Orientational dependence of vicinal proton‐proton NMR coupling constants: The Karplus relationship

Abstract

Vicinal proton-proton coupling constants depend on a variety of stereochemical parameters such as bond angle, bond length, substituent electronegativity and orientation, andmost importantlyon the torsion angle between the coupling protons. The sensitivity of vicinal proton-proton coupling constants '.THH, to variations of dihedral angle $ was first rationalized in valence bond terms by Karplus, who showed that the coupling constants could be approximately fitted to a cosz$ function.The Karplus equation 3fHH = Aces*# + Bcos# + C (or variants thereof) has been a major tool of the structural chemist for 35 years. Karplus started with the Ramsey formula for Fermi contact contribution, expressed by ground-state wave functions and a mean excitation energy. More sophisticated molecular orbital (MO) treatments have afforded analogous expressions that may be used to predict trends correctly but are rarely useful for accurate estimations of dihedral angles. Numerous attempts have been made to account for the effect of substituents, bond angles, and lengths -either empirically by the choice of A, B , and C (with different values for each type of compound) or semiempirically, starting with theoretically more sophisticated expressions with statistically adjustable parameters.Theoretical and empirical approaches are reviewed and compared.

The Spin–Spin Coupling Constants in Ethane, Methanol and Methylamine: A Comparison of DFT, MCSCF and CCSD Results

“…The performance of DFT for the calculation of spin-spin coupling constants has been examined on the basis of the couplings in CH [22]) and the CCSD level with an empirical curve [3].…”

“…Progress in NMR techniques-in particular, the use of high magnetic fields-has made possible the accurate measurement of a wide variety of NMR coupling constants, even in proteins and nucleic acids (and their complexes) of substantial size. In particular, since the nuclear spin-spin coupling constants are extremely sensitive to the molecular geometry, they have for a long time been used for structure assignments of such systems [1][2][3][4]. Such advances in NMR measurement techniques call for a concomitant development of computational methods suitable for the modelling of spin-spin coupling constants in large molecules, allowing for a better understanding of the correlation between NMR parameters and molecular structure.…”

“…On the other hand, all the important coupling constants of organic chemistry are present in CH 3 CH 3 , CH 3 NH 2 and CH 3 OH, making these molecules particularly suitable for testing DFT against high-level wave-function methods. In addition, the molecules under study here offer the possibility of calculating the dependence of 3 J(HH) on the dihedral angle-that is, the Karplus curve [1,2], an important relationship in structural chemistry [1][2][3].…”

Conformation of Sterically Hindered 4-Methyl-2-oxo-2-trityl-1,3,2-dioxaphosphorinane in the Solid State and the Solution

“…These couplings are between axial and equatorial protons, and they exist through three bonds. On the basis of Karplus equation (correlation of changes of coupling constant with changes of dihedral angle [93]) it can be stated that two preferable groups of H-C-C-H torsion angles exist, one ives the coupling constant about 4 Hz and angle close to 120°leads to the coupling constant equals about 6 Hz [91], thus it can be postulated that H-C-C-H torsion angles of the first mentioned group are slightly larger than 60°, and those ones of second group are about 120-140°. 13 C NMR spectra were recorded in the solution (deuterated chloroform) and in the solid state.…”

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.…”