Weakly coupled spectra

Our discussions of spin-spin splitting and multiplicity have been based on first-order or weakly coupled spectra which are spin systems where Av/J > 10. The difference in chemical shift in hertz of coupled protons divided by the coupling constant is 10 or more. In such a case clean 1 1 doublets, 1 2 1 triplets, and so on, are observed and coupling constants and chemical shifts can be read directly from line positions in the spectrum. 

As Av/J decreases, the simple multiplets observed in weakly coupled spectra become increasingly distorted new lines can appear and others merge or disappear. Such spectra are termed second-order or strongly coupled spectra. In these cases the chemical shift does not lie in the center of the multiplet and coupling constants are not always obvious. A simple example of such a change is seen... 

The xy magnetizations can also be complicated. Eor n weakly coupled spins, there can be n 2" lines in the spectrum and a strongly coupled spin system can have up to (2n )/((n-l) (n+l) ) transitions. Because of small couplings, and because some lines are weak combination lines, it is rare to be able to observe all possible lines. It is important to maintain the distinction between mathematical and practical relationships for the density matrix elements. 

The NMR spectrum of methyl kasugaminide in deuterium oxide at 100 Me is shown in Figure 3. The anomeric proton at C-l linking with methoxyl group is shown as a doublet at 4.57 p.p.m. indicating one proton at C-2. The weak coupling, 1.6 c.p.s., is possible between protons in cis relation (28) or in equatorial-equatorial relation (6) at C-l and C-2 of the six-membered ring. 

Protons on carbon geminal to -NCS or -NHCHO functions do not experience the weak coupling with nitrogen due to the normal hybridization of the nitrogen atom. In the case of formamides, however, both E- and Z-rotamers are possible as revealed by resonances in the H NMR spectrum. 

The studies on [LaTb], [TbLu], [LaEr] and [CeY] established that the individual ions ofthe molecules [Tb2(HL)2(H2L)Cl(py)(H20)] and [CeEr(HL)2(H2L)(N03) (py)(H20)] exhibit isolated, well-defined ground state doublets, thus leading to proper definitions of qubit states. The next step is to prove the existence of a weak coupling within each molecule conducive to the appropriate energy level spectrum for the realization of quantum gate operations. 

G.A. Ozin, University of Toronto In our Cr/CO matrix cocondensation experiments (Angew. Chem., Int. Ed. Eng. 1975, 14, 292), we reported evidence for the facile formation of a binuclear chromium carbonyl complex Cr2(CO)i0 or Cr2 (CCOi x which could be described as square pyramidal Cr(CO)5 weakly interacting with either a Cr(CO)5 or Cr(CO)6 moiety in the vacant (sixth) site. As a result, the infrared spectrum of this "weakly-coupled" binuclear species closely resembled that of the mononuclear fragment Cr(CO)5. I would like to ask you, whether or not you have any evidence for the existence of such a binuclear species in your Cr(CO)6 /Xe cryogenic solutions following various photolysis treatments. 

The Markov processes associated with quantum star graphs correspond to systems of weakly coupled edges. Its dynamical properties are determined by the spectrum of the stochastic matrix associated with (14) which is highly degenerate and can be given explicitly (Kottos and Smilansky 1999), that is,... 

Fig. 4.12. Energy level scheme of donor and acceptor molecules showing the coupled transitions in the case where vibrational relaxation is faster than energy transfer (very weak coupling) and illustration of the integral overlap between the emission spectrum of the donor and the absorption of the acceptor.

Weak coupling leads to minor alterations of the absorption spectrum (hypo-chromism or hyperchromism, Davidov splitting of certain vibronic bands). 

The magnetic properties of deoxyHr indicate that a bridge between the iron centers persists but may be altered from that in oxyHr. The NMR spectrum of deoxyHr exhibits large isotropic shifts for the N-H s on histidines coordinated to the binuclear unit. Mossbauer parameters of deoxyHr (Table II) are typical of high spin iron(II) centers which are at best weakly coupled (37,38,39). Room temperature magnetic susceptibility measurements using the Evans NMR technique... 

A very interesting (Cu ,Cu )-derivative of BESOD was prepared with 2 Cu per subunit. The EPR spectrum between 5 and 10 K indicated an antiferromagnetic interaction of the two Cu with a coupling constant of 52 cm , which seems very good evidence for an imidazolate-anion bridge as borne out with model complexes Similarly the (Cu , Co )-derivative of BESOD showed only a weak EPR spectrum reduction of Cu(II) to Cu(I) a normal EPR spectrum... 

A combination of the two techniques was shown to be a useful method for the determination of solution structures of weakly coupled dicopper(II) complexes (Fig. 9.4)[119]. The MM-EPR approach involves a conformational analysis of the dimeric structure, the simulation of the EPR spectrum with the geometric parameters resulting from the calculated structures and spin hamiltonian parameters derived from similar complexes, and the refinement of the structure by successive molecular mechanics calculation and EPR simulation cycles. This method was successfully tested with two dinuclear complexes with known X-ray structures and applied to the determination of a copper(II) dimer with unknown structure (Fig. 9.5 and Table 9.9)[119]. 

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