Karplus-type relationship

As mentioned in the Introduction, in iron—sulfur proteins, the hyperfine shifts of the nuclei of the coordinating cysteines are essentially contact in origin (21, 22). In the case of [Fe4S4l (17) and [FegS4] (112) cluster, it has been shown that the hyperfine shift of the cysteinyl H/3 and Ca nuclei can be related to the value of the Fe-Sy-C/S-H/S/Ca dihedral angle (6) through a Karplus-type relationship of the form... 

V ( C, F). This coupling shows the same angular dependences as the corresponding fluorine-proton or proton-proton counterpart, thus permitting the development of Karplus-type relationships " the sign was assumed to be positive. " ... 

C-0-C-1H couplings have been determined in methyl /i-cellobioside after deuterium substitution of all protons on carbon atoms with a free hydroxy group. Assuming a Karplus type relationship between 3JC H and the dihedral angle in 13C-0-C-1H groups, the torsional angles 0 and / of methyl / -cellobioside were determined to be 25 30" [734],... 

Correlations have been established between values of /(" Sn- H) or /(" Sn- C) and the C-Sn-C valency angles in series of diorganotin compounds. A Karplus-type relationship has been indicated between dihedral angle, (j>, and the /(" Sn- C) values in cyclic systems. 

Contact shifts for nuclei three bonds from the metal are dependent on dihedral angle 9 through a Karplus-type relationship ... 

In dimethyl sulfoxide, exchange of hydroxyl protons is slow enough that hydroxyl protons are observed separately coupled to adjacent CH protons in the NMR spectra of carbohydrates [237,238,239]. Hydroxyl protons involved in intramolecular hydrogen bonds are shielded in comparison to those involved in intermolecular hydrogen bonds to dimethyl sulfoxide [240,241]. The coupling constants can be used in conjunction with Karplus-type relationships [242,243] to identify the orientation of the OH groups. The J values observed for... 

Six homo- and heteronuclear Karplus relationships of vicinal couplings related to the

torsional angle have been analysed with MD/DFT calculations and model peptides by Case et It appeared that the average torsion angle fluctuation amplitudes of 24° had to be taken into account for ubiquitin in order to fit the calculated coupling values to the experimental ones. In addition, the authors have suggested that the / related Vnn coupling does not obey the usual Karplus type relationship. 

Schaefer et al studied departures from the Karplus-type relationship ( Barfield effect ) to determine the ring pucker in 2-phenyl-1,3-dithiane. The dependence of the 7(H,H) Karplus equation on the internal C—C—H angles was given in mathematical form by Barfield et al., who also recalculated the... 

The long-range couplings of a series of acetylenic derivatives have been calculated by Alkorta and Elguero by the use of the finite perturbation method. In the case of dimethylated derivatives a Karplus-type relationship has been observed by them for couplings of hydrogen atoms separated up to 15 bonds. 

By the study of 12 isotopomers of protoadamantane, the stereochemical dependence of isotope effects was also observed. A Karplus-type relationship similar to that for spin-spin coupling constants was proposed Recently, the first quantitative stereochemical dependence between isotope effects and dihedral angle was reported for a series of deuteriated norbornanes, as shown in Figure Observations of the influence of substitution with deuterium on conformational equilibria led to a new method in physical organic chemistry called isotopic perturbation of equilibrium. Details can be found in a recent review The effect was first observed for the chair-tO"Chair interconversion of deuteriated 1,3-dimethylcyclohexane 43 and later in 4-ethyl-l-methylcyclohexane " as well as in 1,1,4,4-tetramethylcyclohexane. In contrast, the isotope effect on conformational equilibrium in related systems turned out to be too small to be observable... 

Couplings via connecting atoms other than carbon also follow Karplus-type relationships. In particular, such relationship for the vicinal couplings of protons with T, and P can provide a useful tool for... 

Nazarski et al. have studied extensively conformational equilibriums of some flexible pyrrolidin-2-ones and -thiones (Fig. 4) in solution by means of experimental NMR parameters ( H and C chemical shifts, and and their DFT predictions. Among others, the authors have calculated three-bond J(H,H) couplings applying DFT approach (B3LYP/IGLO-II// B3LYP/6-31G(d) theory levels) or using the Karplus-type relationships. The former appeared to perform better. 

I. Alkorta, J. Elguero, The influence of chain elongation on Karplus-type relationships a DPT study of scalar coupling constants in polyacetylene derivatives, Org. Biomol. Chem. 1 (2003) 585. 

I. Alkorta, J. Elguero, Karplus-type relationships between scalar couphng constants Jhh molecular versus [Jhh supramolecular coupling constants, Theor. Chem. Acc. Ill (2004) 31. 

Jc.H Values have been obtained for COCH fragments in various carbohydrates by means of 2D heteronuclear J-resolved n.m.r. spectroscopy. Measurements on rigid model- substrates (fijjgU/ iIc-o.K-i of 1,6-anhydroglucose) were used to establish a Karplus-type relationship between Zcoch and dihedral angles. 

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