Molecular correlation time

In addition to the dipole-dipole relaxation processes, which depend on the strength and frequency of the fluctuating magnetic fields around the nuclei, there are other factors that affect nOe (a) the intrinsic nature of the nuclei I and S, (b) the internuclear distance (r,s) between them, and (c) the rate of tumbling of the relevant segment of the molecule in which the nuclei 1 and S are present (i.e., the effective molecular correlation time, Tf). 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

While the rate of change of dipolar interaction depends on t its magnitude depends only on the internuclear distance and is independent of t,. Thus the dipole-dipole relaxation depends on the molecular correlation time T the internuclear distance r, and the gyromagnetic ratios of the two nuclei, y and js -... 

Fig. 1.50. Relaxation time as a function of the molecular correlation time for two spectrometer frequencies 60 MHz and 220 MHz. rSGR, spin-lattice relaxation time rSSR, spin-spin relaxation time (Fig. 2.24 from [ 1.105]).

LIG. 22 A schematic illustration of the dependence of NMR relaxation times T and T2 on the molecular correlation time, xc, characterizing molecular mobility in a singlecomponent system. Both slow and fast motions are effective for T2 relaxation, but only fast motions near w0 are effective in Tx relaxation. 

Structural information on aromatic donor molecule binding was obtained initially by using H NMR relaxation measurements to give distances from the heme iron atom to protons of the bound molecule. For example, indole-3-propionic acid, a structural homologue of the plant hormone indole-3-acetic acid, was found to bind approximately 9-10 A from the heme iron atom and at a particular angle to the heme plane (234). The disadvantage of this method is that the orientation with respect to the polypeptide chain cannot be defined. Other donor molecules examined include 4-methylphenol (p-cresol) (235), 3-hydroxyphenol (resorcinol), 2-methoxy-4-methylphenol and benzhydroxamic acid (236), methyl 2-pyridyl sulfide and methylp-tolyl sulfide (237), and L-tyrosine and D-tyrosine (238). Distance constraints of between 8.4 and 12.0 A have been reported (235-238). Aromatic donor proton to heme iron distances of 6 A reported earlier for aminotriazole and 3-hydroxyphenol (resorcinol) are too short because of an inappropriate estimate of the molecular correlation time (239), a parameter required for the calculations. Distance information for a series of aromatic phenols and amines bound to Mn(III)-substituted HRP C has been published (240). 

Indeed, 13C spin-lattice relaxation times can also reflect conformational changes of a protein, i.e. helix to random coil transitions. This was demonstrated with models of polyamino acids [178-180], in which definite conformations can be generated, e.g. by addition of chemicals or by changes in temperature. Thus effective molecular correlation times tc determined from spin-lattice relaxation times and the NOE factors were 24-32 ns/rad for the a carbons of poly-(/f-benzyl L-glutamate) in the more rigid helical form and about 0.8 ms/rad for the more flexible random coil form [180],... 

It can be shown4 for the simple case of isotropic rotational diffusion that the TCF is a single exponential function of time, decaying with a time constant, rc, the molecular correlation time ... 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

One of the classical NMR methods used to determine molecular correlation times is provided by spin-lattice relaxation experiments. The spin-lattice relaxation rate 1 /T is determined by transitions among the Zeeman levels. For a liquid, the expression for the spin-lattice relaxation rate [81] is... 

As with Ti relaxation, T2 relaxation has a strong dependence upon the molecular correlation time. Unlike U relaxation, T2 relaxation does not reach a minimum and then increase, but continues to decrease, as shown in Fig. 3. Therefore large, slowly tumbling molecules have very short T2 times. This poses a great challenge in the study of large molecules or molecules in the solid state since the lifetime of the signal is very short and the linewidths are very broad. 

Figure 7 Schematic plot of the relationship between 7"i (longitudinal relaxation time), T2 (transverse relaxation time), and the molecular correlation time (r0). In general, small molecules have short correlation times, whereas large molecules have longer correlation times. Ti and T2 are equal in small molecules, whereas T2 is the dominant relaxation mechanism for large molecules.

Under extreme narrowing conditions the molecular correlation time, rc is related to the nuclear resonance frequency by equation (23). These conditions are usually found in low viscosity solutions and within their... 

From a comparable investigation on 14N2 it is found that the molecular correlation time exhibits a discontinuity at the triple point implying that the molecules reorient more rapidly in the solid than in the liquid. It is reported that the Hubbard relationship for the rotational diffusion of spherical molecules in a liquid is approached below 85 K for nitrogen in the liquid state and may be applicable in the solid also. (211)... 

The Nb chemical shift in (775-C5H5)Nb(CO)4 in tetrahydrofuran had a thermal sensitivity measured as 0.38 ppmK from 210 to 340 K, " and the same compound in CH2CI2 a value of 0.42 ppmK . A linear decrease in shielding of the Nb nucleus, with increased temperature, of 0.25 ppmK for [CpNb(H)(CO)3] and [CpNb(D)(CO)3] has been measured, and also a non-linear decrease in linewidths with increased temperature for both of these compounds, indicative of increased molecular correlation times. [Et4N][Nb (CO)6] in THF showed a linear temperature dependence with a sensitivity of 0.18 ppmK over a range 203 to 323 K, and an increase in linewidth from 9.8 Hz (323 K) to 23 Hz (203 K). -... 

In this section, the reader will be confronted with and introduced to some comparatively elemental facts on the theory underlying interpretation of the shielding parameter accessible for normal molecules in isotropic solutions, where normal refers to molecules which are not oversized (such as vanadium bound to proteins), and were we therefore are in the so-called extreme narrowing limit , characterised by the condition 2TruQT << 1, where vq is the measuring frequency and the molecular correlation time, a measure of the mobility of a solute molecule in a solvent. Extreme narrowing simply means that the molecule is freely mobile and the frequency applied to obtain NMR information does not influence the respective parameters. Although the term contains the component extreme , we are well in the domain of normal conditions. 

The constants of proportionality here contain the molecular correlation time, Tc, in addition to a number of known physical constants, and B is now taken to signify inversion rather than saturation of B. In principle, if tc were known, this would directly provide a measure of rAB- Whilst it is possible to determine this (such as from relaxation time measurements) this is rarely done in practice, and it is more common to use a known internal distance as a reference and avoid the need for such laborious measurements. If the NOE between reference nuclei X and Y of internuclear separation rxy is also measured then ... 

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