An ab initio and density functional theory study of keto-enol equilibria of hydroxycyclopropenone in gas and aqueous solution phase

Keto-enol tautomerism in hydroxycyclopropenone (2-hydroxy-2-cyclopropen-1-one) has been studied using ab initio methods, the B3LYP functional of density functional theory, as well as complete basis set (CBS-QB3 and CBS-APNO) and G3 methods. Absolute and relative energies were calculated with each of the methods, whereas computations of geometries and harmonic frequencies for hydroxycyclopropenone and 1,2-cyclopropanedione were computed in the gas phase but were limited to HF, MP2 and CCSD levels of theory, and the B3LYP functional, in combination with the 6-31++G** basis set. Using the MP2/6-31++G** gas phase optimized structure, each species was then optimized fully in aqueous solution by employing the polarizable continuum model (PCM) self-consistent reaction field approach, in which HF, MP2 and B3LYP levels of theory were utilized, with the same 6-31++G** basis set. In both gas and aqueous solution phases, the keto form is higher in energy for all of the model chemistries considered. The presence of the solvent, however, is found to have very little effect on the bond lengths, angles and harmonic frequencies. From the B3LYP/6-31++G** Gibbs free energy, the keto-enol tautomeric equilibrium constant for 2-hydroxy-2-cyclopropen-1-one <==> 1,2-cyclopropanedione is computed to be K(T)(gas) = 2.35 x 10(-6), K(T)(aq) = 5.61 x 10(-14). It is concluded that the enol form is overwhelmingly predominant in both environments, with the effect of the solvent shifting the direction of equilibrium even more strongly in the favor of hydroxycyclopropenone. The almost exclusive nature of this species is attributed to stabilization resulting from aromaticity. Confirmation is provided by comparison of the simulated vibrational spectra of hydroxycyclopropenone with the measured infrared spectrum in an argon matrix.     

Error Estimates in the Sampling From Particle Size Distributions

It is often necessary to estimate the properties of particle size distributions from limited samples taken from large populations. When the distributions are broad, and higher order moments required, as in the case of volume based particle size distributions, the inferred parameters d_3,50 (volume median diameter) and GSD (geometric standard deviation) can have high intrinsic errors not immediately obvious to the measuring scientist. We show that there is a critical number of particles, N_crit, which must be counted or else the error may blow up catastrophically. N_crit is very sensitive to the width of the distribution, and is approximately proportional to GSD¹¹ We develop formulae to estimate the random sampling error inherent in measured values of the d_3,50 and GSD for the log-normal distribution; compare the predictions to a typical experimental particle size measurement; and then generalize to the median of any arbitrary moment, d_{r, 50}.     

Reactivity of nickel(II) and copper(II) complexes of a β-aminohydrazone ligand with pyridine-2-aldehyde: macrocyclization vs unprecedented pyrazole ring synthesis via C-C bond-forming reaction

The synthesis and characterization of a mononuclear nickel(II) complex [Ni(L(2))](ClO(4))(2) (1) and an analogous mononuclear copper(II) complex [Cu(L(2))](ClO(4))(2) (2) of a 15-membered azamacrocycle (L(2) = 3-(2-pyridyl)-6,8,8,13,13,15-hexamethyl-1,2,4,5,9,12-hexaazacyclopentadeca-5,15-diene) are reported. The macrocyclic ligand is formed during the reaction of 4,4,9,9-tetramethyl-5,8-diazadodecane-2,11-dione dihydrazone (L(1)) with pyridine-2-aldehyde (PyCHO) templated by metal ions. The X-ray crystal structure of 1 exhibits a distorted square-pyramidal coordination geometry, where the metal ion sits in the macrocyclic cavity and the pendant pyridine group of L(2) occupies the axial position. While 1 is stable in the presence of an excess of PyCHO, 2 reacts further with copper(II) salt and PyCHO to form a mononuclear copper(I) complex, [Cu(H(2)L(3))](ClO(4))(3) (3). The structure of the complex cation of 3 reveals a distorted tetrahedral coordination geometry at the copper center with a pseudo 2-fold screw axis. A two-dimensional (2D) polymeric copper(II) complex, {[Cu(2)(L(4))(2)](ClO(4))(2)}(n) (4) is obtained by reacting complex 2 (or [Ni(L(1))](ClO(4))(2)) with copper(II) perchlorate and pyridine-2-aldehyde in a methanol-water solvent mixture. Complex 4 is also obtained by treating 3 with copper(II) perchlorate and pyridine-2-aldehyde in the presence of a base. The X-ray structural analysis of 4 confirms the formation of a pyrazolate bridged dimeric copper(II) complex. The extended structure in the solid state of 4 revealed the formation of a 2D coordination polymer with the dimeric core as the repeating unit. The ligand (HL(4)) in 4 is a 3,4,5-trisubstituted pyrazole ring formed in situ via C-C bond formation and represents an unprecedented transformation reaction.