Dividing a system into subsystems is a widely used approach that allows one to calculate the electronic structure of large and complex systems. Quite often, the first order reduced density matrix of the system is employed in this approach. Unfortunately, it turns out that the obtained values of the electronic populations of subsystems, which must correspond to the number of electrons in the subsystem, are fractional and they noticeably deviate from integers. In the present paper for a system in the state of a particular type it is shown that if the second order reduced density matrix is also taken into account in the subsystem generations, then the orthogonal one electron basis can be found with which the calculated populations of subsystems will be practically equal to integer numbers. The said state of a particular type is the state whose wave function is a single determinant with doubly occupied orbitals. This is a reasonable approximation to the wave function for the singlet ground state of a standard atomic-molecular system.

Soft X-ray Li-K and Si-L 2 , 3 emission spectra of crystalline and amorphous lithium silicides Li 13 Si 4 and Li 15 Si 4 forming upon electrochemical lithiation of silicon anode in lithium-ion batteries (LIBs) have been investigated theoretically. It is shown that shape and energy position of X-ray emission bands can be used for determination of the chemical structure and composition of the electrochemically lithiated silicon, while the intensities of Li-K and Si-L 2 , 3 bands provide information on Li concentration. It is demonstrated that theoretical methods of soft X-ray emission spectroscopy (XES) can be used as a powerful tool for the detailed analysis of the electronic and structural properties of Li-Si alloys in LIBs.

Because of its exceptional lithium storage capacity, silicon is considered as a promising candidate for anode material in lithium-ion batteries (LIBs). In the present work, we demonstrate that methods of soft X-ray emission spectroscopy can be used as a powerful tool for the comprehensive analysis of the electronic and structural properties of lithium silicides LixSi forming in LIB’s anode upon Si lithiation. On the basis of density functional theory and molecular dynamics simulations, it is shown that the coordination number of Si atoms in LixSi decreases with an increase in Li concentration both for the crystalline and amorphous phases. In amorphous a-LixSi alloys, Si tends to cluster, forming Si–Si covalent bonds even at the high lithium concentration. It is demonstrated that the Si-L2,3 emission bands of the crystalline and amorphous LixSi alloys show different spectral dependencies, reflecting the process of disintegration of Si–Si network into Si clusters and chains of the different sizes upon Si li...

Many important properties of crystals are the result of the local defects. However, when one address directly the problem of a crystal with a local defect one must consider a very large system despite the fact that only a small part of it is really essential. This part is responsible for the properties one is interested in. By extracting this part from the crystal one obtains a so-called cluster. At the same time, properties of a single cluster can deviate significantly from properties of the same cluster embedded in crystal. In many cases, a single cluster can even be unstable. To bring the state of the extracted cluster to that of the cluster in the crystal one must apply a so-called embedding potential to the cluster. This article discusses a case study of embedding for ion-covalent crystals. In the case considered, the embedding potential has two qualitatively different components, a long-range (Coulomb), and a short-range. Different methods should be used to generate different components. A number of approximations are used in the method of generating an embedding potential. Most of these approximations are imposed to make the equations and their derivation simple and these approximations can be easily lifted. Besides, the one-determinant approximation for the wave function is used. This is a reasonably good approximation for ion-covalent systems with closed shells, which simplifies the problem considerably and makes it tractable. All employed approximations are explicitly stated and discussed. Every component of generation methods is described in details. The proofs of used statements are provided in a relevant appendix. © 2015 Wiley Periodicals, Inc.

K and L X-ray emission spectra of Mg atoms in a MgO crystal are calculated. The wave functions and energies of the crystal needed for calculating the intensities of these spectra are obtained in calculations of crystalline clusters by the embedding potential method. In this method, a finite cluster is considered instead of an infinite crystal and the effect of the crystalline environment on the cluster is simulated by a potential that is usually called the “embedding potential.” The electronic structure of clusters of different sizes and geometries in the embedding potential field is calculated by the Hartree-Fock and density functional methods. Qualitative agreement between calculated spectra and experimental data testifies that the embedding potential correctly describes the effect of the crystalline environment on the cluster.

The embedded cluster method for ion–covalent crystal band structure calculations is proposed. This method uses the results of embedded cluster electronic structure calculations within one‐determinant Hartree–Fock approximations. The band structure of high‐temperature cubic phase ZrO2 crystal is calculated and found to be in good agreement with calculations in the literature, which applied periodic boundary conditions at the same theory level. © 2013 Wiley Periodicals, Inc.

