A topological analysis of electron density and chemical bonding in cyclophosphazenes PnNnX2n (X = H, F, Cl; n = 2, 3, 4)

The restricted Hartree-Fock method was used to determine the cycle size effects on the geometric parameters of several inorganic templates, cyclophosphazenes P_nN_nX_2n (X = H, F, Cl; n = 2, 3, 4). A topological analysis of local electronic properties at the electron density critical points of bonds allowed us to quantitatively characterize the chemical bond in cyclophosphazenes and its dependence on the cycle size and substituents at phosphorus. The calculated distributions of the electron density Laplacian and electron pair localization functions revealed the special features of the electronic structure of the nitrogen and phosphorus atoms. These results explain the nature of noncovalent interactions between the P atoms of one cyclophosphazene molecule and the N atoms of the other.     

Critical Points in a Crystal and Procrystal

The critical points in the model electron density distributions of LiF, NaF, NaCl, and MgO crystals, constructed from accurate X-ray diffraction data, are determined. For LiF and MgO they are compared with those obtained from a Hartree–Fock electron density calculation. Both experiment and theory show the same type of critical points on the bond lines. The topological features in areas between structural units, where the electron density is low and near-uniform, turn out to be model dependent and cannot be established well with the data available. Topological analysis of procrystals (hypothetical systems consisting of spherical atoms or ions placed on the same sites as atoms in real crystal) show that (3, –1) critical points, usually connected with bonding interaction, are observed on interatomic lines in these nonbonded systems as well.     

Uniformly spread measures and vector fields

We show that two different ideas of uniform spreading of locally finite measures on the d-dimensional Euclidean space are equivalent. The first idea is formulated in terms of finite distance transportations to the Lebesgue measure, while the second idea is formulated in terms of vector fields connecting a given measure with the Lebesgue measure. Bibliography: 11 titles.     

Random complex zeroes,III. Decay of the hole probability

The ‘hoe probability’ that a random entire function where ζ₀, ζ₁, ... are Gaussian i.i.d. random variables, has no zeroes in the disc of radiusr decays as exp(−cr ⁴) for larger. Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.     

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields**

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic and kinetic potentials and electron density allowed partitioning any molecules and crystals into atomic - and potential-based -basins; -basins explicitly account for the electron exchange effect, which is missed for -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of - and -basins. The gap between - and -basins represents the charge transfer, while the gap between - and -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of -, -, and - basin boundaries between interacting atoms was proposed. The position of -boundary between - and -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's -basin penetrates oxygen atom's -basin, while for covalent bonds a -boundary closely approaches a -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the -basin of an electron occupier atom.     

Energy properties and structure of 2- and 8-allylthioquinoline complexes with iodine

The study focuses on the energy and quantum topological properties of substituted 2- and 8-allylthioquinoline complexes with iodine, which are assumed to correspond to prereaction states in the iodocyclization reaction leading to the formation of thiazolo- and tiazinoquinoline systems. The structures of the complexes and the corresponding atomic interactions are modeled considering the different conformational states of allyl-substituted quinolinethiols (thioquinolines). The energy values are analyzed for the interactions between the iodine molecule and different donor centers of the substituted quinoline system: the nitrogen heteroatom, sulfur, and π-system of the allyl group. It is shown that the formation of stable complexes with the nitrogen of the quinoline ring is complicated by steric hindrances posed by the S-allyl group at positions 2 and 8 of the quinoline system, which in turn contributes to the convergence of the cyclization centers.     

Chemical Bonding in the Complexes XeF<Stack><Subscript>5</Subscript><Superscript>+</Superscript></Stack>XF<Stack><Subscript>6</Subscript><Superscript>−</Superscript></Stack> (X = P,As, Sb,and Bi)

Ab initio quantum-chemical calculations of the complexes XeF ₅ ⁺ XF ₆ ^? (X = P, As, Sb, and Bi) were performed with the use of relativistic pseudopotentials for heavy atoms and full-electron basis sets. The chemical bonds were characterized by the parameters of critical points (electron density, its Laplacian, total electron energy, and its kinetic and potential components). It was demonstrated that the interaction between the XeF ₅ ⁺ cation and the XF ₆ ^? anion in XeF ₅ ⁺ XF ₆ ^? follows a key-lock scheme involving directed interactions of bridging fluorine atoms F_b → Xe and that the structuring function of the lone electron pair of the Xe atom is to compensate the destabilizing electrostatic interaction between the Xe and X atoms bearing excess positive charges.     

The N···H hydrogen bond strength in the transition state at the limiting step determines the reactivity of cephalosporins in the active site of L1 metallo-β-lactamase

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Random complex zeroes, II. Perturbed lattice

We show that the flat chaotic analytic zero points (i.e. zeroes of a random entire function where ζ₀, ζ₁, … are independent standard complex-valued Gaussian variables) can be regarded as a random perturbation of a lattice in the plane. The distribution of the distances between the zeroes and the corresponding lattice points is shift-invariant and has a Gaussian-type decay of the tails. Supported by the Israel Science Foundation of the Israel Academy of Sciences and Humanities.