NMR tensors in planar hydrocarbons of increasing size

Abstract

¹³C nuclear shielding and ¹³C–¹³C spin–spin coupling tensors were calculated using density functional theory linear response methods for a series of planar hydrocarbons. As calculation of the spin–spin coupling is computationally demanding for large molecules due to demands placed on basis-set quality, novel, compact completeness-optimized (co) basis sets of high quality were employed. To maximize the predictive value of the data, the convergence of the co basis sets was compared to well-known basis-set families. The selection of the exchange–correlation functional was performed based on the available experimental data and coupled-cluster calculations for ethene and benzene. The series of hydrocarbons, benzene, coronene, circumcoronene and circumcircumcoronene, was chosen to simulate increasingly large fragments of carbon nanosheets. It was found that the nuclear shielding and the one-, two-, and three-bond spin–spin coupling constants, as well as the corresponding anisotropies with respect to the direction normal to the plane, approach convergence as the number of carbon atoms in the fragment is increased. Predictions of the investigated properties can then be done for the limit of large planar hydrocarbons or carbon nanosheets. From the results obtained with a judicious choice of the functional, PBE, and co basis close to convergence, limiting values are estimated as follows: σ = 54 ± 1 ppm [corresponding to the chemical shift of 134 ppm with methane (CH₄) as a reference], Δσ = 207 ± 4 ppm, ¹J = 59.0 ± 0.5 Hz, Δ¹J = −1.5 ± 0.5 Hz, ²J = 0.2 ± 0.4 Hz, Δ²J = −4.6 ± 0.2 Hz, ³J = 6 ± 1 Hz, and Δ³J = 3 ± 1 Hz.