The determinant of a class of skew-symmetric toeplitz matrices

The determinant of the n×n matrix associated with the finite-difference operator μδ^2r+1 is obtained explicitly for all n and all integral r?0. An interesting combinatorial identity results.     

Bootstrapping and Askey–Wilson polynomials

The mixed moments for the Askey–Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey–Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied.     

Structural and pH dependence of excited state PCET reactions involving reductive quenching of the MLCT excited state of [RuII(bpy)2(bpz)]2+ by hydroquinones

The proton-coupled electron transfer (PCET) reaction between the bpz-based photoexcited (3)MLCT state of [Ru(II)(bpy)(2)(bpz)](2+) (bpy = 2,2'-bipyridine, bpz = 2,2'-bipyrazine) and a series of substituted hydroquinones (H(2)Q) has been studied by transient absorption (TA) and time-resolved electron paramagnetic resonance (TREPR) spectroscopy at X-band. When the reaction is carried out in a CH(3)CN/H(2)O mixed solvent system with unsubstituted hydroquinone, the neutral semiquinone radical (4a) and its conjugate base, the semiquinone radical anion (4b), are both observed. Variation of the acid strength in the solvent mixture allows the acid/base dependence of the PCET reaction to be investigated. In solutions with very low acid concentrations, TREPR spectra exclusively derived from radical anion 4b are observed, while at very high acid concentrations, the spectrum is assigned to the protonated structure 4a. At intermediate acid concentrations, either a superposition of spectra is observed (slow exchange between 4a and 4b) or substantial broadening in the TREPR spectrum is observed (fast exchange between 4a and 4b). Variation of substituents on the H(2)Q ring substantially alter this acid/base dependence and provide a means to investigate electronic effects on both the ET and PT components of the PCET process. The TA results suggest a change in mechanism from PCET to direct ET quenching in strongly basic solutions and with electron withdrawing groups on the H(2)Q ring system. Changing the ligand on the Ru complex also alters the acid/base dependence of the TREPR spectra through a series of complex equilibria between protonated and deprotonated hydroquinone radicals and anions. The relative intensities of the signals from radical 4a versus 4b can be rationalized quantitatively in terms of these equilibria and the relevant pK(a) values. An observed equilibrium deuterium isotope effect supports the conclusion that the post-PCET HQ(?)/Q(?-) equilibrium is the most important in determining the 4a/4b ratio at early delay times.     

Hydrophobic/hydrophilic solvation: inferences from Monte Carlo simulations and experiments

In this study Monte Carlo simulations are used to determine the solvation properties of model hydrophobic (xenon and hard sphere) and hydrophilic (dimethyl ether) solutes in SPC/E water. Various contributions to the experimental solvation entropy, including the solvent reorganization entropy, have been determined. The main conclusion drawn, which is in accord with solubility data, is that poor solubility correlates with poor solute-water interaction. At room temperature, energy dominates the aqueous solubility of both hydrophobic and hydrophilic solutes, rather than entropy. However, at higher temperatures the solubility can pass through a minimum, and then entropy becomes dominant. Another interesting finding is the presence of larger than expected cavities in water. Two different simulation results support this finding. This unexpected hollow structure in water explains why a hard sphere solute is more soluble in water than in a comparable hard sphere or Lennard-Jones solvent. Hydrogen bonding causes water to aggregate into clusters that produce a few large cavities rather than many smaller cavities. The propensity for clustering also explains why water gives the illusion of being a low density liquid. Sufficient theoretical apparatus is developed to connect theoretical solvation properties to those measured by simulation and experiment. Finally, based on gas solubility, an intuitive hydrophobic/hydrophilic scale is developed.     

An alternative preparation of the 2-dimethylaminomethylene-1,3-bis(dimethylimmonio)propane salt from phosphonoacetic acids and some applications in heterocyclic synthesis

An alternative preparation of a 2-iminovinamidinium salt from phosphonoacetic acids is described along with its application to the synthesis of 5-formylpyrimidines and masked 4-formylpyrazoles.     

Zement

Ohne Zusammenfassung     

Infrared overtone spectroscopy and vibrational analysis of a Fermi resonance in nitric acid: Experiment and theory

High resolution infrared spectra of nitric acid have been recorded in the first OH overtone region under jet-cooled conditions using a sequential IR-UV excitation method. Vibrational bands observed at 6933.39(3), 6938.75(4), and 6951.985(3) cm(-1) (origins) with relative intensities of 0.42(1), 0.38(1), and 0.20(1) are attributed to strongly mixed states involved in a Fermi resonance. A vibrational deperturbation analysis suggests that the optically bright OH overtone stretch (2nu1) at 6939.2(1) cm(-1) is coupled directly to the nu1 + 2nu2 state at 6946.4(1) cm(-1) and indirectly to the 3nu2 + nu3 + nu7 state at 6938.5(1) cm(-1). Both the identity of the zero-order states and the indirect coupling scheme are deduced from complementary CCSD(T) calculations in conjunction with second-order vibrational perturbation theory. The deperturbation analysis also yields the experimental coupling between 2nu1 and nu1 + 2nu2 of -6.9(1) cm(-1), and that between the two dark states of +5.0(1) cm(-1). The calculated vibrational energies and couplings are in near quantitative agreement with experimentally derived values except for a predicted twofold stronger coupling of 2nu1 to nu1 + 2nu2. Weaker coupling of the strongly mixed states to a dense background of vibrational states via intramolecular vibrational energy redistribution is evident from the experimental linewidths of 0.08 and 0.25 cm(-1) for the higher energy and two overlapping lower energy bands, respectively. A comprehensive rotational analysis of the higher energy band yields spectroscopic parameters and the direction of the OH overtone transition dipole moment.