Riddles of the structure and vibrational dynamics of HO resolved near the ab initio limit.

The hydridotrioxygen (HO) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HO cycle but more recently because of its fascinating chemical bonding, geometric structure, and vibrational dynamics. We have executed new, comprehensive research on this vexing molecule via focal point analyses (FPA) to approach the ab initio limit of optimized geometric structures, relative energies, complete quartic force fields, and the entire reaction path for cis-trans isomerization. High-order coupled cluster theory was applied through the CCSDT(Q) and even CCSDTQ(P) levels, and CBS extrapolations were performed using cc-pVXZ (X = 2-6) basis sets.

Exact Ligand Solid Angles.

Steric demands of a ligand can be quantified by the area occluded by the ligand on the surface of an encompassing sphere centered at the metal atom. When viewed as solid spheres illuminated by the metal center, the ligand atoms generally cast a very complicated collective shadow onto the encompassing sphere, causing mathematical difficulties in computing the subtended solid angle. Herein, an exact, analytic solution to the ligand solid angle integration problem is presented based on a line integral around the multisegmented perimeter of the ligand shadow.

Exact ligand cone angles.

Many properties of transition-metal complexes depend on the steric bulk of bound ligands, usually quantified by the Tolman (θ) and solid (Θ) cone angles, which have proven utility but suffer from various limitations and coarse approximations. Here, we present an improved, mathematically rigorous method to determine an exact cone angle (θ°) by solving for the most acute right circular cone that contains the entire ligand. The procedure is applicable to any ligand, planar or nonplanar, monodentate or polydentate, bound to any metal center in any environment, and it is ideal for analyzing structures from quantum chemical computations as well as X-ray crystallography experiments.