Extension of the Karplus relationship for NMR spin-spin coupling constants to nonplanar ring systems: Pseudorotation of cyclopentane

A new Karplus equation for pseudorotating five-membered rings is derived by expanding calculated NMR spin-spin coupling constants (SSCCs) J as a function J(q,phi) of the puckering amplitude q and the pseudorotational phase angle phi. The approach was tested for cyclopentane but is equally applicable to ribose sugars and other biochemically interesting five-membered rings. It is based on the calculation of the conformational potential V(q,phi), which in the case of cyclopentane was determined at the MBPT(2)/cc-pVTZ level of theory. Cyclopentane is a free pseudorotor (barriers DeltaE and DeltaH less than or equal to 0.01 kcal/mol) with a puckering amplitude q = 0.43 Angstrom and a barrier to inversion DeltaH = 5.1 kcal/mol, in perfect agreement with experimental data. The SSCCs of cyclopentane were calculated at MBPT(2)/cc-pVTZ geometries by use of coupled perturbed density functional theory (CP-DFT) with the B3LYP functional and a (9s,5p,1d/5s,1p)[6s,4p, 1d/3s,1p] basis set. In addition, coupled-cluster singles and doubles (CCSD) calculations were carried out to verify the CP-DFT results. All geometrical parameters and the 10 SSCCs of cyclopentane are determined as functions of the phase angle 0 and averaged to give (V) values that can be compared with experimental data. The following SSCCs (in hertz) were obtained at CP-DFT[B3LYP/[6s,4p,1d/3s,1p]: <(1)J(CC)> = 34.0; <(1)J(CH)> = 127.6, exp 128.2; <(2)J(CCC)> = 2.3, exp (+)2.8; <(2)J(CCH)> = -2.6, exp (-)3.0; <(2)J(HCH)> = - 12.4, exp (-) 12.4; <(3)J(CCCH)> = 3.9; <(3)J(HCCH, cis)> = 7.7, exp 7.7; <(3)J(HCCH, trans)> = 5.6, exp 6.3; <(4)J(HCCCH, cis)> = 0. 1; <(4)J(HCCCH, trans)> = -0.6. Magnitude and trends in calculated SSCCs are dominated by the Fermi contact term [with the exception of (1)J(CC)]. A new way of determining puckering amplitude and pseudorotational angle by a combination of measured and calculated SSCCs is presented.