A variation principle for energy differences between states of two different Hamiltonians

A modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ??] = 〈X₀| ??_x – W_x|X₁〉 – 〈Y₀|??_y – W_y|y₁〉 + 〈X₀| Δ ??|Y₀〉 · 〈X₀| Y₀〉^?1. Δ ?? = ??_y – ??_x, |X₀〉 and |Y₀〉 are the wave functions for the X and Y states and |X₁〉 and |Y₁〉 are functions defined in the text. The principle is applied to a few simple examples.     

4‐Methyl‐2‐[N‐(3,4‐methyl­ene­dioxy­benzyl­idene)hydrazino]­thia­zole and its reduction product, 4‐methyl‐2‐[N‐(3,4‐methyl­ene­dioxybenzyl­idene)hydrazono]‐4,5‐di­hydro­thia­zole

The crystal structures of 4‐methyl‐2‐[N‐(3,4‐methyl­ene­dioxybenzyl­idene)hydrazino]­thia­zole, C₁₂H₁₁N₃O₂S, and its reduction product 4‐methyl‐2‐[N‐(3,4‐methyl­ene­dioxybenzyl­idene)hydrazono]‐4,5‐di­hydro­thia­zole, C₁₂H₁₃N₃O₂S, have been determined and compared. In the reduction product, the tautomer observed bears an H atom on the exocyclic N atom. Both compounds form hydrogen‐bonded dimers over centers of inversion.     

Effects of methyl substitution on radiative and solvent quenching rate constants of [Ru(phen)2dppz]2+ in polyol solvents and bound to DNA

Methyl substituents on the distant benzene ring of the dppz ligand in the "light switch" complex [Ru(phen)(2)dppz](2+) have profound effects on the photophysics of the complexes in water as well as in the polyol solvents ethylene glycol, glycerol, and 1,2- and 1,3-propanediol. Whereas 11,12-dimethyl substitution decreases the rate of quenching by diminishing hydrogen bonding by solvent, the 10-methyl substituent in addition also decreases both the radiative and the nonradiative rate constant for decay to the ground state of the non-hydrogen-bonded excited state species. For both the 10-methyl and the 11,12-dimethyl derivatives, the effect of methyl substitution on the equilibrium of solvent hydrogen bonding to the excited state is due to changes in the entropy terms, rather than in the enthalpy, indicating that the effect is a steric perturbation of the solvent cage around the molecule. When intercalated into DNA, the effects of methyl substitution is smaller than those in polyol solvent or water, suggesting that the water molecules that quench the excited state by hydrogen bonding to the phenazine aza nitrogens mainly access them from the same groove as in which the Ru(II) ion resides. Since the Delta-enantiomer of [Ru(phen)(2)10-methyl-dppz](2+) has an absolute quantum yield of up to 0.23 when bound to DNA, a value 7000 times higher than in pure water solution, it is promising as a new luminescent DNA probe.     

The satellite-shaped Co-15 Polyoxotungstate, [Co6(H2O)30{Co9Cl2(OH)3(H2O)9(beta-SiW8O31)3}]5-

The 15-cobalt-substituted polyoxotungstate [Co(6)(H(2)O)(30){Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}](5-) (1) has been characterized by single-crystal XRD, elemental analysis, IR, electrochemistry, magnetic measurements, and EPR. Single-crystal X-ray analysis was carried out on Na(5)[Co(6)(H(2)O)(30){Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}].37H(2)O, which crystallizes in the hexagonal system, space group P6(3)/m, with a = 19.8754(17) A, b = 19.8754(17) A, c = 22.344(4) A, alpha= 90 degrees, beta = 90 degrees, gamma = 120 degrees, and Z = 2. The trimeric polyanion 1 has a core of nine Co(II) ions encapsulated by three unprecedented (beta-SiW(8)O(31)) fragments and two Cl(-) ligands. This central assembly {Co(9)Cl(2)(OH)(3)(H(2)O)(9)(beta-SiW(8)O(31))(3)}(17-) is surrounded by six antenna-like Co(II)(H(2)O)(5) groups resulting in the satellite-like structure 1. Synthesis of 1 is accomplished in a simple one-pot procedure by interaction of Co(II) ions with [gamma-SiW(10)O(36)](8-) in aqueous, acidic NaCl medium (pH 5.4). Polyanion 1 was studied by cyclic voltammetry as a function of pH. The current intensity of its Co(II) centers was compared with that of free Co(II) in solution. Our results suggest that 1 keeps its integrity in solution. Magnetic susceptibility results show the presence of both antiferro- and ferromagnetic coupling within the (Co(II))(9) core. A fully anisotropic Ising model has been employed to describe the exchange-coupling and yields g = 2.42 +/- 0.01, J(1) = 17.0 +/- 1.5 cm(-1), and J(2) = -13 +/- 1 cm(-(1). Variable frequency EPR studies reveal an anisotropic Kramer's doublet.     

