40
1
General Principles
2.3.3 Dipolar Coupling
In normal liquids, most molecules move isotropically and dipolar couplings are averaged to
0. In static solids and in liquid crystals, molecular motion is non-existent or anisotropic and
dipolar couplings are observed. In solids, dipolar couplings are obscured by chemical shift
anisotropy but in liquid crystals, they are observed and can be large, up to the kHz range [423].
The size of the direct dipolar coupling (D ij ) between nuclei i and j is:
D ij =
−K ij S ij
r 3
ij
(5)
where K ij is equal to a constant times the product of γ i and γ j and S ij is a traceless symmetric tensor, the order tensor, indicating how the spins are oriented with respect to the liquid crystal axis and the magnetic field [424]. Analysis of these spectra is complex since
every spin 1/2 nucleus is coupled to every other nucleus. However, Tjandra and Bax showed
that partial orientation of small proteins can be achieved in phospholipid bilayers known as
bicelles [425]. The value of the order parameter increases with increasing bicelle concentrations allowing separation of dipolar and scalar couplings. This technique has been applied to
carbohydrates [236,333,426,427,428,429,430,431]. Measurements of dipolar couplings provide a valuable complement to NOE measurements to define internuclear distances since the
distance dependence of this interaction is r −3 , rather than r −6 . A concern is that interaction
of the carbohydrate with the liquid crystal may alter the populations of individual conformers [432].
2.3.4 Nuclear Overhauser Effect
Techniques based on the nuclear Overhauser effect (nOe) are now the most important methods
used for defining three-dimensional structures of carbohydrates. There is a recent edition [433]
of earlier texts [434,435]. Overhauser originally predicted that saturation of electrons in a metal
would polarize the metal nuclear spins [436] and the term nOe refers to the change in intensity
of a signal resulting upon irradiation of another signal. For a two-spin system, IS, the nOe
effect f I (S) is defined as the fractional change in the intensity of I on saturating S:
f I (S) =
(I − I ◦ )
I ◦
(6)
where I° is the equilibrium intensity of I [435]. > Figure 28 shows a diagram of transition probabilities (W 0IS , W 1I , W 1S , and W 2IS ) and spin states for the two-spin system.
Solomon [437] showed that on saturating S:
f I (S) =
γ S
γ I
W 2IS − W 0IS
W 0IS + 2W 1I + W 2IS
=
γ S
γ I
σ IS
IS
(7)
where γ I and γ S are the magnetogyric ratios for the two nuclei, σ IS is the cross-relaxation rate,
and IS is the longitudinal relaxation rate. Relaxation for 1 H and 13 C nuclei normally occurs
via the dipole-dipole mechanism where the motion of nearby magnets, usually 1 H nuclei that
move with the molecular motion, creates a magnetic field that has a frequency component that
matches the transition frequency. For small molecules in solution at room temperature, the
1
General Principles
2.3.3 Dipolar Coupling
In normal liquids, most molecules move isotropically and dipolar couplings are averaged to
0. In static solids and in liquid crystals, molecular motion is non-existent or anisotropic and
dipolar couplings are observed. In solids, dipolar couplings are obscured by chemical shift
anisotropy but in liquid crystals, they are observed and can be large, up to the kHz range [423].
The size of the direct dipolar coupling (D ij ) between nuclei i and j is:
D ij =
−K ij S ij
r 3
ij
(5)
where K ij is equal to a constant times the product of γ i and γ j and S ij is a traceless symmetric tensor, the order tensor, indicating how the spins are oriented with respect to the liquid crystal axis and the magnetic field [424]. Analysis of these spectra is complex since
every spin 1/2 nucleus is coupled to every other nucleus. However, Tjandra and Bax showed
that partial orientation of small proteins can be achieved in phospholipid bilayers known as
bicelles [425]. The value of the order parameter increases with increasing bicelle concentrations allowing separation of dipolar and scalar couplings. This technique has been applied to
carbohydrates [236,333,426,427,428,429,430,431]. Measurements of dipolar couplings provide a valuable complement to NOE measurements to define internuclear distances since the
distance dependence of this interaction is r −3 , rather than r −6 . A concern is that interaction
of the carbohydrate with the liquid crystal may alter the populations of individual conformers [432].
2.3.4 Nuclear Overhauser Effect
Techniques based on the nuclear Overhauser effect (nOe) are now the most important methods
used for defining three-dimensional structures of carbohydrates. There is a recent edition [433]
of earlier texts [434,435]. Overhauser originally predicted that saturation of electrons in a metal
would polarize the metal nuclear spins [436] and the term nOe refers to the change in intensity
of a signal resulting upon irradiation of another signal. For a two-spin system, IS, the nOe
effect f I (S) is defined as the fractional change in the intensity of I on saturating S:
f I (S) =
(I − I ◦ )
I ◦
(6)
where I° is the equilibrium intensity of I [435]. > Figure 28 shows a diagram of transition probabilities (W 0IS , W 1I , W 1S , and W 2IS ) and spin states for the two-spin system.
Solomon [437] showed that on saturating S:
f I (S) =
γ S
γ I
W 2IS − W 0IS
W 0IS + 2W 1I + W 2IS
=
γ S
γ I
σ IS
IS
(7)
where γ I and γ S are the magnetogyric ratios for the two nuclei, σ IS is the cross-relaxation rate,
and IS is the longitudinal relaxation rate. Relaxation for 1 H and 13 C nuclei normally occurs
via the dipole-dipole mechanism where the motion of nearby magnets, usually 1 H nuclei that
move with the molecular motion, creates a magnetic field that has a frequency component that
matches the transition frequency. For small molecules in solution at room temperature, the