The heisenberg exchange integral in a non-orthogonal basis for antiferromagnetic and ferromagnetic systems

The Dirac-Van Vleck-Serber permutation degeneracy method is used to demonstrate that the Heisenberg spin exchange Hamiltonian, –2J ₁₂s₁·s₂, is a good approximate Hamiltonian for the theoretical interpretation of antiferromagnetic and ferromagnetic systems. The approach does not neglect double or higher-order permutations and covers the general case of a singleN-electron configuration as well as that of configuration interaction. An analogy between antiferromagnetic and hydrogen-molecule-like systems is established, and a formula for the estimation of the Heisenberg exchange integral is derived.     

Photochemical transformation of metal-free phthalocyanine in a Shpol'skii matrix

Low lying vibronics within ∼700 cm⁻¹ above the origins of the first excited states of the two isomeric forms of metal-free phthalocyanine (H₂Pc) in mixed solvent matrix were re-examined by fluorescence excitation. Based on the obtained information, direct observation of photoisomeric transformation in the complex was made both from the fluorescence intensity decline under continuous resonance pumping and from the asymmetry of the fluorescence excitation intensity ratios upon two opposite laser scanning directions.     

Perturbation theory for the density matrix in the MO LCAO method

The problem of calculating the density matrix of perturbed electron shells in complex molecules has been solved in the MO LCAO [molecular orbital linear combination atomic orbitals] approximation. Considering the electron interaction in correcting the density matrix in each order of the perturbation theory yields one matrix equation uniquely defining the correction. This equation is formulated as an ordinary, linear nonhomogeneous system with respect to the individual matrix elements; this provided the possibility of establishing the convergence region of the self-consistent method. The solution of this system is accomplished by the method of steepest descent which, as has been shown, is always convergent in this case. It was established that just as in the conventional perturbation theory, the (2i + 1)th correction for the energy in terms of the Hartree-Fock method may be expressed by a correction of the density matrix not exceeding the i-th order. Detailed expressions are presented up to the eighth energy correction.     

Density matrix in the open shell theory

All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.     

The matrix theory of electron spin multiplets for atoms and molecules

In this article a matrix method for the construction of spin multiplets (spinconfigurations) is suggested in order to solve the multielectron problem for atoms and mulecules by means of configuration interaction.A simple graphical way is given to enumerate configurations and to break their set into subsets of configurations related to the given projection of the total spin of a system S _z . It is found that all matrices in the theory of spin multiplets are convex and in cases of two, three, and four electrons are broken into blocks of an order no higher than 3.The model of the solution of the multielectron Schrödinger equation, in which the total spin of core electrons is zero, is considered. In this model the construction of linear combinations of configurations is reduced to the construction of those for but valence electrons.     

The final catalytic step of cytochrome p450 aromatase: a density functional theory study

B3LYP density functional theory calculations are used to unravel the mysterious third step of aromatase catalysis. The feasibility of mechanisms in which the reduced ferrous dioxygen intermediate mediates androgen aromatization is explored and determined to be unlikely. However, proton-assisted homolysis of the peroxo hemiacetal intermediate to produce P450 compound I and the C19 gem-diol likely proceeds with a low energetic barrier. Mechanisms for the aromatization and deformylation sequence which are initiated by 1beta-hydrogen atom abstraction by P450 compound I are considered. 1beta-Hydrogen atom abstraction from substrates in the presence of the 2,3-enol encounters strikingly low barriers (5.3-7.8 kcal/mol), whereas barriers for this same process rise to 17.0-27.1 kcal/mol in the keto tautomer. Transition states for 1beta-hydrogen atom abstraction from enolized substrates in the presence of the 19-gem-diol decayed directly to the experimentally observed products. If the C19 aldehyde remains unhydrated, aromatization occurs with concomitant decarbonylation and therefore does not support dehydration of the C19 aldehyde prior to the final catalytic step. On the doublet surface, the transition state connects to a potentially labile 1(10) dehydrogenated product, which may undergo rapid aromatization, as well as formic acid. Ab initio molecular dynamics confirmed that the 1beta-hydrogen atom abstraction and deformylation or decarbonylation occur in a nonsynchronous, coordinated manner. These calculations support a dehydrogenase behavior of aromatase in the final catalytic step, which can be summarized by 1beta-hydrogen atom abstraction followed by gem-diol deprotonation.     

