The Origin Of The Chemical Shift

Each type of nucleus (each specific isotope like 1H) has a characteristic resonant frequency (precession frequency or Larmor frequency) in a given external magnetic field, Bo. The simple relationship vo = y Bo/2n shows that the Larmor frequency depends only on the "magnet strength" of the nuclear magnet (the magnetogyric ratio y) and the strength of the external magnetic field Bo. This is how we can "tune in" to a particular nucleus on the spectrometer, by setting the base frequency (e.g., 500 MHz for 1H and 125 MHz for 13C on an 11.7 T spectrometer). But if all protons in a molecule had exactly the same resonant frequency, the technique would be useless because we would see a single peak in the spectrum representing all of the protons. In fact, as we have seen, there are slight differences in resonant frequency depending on the chemical environment of the nucleus within a molecule. The relationship still holds that resonant frequency is exactly proportional to external field strength, but it is the local magnetic field strength at the position of the nucleus that is important: the effective field Beff,

This local magnetic field is slightly less than the applied magnetic field, Bo, due to the effect of the electron cloud (bonding and nonbonding electrons) surrounding the nucleus. This cloud of electrons "shields" the nucleus from the applied magnetic field by a tiny factor, on the order of parts per million, of the applied field:

The shielding factor, a, is related to the chemical shift in parts per million:

where ao is the shielding factor for a reference compound such as tetramethylsilane (TMS) that defines the zero of the chemical shift scale. Note that 5 gets smaller as there is more shielding and larger as there is less shielding. We can view the right-hand side of the spectrum as relatively "shielded" (upfield, small 5) and the left-hand side as relatively "deshielded" (downfield, large 5).

The physical origin of this shielding by electrons is relatively easy to explain. The cloud of electrons surrounding a nucleus begins to circulate when the sample is placed in a magnetic field. This is a general phenomenon of physics: If you place a closed circle of wire in a magnetic field, a current will be induced to flow around the circle. This induced current will create a new magnetic field, just as any coil of wire with a current, and the direction of the induced current will always be such that the new magnetic field will oppose the original magnetic field that created it. This is called Lenz's law. The stronger the original magnetic field, the more the current will flow in the wire loop and the stronger will be the new, opposing magnetic field. Thus, the opposing field is proportional to the original field. Returning to the nucleus in a cloud of electrons, the electrons are mobile and thus form a kind of circle of wire around the nucleus (Fig. 2.14). When the sample is inserted in the magnetic field, the electrons begins to circulate around the nucleus (the induced current) and produce a magnetic field that opposes the Bo field at the center of the current (i.e., at the nucleus). This induced field (Bi) is proportional to the external field and subtracts from it, reducing the effective field felt by the nucleus:

vo = yBeff /2n = yBo(1 - a)/2n = yBo/2n - yBoa/2n (a ^ 1)

The change in resonant frequency (in hertz) is thus proportional to Bo for a given shielding constant a, that is, for a given nucleus at a particular position in a molecule. This is exactly the effect we saw in Figure 2.1, as the field strength Bo is increased. To make chemical shifts the same regardless of magnet strength, we use the 5 scale in parts per million, where the proportionality to Bo is already taken into account:

Shielding is just a combination of electron density in the vicinity of the nucleus and the ease of circulation of those electrons. For a proton, there is only one bond to the rest of the molecule, and the electron density around the proton is affected primarily by the electron-withdrawing effect of electronegative atoms that are nearby in the bonding network. For

Figure 2.14

example, a proton bound to an oxygenated carbon (H-C-O) experiences a "deshielding" effect (downfield shift) because the electronegative oxygen pulls electron density toward it, making the carbon atom slightly positive and displacing electron density away from the proton and toward the carbon. This reduction of electron density reduces the circulating current around the proton, leading to a reduction in the opposing magnetic field created by that current. Thus, the proton is less shielded from (more "exposed" to) the applied magnetic field, Bo, and its resonant frequency increases (downfield shift). The magnitude of this change in electron density is miniscule, on the order of a few parts per million.