End-evaporation dynamics revisited

We present analytical results on the so-called end-evaporation kinetics in equilibrium polymeric systems following a temperature jump (T jump). A T jump prepares the system with a nonequilibrium length distribution, after which it relaxes back to its equilibrium state. Starting from a master equation, we develop a mean-field analytical theory based on a generating function approach, which allows explicit approximate expressions for the monomer and dimer concentrations to be derived in a discrete setting; the concentrations of the other chains as well as the average chain length were shown to be entirely expressible in terms of the monomer and dimer concentrations. We find that the calculated monomer and dimer concentrations as well as the average chain length are in good agreement with numerical simulation results and do not suffer from some of the defects of earlier continuum theories. Furthermore, the relaxation was shown to take place in three different stages. The first stage comprises the very fast relaxation of the monomers to almost their equilibrium concentration; the other polymer chains have hardly relaxed. During the second stage, which is highly nonlinear, a redistribution of material at practically constant monomer density takes place. Only in the final stage of the relaxation process the chain concentrations approach their true equilibrium values. In this stage there are only very small shifts in the concentrations of chains, which are governed by extremely slow "indirect" monomer-mediated processes.     

Quantitative accuracy in the gas chromatographic analysis of solvent mixtures

Quantitative accuracy is of great importance in the analysis of bulk mixtures of solvents, particularly when the analysis is related to quality control of very large product volumes like in solvent recovery plants. Serious errors can be made if the effects of density differences between the pure solvents and volume contractions are not properly addressed. In earlier work, the use of an iterative process for correcting such errors has been suggested. However, in the case of volume contractions and mixtures of several solvents, this procedure is difficult to apply. In the present paper, we describe a simple procedure where calibration curves based on mass concentration are utilized. The densities of calibration mixtures of known compositions are determined with a density meter, in order to provide for correction factors caused by volume contractions. Model experiments with mixtures of water, ethanol, acetone and methanol showed a significant improvement in quantitative accuracy. when the suggested calibration strategy was applied.     

Single molecule spectroscopy as a probe for dye-polymer interactions

Experimental (Single Molecule Spectroscopy) and theoretical (quantum-chemical calculations and Monte Carlo and molecular dynamics simulations) techniques are combined to investigate the behavior and dynamics of a polymer-dye molecule system. It is shown that the dye molecule of interest (1,1'-dioctadecyl-3,3,3',3'-tetramethylindo-dicarbocyanine) adopts two classes of conformations, namely planar and nonplanar ones, when embedded in a poly(styrene) matrix. From an in-depth analysis of the fluorescence lifetime trajectories, the planar conformers can be further classified according to the way their alkyl side chains interact with the surrounding poly(styrene) chains.     

The unimolecular chemistry of [1,2-propanediol]+˙: a rationale in terms of hydrogen-bridged radical cations

By combining results from a variety of mass spectrometric techniques (metastatle ion, collisional activation, collision-induced dissociative ionization, neutralization–reionization spectrometry and appearance energy measurements) and the classical method of isotopic labelling, a unified mechanism is proposed for the complex unimolecular chemistry of ionized 1,2-propanediol. The key intermediates involved are the stable hydrogen-bridged radical cations [CH₂?C(H)? H…?O…?O(H)CH₃]⁺˙, which were generated independently from [4-methoxy, 1-butanol]⁺˙ (loss of C₂H₄) and [1-methoxyglycerol]⁺˙ (loss of CH₂O), [CH₃? C?O…?H…?O(H)CH₃]⁺˙ and the related ion-dipole complex [CH₂?C(OH)CH₃/H₂O]⁺˙. The latter species serves as the precursor for the loss of CH³˙ and in this reaction the same non-ergodic behaviour is observed as in the loss of CH³˙ from the ionized enol of acetone.     

Structure-Photodynamic Activity Relationships of a Series of 4-Substituted Zinc Phthalocyanines

Abstract— Radioiodinated zinc phthalocyanine including [¹²⁵I]ZnPcI₄ and differently sulfonated [⁶⁵Zn]ZnPcS (ZnPcS₄, ZnPcS₃, ZnPcS₂ and ZnPcS_1.75, a mixture of adjacent di and 25% mono) were prepared in order to study cell uptake and release kinetics in EMT-6 cells. The same compounds were evaluated for their in vitro phototoxicity and the biological parameters were compared to partition coefficients to arrive at quantitative structure-activity relationships (QSAR). At 1 μM in 1% serum, at 37°C, all dyes showed rapid cell uptake during the first hour followed by a slow accumulation phase. After 24 h, the highest cellular concentration was observed with the lipophilic ZnPcI₄, followed by the amphiphilic ZnPcS₂ and ZnPcS_1.75. The hydrophilic ZnPcS₄ and ZnPcS₃ showed lower uptake. Dye release from dyeloaded cells during incubation in dye-free medium could reach up to 60% and was shown to depend mainly on the amount of drug incorporated rather than the type of compound. These results suggest that care should be taken in interpreting dye toxicity data, which involve in vitro cell manipulations in dye-free medium, particularly during in vitro/in vivo protocols. The EMT-6 cell survival after 1 h or 24 h incubation with 1 μM dye in 1% serum followed by exposure to red light was assessed by means of the colorimetric 3-(4,5-dimethylthiazol-2-yl)-diphenyl-tetrazolium bromide (MTT) assay. Photocytotoxicities correlated inversely with the tendencies of the dyes to aggregate. Increased dye uptake by the cells also correlated with their activities, except for the lipophilic ZnPcI₄, which showed the highest cell uptake but little phototoxicity. The QSAR between phototoxicity and the log of the partition coefficients (phosphate-buffered saline and n-octanol) gave a parabola with optimal partition values corresponding to the adjacent sulfonated ZnPcS₂.