Nonempirical Quantum-Chemical Calculations of the Structure and Conformations of the 2,2-Dichloroethanal Molecule in the Lowest Excited Singlet State

The structure of the 2,2-dichloroethanal molecule (CHC_l2CHO) in the lowest excited singlet state was calculated by the nonempirical multiconfigurational self-consistent field method. The electron transition of CHC_l2CHO from the ground to lowest excited singlet state is accompanied by rotation of the CHC₁₂ group, and the carbonyl fragment becomes nonplanar. The potential energy surface for the excited CHCl₂CHO molecule contains six minima corresponding to three pairs of enantiomers. This surface was used to solve torsion and inversion motion problems in the one-dimensional approximation and also two-dimensional torsion-inversion problem. Comparison of the results showed a relation between torsion and inversion motions.     

A quantum-chemical study of the structure and conformational dynamics of the acrolein molecule in the ground electronic state

The geometric parameters (including vibrationally averaged parameters), energy differences (ΔE) between the s-cis and s-trans conformers, and barrier to internal rotation (V _t ) were calculated for the acrolein molecule CH₂=CHCHO by various quantum-chemical methods (MP2, DFT, CASSCF, QCISD, CCSD(T), and MR-AQCC). The MP2 and B3LYP methods were used to calculate internal rotation potential functions and vibrational frequencies; the calculations were performed in various anharmonic approximations. To refine the ΔE and V _t values, two-dimensional (using a basis set of atomic orbitals) VFPA extrapolation procedure was applied, which allowed the results to be estimated in the FCI/CBS approximation taking into account nonadiabaticity, core correlation effects, and changes in the difference between zero point energies.     

Computation of discontinuous solutions of fluid dynamics equations with entropy nondecrease guarantee

A new formulation of the Godunov scheme with linear Riemann problems is proposed that guarantees a nondecrease in entropy. The new version of the method is described for the simplest example of one-dimensional gas dynamics in Lagrangian coordinates.     

Thermodynamic formalization of the fluid dynamics equations for a charged dielectric in an electromagnetic field

Minkowski??s classical work underlying modern electrodynamics is described. Primary attention is given to the mathematical refinements that are required if the parameters ? and ?? depend on the properties of the dielectric fluid, i.e., the medium carrying charges in the field under study. It is shown that the motion of the medium and the accompanying evolution of the electromagnetic field are described by differential equations that are symmetric and hyperbolic in the sense of Friedrichs. This property guarantees their well-posedness. Note that this class of equations was not known in Minkowski??s time. At present, it plays an important role in the mathematical simulation of nonstationary processes and in the design of numerical algorithms. The author??s view of the mathematical foundations of Minkowski??s work is presented, which relates the latter to present-day insights into the theory of differential equations. This paper can possibly be of interest to physicists.     

Neutrino oscillations in the general spherically symmetric gravitational field

The results for neutrino oscillations in the gravitational field described by the Schwarzschild metric are generalized to the general spherically symmetric gravitational field.     

Hausdorff sets of matrices and an estimate for the angle between invariant subspaces

The research was financially supported by the Russian Foundation for Fundamental Research (Grant 93-01-01515).     

Experimental analysis of convergence of the numerical solution to a generalized solution in fluid dynamics

Convergence of the approximate solution of fluid dynamics problems obtained using Godunov’s scheme to the discontinuous solution is investigated.     

Double Higgs production at LHC,see-saw type-II and Georgi-Machacek model

Journal of Experimental and Theoretical Physics - The double Higgs production in the models with isospin-triplet scalars is studied. It is shown that in the see-saw type-II model, the mode with an...     

On the difference approximations of overdetermined hyperbolic equations of classical mathematical physics

Issues concerning difference approximations of overdetermined systems of hyperbolic equations are examined. The formulations of extended overdetermined systems are given for hydrodynamics equations, magnetohydrodynamics equations, Maxwell equations, and elasticity equations. Some approaches to the construction of difference schemes are discussed for these systems.     

Singular numbers of a boundary-value problem on the halfline for a linear system of ordinary differential equations

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 4, pp. 5–12, July–August, 1989.