Dipolmoment und Konformation von Imino-äther-Derivaten

By means of the dipole moments of several imidic acid esters the conformation at the C? O bond and the configuration at the C?N bond have been determined. Use was made of the graphical comparison of a phenyl-derivative with the para-substituted analogue [7] in combination with cyclic model compounds having forced stereochemistry. The results obtained are conclusive for the N-alkyl-derivatives which are in the Eap form A. The imidic acid esters which are unsubstituted at the nitrogen are prevailingly in the same Eap conformation A; another conformation, probably the Zap form B, may also be present in smaller amounts.     

A program for linear regression with a common point of intersection: the isokinetic relationship

A program is described for statistically correct calculations of the enthalpy-entropy relationship, applicable also generally for linear regression when several regression lines are constrained by a common point of intersection. Examples from the chemical literature show the difference between a correct and incorrect statistical treatment.     

Matrix canonical realizations of the Lie algebra o(m,n). II. Casimir operators

The matrix canonical realizations of the Lie algebra of pseudo-orthogonal group O(m, n) described in the first part of this paper are further investigated. The explicit formulae for values of the Casimir operators (which are multiples of identity in these realizations) are obtained.     

Path-integral expression of dissipative dynamics

The Feynman-Ito formula for a wide class of bounded absorptive potentials as well as for the multidimensional damped harmonic oscillator is derived within the framework of the path-integral theory of Albeverio, Høegh-Krohn and Truman.     

Geometry and conformation of dimethyl sulphate as investigated by electron diffraction and dipolometry

Electron diffraction data of dimethyl sulphate are interpreted by a 2:1 mixture of the C₂ and C_2v rotamers. This finding is also in agreement with the dipole moments of dimethyl sulphate and diethyl sulphate in benzene solution. The SO bond length and OSO bond angle are in agreement with the previously described empirical relationships. The variations in the O ?O distances in the different moieties OSO , OS-O, O-S-O, deserve special attention.     

Infinite quantum graphs

Infinite quantum graphs with δ-interactions at vertices are studied without any assumptions on the lengths of edges of the underlying metric graphs. A connection between spectral properties of a quantum graph and a certain discrete Laplacian given on a graph with infinitely many vertices and edges is established. In particular, it is shown that these operators are self-adjoint, lower semibounded, nonnegative, discrete, etc. only simultaneously.     

pK<Subscript>a</Subscript> based protonation states and microspecies for protein–ligand docking

In this paper we present our reworked approach to generate ligand protonation states with our structure preparation tool SPORES (Structure PrOtonation and REcognition System). SPORES can be used for the preprocessing of proteins and protein–ligand complexes as e.g. taken from the Protein Data Bank as well as for the setup of 3D ligand databases. It automatically assigns atom and bond types, generates different protonation, tautomeric states as well as different stereoisomers. In the revised version, pKa calculations with the ChemAxon software MARVIN are used either to determine the likeliness of a combinatorial generated protonation state or to determine the titrable atoms used in the combinatorial approach. Additionally, the MARVIN software is used to predict microspecies distributions of ligand molecules. Docking studies were performed with our recently introduced program PLANTS (Protein–Ligand ANT System) on all protomers resulting from the three different selection methods for the well established CCDC/ASTEX clean data set demonstrating the usefulness of especially the latter approach.     

A short perspective of modeling electrode materials in lithium-ion batteries by the ab initio atomistic thermodynamics approach

Atomic-scale insights into the performance of electrode materials in lithium-ion batteries require thermodynamic considerations as first step in order to determine potential surface structures that are relevant for subsequent kinetic studies. Within the last 20 years, research in heterogeneous catalysis as well as in electrocatalysis has been spurred by the ab initio atomistic thermodynamics approach, whose application for electrode materials in lithium-ion batteries is eyed and discussed in this perspective article.     

Remarks on the Trotter–Kato Product Formula for Unitary Groups

Let A and B be non-negative self-adjoint operators in a separable Hilbert space such that their form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary parameter values in the L ²-norm, that is, one has

$ \lim_{n\to+\infty} \int\limits^T_{-T} \left\|\left(e^{-itA/n}e^{-itB/n} \right)^nh - e^{-itC}h\right\|^2dt = 0 $

for each element h of the Hilbert space and any T > 0. This result is extended to the class of holomorphic Kato functions, to which the exponential function belongs. Moreover, for a class of admissible functions: \({\phi(\cdot),\psi(\cdot):{\mathbb R}_+ \longrightarrow {\mathbb C}}\), where \({{\mathbb R}_+ := [0,\infty)}\), satisfying in addition \({{\Re{\rm e}}\,(\phi(y))\ge 0, {\Im{\rm m}}\,(\phi(y) \le 0}\) and \({{\Im{\rm m}}\,(\psi(y)) \le 0}\) for \({y \in {\mathbb R}_+}\), we prove that

$ \,\mbox{\rm s-}\hspace{-2pt} \lim_{n\to\infty}(\phi(tA/n)\psi(tB/n))^n = e^{-itC} $

holds true uniformly on \({[0,T]\ni t}\) for any T > 0.