On spin and matrix models in the complex plane

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of two-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-N partition function zeros in the complex plane.     

Electrochemical behavior of the tris(pyridine)-Cu funnel complexes: an overall induced-fit process involving an entatic state through a supramolecular stress

The electrochemical behavior of the tris(pyridine) calix[6]arene Cu adducts is unique as compared to that of most classical Cu complexes in a strain-free environment. The presence of MeCN buried inside the cavity is a prerequisite for a quasi-reversible behavior in a dynamic mode. The CV behavior assisted by simulation outlines that the coordination adaptability of the Cu(II)/Cu(I) redox states is completely reversed, with a Td geometry enforced at either redox states. Hence, the supramolecular control of the Cu coordination by a protein-like pocket determines the dynamics of the electron transfer process, its thermodynamics, and the kinetics of the reorganizational barrier and generates a preorganized state for oxidation. This redox behavior corresponds to an overall induced-fit process generating a truly entatic highly oxidizing Cu(II) state through a protein-like strain by involvement of the secondary coordination sphere.     

Bicyclic nucleosides; stereoselective dihydroxylation and 2'-deoxygenation

A series of polyhydroxylated bicyclic nucleoside derivatives is approached applying stereoselective dihydroxylation reactions. Three out of four isomeric and protected products were obtained after the stereoselectivity of dihydroxylation has been completely inverted comparing a bicyclic nucleoside with a tricyclic furanose substrate. A corresponding 2'-deoxynucleoside derivative has been obtained after an optimized deoxygenation procedure.     

Configuration-interaction energy derivatives in a fully variational formulation

A configuration-interaction energy function (Lagrange) which is variational in all variables, including the orbital rotational parameters, is constructed. When this Lagrangian is used for obtaining configuration-interaction derivatives, all the important simplifications which occur for derivatives of variational wave functions carry over in a straightforward way. In particular, the state and orbital rotational response parameters obey the 2n+1 rule and the Lagrange multipliers obey the somewhat stronger 2n+2 rule. The simplifications which are normally obtained by invoking the Handy-Schaefer technique are automatically incorporated to all orders. Simple expressions for energy derivatives up to third order are presented. The relationship between the numerical errors in the variational parameters and the errors in the calculated energy derivatives is discussed.     

Mono- and diprotonation of dihydropyrene, 2,7-di-tert-butyl-dihydropyrene,and their conversion to pyrenium ions; Influence of the radical cation and its potential utility in NMR assignments of the arenium ions of readily oxidizable PAHs

Parent dihydropyrene 1 and 2,7-di-tert-butyldihydropyrene 3 are monoprotonated with FSO₃H/SO₂CIF to give their persistent monoarenium ions 1H ⁺ and 3H ⁺ by the attack of proton at C-3 (peri to the ethano-bridge not at C-1 as previously suggested). Dihydropyrene 3 is diprotonated in FSO₃H.SbF₅ 1∶1 “Magic Acid”^R/SO₂CIF to give the symmetrical dication 3H ₂ ⁺², similar diprotonation of 1 with “Magic Acid”/SO₂CIF or with FSO₃H.SbF₅ (4∶1)/SO₂CIF gave the diprotonated species 1H ₂ ⁺² in a mixture. NMR characteristics of the mono- and dications are discussed. On raising temperature or on prolonged cold storage, 1H ⁺ and 3H ⁺ are converted to their corresponding pyrenium cations (2H ⁺ and 4H ⁺). Formation of 2H ⁺ from 1 is more rapid than conversion of 3 to 4H ⁺. Parent pyrenium cation was independently generated by protonation with FSO₃H/SO₂CIF. When a mixture of 2 and 1 is reacted with FSO₃H/SO₂CIF (dry ice/acetone temperature) only 2H ⁺ is seen in the NMR (concomitant presence of the radical cation 1 ⁺⁺ is inferred from EPR). Similar protonation of a mixture of 6-chlorochrysene 5 and 1 with FSO₃H/SO₂CIF leads to NMR observation of 1H ⁺ (with concomitant presence of 5 ⁺⁺); on raising temperature 1H ⁺ is converted to 2H ⁺. The nature of the paramagnetic radical cation (RC) present in the arenium ion samples influences the position, and resolution of the NMR spectra. This approach may prove useful in NMR studies of large polycyclic aromatic hydrocarbons PAHs where concomitant RC formation greatly diminishes the quality of the NMR spectra.     

Deuterium isotope effects on 13C chemical shifts of nitromalonamide

The OH chemical shift of the enol form of nitromalonamide is found at 18.9 ppm both in DMSO-d(6) and in DMF-d(7) indicating a very strong hydrogen bond. The OH chemical shift is insensitive to temperature changes. Contrary to the large OH chemical shift, a small two-bond deuterium isotope effect of 0.135 ppm due to deuteration at the OH position is found at the enolic carbon. This is confirmed by density functional theory calculations. The observed effects are interpreted as due to an equilibrium between identical enolic forms. These show a strong OH...O hydrogen bond as well as a NH...O-N=O hydrogen bond.     

Density functional theory study of intramolecular hydrogen bonding and proton transfer in o-hydroxyaryl ketimines

The potential energy surface and the reaction pathway for the intramolecular hydrogen transfer in o-hydroxyaryl ketimines are characterized using DFT methods. Structural changes in the proton-transfer process in quasi-aromatic hydrogen bonding are described. A transition state and a state with a low proton-transfer barrier were studied in sterically compressed o-hydroxyaryl ketimines (2(N-methyl-alpha-iminoethyl)phenols) possessing two potential minimums. The potentials for proton vibration in the OH and HN tautomers of o-hydroxyaryl ketimines were investigated and anharmonic frequencies were determined. Solvent and substituent effects were analyzed. The energies of the various conformers of the OH and HN tautomers were compared with the related forms of o-hydroxyaryl aldimine.     

Deuterium isotope effects on 13C nuclear shielding as a measure of tautomeric equilibria

Large deuterium isotope effects of both signs have been observed on the ¹³C nuclear shielding in proton-chelating tautomeric forms of β-thioxoketones, and small isotope effects of both signs have been found in related forms of Schiff's bases of salicylaldehydes. These effects are interpreted in terms of shifts in the tautomeric equilibria on deuterium substitution of the enolic proton. The observation of deuterium isotope effects is suggested as a useful method for the detection of fast tautomeric equilibria in systems of the following type. .