Semi-experimental equilibrium (r_e ^SE) and theoretical structures of hydrazoic acid (HN₃)

Hydrazoic acid (HN₃) is used as a case study for investigating the accuracy and precision by which a molecular structure-specifically, a semi-experimental equilibrium structure (r_e ^SE)-may be determined using current state-of-the-art methodology. The influence of the theoretical corrections for effects of vibration-rotation coupling and electron-mass distribution that are employed in the analysis is explored in detail. The small size of HN₃ allowed us to deploy considerable computational resources to probe the basis-set dependence of these corrections using a series of coupled-cluster single, double, perturbative triple [CCSD(T)] calculations with cc-pCVXZ (X = D, T, Q, 5) basis sets. We extrapolated the resulting corrections to the complete basis set (CBS) limit to obtain CCSD(T)/CBS corrections, which were used in a subsequent r_e ^SE structure determination. The r_e ^SE parameters obtained using the CCSD(T)/cc-pCV5Z corrections are nearly identical to those obtained using the CCSD(T)/CBS corrections, with uncertainties in the bond distances and angles of less than 0.0006 Å and 0.08°, respectively. The previously obtained r_e ^SE structure using CCSD(T)/ANO2 agrees with that using CCSD(T)/cc-pCV5Z to within 0.000 08 Å and 0.016° for bond distances and angles, respectively, and with only 25% larger uncertainties, validating the idea that r_e ^SE structure determinations can be carried out with significantly smaller basis sets than those needed for similarly accurate, strictly ab initio determinations. Although the purely computational r_e structural parameters [CCSD(T)/cc-pCV6Z] fall outside of the statistical uncertainties (2σ) of the corresponding r_e ^SE structural parameters, the discrepancy is rectified by applying corrections to address the theoretical limitations of the CCSD(T)/cc-pCV6Z geometry with respect to basis set, electron correlation, relativity, and the Born-Oppenheimer approximation, thereby supporting the contention that the semi-experimental approach is both an accurate and vastly more efficient method for structure determinations than is brute-force computation.