2.6.1 Through-space Effects

The deshielding effect of electronegative groups operates by displacing electrons in bonds, effectively decreasing the electron density immediately surrounding the proton. Another effect arises when induced magnetic fields are strong enough to extend through space from other atoms or molecular subunits to the point occupied by the proton. The classic example of this is the benzene ring, which has two mobile clouds of n electrons, one above and one below the plane of the ring (Fig. 2.15). In the external (Bo) magnetic field, the n electrons circulate according to Lenz's law, generating an induced magnetic field (Bi) that opposes Bo at the center of the circulating current. The induced field lines are circular, however, extending from the bottom upward around the outside of the benzene ring and then descending again into the center of the ring. At the position of the proton, at the outside of the benzene ring, the induced field is aligned with the Bo field so that it adds to the laboratory field. This strong deshielding effect shifts the benzene protons downfield to more than 7 ppm on the 8 scale. These larger scale electron currents due to loosely bound n electrons in double bonds and conjugated systems generate stronger induced fields that can extend

through space several Angstroms and influence chemical shifts. For the benzene ring, the effect is shielding (upfield shifting) in the region directly above and below the ring, while it is deshielding (downfield shifting) in the plane of the aromatic ring. One can imagine two cones extending from the center of the ring, one above the ring and another cone below the ring; protons inside one of the cones will be shielded (upfield shifted) and protons outside of the cones will be deshielded (downfield shifted). The effect diminishes as the proton moves away from the center of the ring. The same pair of cones can be visualized above and below the plane of a single unsaturation (C=C or C=O), leading to zones of "anisotropic" shielding and deshielding.

In rigid molecules, we sometimes see large chemical shift differences (up to 2 ppm) between the two protons of a CH2 group if there is a double bond or aromatic ring nearby. The inductive effects of electronegative groups will be the same for these two protons because each one has the same through-bond relationship to the rest of the molecule, but the difference in chemical shift is largely due to their different positions in space relative to the plane of the unsaturated group (n bond). In globular proteins the monomer unit (-NH-CH(R)-CO-) of the biological polymer can have unique chemical shifts even when there are many of the same monomer unit (e.g., alanine: R = CH3) in the polypeptide chain. For example, if there are six alanine residues (A4, A15, A26, A78, A92, and A126) in a protein, there might be six different chemical shifts for the six methyl doublets. This "dispersion" or spreading out of chemical shifts for identical monomer units is due in large part to the proximity and orientation of aromatic rings (side chains of nearby aromatic amino acids). Proteins with few aromatic amino acids usually show more overlap and are more difficult to work with in NMR structure determination. In NMR of natural products, the use of d6-benzene (C6D6) as a solvent can sometimes "spread out" overlapped chemical shifts in the same way, due to the anisotropic (relative orientation dependent) effects of n-electron circulation in the solvent molecules on solute chemical shifts.

245 ppm 110 ppm 35 ppm

Figure 2.16

2.6.2 Chemical Shift Anisotropy

The amount of electron circulation (and thus the intensity of the induced field) is dependent on the orientation of the molecule with respect to the Bo field direction. In the above example of the benzene ring, we assumed that the plane of the aromatic ring is perpendicular to the Bo field vector. In fact, in solution the molecule is rapidly reorienting itself and samples all orientations equally over time (rapid isotropic tumbling). If we could lock the ring in place and measure chemical shifts, we would see three different chemical shifts for the three principle orthogonal orientations of the molecule. For example, the 13 C chemical shift of benzene is 245 ppm for the orientation with the ring plane perpendicular to Bo (Fig. 2.16) because this orientation gives the maximum electron circulation. For the orientation with the ring plane parallel to the Bo field and the 13C-H vector perpendicular to Bo, the chemical shift is 110 ppm, and for the other parallel orientation with the 13C-H vector parallel to Bo, the shift is only 35 ppm. In the two parallel cases, the electron circulation would have to cross the plane of the benzene ring, which is a node (zero electron density) in the n orbital. The observed chemical shift in solution (the "isotropic" chemical shift) is the average of these three fixed-orientation chemical shifts:

The amount of variation of chemical shift with the orientation is called the chemical shift anisotropy, or CSA. CSA is simply the difference between the smallest fixed-position chemical shift and the average of the other two fixed-position chemical shifts:

By comparison, a saturated methine carbon (C-H) has a CSA of only 25 ppm because the mobility of electrons around the carbon nucleus is much less in an sp3-hybridized carbon and depends much less on the orientation of the C-H bond with respect to Bo. In solution-state NMR we only see the isotropic chemical shift, ┬┐iso, and the fixed-position chemical shifts and the CSA value are obtained from solid-state NMR measurements. Although CSA does not affect chemical shifts in solution, it does contribute to NMR relaxation and can be exploited to sharpen peaks of large molecules such as proteins in solution. For large molecules, such as proteins, nucleic acids, and polymers, or in viscous solutions, molecular tumbling is slow and CSA broadens NMR lines due to incomplete averaging of the three principle chemical shift values on the NMR timescale. Like isotropic chemical shifts, CSA in parts per million is independent of magnetic field strength Bo but is proportional to Bo when expressed in hertz. Because linewidths are measured in hertz, the line-broadening effect of CSA becomes more significant as we increase the field strength.

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