Moscow Center for Continuous Mathematical Education

Moscow, Russia

Moscow Center for Continuous Mathematical Education

Moscow, Russia
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Litvinov G.L.,National Research University Higher School of Economics | Rodionov A.Y.,Moscow Center for Continuous Mathematical Education | Sergeev S.N.,University of Birmingham | Sobolevski A.N.,National Research University Higher School of Economics
Soft Computing | Year: 2013

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed. © 2013 Springer-Verlag Berlin Heidelberg.


Tchougreeff A.L.,RWTH Aachen | Tchougreeff A.L.,Moscow Center for Continuous Mathematical Education | Tokmachev A.M.,RAS Research Center Kurchatov Institute | Dronskowski R.,RWTH Aachen
International Journal of Quantum Chemistry | Year: 2013

The theory of catalytic activity of transition-metal compounds is a fascinating problem especially if a comparison of different catalysts is necessary. The isomerization of quadricyclane (QC) to norbornadiene (NB) catalyzed by transition-metal porphyrins is a challenge and incidentally a suitable benchmark for various theories of catalysis. We analyze this process in detail using a valence bond-like scheme adjusted for the description of reaction centers containing transition-metal atoms. A qualitative explanation of contrasting catalytic behavior of Mn-phthalocyanine and Co-tetraphenylporphyrin is obtained from the analysis of the spectra of local many electron states of free catalysts and their complexes with the reactant/product. This picture is supported by the numerical analysis of potential energy profiles for the QC to NB isomerization in the presence of a catalyst performed in the effective Hamiltonian approximation. This exemplary reaction is put in a more general perspective of theories of catalytic activity of transition-metal complexes and in relation with oxygenation reactions. © 2012 Wiley Periodicals, Inc.


Tchougreeff A.L.,RWTH Aachen | Tchougreeff A.L.,Moscow Center for Continuous Mathematical Education | Dronskowski R.,RWTH Aachen
Journal of Physical Chemistry A | Year: 2013

The calculation of the 3d-intrashell excitations in coordination compounds by means of the Effective Hamiltonian Crystal Field (EHCF) method is generalized to their polynuclear analogues to properly describe several open d-shells and their magnetic interactions. This challenge requires improving the precision of ca. 1000 cm-1 to ca. 100 cm-1 characteristic for the spin-reorientation energies. The method follows the successful EHCF paradigm, namely, the concerted usage of McWeeny's group-function approximation and Löwdin's partitioning technique, for an effective description of the multicenter d-systems. The novel approach is implemented in the MagAIîxTic package and validated against a series of binuclear complexes of Cr(III) featuring μ-oxygen superexchange paths. The trends in the compound series in terms of exchange constants are correctly reproduced, despite differing details of composition and structure, and the numerical results agree by order of magnitude with available experimental data and other theoretical methods. © 2013 American Chemical Society.


Tokmachev A.M.,RWTH Aachen | Tchougreeff A.L.,RWTH Aachen | Tchougreeff A.L.,Moscow Center for Continuous Mathematical Education | Dronskowski R.,RWTH Aachen
ChemPhysChem | Year: 2010

Water aggregates allow for numerous configurations due to different distributions of hydrogen bonds. The total number of possible hydrogen-bond networks is very large even for medium-sized systems. We demonstrate that targeted ultrafast methods of quantum chemistry make an exhaustive analysis of all configurations possible. The cage of (H2O)20 in the form of the pentagonal dodecahedron is a common motif in water structures. We calculated the spatial and electronic structure of all hydrogen-bond configurations for three systems: idealized cage (H2O)20 and defect cages with one or two hydrogen bonds broken. More than 3 million configurations studied provide unique data on the structure and properties of water clusters. We performed a thorough analysis of the results with the emphasis on the cooperativity in water systems and the structure-property relations. © 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.


Tchougreeff A.L.,RWTH Aachen | Tchougreeff A.L.,Moscow Center for Continuous Mathematical Education | Tchougreeff A.L.,Moscow State University | Dronskowski R.,RWTH Aachen
Molecular Physics | Year: 2016

The story of C2 continues to fascinate chemists spinning around a possibility of quadruple bonds for p-elements and discussing a wealth of options for the nature of an unconventional fourth bond. This led to lively discussions about the ways of counting or measuring bonds, and the interplay between the bond strength (energy), its length, and rigidity/stiffness (elasticity). Even old concerns about the possibility of theorems in chemistry and thus of the place of chemistry among ‘true’ sciences had been revived. We show that under some mild conditions certain exact statements (lemmas and theorems) about the C2 molecule can be relatively easily proven which, if not resolves the controversy entirely, at least provides some theoretical reference points to the discussion. Some more general consequences from this experience are discussed as well. © 2016 Taylor & Francis

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