs)/§tef]

where vref, vs and vo are resonance frequencies of a reference compound, sample in hertz (Hz) and operating frequency in MHz respectively. 8ref and 8obs are the positions (in Hz) for a reference compound and the signal of interest. The numerator is expressed in Hz as opposed to the denominator, which is expressed in MHz and therefore the unit of chemical shift parameter, 8, is expressed in parts per million (ppm). This permits us to compare spectra obtained on instruments operating at different field strengths since the frequency of a particular resonance increases in direct proportion to the increase in the field strength. Usually a compound with shield nuclei that resonate at particularly high frequencies is used as the reference. For example, tetramethylsilane (TMS) or sodium 2,2-methyl-2-silapentane-5-sulfonate (DSS) are commonly used to calibrate the instrument in proton magnetic resonance (PMR). In some literatures (especially organic chemistry), T-scale of chemicals shifts where t = 10 - 8 is used.

Two classes of shift are:

1. primary or intrinsic shift which is characteristic of a particular chemical group; and

2. secondary or induced shift arising from the influence, through space, of neighboring magnetic centers.

The primary shifts vary widely with different nuclei of different groups and are sensitive to the ionization state of the molecule.

The primary shifts depend on the electron cloud around the proton that is undergoing resonance. Electronegative substituents withdraw electron density from the proton, giving less shielding and therefore larger 8 values. The secondary (induced) shifts are important in macromolecular spectra. NMR spectra of native (folded) biopolymers are generally different from those of the denatured (unfolded) biopolymers. An analysis of the difference spectra provides useful information about the conformation of the biopolymers. Interatomic shielding forming neighboring atoms can augment or oppose the applied field, and therefore the shift of the resonating nuclei. A special kind of interatomic shielding is ring current (delocalized n electrons) shifts of aromatic rings that are particularly important in biomacromolecules. The induced electron currents create large magnetic field affecting (positively or negatively) the resonating nucleus, depending on its position relative to the aromatic ring. The resonating nucleus on the side of the ring experiences an augmentation of the applied field while that over the center of the ring sees an opposing effect. Hydrogen bonding affects the bonded proton by causing a downfield shift relative to the unbonded state.

7.5.1.3 Multiplicity and spin-spin coupling. Spin-spin interactions (couplings) between magnetic nuclei are responsible for multiplet structure of NMR spectra. These interactions are communicated between the nuclei by electrons in a chemical bond. Thus spin-spin interactions are often referred to as through-bond interactions. The splitting (of multiplet) is independent of the field, and depends only on the nature of the bonding between the two groups, thus it is informative of the neighboring groups. The size of the interaction is defined by the spin-spin coupling constant (J), which measures the splitting between two different nuclei in a given molecule in hertz (Hz).

For the spin-spin coupling to systems containing n bond-sharing protons, the following rules can be formulated:

1. If a proton has a neighbors, sets na, nb, nc... of chemically equivalent protons, the multiplicity of its resonance will be (na + 1)(nb + 1)(nc + 1)

2. For one neighboring group of n equivalent protons, the relative intensities of the n + 1 multiplet components are given by the coefficients of the terms in the expansion of (x + 1)n.

These two generalizations form the basis for interpreting spin-spin coupling patterns in NMR spectra by the first-order approximation, if J is smaller than the chemical shift frequency Av between adjacent groups (typically J < Av). If J > Av, the spectrum can be more complex than the first-order splitting pattern. An increase in field strength raises Av (chemical shifts are independent of field strength) to the point where simple first-order splitting can be seen (J < Av).

The appearance of a multiplet also depends on the relative magnitudes of 8 and J for the coupled nuclei. If A8 >> J, then a well-splitted multiplet is observed. However, the nuclei are said to be equivalent and no multiplet structure is observed if A8 ~ J. The spin-spin coupling between protons three bonds apart depends on the relative orientation of the nuclei involved in the coupling according to the Karplus equation (Karplus, 1959):

For protons, 0 is the angle between the protons for germinal (two-bond) coupling (x = 2) or the dihedral angle between the protons for vicinal (three-bond) coupling. Subscripts, y and z define the nuclei that are interacting. A, B and C are empirical constants, e.g. for vicinal couplings (*0 = $ - 60° for proteins):

y

z

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