Precise Equilibrium Structure of Benzene

Abstract

Recent advances in gas-phase structure determination afford outstanding agreement between the CCSD­(T)/cc-pCVTZ-corrected semi-experimental (re SE) equilibrium structures and their corresponding best theoretical estimates (BTEs) of the equilibrium structures (re ) based upon corrections to the CCSD­(T)/cc-pCV5Z geometries for the aromatic heterocycles pyrimidine and pyridazine. Herein, that same analysis is extended to the fundamental aromatic molecule benzene, using published experimental spectroscopic data for a total of 11 available isotopologues. The incorporation of rotational constants from all of these isotopologues and CCSD­(T) corrections to address the impacts of both the vibration-rotation interaction and electron-mass distribution results in a highly precise and accurate re SE structure. The CCSD­(T)/cc-pCV5Z optimized geometry has been further corrected to address a finite basis set, untreated electron correlation, relativistic effects, and a breakdown of the Born–Oppenheimer approximation. This analysis achieves outstanding agreement between the re (BTE) and re SE structural parameters of benzene to a highly satisfying level (0.0001 Å), an agreement that surpasses our recently published structures of the aforementioned nitrogen-substituted benzene analogues. The D 6h geometry of benzene is now known to an unprecedented precision: R C–C = 1.3913 (1) Å and R C–H = 1.0809 (1) Å. The mutual agreement between theory and experiment presented in this work validates both, substantially resolving all discrepancies between the re SE and theoretical re structures available in the literature.

Neutral inverse-sandwich rare-earth metal complexes of the benzene tetraanion

“…The C–C distances within the bound ring have been correlated with the extent of reduction of the bound arene as well as the distribution of negative charges. 12,13,61 The average C–C distances of 2-M (Y 1.452(8) Å; Sm 1.453(4) Å) and 3-M (Y 1.455(7) Å; Sm 1.469(5) Å) are significantly longer than that of free benzene (1.39 Å), 62 but close to the average C–C distances of the bound ring in [(NN TBS )Y] 2 (μ-η 6 ,η 6 -C 6 H 5 Ph)[K(toluene)] 2 (1.46 Å) and [K(18-crown-6)(THF) 2 ] 2 [[(NN TBS )Y] 2 (μ-η 6 ,η 6 -C 6 H 5 Ph)] (1.47 Å), 20 as well as [(NN TBS )Sm] 2 (μ-η 6 ,η 6 -C 6 H 5 Ph)[K(toluene)] 2 (1.45 Å), [K(18-crown-6)(THF) 2 ] 2 [[(NN TBS )Sm] 2 (μ-η 6 ,η 6 -C 6 H 5 Ph)] (1.46 Å), 22 [(NN TBS )Th] 2 (μ-η 6 ,η 6 -C 6 H 6 ) (1.46 Å), and [(NN TBS )Th] 2 (μ-η 6 ,η 6 -C 6 H 5 Me) (1.45 Å), 42 in line with quadruply reduced bridging arene ligands in 2-M and 3-M . Moreover, the C–C distances of the bound ring are all within a relatively narrow range for 2-M and 3-M (Table 1, entry 5 & Fig.…”

Rotational Spectrum of the Phenoxy Radical

“…Although the lack of data from isotopically substituted species prevents a complete (semi)­experimental equilibrium structure determination at this juncture, the good agreement (∼0.1%) between the measured and best estimate theoretical rotational constants (Table ) lends confidence to the accuracy of the corresponding theoretical equilibrium structure, which is illustrated in Figure . The calculated C– C bond lengths show significant differences from their reference semi-experimental equilibrium values in a normal benzene ring [ r CC = 1.3913(3) Å]. As the accompanying resonance structures illustrate, the delocalization of the unpaired π electron in phenoxy results in an approximate O– C 1 double bond (1.247 Å), a C 1 – C 2 single bond (1.449 Å), a C 2 – C 3 double bond (1.373 Å), and an intermediate C 3 – C 4 single/double bond (1.406 Å).…”