On the asymptotic behavior of dynamical maps for a finite quantum system

We give some remarks on the dynamical evolution (also nonlinear) of finite quantum system. We are interested int-asymptotic behavior of density matrices in the Liouville space formalism and we show that for nonlinear dynamical semigroups, as well as for the dynamical maps that do not form semigroups, the stationary time evolution may be attained for finite time in contrast to the motion generated by the linear dynamical semigroup. Recently the problem of constructing a nonlinear analog of quantum mechanics with nonlinear wave equation playing the role of the Schrödinger equation has been investigated by some authors; see for example Mielnik (1974), Bergmann (1968). Our work is related to this investigation and gives a characteristic feature of the nonlinear time evolution.     

Characteristic of the Ag(bipy) 2 2+ /Ag(bipy) 2 + and Ag(phen) 2 2+ /Ag(phen) 2 + systems in acetonitrile

The values of standard potentials of redox systems formed by the complexes of Ag(II) and Ag(I) with 2,2-bipyridine and 1,10-phenanthroline in acetonitrile have been determined. The properties of the above systems in water and acetonitrile are compared. The possibility of application of these systems for the construction of electrodes with a constant potential in different solvents is discussed.

---

Charakteristik der Systeme Ag(bipy) ₂ ²⁺ /Ag(bipy) ₂ ⁺ und Ag(phen) ₂ ²⁺ /Ag(phen) ₂ ⁺ in Acetonitril

Zusammenfassung Die Standardpotentialwerte der Redoxsysteme, die durch Komplexbildung von Ag(II)- und Ag(I)-Ionen mit 2,2-Bipyridin und 1,10-Phenantrolin gebildet werden, wurden in Acetonitril bestimmt. Die Eigenschaften dieser Redoxsysteme in Wasser und Acetonitril wurden verglichen.Es wurde weiterhin die Möglichkeit der Anwendung dieser Systeme zur Konstruktion einer Elektrode mit unveränderbarem Potential in verschiedenen Lösungsmitteln diskutiert.

     

Monomer basis-set truncation effects in calculations of interaction energies: A model study

Supermolecular interaction energies are analyzed in terms of the symmetry-adapted perturbation theory and operators defining the inaccuracy of the monomer wave functions. The basis set truncation effects are shown to be of first order in the monomer inaccuracy operators. On the contrary, the usual counterpoise correction schemes are of second order in these operators. Recognition of this difference is used to suggest an approach to corrections for basis-set truncation effects. Also earlier claims--that dimer-centered basis sets may lead to interaction energies free of basis-set superposition effects--are shown to be misleading. According to the present study the basis-set truncation contributions, evaluated by means of the symmetry-adapted perturbation theory with monomer-centered basis sets, provide physically and mathematically justified corrections to supermolecular results for interaction energies.     

Single-site mutation and secondary structure stability: an isodesmic reaction approach. The case of unnatural amino acid mutagenesis Ala-->Lac

