Effects of complex-valued electronic wave functions on nuclear motions

Moleculer species and colliding groups of atoms are considered for which the electronic wave functions are complex-valued, having arguments that depend parametrically on the nuclear coordinates. The effective Hamiltonian for nuclear motions in the adiabatic approximation that arises in the present case differs from the ordinary Born–Oppeneheimer Hamiltonian, the latter being obtained when restriction to real-valued electronic functions is made. The asymptotic boundary conditions imposed in collision theory lead to in- and out- states [8], and hence to complex-valued wave functions in the coordinate representation. The study of the influence of electron–molecule scattering on nuclear motions therefore necessitates the use of the new effective Hamiltonian, which leads to results differing from those predicted on the basis of the Born–Oppenheimer operator. It is shown that momentum-dependent potentials occurring in the new Hamiltonian might cause “distortions” to the vibrational patterns of some electron–molecule metastable states. Also, these terms can give rise to non-Born–Oppenheimer resonances when motions in an internuclear coordinate become unbounded. We derive expressions for the relevant level widths and line shapes, showing them to be subject to an isotope effect. Even when real-valued electronic functions may be used, the selections of complex-valued functions in their linear span is still optional. Although exact treatments lead to the same results in both real and complex cases we show how the choice of the argument of the electronic function to be non-zero and dependent on nuclear coordinates may be useful for the application of certain approximation schemes. It is demonstrated that for certain systems a suitable choice of the argument assures convergence when the related Lippmann–Schwinger Equation is iterated. It is also shown that in this way an nth order term in the series expansion of the T matrix [8] for moleculer systems can be made negligibly small.     

Neue neutrale und kationische Mono‐Aziridin‐Komplexe des Typs [CpMn(CO)2Az], [CpCr(NO)2Az]+ und [(Ph3P)(CO)4ReAz]+ über CO‐, Hydrid‐ und Chlorid‐Abspaltungsreaktionen

Novel Neutral and Cationic Mono‐Aziridine Complexes of the Type [CpMn(CO)₂Az], [CpCr(NO)₂Az]⁺, and [(Ph₃P)(CO)₄ReAz]⁺ via CO‐, Hydride‐, and Chloride‐Elimination Reactions The monoaziridine complexes 1 — 5 are obtained by three differently induced substitution reactions. The photolytically induced CO substitution reaction of [CpMn(CO)₃] with 2, 2‐dimethylaziridine leads to the neutral N‐coordinate aziridine complex [Cp(CO)₂Mn{$\overline{N(H)CMe₂C}$ H₂}] ( 1 ). The protonation of [(Ph₃P)(CO)₄ReH] with CF₃SO₃H and consecutive treatment with 2, 2‐dimethylaziridine or 2‐ethylaziridine gives the salt‐like aziridine complexes [(Ph₃P)(CO)₄Re{$\overline{N(H)CMe₂C}$ H₂}](CF₃SO₃) ( 2 ) or [(Ph₃P)(CO)₄Re{ H₂}](CF₃SO₃) ( 3 ) by hydride elimination reactions. The like‐wise salt‐like complexes [Cp(NO)₂Cr{$\overline{N(H)CMe₂C}$ H₂}](BF₄) ( 4 ) and [Cp(NO)₂Cr{ H₂}](CF₃SO₃) ( 5 ) are synthesized from [CpCr(NO)₂Cl] by chloride elimination with AgX (X = BF₄, CF₃SO₃) in the presence of 2, 2‐dimethylaziridine or 2‐ethylaziridine, respectively. As a result of X‐ray structure analyses, the metal atoms are trigonal pyramidally ( 1, 4, 5 ) or octahedrally ( 2, 3 , cis‐position) configurated; the intact three‐membered rings coordinate through the distorted tetrahedrally configurated N atoms. All compounds 1‐5 are stable with respect to the directed thermal alkene elimination to give the corresponding nitrene complexes; the IR, ¹H‐ and ¹³C{¹H}‐NMR, and MS spectra are reported and discussed.     

Determination of the diastereomers of vitamin K1

A method is described for the gas-chromatographic determination of the diastereomers of vitamin K₁ (phylloquinone) in the form of their dihydro dimethyl ethers. The reported method of derivatization and chromatographic analysis in conjunction with optical rotation measurements are useful approaches for characterization of vitamin K₁ samples with respect to their origin.     

