On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

The stressed state in an infinite medium having a system of rectilinear thin elastic inclusions with cyclic symmetry

Using the machinery of complex variable theory we study the stressed state in an unbouned medium of cyclically located thin elastic inclusions of finite length. The problem is reduced to solving a system of two singular integro-differential equations. A numerical analysis is carried out for the stress intensity factors in the vicinity of the ends of the inclusions. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 87–90.     

Inorganic Molecular Electride Mg4O3: Structure,Bonding, and Nonlinear Optical Properties

Growing demands of material science and, in particular, in the field of nonlinear optics (NLO) encourage us to look for stable highly polarizable molecules with excess diffuse electrons. An unusual class of compounds called electrides comply with these requirements. Many attempts have been made, yet only few electrides have been synthesized as solids and none of them as molecular species. In this paper, a new theoretically designed molecular species with electride characteristics is reported. The idea of this molecular electride comes from the formation of electride-like features in the MgO crystal with defect F-centers. The geometry of the investigated molecule can be described as a Mg₄O₄ cube with one oxygen atom removed. In Mg₄O₃, two 3s electrons are pushed out from the inner area of the molecule forming a diffuse electride multicentered bond. Our calculations show that this electride-like cluster possesses a noticeably large first hyperpolarizability β=5733 au. At the same time, a complete cube Mg₄O₄ and Mg₄O₃²⁺ without electride electron pair have much smaller β: 0 au and 741 au, respectively. This fact indicates the decisive role of the electride electron pair in NLO properties. Additionally, vertical detachment energies of isomers (VDE), excitation energies ΔE, polarizabilities α, and IR spectra were calculated. These properties, including β, are supposed to be observable experimentally and can serve as indirect evidence of the stable molecular electride formation.     

Reply to the Comment on “Realization of Lewis Basic Sodium Anion in the NaBH3− Cluster”

We reply to the comment by S. Pan and G. Frenking who challenged our interpretation of the Na^?:→BH₃ dative bond in the recently synthesized NaBH₃^? cluster. Our conclusion remains the same as that in our original paper ( https://doi.org/10.1002/anie.201907089 and https://doi.org/10.1002/ange.201907089 ). This conclusion is additionally supported by the energetic pathways and NBO charges calculated at UCCSD and CASMP2(4,4) levels of theory. We also discussed the suitability of the Laplacian of electron density (QTAIM) and Adaptive Natural Density Partitioning (AdNDP) method for bond type assignment. It seems that AdNDP yields more sensible results. This discussion reveals that the complex realm of bonding is full of semantic inconsistencies, and we invite experimentalists and theoreticians to elaborate this topic and find solutions incorporating different views on the dative bond.     

Elastic stresses in a half-plane with a periodic system of exogeneous circular inclusions located along the boundary of the half-plane

Podol'sk Engineering Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 6, pp. 59–64, June, 1991.