Extension of the Karplus Relationship for NMR Spin-Spin Coupling Constants to Nonplanar Ring Systems: Pseudorotation of Tetrahydrofuran

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Abstract
Karplus relationships for all 26 NMR spin-spin coupling constants (SSCCS) J of the pseudorotating tetrahydrofuran (THF) molecule were derived by expanding J as a function J(q,phi) of the puckering amplitude q and the pseudorotational phase angle phi. For this purpose, the conformational potential V(q,phi) of THF was determined at the MBPT(2)/cc-pVTZ and B3LYP/6-31G(d,p) levels of theory. THF is a slightly hindered pseudorotor (MP2 barriers DeltaE and DeltaH are 0.1 - 0.2 kcal/mol) with a puckering amplitude q = 0.396 Angstrom and a barrier to inversion DeltaH = 4.1 kcal/mol in reasonable agreement with experimental data. The SSCCs of THF were calculated both at MBPT(2)/cc-pVTZ and B3LYP/6-31G(d,p) geometries using coupled perturbed density functional theory (CPDFT) with the B3LYP functional and a (9s,5p,1d/5s,1p)[6s,4p,1d/3s,1p] basis set. All geometrical parameters and the 26 SSCCs of THF were computed as functions of the phase angle 0 and averaged to give [(n)J] values that can be compared with measured data. The following SSCCs were obtained: [(1)J(CC)] = 34.2, 34.0; [(1)J(CO)] = 26.4; [(1)J(CH)] = 142.6, 130.9; [(2)J(CXC)] = 0.5, 0.8; [2J(OCC)] = 0.3; [(2)J(CCH)] = -1.5, -0.7. -2.8; [(2)J(OCH)] = -8.6; [(2)J(HCH)] = -8.7, -12.0; [(3)J(CXCH)} = 3.0, 4.0, 2.9; [(3)J(OCCH)} = -1.2; [(3)J(HCCH, cis)] = 7.3, 8.5; [(3)J(HCCH, trans)] = 5.3, 5.5; [(4)J(HCXCH, cis)] =-0. 2, -0.2; [(4)J(HCXCH, trans)] = -0.5, -0.6 Hz (X = C or O). Magnitude and trends in calculated SSCCs are dominated by the Fermi contact term although other contributions are not negligible. Those SSCCs that strongly depend on the pseudorotational mode of THF were identified as suitable descriptors for the conformation of THF in solution. THF is discussed as a suitable model for ribose.