The dipolar interaction under all angles

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

“…When the CSG strength G and the evolution time t 1 have the values given in Table 1, the magnetization is modulated under the combined effect of the background gradient and CSG. When the magic angle gradient condition of magnetization modulation is satisfied, it results in null DDF [39,40]. It is noted that the simulation results for the t 1 value in Table 1 correspond to the minimal relative signal intensities in the curves of Fig.…”

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

“…When the CSG strength G and the evolution time t 1 have the values given in Table 1, the magnetization is modulated under the combined effect of the background gradient and CSG. When the magic angle gradient condition of magnetization modulation is satisfied, it results in null DDF [39,40]. It is noted that the simulation results for the t 1 value in Table 1 correspond to the minimal relative signal intensities in the curves of Fig.…”

Resin Dynamics Contributes to the NMR Line Broadening of Organic Molecules Grafted onto a Polystyrene Resin

“…Both semiclassical (35) and quantum mechanical (36 ) calculations showed that this field can be modeled as originating from a dipole, if the proton under consideration is reasonably far from the ring system. This dipolar field is not averaged out to zero by the rapid isotropic motion of the protein molecule because the dipole moment associated with the aromatic ring is not constant, but depends on the orientation of the ring normal with respect to B 0 (33,37,38). The resulting average field leads to differential chemical shift values and is one of the important contributions in semiempirical chemical shift calculation routines (39).…”

From NMR spectra to structure

“…Direct methods are based on the explicit dependence of the direct dipolar coupling on the distances between magnetically active nuclei. Two magnetically active nuclear spins interact via a direct dipolar interaction which is analogous to the classical interaction between two magnetic point dipoles, m 1 and m 2 . The direct‐dipolar coupling constant, α, characterize the direct interaction, where is the permeability constant, is the Planck's constant and are the magnetogyric ratio of nuclei 1 and 2, respectively.…”

“…It is important to recall that α depends on the average of the inverse cube separation between the magnetic dipoles, . For an isolated spin pair, the direct dipolar contribution to the spin–spin Hamiltonian is where D is the direct dipolar tensor, which averages to zero for rapidly tumbling molecules because it is traceless, i.e. the sum of its diagonal elements is zero.…”

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

“…When the CSG strength G and the evolution time t 1 have the values given in Table 1, the magnetization is modulated under the combined effect of the background gradient and CSG. When the magic angle gradient condition of magnetization modulation is satisfied, it results in null DDF [39,40]. It is noted that the simulation results for the t 1 value in Table 1 correspond to the minimal relative signal intensities in the curves of Fig.…”

Resin Dynamics Contributes to the NMR Line Broadening of Organic Molecules Grafted onto a Polystyrene Resin

“…Both semiclassical (35) and quantum mechanical (36 ) calculations showed that this field can be modeled as originating from a dipole, if the proton under consideration is reasonably far from the ring system. This dipolar field is not averaged out to zero by the rapid isotropic motion of the protein molecule because the dipole moment associated with the aromatic ring is not constant, but depends on the orientation of the ring normal with respect to B 0 (33,37,38). The resulting average field leads to differential chemical shift values and is one of the important contributions in semiempirical chemical shift calculation routines (39).…”

From NMR spectra to structure

“…Direct methods are based on the explicit dependence of the direct dipolar coupling on the distances between magnetically active nuclei. Two magnetically active nuclear spins interact via a direct dipolar interaction which is analogous to the classical interaction between two magnetic point dipoles, m 1 and m 2 . The direct‐dipolar coupling constant, α, characterize the direct interaction, where is the permeability constant, is the Planck's constant and are the magnetogyric ratio of nuclei 1 and 2, respectively.…”

“…It is important to recall that α depends on the average of the inverse cube separation between the magnetic dipoles, . For an isolated spin pair, the direct dipolar contribution to the spin–spin Hamiltonian is where D is the direct dipolar tensor, which averages to zero for rapidly tumbling molecules because it is traceless, i.e. the sum of its diagonal elements is zero.…”

High-resolution NMR spectra in inhomogeneous fields utilizing the CRAZED sequence without coherence selection gradients

“…When the CSG strength G and the evolution time t 1 have the values given in Table 1, the magnetization is modulated under the combined effect of the background gradient and CSG. When the magic angle gradient condition of magnetization modulation is satisfied, it results in null DDF [39,40]. It is noted that the simulation results for the t 1 value in Table 1 correspond to the minimal relative signal intensities in the curves of Fig.…”

Resin Dynamics Contributes to the NMR Line Broadening of Organic Molecules Grafted onto a Polystyrene Resin

“…Both semiclassical (35) and quantum mechanical (36 ) calculations showed that this field can be modeled as originating from a dipole, if the proton under consideration is reasonably far from the ring system. This dipolar field is not averaged out to zero by the rapid isotropic motion of the protein molecule because the dipole moment associated with the aromatic ring is not constant, but depends on the orientation of the ring normal with respect to B 0 (33,37,38). The resulting average field leads to differential chemical shift values and is one of the important contributions in semiempirical chemical shift calculation routines (39).…”

From NMR spectra to structure

“…Direct methods are based on the explicit dependence of the direct dipolar coupling on the distances between magnetically active nuclei. Two magnetically active nuclear spins interact via a direct dipolar interaction which is analogous to the classical interaction between two magnetic point dipoles, m 1 and m 2 . The direct‐dipolar coupling constant, α, characterize the direct interaction, where is the permeability constant, is the Planck's constant and are the magnetogyric ratio of nuclei 1 and 2, respectively.…”

“…It is important to recall that α depends on the average of the inverse cube separation between the magnetic dipoles, . For an isolated spin pair, the direct dipolar contribution to the spin–spin Hamiltonian is where D is the direct dipolar tensor, which averages to zero for rapidly tumbling molecules because it is traceless, i.e. the sum of its diagonal elements is zero.…”