Quantitative prediction of gas-phase $C13$ nuclear magnetic shielding constants

Benchmark calculations of $C13$ nuclear magnetic shielding constants are performed for a set of 16 molecules. It is demonstrated that near-quantitative accuracy $(∼1–2 ppm$ deviation from experiment) can be achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by perturbative corrections for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) calculations are performed at accurate equilibrium geometries (obtained from CCSD(T)/cc-pVTZ or CCSD(T)/cc-pVQZ calculations), and (4) vibrational averaging is included. In this way $[CCSD(T)/13s9p4d3f$ calculations corrected for vibrational effects], the mean deviation and standard deviation from experiment are 1.6 and 0.8 ppm, respectively. Less complete theoretical treatments result in larger errors. Consideration of relative shifts might reduce the mean deviation (through an appropriately chosen reference compound), but cannot change the standard deviation. Density-functional theory calculations of nuclear magnetic shielding constants are found to be less accurate, intermediate between Hartree–Fock self-consistent-field and second-order Møller–Plesset perturbation theory.