On localized orbitals in infinite,periodic systems

It is shown that in two- or three-dimensional periodic systems with an odd number of electrons per unit cell no unitary transformation of the canonical Hartree - Fock orbitals can produce equivalent, localized orbitals for all electrons. However, in one-dimensional systems such orbitals can be found. The physical implications are discussed.     

On solving the master equation in spatially periodic systems

We present a new method for solving the master equation for a system evolving on a spatially periodic network of states. The network contains 2(ν) images of a "unit cell" of n states, arranged along one direction with periodic boundary conditions at the ends. We analyze the structure of the symmetrized (2(ν)n) × (2(ν)n) rate constant matrix for this system and derive a recursive scheme for determining its eigenvalues and eigenvectors, and therefore analytically expressing the time-dependent probabilities of all states in the network, based on diagonalizations of n × n matrices formed by consideration of a single unit cell. We apply our new method to the problem of low-temperature, low-occupancy diffusion of xenon in the zeolite silicalite-1 using the states, interstate transitions, and transition state theory-based rate constants previously derived by June et al. [J. Phys. Chem. 95, 8866 (1991)]. The new method yields a diffusion tensor for this system which differs by less than 3% from the values derived previously via kinetic Monte Carlo (KMC) simulations and confirmed by new KMC simulations conducted in the present work. The computational requirements of the new method are compared against those of KMC, numerical solution of the master equation by the Euler method, and direct molecular dynamics. In the problem of diffusion of xenon in silicalite-1, the new method is shown to be faster than these alternative methods by factors of about 3.177 × 10(4), 4.237 × 10(3), and 1.75 × 10(7), respectively. The computational savings and ease of setting up calculations afforded by the new method of master equation solution by recursive reduction of dimensionality in diagonalizing the rate constant matrix make it attractive as a means of predicting long-time dynamical phenomena in spatially periodic systems from atomic-level information.     

Self-enhanced multicolor electrochemiluminescence by competitive electron-transfer processes

Controlling electrochemiluminescence (ECL) color(s) is crucial for many applications ranging from multiplexed bioassays to ECL microscopy. This can only be achieved through the fundamental understanding of high-energy electron-transfer processes in complex and competitive reaction schemes. Recently, this field has generated huge interest, but the effective implementation of multicolor ECL is constrained by the limited number of ECL-active organometallic dyes. Herein, the first self-enhanced organic ECL dye, a chiral red-emitting cationic diaza [4]helicene connected to a dimethylamino moiety by a short linker, is reported. This molecular system integrates bifunctional ECL features (i.e. luminophore and coreactant) and each function may be operated either separately or simultaneously. This unique level of control is enabled by integrating but decoupling both molecular functions in a single molecule. Through this dual molecular reactivity, concomitant multicolor ECL emission from red to blue with tunable intensity is readily obtained in aqueous media. This is done through competitive electron-transfer processes between the helicene and a ruthenium or iridium dye. The reported approach provides a general methodology to extend to other coreactant/luminophore systems, opening enticing perspectives for spectrally distinct detection of several analytes, and original analytical and imaging strategies.

Controlling electrochemiluminescence (ECL) color(s) is crucial for many applications ranging from multiplexed bioassays to ECL microscopy.     

On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

The symmetry properties of the mono- and bielectronic terms contributing to the Fock matrix in the ab initio Hartree–Fock treatment of periodic systems are discussed. A computational scheme which takes full advantage of the point symmetry is presented; in this respect, it represents a generalization of the scheme proposed in Int. J. Quantum Chem. 17 , 501 (1980). Computational details and numerical examples are reported; it is shown that with respect to two of the bottlenecks of this kind of calculation, namely, computer time and backing storage required for the bielectronic integrals, it is possible to obtain saving factors as large as h and h², respectively, where h is the order of the point group. Preliminary tests are reported which indicate that the study of relatively complicated systems, like quartz or corundum (9 and 10 atoms in the unit cell, respectively) at an ab initio Hartree–Fock level is now within reach.     

Permanence and partial extinction in an impulsive delay competitive system with the effect of toxic substances

In this paper we propose a periodic impulsive delay two-species competitive system in which two species have toxic inhibitory effects on each other. It is assumed that the system is impulsively controlled by means of harvesting and stocking controls. By using the theory of impulsive differential equation and analysis techniques, a set of sufficient conditions are derived for the permanence and partial extinction of the system. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.     