We propose a new method for decomposing electron density of a crystal into contributions associated with pair‐wise chemical bonds. To this end, an ion‐covalent crystal is represented using a neutral, closed shell cluster assembled from identical structural elements (SE) and embedded into the lattice electrostatic potential. The wave function of this cluster is calculated using the one determinant approximation. Then, a set of orthonormal, noncanonical, multicenter orbitals of the cluster valence states is generated, so as each orbital is localized on one structural element. The projection operators technique is used here, the valence molecular orbitals of the cluster being taken for the orthonormal basis set. In this construction, the first‐order reduced density matrix of the cluster valence electrons is exactly the sum of the first‐order reduced density matrices of the SE, and the latter is the exact sum of localized on this cluster orbitals densities. The localized orbitals are then transformed into directed orbitals corresponding to the ion‐covalent bonds in each structural element. The first‐order reduced density matrix of each structural element is exactly the sum of densities of all such corresponding directed orbitals. This method is demonstrated on the examples of MgO, cubic ZrO 2 , and rutile TiO 2 crystals. © 2012 Wiley Periodicals, Inc.

the field of atomic physics, one of the creators of the modern theory of atomic collisions, Honored Scientist of Russia, Professor Emeritus at St. Petersburg University, died on 15 November 2010. Yu N Demkov was born on 12 April 1926 in Leningrad into the family of engineer-architects designing many public buildings in Leningrad and other cities in the USSR. He graduated magna cum laude from high school in 1942 in the city of Yaroslavl' during the evacuation and entered the Moscow Institute of Steel in 1943. In 1944, when he was 18 years old, Y N Demkov was drafted into the acting army and served as a soldier in the First Ukrainian Front during World War II. In September 1945 he was demobilized, went back to Leningrad, and joined the sophomore class of the Department of Physics at Leningrad State University, where he worked all his life. After graduating with summa cum laude from Leningrad State University in 1949, YuNDemkov joined as an assistant the Chair of Theoretical Physics headed at that time by Academician V A Fock. His graduation thesis, ``Charge exchange in atomic collisions'', proved to be quite relevant and determined the main direction of his research for many years. Yurii Nikolaevich's PhD thesis was devoted to the variation principles in collision theory, which were closely related to the investigations of V A Fock. He defended a PhD thesis in 1954 and later wrote amonograph on the same topic, which was then translated into English and received a university prize in 1962. Yu N Demkov defended his doctoral dissertation, ``Slow collisions of atoms and molecules'', in 1967 and became a full professor in 1970. Yurii Nikolaevich worked successively as an assistant, senior researcher, associate professor, head of the laboratory of the theory of atomic collisions, and professor. From 1975 to 1991, he was the head of the Chair of QuantumMechanics. The work of Yu N Demkov on the collision theory of atoms and ions brought him scientific authority in theoretical physics in our country and later worldwide prominence. He obtained pioneering results in the theories of charge exchange, electron detachment, and other processes. The concepts of the `Demkov model' and `Demkov coupling' are well known in modern atomic physics. The second set of results obtained by Yu N Demkov concerns the problems of symmetry in atomic physics, in particular, when applied to the Fock symmetry of the hydrogen atom and harmonic oscillator. The most important among these results was the explanation of the internal symmetry of the Mendeleev Periodic Table and the so-called (n‡ l, n) energy-level occupation rule. Here, he managed to combine in whole the work of Maxwell on the so-called `fish eye', of Mendeleev, Bohr, and Fock on the hydrogen atom symmetry. Yurii Nikolaevich also obtained, together with G F Drukarev and V N Ostrovskii, fundamental results in the development of the method of zero-radius potentials in atomic physics. The results of these studies are presented in the monograph Method of Zero-Radius Potentials by Yu N Demkov and V N Ostrovskii [(Leningrad: Leningrad State University, 1975), which was translated into English (Plenum Press, 1988)] and awarded a University First-Class Prize. Yu N Demkov's significant achievement was the discovery of a new class of problems in collision theory, so-called harmonic scattering, and the development (together with I V Komarov, A P Shcherbakov, and D I Abramov) of the original theory of this scattering using conformal mappings. This work was awarded an Academician V A Fock Prize of the Russian Academy of Sciences. Other work of Demkov includes original and unexpected results obtained in neutrino focusing studies; polynomial solutions of the problem of the Uspekhi Fizicheskikh Nauk 181 (5) 565 ± 566 (2011) DOI: 10.3367/UFNr.0181.201105l.0565 Translated by M N Sapozhnikov PERSONALIA PACS number: 01.60.+q

