Intramolecular surfaces for vicinal proton–proton coupling constants ³J_HH

Abstract

Equations for the intramolecular surfaces of the ³J_HH coupling constants in ethane, ethylene, and acetylene are formulated, and the corresponding coefficients are estimated from calculations at the DFT/B3LYP level. The chosen variables are changes in bond lengths, in the torsion angle φ between the coupled protons H_a and H_b, in bond angles, and in dihedral angles. The ³J_HH surface of ethane is formulated as an extended Karplus equation with the coefficients of a truncated Fourier series on the torsion angle φ expanded as second-order Taylor series in the chosen variables taking into account the invariance of ³J_HH under reflections and rotations of nuclear coordinates. Partial vibrational contributions from linear and square terms corresponding to changes in the geometry of the H_a − C_a − C_b − H_b fragment are important while those from cross terms are small with a few exceptions. The ³J_HH surface of ethane is useful to predict contributions to ³J_HH from changes in local geometry of derivatives but vibrational contributions are predicted less satisfactorily. The predicted values at the B3LYP/BS2 level of the ³J_HH couplings (vibrational contributions at 300 K) from equilibrium geometries are 9.79 (−0.17) for acetylene, and 17.08 (1.93) and 10.73(0.93) for the trans and cis couplings of ethylene.

Keywords:

• vicinal coupling constants
• intramolecular surfaces
• vibrational contributions
• extended Karplus equations
• DFT/B3LYP

Acknowledgements

Computer time provided by the Centro de Computación Científica of Universidad Autónoma de Madrid is gratefully acknowledged.

Additional information

Funding

Financial support from the Dirección General de Enseñanza Superior e Investigación Científica (DGESIC), Spain [grant number CTQ2006-15141] is gratefully acknowledged. R.H. Contreras gratefully acknowledge financial support from Universidad de Buenos Aires Ciencia y Técnica UBACyT (2011–2013) and Consejo Nacional de Investigaciones Científicas y Técnicas CONICET [grant number PIP 0369/10].