Wannier-type atomic orbitals for periodic systems

The results of an application of Wannier-type atomic orbitals for calculations of local properties of electronic structure for periodic systems (atomic charges and covalencies, bond orders and total valencies), published earlier by the authors, are summarized. The numerical results are given for bulk crystals with the perovskite structure ATiO₃, A=Sr,Ba,Pb and LaMnO₃ (the Bloch functions are calculated in LCAO basis), for bulk MgO crystal (the Bloch functions are calculated both in LCAO and PW basis) and for the two periodic slab models of surfaces (001) of MgO and (110) of rutile TiO₂.     

Dressed coupled-electron-pair-approximation methods for periodic systems

 The techniques of matrix dressing for configuration-interaction (CI)-type or coupled-electron-pair-approximation (CEPA)-type correlation treatments are reviewed with respect to the application to periodic systems. All methods ranging from canonical second-order M?ller–Plesset perturbation theory over CI of single and double excitation, CEPA-0 or the averaged-coupled-pair-functional to self-consistent size-consistent CI can be formulated completely equivalently as an eigenvalue problem or as a solution to a system of linear equations. The size consistency of each method is obtained in a natural way, and invariance under orbital rotations is clearly assessible. A remark on the size consistency of the Davidson correction is presented. Additionally, the direct generation of localized Hartree–Fock orbitals as basic ingredients for the correlation calculations are addressed, as well as selected results on ring molecules, polymers, and 3D cubic beryllium as a model crystal. Received: 28 August 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

Grid-free density functional calculations on periodic systems

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.     

Stress tensor in model polymer systems with periodic boundaries

The calculation of the stress tensor from molecular simulations of atomistic model polymer systems employing periodic boundary conditions is discussed. Starting from the dynamical equations governing the motion of sites, correct double summation forms of the atomic and the molecular virial equations are derived, which are valid for flexible, infinitely stiff and rigid chain models even in the presence of interactions between different images of the same parent macromolecule. A new expression for the true instantaneous stress (flux of momentum through the faces of the simulation box) is derived and shown to exhibit large fluctuations when applied in molecular dynamics simulations. A new equation for the thermodynamic stress, cast exclusively in terms of intermolecular forces on interaction sites, is also derived. Application to Monte Carlo simulations shows that the molecular virial expression exhibits the smallest fluctuations among all stress expressions discussed, and thus allows computation of the thermodynamic stress with least uncertainty. A scheme is developed for the calculation of surface tension from intermolecular forces only.     

超分子体系中的光物理和光化学过程

总结了我们组近几年来对超分子体系中的光物理和光化学过程所做的工作,包括三个部分：(1)微反应器控制的有机光化学反应的选择性,(2)疏水、疏脂作用对光物理和光化学过程的影响,(3)超分子体系中的电子转移、能量传递和光化学转换。     

Förster-type processes in cascading systems

The deactivation of molecules (donors) excited to high vibrational states by consecutively transferring single vibrational quanta to randomly placed acceptors is investigated. Whereas the microscopic master equation is governed by constant step-down rates, the corresponding macroscopic reaction system exhibits not only time-dependent effective rates but also deactivating rates connecting all the levels to each other.     

On the planar periodic table

We reconsider, in this work, the construction of the two‐dimensional (2‐D) periodic table. The two‐dimensional logarithmic Coulomb system is used to generate atomic shells for the 2‐D atoms. A q‐deformed model is developed to explain the ordering of the shells predicted by the 2‐D Madelung rule. Our model, with the value q=1.26 for the deformation parameter, reproduce very well the above rule. We also compute the key function and the address function which, together with our model for the Madelung rule, permit us to give a new format of the 2‐D periodic table. It is shown that this table is different from the one existing in the literature, and we have a new family of elements, the g family. The question of the existence of 2‐D “ions” is briefly discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 206–211, 2000     

Laplace-transformed diagonal Dyson correction to quasiparticle energies in periodic systems

We present a method to self-consistently evaluate quasiparticle energies of periodic systems within the diagonal approximation for solving Dyson's equation. Our method is based on the Laplace transform of the second-order M?ller-Plesset perturbation (MP2) theory kernel in the atomic basis formulation. The overhead computational cost of evaluating the fully self-consistent diagonal correction over the MP2 band energy calculation is negligible. We present numerical benchmark results for the band structure of trans-polyacetylene and compare it with MP2 and other approaches.     

