Chapter 3 Developments in the Karplus Equation as they Relate to the NMR Coupling Constants of Carbohydrates

Measurement and Applications of Long‐Range Heteronuclear Scalar Couplings: Recent Experimental and Theoretical Developments

“…The long-range heteronuclear scalar couplings ( n J XH , X= 13 C and 15 N, n > 1) associated with low gyromagnetic ratio nuclei, such as 13 C or 15 N, are usually very small in magnitude (1)(2)(3)(4)(5)(6)(7)(8). Therefore, the routine application of such couplings is severely hindered because of the inherent difficulties in their measurement.…”

“…[61] For instance, the E configuration around the exocyclic C=C bond in enaminone (9 in Scheme 2) was established on the basis of 3 J CH between the methylidene proton (H2') and the carbonyl carbon atoms [O-C(1) and O-C(3)], measured from the anti-phase splitting of cross peaks in the HMBC spectrum. It is also well known that the magnitudes of the coupling constant ( 3 J CH ) between nuclei with cis configuration around the C=C double bond are smaller (2-6 Hz) than those of trans-oriented nuclei (8)(9)(10)(11)(12). [62,64] The magnitudes of couplings 3 J C(1)ÀH(2') = 7 Hz (trans) and 3 J C(3)ÀH(2') = 5 Hz (cis) confirms the E configuration around the exocyclic C=C double bond.…”

“…These modified versions contain both sine and cosine terms of the dihedral angle f. As an example a recent review discusses these modified equations, where the correlation of coupling constants with dihedral angle is obtained for carbohydrates. [8] The basic Karplus equation is a quadratic function of cos f. From the measured coupling constant the explicit value of f can be determined. Cosine being an even function for a particular value of coupling constant, there will be a maximum of four solutions.…”

Development of a Karplus equation for 3JCOCH in ester-functionalized glucopyranoses and methylglucuronate.

“…Nowadays, such equations are based on a multitude of experimental data and extensive quantum mechanical calculations, which take bond lengths, electron densities, electron orbital terms, and dipolar electron spin terms into account. [9][10][11][12] In our research efforts to investigate the conformational changes imparted by an ester linkage to novel ester-linked disaccharides, we required an accurate description of the flexibility of the C(sp 2 )-O-C-H torsional angle to more accurately describe the solution state structure of these molecules. Many Karplus equations have been derived based on both experimental and computational data for HCCH, CCCH and COCH torsions, both for generalized and carbohydrate-specific cases.…”

“…Many Karplus equations have been derived based on both experimental and computational data for HCCH, CCCH and COCH torsions, both for generalized and carbohydrate-specific cases. 10,13 However, as became evident based on preliminary work (as detailed in the Supplemental Material), the available Karplus equations for C(sp 3 )OCH torsions were not well suited for ester-linked compounds due to the different hybridization of the carbonyl carbon. Specifically, the Karplus equations yield lower absolute values for the coupling in the sp 3 -hybridized case compared to C(sp 2 )-O-C-H in ester-functionalized compounds.…”