Equivalence of nuclei

Apparent NMR equivalence of nuclei can also arise by a quantum mechanical intramolecular tunneling process. In principle, this process may be differentiated from intermolecular exchange processes because although the exchanging nuclei are rendered equivalent insofar as the NMR experiment is concerned, spin-spin splitting by other magnetic nuclei is not washed out. This type of intramolecular exchange is manifested in several boron hydride derivatives. It was first proposed by Ogg and Ray (98) to explain the NMR spectra of aluminum borohydride, whose structure is... 

Perhaps, it will be useful to the reader to realize that the perversions and predilections found in the present chapter arise since the author is not a typical NMR guru, but rather has primarily practiced solid-state EPR spectroscopy. On the other hand, he has accumulated appreciable liquid-solution NMR experience. The author, together with S.M. Nokhrin and D.F. Howarth, has teamed on some studies of equivalence of nuclei as implying certain subtle phenomena in EPR.13 14... 

When there is rapid internal motion in a molecule, such as internal rotation or inversion, the equivalence of nuclei should be determined on an overall average basis, rather than in one of the individual conformations. For example, in CH3CH2Br, the three CH3 protons are magnetically equivalent because they couple equally on the average with each of the methylene protons, even though... 

Equation (3.40) is the DFT equivalent of the Schrbdinger equation. The subscript Vext indicates that this is under conditions of constant external potential (i.e. fixed nuclear po.-,ilions). It is interesting to note that the Lagrange multiplier, p, can be identified with (lu chemical potential of an electron cloud for its nuclei, which in turn is related to the... 

The reaction of bis(benzene)vanadium [12129-72-5] with TCNE affords an insoluble amorphous black soHd that exhibits field-dependent magnetization and hysteresis at room temperature, an organic-based magnet (12). The anion radical is quite stable in the soHd state. It is paramagnetic, and its intense electron paramagnetic resonance (epr) spectmm has nine principal lines with the intensity ratios expected for four equivalent N nuclei (13) and may be used as an internal reference in epr work (see Magnetic spin resonance). 

Chemical equivalence atomic nuclei in the same chemical environment are chemically equivalent and thus show the same ehemieal shift. The 2,2 - and 3,3 -protons of a 1,4-disubstituted benzene ring, for example, are ehemically equivalent because of molecular symmetry. 

The equivalent of the spin-other-orbit operator in eq. (8.30) splits into two contributions, one involving the interaction of the electron spin with the magnetic field generated by the movement of the nuclei, and one describing the interaction of the nuclear spin with the magnetic field generated by the movement of the electrons. Only the latter survives in the Born-Oppenheimer approximation, and is normally called the Paramagnetic Spin-Orbit (PSO) operator. The operator is the one-electron part of... 

Beta radiation Electron emission from unstable nuclei, 26,30,528 Binary molecular compound, 41-42,190 Binding energy Energy equivalent of the mass defect measure of nuclear stability, 522,523 Bismuth (m) sulfide, 540 Blassie, Michael, 629 Blind staggers, 574 Blister copper, 539 Blood alcohol concentrations, 43t Body-centered cubic cell (BCC) A cubic unit cell with an atom at each comer and one at the center, 246 Bohrmodd Model of the hydrogen atom... 

To treat the reagents and products as indistinguishable, one must make the total (electronic + nuclear) wave function symmetric under a cyclic exchange of nuclei, which is equivalent to making it symmetric under rotations 2n/3, 4n/3. about the threefold axis of symmetry. Mead showed that, because the electronic wave function >]> is antisymmetric under 2ti/3> must be symmetrized... 

The ESR spectra of the radicals RsE exhibited the anticipated splitting patterns, for example, [(Me3Si)2CH]3Ge gives a decet (coupling with Ge nucleus, I = 9/2) of septets (coupling with the 3 equivalent N nuclei, I = 1). ° ... 

Depending on how the secondary magnetic field is applied, there are two fundamentally different types of spectrometers, namely, continuous wave (CW) and pulse Fourier transform (PFT) spectrometers. The older continuous wave NMR spectrometers (the equivalent of dispersive spectrometry) were operated in one of two modes (i) fixed magnetic field strength and frequency (vi) sweeping of Bi irradiation or (ii) fixed irradiation frequency and variable field strength. In this way, when the resonance condition is reached for a particular type of nuclei (vi = vo), the energy is absorbed and... 

Since the phosphorus spectra of compounds 1 to 5 are rather boring (only one phosphorus resonance), we shall also use compound 6, which contains three non-equivalent phosphorus nuclei, to demonstrate the results of the experiments we describe. 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

If all the nuclei are non-equivalent, then all lines should have the same intensity (barring accidental overlap). If there are equivalent sets of nuclei, then the expected ratio is the product of the largest-to-smallest ratios of the various multiplets. Thus, for the above examples, three groups of two spin-1/2 nuclei gives a 1 2 1 triplet of 1 2 1 triplets of 1 2 1 triplets thus the maximum... 

Figure 3.3 Stick spectrum showing hyperfine pattern for coupling to three equivalent 59Co nuclei (1=1/2) computed to (a) first-order and (b) second-order in perturbation theory. (Adapted from ref. 7.) (c) Isotropic ESR spectrum of [PhCCo3(CO)9r in THF solution at 40°C.

A very similar application of the modified Bloch equations was based in the work of Adams and Connelly.4 ESR spectra (Figure 5.8) of [Mo P(0 Me)3 2(MeC = CMc)Cp] show the expected triplet (two equivalent 31P nuclei) at 280 K, but only a doublet at 160 K. At intermediate temperatures, the lines broaden. The interpretation is that the alkyne undergoes a pendulum oscillation, which in the extrema diverts spin density from one or the other phosphite. Interestingly, the diamagnetic cation undergoes a similar motion on the NMR time scale, but then the alkyne undergoes a complete rotation. Thus, analysis of the effect leads to a measure of the rate of the oscillation. The... 

---