Karplus dependence of spin-spin coupling constants revisited theoretically. Part 1: second-order double perturbation theory.
A double perturbation theory (DPT) at the second order level of approximation formalism has been applied to examine the dihedral angle dependence of the Fermi-contact (FC) contribution to nuclear spin-spin coupling constants. The unperturbed wave function of the ground state in DPT was approximated by the Hartree-Fock Slater determinant, while the excited states were treated as the single excited determinants. An analytical expression relating the FC term of vicinal proton-proton spin-spin coupling constants across the aliphatic single carbon-carbon bond to the dihedral angle describing inner rotation around the C-C bond in the ten-electron ten-orbital moiety H-C-C-H has been derived and analyzed. In particular, it has been shown that extrema of (3)J(H,H) are observed at φ = πn, n = 0, ±1, ±2,…, which provides a theoretical background of a well-known semiempirical Karplus equation.
A.E. Favorsky Irkutsk Institute of Chemistry, Russian Academy of Sciences, Siberian Branch, 1 Favorsky St., 664033 Irkutsk, Russia. krivdin_office@irioch.irk.ru.
Irina L
IL
Rusakova
Leonid B
LB
Krivdin
D002244:Carbon / Q000737:chemistry; D009682:Magnetic Resonance Spectroscopy; D008958:Models, Molecular; D011522:Protons; D011789:Quantum Theory
D011522:Protons; D002244:Carbon