Geometry optimization of periodic systems using internal coordinates

An algorithm is proposed for the structural optimization of periodic systems in internal (chemical) coordinates. Internal coordinates may include in addition to the usual bond lengths, bond angles, out-of-plane and dihedral angles, various "lattice internal coordinates" such as cell edge lengths, cell angles, cell volume, etc. The coordinate transformations between Cartesian (or fractional) and internal coordinates are performed by a generalized Wilson B-matrix, which in contrast to the previous formulation by Kudin et al. [J. Chem. Phys. 114, 2919 (2001)] includes the explicit dependence of the lattice parameters on the positions of all unit cell atoms. The performance of the method, including constrained optimizations, is demonstrated on several examples, such as layered and microporous materials (gibbsite and chabazite) as well as the urea molecular crystal. The calculations used energies and forces from the ab initio density functional theory plane wave method in the projector-augmented wave formalism.     

RRS-PBC: a molecular approach for periodic systems

Technically, when dealing with a perfect crystal, methods in k-(reciprocal) space that impose periodic boundary conditions(PBC) in conjunction with plane-wave basis sets are widely used. Chemists, however, tend to think of a solid as a giant molecule, which offers a molecular way to describe a solid by using a finite cluster model(FCM). However, FCM may fail to simulate a perfect crystal due to its inevitable boundary effects. We propose an RRS-PBC method that extracts the k-space information of a perfect crystalline solid out of a reduced real space(RRS) of an FCM. We show that the inevitable boundary effects in an FCM are eliminated naturally to achieve converged high-quality band structures.     

Physical aging and relaxation processes in epoxy systems

Relaxation transitions in epoxy oligomers of various chemical nature and three-dimensional polymer networks on their basis are considered. Additional factors affecting relaxation of the networks, namely, the conversion of reactive functional groups of monomers during curing and the crosslink density of the network being formed, are discussed. Special attention is given to the phenomenon of physical aging in glassy crosslinked epoxy systems, which is analyzed from the experimental and theoretical viewpoints.     

Energetics of electron processes in semiconductor photocatalytic systems

The energetics of electron processes in photocatalytic systems based on dispersed semiconductors, their nanocomposites and heterostructures are examined. Methods for the approximate estimation and quantitative determination of their energetic characteristics are evaluated and energy diagrams of photocatalytic systems based on semiconductor nanocomposites and their heterostructures are plotted. Analysis of the diagrams permits the elucidation of the nature of their photocatalytic effects in redox reactions. L. V. Pisarzhevskii Institute of Physical Chemistry, National Academy of Sciences of Ukraine, 31 Prospekt Nauki, Kiev 03039, Ukraine. Translated from Teoreticheskaya i éksperimental'naya Khimiya, Vol. 36, No. 2, pp. 69–89, March–April, 2000.     

Thermodynamic description of sorption processes in swelling systems

The thermodynamics of sorptive moistening of various types of swelling sorbents have been analyzed. The energy and entropy characteristics of the sorbed substance have been calculated.Institute of Physical Chemistry, Russian Academy of Sciences, Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 29–33, January, 1992.     

The kinetics of photochemical processes in polymer-salt systems

The kinetics of photochemical reactions in aqueous polymer-salt systems containing ammonium heptamolybdate, dodecatungstate, or metavanadate and polyvinyl alcohol or polyvinylpyrrolidone was studied by measurements of photoinduced electrode potential difference. The rate of primary accumulation of reduced d metal forms was evaluated for different systems. Possible reasons for complex oscillatory processes in the systems were analyzed. Comparative data were obtained for compositions containing polyoxometallate shaped like buckyball:(NH₄)₄₂[Mo₇₂^VIMo₆₀^VO₃₇₂(HCOO)₃₀(H₂O)₇₂] · 30HCOONH₄ · 250H₂O. UV irradiation of this system caused the oxidation of molybdenum(V). Original Russian Text ? A.A. Ostroushko, M.Yu. Sennikov, 2009, published in Zhurnal Fizicheskoi Khimii, 2009, Vol. 83, No. 1, pp. 127–131.