A method is described to evaluate backbone interactions in proteins via computational unnatural amino acid mutagenesis. Several N-acetyl polyalanyl amides (AcA(n)NH(2)) were optimized in the representative helical (3(10)-, 4(13)-, and a "hybrid" kappa-helix, n = 7, 9, 10, 14) and hairpin (two- and three-stranded antiparallel beta-sheets with type I turns betaalphaalphaepsilon, n = 6, 9, 10) conformations, and extended conformers of N-acetyl polyalanyl methylamides (n = 2, 3) were used to derive multistranded beta-sheet fragments. Subsequently, each residue of every model structure was substituted, one at a time, with l-lactic acid. The resulting mutant structures were again optimized, and group-transfer energies DeltaE(GT) were obtained as heats of the isodesmic reactions: AcA(n)NHR + AcOMe --> AcA(x)LacA(y)NHR + AcNHMe (R = H, CH(3)). These group-transfer energies correlate with the degree of charge polarization of the substituted peptide linkages as measured by the difference Deltae in H and O Mulliken populations in HN-C=O and with the H-bond distances in the "wild-type" structures. A good correlation obtains for the HF/3-21G and B3LYP/6-31G* group-transfer energies. The destabilization effects are interpreted in terms of loss of interstrand and intrastrand H-bonds, decrease in Lewis basicity of the C=O group, and O...O repulsion. On the basis of several comparisons of Ala --> Lac DeltaE(GT)'s with heats of the NH --> CH(2) substitutions, the latter contribution is estimated (B3LYP/6-31G*) to range between 1.5 and 2.4 kcal mol(-1), a figure close to the recent experimental DeltaDeltaG(o) value of 2.6 kcal mol(-1) (McComas, C. C.; Crowley, B. M.; Boger, D. L. J. Am.Chem. Soc. 2003, 125, 9314). The partitioning yields the following maximum values of the electronic association energy of H-bonds in the examined sample of model structures (B3LYP/6-31G* estimates): 3(10)-helix D(e) = -1.7 kcal mol(-1), alpha-helix D(e) = -3.8 kcal mol(-1), beta-sheet D(e) = -6.1 kcal mol(-1). The premise of experimental evaluations of the backbone-backbone H-bonding that Ala --> Lac substitution in proteins is isosteric (e.g., Koh, J. T.; Cornish, V. W.; Schultz, P. G. Biochemistry 1997, 36, 11314) is often but not always corroborated. Examination of the integrity of H-bonding pattern and phi(i), psi(i) distribution identified several mutants with significant distortions of the "wild-type" structure resulting inter alia from the transitions between i, i + 3 and i, i + 4 H-bonding in helices, observed previously in the crystallographic studies of depsipeptides (Ohyama, T.; Oku, H.; Hiroki, A.; Maekawa, Y.; Yoshida, M.; Katakai, R. Biopolymers 2000, 54, 375; Karle, I. L.; Das, C.; Balaram, P. Biopolymers 2001, 59, 276). Thus, the isodesmic reaction approach provides a simple way to gauge how conformation of the polypeptide chain and dimensions of the H-bonding network affect the strength of backbone-backbone C=O...HN bonds. The results indicate that the stabilization provided by such interactions increases on going from 3(10)-helix to alpha-helix to beta-sheet.     

Quantum chemical studies of dioxygen activation by mononuclear non-heme iron enzymes with the 2-His-1-carboxylate facial triad

Density functional theory with the B3LYP hybrid functional has been used to study the mechanisms for dioxygen activation by four families of mononuclear non-heme iron enzymes: alpha-ketoacid-dependent dioxygenases, tetrahydrobiopterin-dependent hydroxylases, extradiol dioxygenases, and Rieske dioxygenases. These enzymes have a common active site with a ferrous ion coordinated to two histidines and one carboxylate group (aspartate or glutamate). In contrast to the heme case, this type of weak field environment always leads to a high-spin ground state. With the exception of the Rieske dioxygenases, which have an electron source outside the active site, the dioxygen activation process passes through the formation of a bridging-peroxide species, which then undergoes O-O bond cleavage finally leading to the four electron reduction of O(2). In the case of tetrahydrobiopterin- and alpha-ketoacid-dependent enzymes, the O-O heterolysis yields a high-valent iron-oxo species, which is capable of performing a two-electron oxidation chemistry on various organic substrates. For the other two families of enzymes (extradiol dioxygenases and Rieske dioxygenases) the substrate oxidation and the O-O bond cleavage are found to be coupled. In the extradiol dioxygenases the product of the O-O bond cleavage is a ferric iron with an oxy-substrate with a mixture of radical and anionic character, which is essential for the selectivity of the catechol cleavage.     