In calculation, the electronic structure of crystals, especially those containing point defects, the embedding approach is proved to be useful and convenient. In this approach, a finite part of the crystal, referred to as cluster, is considered instead of infinite crystal and the influence of the rest of the crystal is simulated by the embedding potential. The key problems of this approach are the cluster selection and the embedding potential generation. To select a cluster, the Wigner-Seitz unit cell is used in the present approach and every border atom, situated at the unit cell face, edge, or vertex is symmetrically "divided" among adjacent unit cells sharing this atom. The atomic hybrid orbitals are used for the border atoms partition between neighboring clusters. It is shown that contrary to the conventional hybridization scheme, the nonorthogonal and even linearly dependent atomic hybrid orbitals can be used to construct the border atom density matrix. This density matrix can be made to satisfy the proper point symmetry and to match the number of equivalent hybrid orbitals and the number of nearest neighbors. Two different types (one-center and multicenters) of the embedding potential corresponding to the border atom are considered in the article. As a particular example of the border atom the oxygen ion in ZrO2, MgO, and TiO2 rutile crystals is considered. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 2602-2619, 2011

We present a method and a computer code for accurate calculation of electrostatic potential in an arbitrary crystalline lattice modeled using a finite system. The method is based on complementing a lattice unit cell with a set of point charges in order to annihilate simultaneously all components of any number of the lowest multipole moments. The positions and the values of the complementary charges are determined analytically. The electrostatic potential produced by each modified cell is short range, and the corresponding lattice series converges absolutely, which makes it convenient to use in embedded cluster calculations of solids, surfaces, and low-dimensional structures. The method is illustrated by application to the rutile TiO(2) and a-quartz SiO(2) lattices and to those of several complex minerals.

We present a QM/MM method for modeling metal/organic interfaces, which incorporates contributions from long‐range electron correlation, characteristic to metals and non‐bonded interactions in organic systems. This method can be used to study structurally irregular systems. We apply the method to model finite size domains of self‐assembled monolayers on the gold (111) surface and discuss the influence of boundary effects on the electrostatic and electronic properties of these systems. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010

Point defects are known to affect transport properties of materials. The effect of oxygen vacancies on the diffusion of Li+ ions in rutile TiO2 is investigated using an embedded cluster method. The calculated Li+ diffusion pathway in vacancy-containing lattice is similar to that found for the ideal lattice. However, vacancies strongly modify the shape of the Li+ potential energy surface and increase the diffusion activation energies by the factor of two.

The spin structure of the first order reduced density matrix (RDM-1) for an arbitrary many-electron state with zero z-projection of the total spin is examined. It is well known that for the state Psi(S0)(r(1)sigma(1),...,r(N)sigma(N)), which is an eigenstate of operators (S-2) over cap and (S-z) over cap with quantum numbers S and M 0, the matrix elements for spins alpha and beta are equal for any r and r': p(s0)(alpha)(r vertical bar r') = rho(beta)(s0)(r vertical bar r'). In the present article, it is shown that the same is true for any state Phi(M=0)(r(1)sigma(1),...,r(N)sigma(N)) with indefinite total spin if in the expansion Phi(M=0) = Sigma(S) D-s Psi(S0) only spins S with the same parity are present. To prove the statement, it is shown that the wave function Psi(S0) acquires the phase factor (-1)(N/2-S) when all spin functions alpha(sigma(i)) are changed for beta(sigma(i)) and vice versa. In the developed proof, the Hamiltonian was not used at all and it was not even assumed that the wave function Psi(S0) is an eigenfunction of some Hamiltonian. Therefore the obtained result is valid for the stationary and non-stationary states, ground and excited states, with and without homogeneous magnetic field imposed, exact and approximate wave functions. From the result obtained it follows, in particular, that for the stationary state to be spin-polarized (p(0)(alpha)(r vertical bar r) not equal rho(beta)(0)(r vertical bar r)) it is necessary for the Hamiltonian to mix states with different parity spins. The consequences from the proved statement for the antiferromagnetic state are discussed. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 108: 2657-2665, 2008

