Effect of structural relaxation on the binding energy in a molecular complex. The role of relaxation in the formation of intermediate for nucleophilic reactions of carbonyl compounds

The problem of a change in the geometry of interacting molecules, based on harmonic approximation, is considered here, to describe the effect of structural relaxation in the formation of a molecular complex on the binding energy. The correlation between the relaxation and deformation energies found earlier was analyzed with the use of an harmonic model of a molecular complex. To verify the correlation, calculations on the molecular complexes of different kinds were carried out using ab initio and semiempirical AM1 quantum chemical methods. The effect of structural relaxation on the properties of the potential energy surface for reactions of nucleophilic addition to carbonyl compounds is discussed.     

Simulation of molecular and electronic structure of polyhydrogenated (n,0)-tubulenes and their analogs intercalated with lithium

Molecular and electronic structure of four polyhydrogenated (n,0)-tubulenes, namely, [−C₂₄H₄−] _m (1), two isomers of composition [−C₂₈H₄−] _m (2 and3), and [−C₃₂H₄−] _m (4) withn benzene rings in the cross section (n=6, 7, 7, and 8, respectively), was simulated atm>1 (m is the number of repeating fragemnts). It was assumed that hydrogen atoms are attached to all carbon atoms lying on the two most distant elements of the cylinders of the corresponding tubulenes. The energy band structures of macromolecules1–4 and their Li-intercalated analogs [−C₂₄H₄Li−] _m (5) [−C₂₈H₄Li−] _m (two isomers,6 and7), and [−C₃₂H₄Li−] _m (8), containing one Li atom per repeating unit at each center, were obtained in the EHT approximation by the crystal orbital method. Geometric parameters of repeating units of structures1–8 were found after MNDO/PM3 optimization of the energies of hydrocarbon molecules C₇₂H₂₄, C₈₄H₂₆ (two geometric isomers), and C₉₆H₂₈, containing three repeating units of corresponding tubulenes1–4 each. The conductivity types of polyhydrogenated tubulenes1–4 are the same as those of their precursors, (6,0)-, (7,0)-, and (8,0)-tubulenes. Dispersion curves of systems5–8 are much the same as those of macromolecules1–4; however, electron energy spectra of5–8 possess metallic conductivity type and the positions of Fermi levels for these systems are higher than for compounds1–4. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2061–2067, November, 1999.     

Electron energy level crossings in the time-dependent Born-Oppenheimer approximation

Summary We summarize the results of a mathematical study of the time-dependent Born-Oppenheimer approximation near crossings of two non-degenerate electron energy surfaces. We illustrate our techniques by relatively simple examples that contain the essential ingredients of the general cases. We discuss all generic types of crossings of two non-degenerate electron energy surfaces.Supported in part by the National Science Foundation under Grant number DMS-8801360     

Propagation of a pre-existing turbulent fluid fracture

The propagation of rough and smooth wall pre-existing turbulent fluid fractures is investigated. The laminar fluid fracture is included as a special case for comparison. Lubrication theory is assumed to apply in the fracture and turbulence is introduced through the wall shear stress. The Perkins–Kern–Nordgren approximation is made in which the fluid pressure is proportional to the half-width of the fracture. The fracture half-width satisfies a non-linear diffusion equation. By using a linear combination of the Lie point symmetries of the non-linear diffusion equation a group invariant solution for the fracture length, volume and half-width is derived. The evolution of the length, half-width and mean flow velocity is analysed for a range of working conditions at the fracture entry. It is found that the mean flow velocity increases approximately linearly along the fracture.     

Many-body and quantum effects in the surface tension and surface energy of liquid neon and argon using the Fowler’s approximation

The Fowler’s expression for calculation of the reduced surface tension and surface energy has been used with Lennard-Jones (LJ) and two-body Hartree-Fock dispersion (HFD)-like potentials for neon and argon, respectively. The required radial distribution functions (RDFs) have been used from two recently determined expressions in the literature and a new equation proposed in this work. Quantum corrections for neon system have been considered using the Feynman-Hibbs (FH) and Wigner-Kirkwood (WK) approaches. To take many-body forces into account for argon system, the simple three-body potentials of Wang and Sadus (2006) [33] and Hauschild and Prausnitz (1993) [30] used with the HFD-like potential without requiring an expensive three-body calculation. The results show that the quantum and three-body effects improve the prediction of the surface tension of liquid neon and argon using the Fowler’s expression.     

Long-time simulation of a highly oscillatory Vlasov equation with an exponential integrator

We change a previous time-stepping algorithm for solving a multi-scale Vlasov–Poisson system within a Particle-In-Cell method, in order to perform accurate long-time simulations. As an exponential integrator, the new scheme allows us to use large time steps compared to the size of the oscillations in the solution.