The general scheme of using non-orthogonal radial orbitals in a complex electronic configuration of the atom

A theory for using non-orthogonal radial orbitals between shells with identical orbital quantum numbers, in the case of complex configurations, is presented. Construction of the antisymmetric wave function of the whole configuration, with the help of antisymmetrical wave functions of individual shells, is described. General methods of calculating matrix elements of one- and two-electron operators are given.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

Effect of the filler on the kinetics of transformation of triplet carbenes in a polymer matrix

The effect of the filler, Aerosil, on the kinetics of quenching of triplet cyclohexadiene carbenes at 100–140 K was detected in polymethyl methacrylate and cellulose triacetate. At a fixed temperature, the average rate constant of the process decreases by one to two orders of magnitude with an increase in the concentration of filler to 65 wt. %. The effect of the filler is due to modification of the physical structure of the polymer in passing into the state of a boundary layer whose thickness was estimated at 15–20 nm based on the kinetic data.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2453–2458, November, 1989.     

Modeling of the elementary step in the chemical transformation of crystals. I. Statement of the problem; description of the model

A model is proposed within the framework of activated-complex (AC) theory for analyzing the elementary chemical step (ECS) in the case of solid state reactions. By ECS is understood the synchronous restructuring (change in configuration, decomposition) of polyatomic structural units (SU) of the crystal or synchronous formation of new molecular groupings from poly- or monatomic SU. Simple physical observations lead to the conclusion that the ECS of solid state transformations does not have high molecularity. The mechanism which controls activation and deactivation is not directly considered. For activated SU that do not experience deactivation, it is suggested that interaction of these reacting SU with their surroundings in the crystal is constant throughout the course of the ECS. In conformity with this, an analysis of elementary steps of chemical transformation in crystals leads to an examination of the transformation of groupings composed of a small number of the SU of the crystal. A comparison of the ECS is carried out based on a comparison of the energies of activation (E_a) corresponding to the transformations. The E_a for various paths of transformation are evaluated by using the correlation diagram (CD) method. In a correlation analysis, experimental data for crystals should be used. Orbital symmetry and multiplicity of terms should be examined on the basis of specific quantum chemical analysis. The problem is formally reduced to a molecular one; however, the separable SU are bearers of properties of the crystal which are important for the ECS (enthalpy of formation, symmetry, electron composition, spectroscopic properties, etc.).     

One step in situ synthesis of Ag/AgCl nanoparticles in a cellulose nanofiber matrix for the development of energy storage paper

Cellulose - In the present work, we prepare Cellulose Nanofibers Films (CNFs) incorporating silver nanostructures (Ag/AgCl nanocubes) in a ratio of 1–20 wt% to the organic matrix. We found...     

The structure of the second-order reduced density matrix in density matrix functional theory and its construction from formal criteria

Some formal requirements for the second-order reduced density matrix are discussed in the context of density matrix functional theory. They serve as a basis for the ad hoc construction of the second-order reduced density matrix in terms of the first-order reduced density matrix and lead to implicit functionals where the occupation numbers of the natural orbitals are obtained as diagonal elements of an idempotent matrix the elements of which represent the variational parameters to be optimized. The numerical results obtained from a first realization of such an implicit density matrix functional give excellent agreement with the results of full configuration interaction calculations for four-electron systems like LiH and Be. Results for H2O taken as an example for a somewhat larger molecule are numerically less satisfactory but still give reasonable occupation numbers of the natural orbitals and indicate the capability of density matrix functional theory to cope with static electron correlation.     

Modified combinatorial factor in the hole theory

To describe the behavior of liquid state by hole theory, Flory's combinatorial factor used in the partition function of the hole theory is modified in a general form by assuming that unit segment of chain molecule can occupy more than one unit cell or lattice. From this combinatorial factor and free volume expression, a new equation of state is derived, and is used to calculate the PVT behaviors of 10 pure low molecular weight liquid systems. In addition, the PVT behavior of carbontetrachloride/cyclohexane binary system is calculated. Good agreements between the theory and experimental data are obtained.