Interactions of porphyrin covalently attached to poly(methacrylic acid) with liposomal membranes

The interactions between the 5-(4-acryloyloxyphenyl)-10,15,20-tritolylporphyrin covalently attached to poly(methacrylic acid) chain (PMA-Po) and phosphatidylcholine liposomes in aqueous solution at different pH values were studied. The binding constants (K(b)) for the liposome- PMA-Po in solutions in the pH range from 6.5 to 9.2 were determined using fluorescence spectroscopy. The binding was found to be efficient. The acid-base properties of the porphyrin chromophores were also studied. Both pK values associated with imine-N protonation of the porphyrin core were found to be 6.4. The quantum yield (Phi(Delta)) of singlet oxygen production by Po in the lipid-PMA-Po system was found to be high (0.88 +/- 0.05).     

Crystal chemistry of protonated 1,2-bis(di-R-aminomethyl)benzenes. Part V. [1,2-bis(diethylaminomethyl)-3,6-dichlorobenzene:1,2-bis(diethylaminomethyl)-3,4,6-trichlorobenzene]perchlorate mixed crystals

The mixed crystals of 1,2-bis(diethylaminomethyl)-3,6-di- and 3,4,6-trichloro-benzene perchlorate at 0.5:0.5 ratio have been studied using X-ray diffraction and FT-IR spectroscopy. The molecules of di- and tri-chloro derivatives are distributed randomly in the crystal lattice; however, this disorder manifested mainly by a partial occupation of the chlorine atom at C(4) and by relatively big atomic temperature parameters even at 99 K, particularly for the oxygens of the perchlorate anion. The proton in the [NHN]⁺ bond refined close to the equidistant position between the nitrogens. The conformations of the diethylaminomethyl substituents are pseudo-symmetrical relative to the plane and twofold axis passing through the midpoint of the hydrogen bond. The IR spectrum of the crystals shows a broad intense band and an intense continuous absorption indicating relatively high proton polarizability in the intramolecular hydrogen bond. In acetonitrile and in chloroform, the proton in the intramolecular hydrogen bond also shows a very high proton polarizability demonstrated by the continuous absorption in the IR spectrum.     

The use of bathoferroine for extraction-spectrophotometric determinations of microamounts of perchlorate and perrhenate

Bathoferroine can be used for anion determinations by a method based on selective ion-pair extraction if the selectivity of extraction has been enhanced by addition of nonelectrolyte to the water phase. The method of perchlorate and perrhenate determinations characterizes parameters similar to those obtained by methods in which other cation complexes have been used. The advantage of the proposed method is the possibility of considerable concentration of ion association compound extracts by nitromethane reextraction.     

Differential transition-state stabilization in enzyme catalysis: quantum chemical analysis of interactions in the chorismate mutase reaction and prediction of the optimal catalytic field

Chorismate mutase is a key model system in the development of theories of enzyme catalysis. To analyze the physical nature of catalytic interactions within the enzyme active site and to estimate the stabilization of the transition state (TS) relative to the substrate (differential transition state stabilization, DTSS), we have carried out nonempirical variation-perturbation analysis of the electrostatic, exchange, delocalization, and correlation interactions of the enzyme-bound substrate and transition-state structures derived from ab initio QM/MM modeling of Bacillus subtilis chorismate mutase. Significant TS stabilization by approximately -23 kcal/mol [MP2/6-31G(d)] relative to the bound substrate is in agreement with that of previous QM/MM modeling and contrasts with suggestions that catalysis by this enzyme arises purely from conformational selection effects. The most important contributions to DTSS come from the residues, Arg90, Arg7, Glu78, a crystallographic water molecule, Arg116, and Arg63, and are dominated by electrostatic effects. Analysis of the differential electrostatic potential of the TS and substrate allows calculation of the catalytic field, predicting the optimal location of charged groups to achieve maximal DTSS. Comparison with the active site of the enzyme from those of several species shows that the positions of charged active site residues correspond closely to the optimal catalytic field, showing that the enzyme has evolved specifically to stabilize the TS relative to the substrate.