Thermisches Verhalten von Caesiumchloroferraten(III) und Caesiumchloroferrat(III)-Hydraten. II. Die Rehydratation der Zersetzungsprodukte von Cs3[FeCl6] – Eine ramanspektroskopische Untersuchung unter definierter Wasserdampfatmosphäre [1]

The Thermal Behaviour of Caesiumchloroferrates(III) and Caesiumehloroferrate(III) Hydrates. II. The Rehydration of Decomposition Products of Cs₃[FeCl₆] — A Raman Spectroscopic Study under Definite Atmosphere of Water Vapour Cs₃[FeCl₆] formed by dehydration of Cs₃[FeCl₆] · H₂O at about 160°C does not change at normal atmosphere within 3 till 4 hours. Rehydration under the vapour pressure of the eliminated water yields the monohydrate in nearly the same time. In the same manner rehydration of the solid mixture of Cs[FeCl₄] and 2 CsCl formed by thermal decomposition of the metastable Cs₃[FeCl₆] (280°C) produces the intermediates Cs₃[Fe₂Cl₉] and Cs₂[Fe(H₂O)Cl₅] in mixtures with CsCl and, finally, Cs₃[FeCl₆] · H₂O. The formation of Cs₃[Fe₂Cl₉] from Cs[FeCl₄] and CsCl is accelerated by water. The reaction cycle has been studied using Raman and IR spectroscopy. The results will be discussed with respect to thermoanalytical data.     

Charge transfer in the Cl-CO cluster induced by core ionization

Ab initio calculations of core-ionization spectra of the anion-molecule Cl-CO cluster are performed. Particular attention is paid to the investigation of charge-transfer screening processes accompanying core ionization of the CO molecule in the cluster. The charge-transfer processes are very efficient and favored by the presence of a low-lying unoccupied pi* orbital in CO capable of accepting an electron from Cl-. The O1s(-1) and C1s(-1) core-ionization spectra are calculated and compared. Both reveal a breakdown of the quasiparticle picture of core ionization caused by the charge-transfer processes. Remarkable differences between these two spectra are found which manifest themselves in distinct intensity distributions in the prominent low-energy spectral bands. The underlying reason for these differences is elucidated and linked with the preference of the pi* orbital to localize mainly on carbon. Core-ionization spectra of anion-molecule clusters are very sensitive to the type of the molecule involved as the comparative analysis of the O1s(-1) core-ionization spectra of the Cl-CO and Cl-H(2)O clusters show.     

Structural basis for recognition of bacterial cell wall teichoic acid by pseudo-symmetric SH3b-like repeats of a viral peptidoglycan hydrolase

Endolysins are bacteriophage-encoded peptidoglycan hydrolases targeting the cell wall of host bacteria via their cell wall-binding domains (CBDs). The molecular basis for selective recognition of surface carbohydrate ligands by CBDs remains elusive. Here, we describe, in atomic detail, the interaction between the Listeria phage endolysin domain CBD500 and its cell wall teichoic acid (WTA) ligands. We show that 3′O-acetylated GlcNAc residues integrated into the WTA polymer chain are the key epitope recognized by a CBD binding cavity located at the interface of tandem copies of beta-barrel, pseudo-symmetric SH3b-like repeats. This cavity consists of multiple aromatic residues making extensive interactions with two GlcNAc acetyl groups via hydrogen bonds and van der Waals contacts, while permitting the docking of the diastereomorphic ligands. Our multidisciplinary approach tackled an extremely challenging protein–glycopolymer complex and delineated a previously unknown recognition mechanism by which a phage endolysin specifically recognizes and targets WTA, suggesting an adaptable model for regulation of endolysin specificity.

Combining genetic, biochemical and computational approaches, we elucidated the molecular mechanisms underlying the recognition of Listeria wall teichoic acid by bacteriophage-encoded SH3b repeats.     

Asymptotic expansions for the truncation error in Ramanujan-type series

The Ramanujan Journal - Many of the fastest known algorithms to compute $$\pi $$ involve generalized hypergeometric series, such as the Ramanujan–Sato series. In this paper, we investigate...