Riddles of the structure and vibrational dynamics of HO3 resolved near the ab initio limit.

The hydridotrioxygen (HO3) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HOx 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. The cis isomer proves to be higher than trans by 0.52 kcal mol-1, but this energetic ordering is achieved only after the CCSDT(Q) milestone is reached; the barrier for cis → trans isomerization is a minute 0.27 kcal mol-1. The FPA central re(O-O) bond length of trans-HO3 is astonishingly long (1.670 Å), consistent with the semiexperimental re distance we extracted from microwave rotational constants of 10 isotopologues using FPA vibration-rotation interaction constants (αi). The D0(HO-O2) dissociation energy converges to a mere 2.80 ± 0.25 kcal mol-1. Contrary to expectation for such a weakly bound system, vibrational perturbation theory performs remarkably well with the FPA anharmonic force fields, even for the torsional fundamental near 130 cm-1. Exact numerical procedures are applied to the potential energy function for the torsional reaction path to obtain energy levels, tunneling rates, and radiative lifetimes. The cis → trans isomerization occurs via tunneling with an inherent half-life of 1.4 × 10-11 s and 8.6 × 10-10 s for HO3 and DO3, respectively, thus resolving the mystery of why the cis species has not been observed in previous experiments executed in dissipative environments that allow collisional cooling of the trans-HO3 product. In contrast, the pure ground eigenstate of the cis species in a vacuum is predicted to have a spontaneous radiative lifetime of about 1 h and 5 days for HO3 and DO3, respectively.

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. Exact cone angles were evaluated for a wide array of phosphine and amine ligands bound to palladium, nickel, or platinum by optimizing structures using B3LYP/6-31G* density functional theory with effective core potentials for the transition metals. The mean absolute deviations of the standard θ and Θ parameters from the exact cone angles were 15-25°, mostly caused by distortions from the assumed idealized structures.

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. The solution, which is valid for any ligand bound to any metal center, provides an excellent method for analyzing geometric structures from quantum chemical computations or X-ray crystallography. Over 275 structures of various metals bound to diverse mono- and multidentate ligands were optimized using B3LYP density functional theory to exhibit exact solid angle (Ω°) computations. Among the intriguing Ω° solutions, Pd(xantphos) and ferrocene exhibit holes in their ligand shadows, and Fe(EDTA)(2-) has a surprisingly simple shadow defined by only four arcs, despite having a multitude of overlaps among individual shadow cones.