The electrostatic potential due to the crystal atoms net charge is present in almost all crystals, except pure covalent ones. The electrostatic potential is described by the series which is divergent for an infinite crystal. Several methods were proposed to address the problem of the electrostatic potential calculation and for the ideal lattice the commonly adopted is the Ewald method. However, for the imperfect lattices, the problem still remains active especially for crystals with complicated unit cell. In the present paper, a method is proposed to construct the Coulomb embedding potential. The crystal is divided into the finite cluster and infinite cluster environment, and the electrostatic potential of the latter is simulated with the embedding potential. It is essential that the embedding potential is produced by a finite number of charges disposed outside the cluster. The embedding potential for the perfect crystal and for the crystal with local defect (the finite radius defect) is the same, provided that the containing defect cluster is large enough. Therefore, the Coulomb embedding potential generated for the perfect crystal can be used for the crystal with various local defects. With the proposed method, the Coulomb embedding potential can be generated for any lattice with any atomic basis. The proposed method is based on the crystal unit cell modification, namely, in construction the unit cell with additional charges. The positions of additional charges are specially selected, and the values of these charges are obtained from the condition that all moments of the unit cell including up to the l th moment are equal to zero. The system of equations for additional charges is solved exactly in the general case. The infinite series of the unit cell potentials with l >= 2 is convergent and it converges to the Ewald potential.

With a rapid downscaling of the complementary metal-oxide-semiconductor (CMOS) devices, the ZrO2 becomes a promising candidate for application in microelectronic and therefore the information about the electronic structure of the perfect and defect ZrO2 crystal becomes important. In the present study, the local orbital Hartree-Fock approximation was applied to the ZrO2 crystal electronic structure calculations. The noncanonical orbitals localized on ions were employed, which are the solutions of the Hartree-Fock equations for ions in the confining potential simulating the crystal environment. The confining potential was calculated selfconsistently to bring the minimum to the crystal energy. The cluster expansion for the crystal energy was employed. The general idea of the method is similar to that of the study (1978, 20, 565), devoted to the electronic structure calculations of MgO crystal. In the present study, the more complicated system is considered. First, ZrO2 crystal has lower symmetry, and second the d-orbitals are present among ions occupied orbitals. (c) 2007 Wiley Periodicals, Inc.

A quasionedimentional spin chain s = 1/2 is considered as a lattice consisting of two sublattices. The attention is paid to the States, which are pure spin states of the whole lattice and both sublattices, the value of the sublattices' spins being maximum. It is shown that the Neel state can be considered as a superposition of such states. The exact equation for this superposition coefficients is developed. The possibility of the Neel state to be the eigenstate of a Hamiltonian is discussed. Several model Hamiltonians are examined, the well known ones and few novel Hamiltonians being considered. The time evolution of the Neel state in different models is studied with the help of Fock-Krylov method. (c) 2007 Wiley Periodicals, Inc.

in the current article, the procedure to separate a molecule into the ion radicals and bonds, proposed earlier by one of authors within the Hartree-Fock (HF) approach, is used. In this procedure the ion-radical-occupied orbitals are defined as solutions of HF equations for ion radical in the basis of occupied molecular orbital (MO) of the whole molecule. The bond orbitals are constructed to complete the functional space span by the occupied MO of ion radicals to the functional space span by occupied MO of the whole molecule. hi this approach it is easy to calculate the electron density of all ion radicals and bonds, which add up to the total electron density of the whole molecule, the densities overlap being taken into account. Hence, the adiabatic potential of the molecule is expressed as a sum of ion radicals and bonds self-energies and of various intramolecular interaction energies. The results of ab initio adiabatic potential calculations and its decomposition for several carbon-containing molecules, such as CH4, CH3Li, CH3F, and C2H6, which can be considered as two ion radicals connected by a single chemical bond, are presented here. The dependence of adiabatic potential components on the bond length is analyzed, and simple approximate equations for them are generated. In addition, the electronic structure of ion-radical CH3+, common for all molecules calculated here, is considered, and its dependence on the molecular environment is analyzed. (C) 2003 Wiley Periodicals, Inc.