Orbits and induced representations in the quantum chemistry of nanostructures

Induced representations are applied to analyze the structures and electronic configurations of complex chemical systems with symmetry subgroups. A correlation is established between the local atomic symmetry and the number of equivalent atoms in a nanoparticle. A procedure is developed for finding additive quantum numbers for molecular orbitals based on the transitivity of induction.     

Application of symmetry groups of four-dimensional space in spectroscopy of crystals

A method of classification of many-electron states that involves symmetry groups of four-dimensional space is developed. Taking into account the spatial and temporal symmetry, the selection rules for electric and magnetic dipole transitions are investigated. The reduction relations for the irreducible representations of the orthogonal group O ₄ and the group R ₄ of pure rotations of the four-dimensional space on the groups and O _h ⁴ and O ⁴ of the four-dimensional cube and of the octahedron on the three-dimensional groups O _h and D _6h of the cubic and hexagonal systems, respectively, are obtained. The four-dimensional classification of the levels of the spin-orbit interaction of rare earth ions for the intermediate reduction on the group of the four-dimensional cube is performed. With the help of the irreducible representations of the O ₄ group, the selection rules of magnetic and forbidden electric dipole transitions, as well as of intercombination transitions, are investigated.     

MALDI-TOF Mass Spectrometry of Nanosized MoO<Subscript>2</Subscript>. Structure and Relative Stability of Isomers of Lower Molybdenum Oxide Cations

MALDI-TOF was used to study molybdenum dioxide (MoO₂) containing a nanosized fraction. The composition of cationic clusters of nonstoichiometric lower molybdenum oxides in the gas phase was determined, and the thermodynamic stabilities and configurations of isomers were calculated for selected symmetric molecular structures and for cations MoSO ₈ ⁺ and Mo₅O ₉ ⁺ . Molecular orbital analysis was performed for two trigonal-bipyramidal clusters Mo₅O₈ and Mo₅O₉. Changes in molybdenum–molybdenum interatomic distances in going from MoO ₈ ⁺ and Mo₅O ₉ ⁺ cations to neutral clusters are discussed.     

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)²] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)²] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p _1/2 and 2p _3/2 shells of elements with 11≤Z≤29 and for the 3d _3/2 and 3d _5/2 shells of elements with 30≤Z≤54.     

Theory of lineshape in photoelectron and Auger spectra

A theory of lineshape in photoelectron spectra is developed based on the Green’s function calculation of the atomic vacancy structure. It is shown that the broadening of photoelectron lines is always somewhat asymmetrical, and the broadening of satellite lines arising in atomic photoionization is generally strongly asymmetrical and inverse. The approach is generalized to low-energy Auger spectra; it is shown that Auger decay lines of excited atomic states may narrow with respect to the width of the initial level. The results are compared with experimental photoelectron spectra. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 985–991, November–December, 1998.