Root-Mean-Square Amplitude of Zero-Point Vibrations in a Crystal

Russian Physics Journal - The paper shows that the values of zero-point energy and vibrations of atoms in a crystal determined by the uncertainty principle, depend on the dynamic response of atoms....     

Optimization of the Ambulance Fleet Location and Relocation

Journal of Applied and Industrial Mathematics - We study the problem of optimal location of the ambulance fleet at the base stations. The objective is to minimize the average waiting time for...     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Transition-Metal Catalysis of Triene 6π Electrocyclization: The π-Complexation Strategy Realized

Triene 6π electrocyclization, wherein a conjugated triene undergoes a concerted stereospecific cycloisomerization to a cyclohexadiene, is a reaction of great historical and practical significance. In order to circumvent limitations imposed by the normally harsh reaction conditions, chemists have long sought to develop catalytic variants based upon the activating power of metal–alkene coordination. Herein, we demonstrate the first successful implementation of such a strategy by utilizing [(C₅H₅)Ru(NCMe)₃]PF₆ as a precatalyst for the disrotatory 6π electrocyclization of highly substituted trienes that are resistant to thermal cyclization. Mechanistic and computational studies implicate hexahapto transition-metal coordination as responsible for lowering the energetic barrier to ring closure. This work establishes a foundation for the development of new catalysts for stereoselective electrocyclizations.     

The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.