Lie and Noether symmetries of geodesic equations and collineations

The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.Comment: 19 page

The mechanism of reactions of phosphorus-containing molecules with chloral: Density functional theory calculations

The most probable mechanisms of bimolecular interactions between a complex heterocyclic salicylic acid derivative, "phosphite," and chloral were for the first time studied by the density functional theory method. It was found theoretically that the reaction could develop in three different channels, (a) with six-membered heteroring opening and the formation of a seven-membered product and (b, c) as a Perkov-type reaction leading to (b) acyclic or (c) cyclic vinyl phosphates. The structures of the reagents, products, intermediates, and transition states were calculated with complete geometry optimization. All stationary points were identified by calculations of force constant matrices. For all transition states, intrinsic reaction coordinates were calculated. A comparison with the experimental data was performed. © 2008 Pleiades Publishing, Ltd

Dynamic intramolecular rearrangements with proton transfer in methanimine oxide

The structures of possible intermediates and transition states on the potential energy surface for the isomerization of methanimine oxide into formamide were determined by UHF/6-311G(3d) quantum-chemical calculations. Two possible reaction channels were revealed. The same processes were studied by the direct molecular mechanics method which also revealed two reaction channels. The time range of the examined dynamic processes was estimated at 90-300 fs

Diagrams of isoshielding lines of C-N bonds and nitrogen and phosphorus lone pairs

Diagrams of isoshielding lines in the vicinity of lone pairs of nitrogen and phosphorus atoms, as well as a C-N bond, have been calculated. The magnetic shielding constants of the protons were calculated by the gauge-invariant atomic-orbital method with the use of localized molecular orbitals and expansions of the atomic wave functions in Gaussian functions. The diagrams of the isoshielding lines have been used for the evaluation of chemical shifts in piperidine derivatives for the purpose of accounting for the experimentally observed tendencies in chemical shifts. © 1986 Plenum Publishing Corporation

Calculations of magnetic susceptibility of some molecules by the variational method using ab initio wave functions

Calculations of magnetic susceptibility were carried out for H2O, CH4 NH3, PH3 and H2S using the variational method with non-empiric wave functions. It was established that the results are weakly sensitive to the basis set. It was shown that the results are comparable with the more precise results obtained by the coupled Hartree-Fock (CHF) method and agree well with experimental data. It should be noted that requirements to gauge invariance are considerably lower than in the CHF method. © 1991

Calculation of nuclear magnetic shielding constants using variation-perturbation method with moderate size basis sets

Within a framework of variation-perturbation formalism of Karplus-Kolker, an algorithm and a program for the nuclear magnetic shielding calculations with ground-state wave functions were developed. The calculations of nuclear magnetic shielding σ in some diatomic molecules and also in methane, water and CH3F molecules with 6-311G ab initio wave functions were carried out. The results were compared with the experimental data and the results obtained by other theoretical methods. This method can be considered as an alternative approach for the calculations of the magnetic anisotropic effects on chemical shifts and can be used for predicting the tendencies in magnetic shielding alteration due to the different fragments in a big molecular systems. © 2001 Elsevier Science B.V. All rights reserved

Rearrangements and proton transfer in nitrones by quantum chemistry and molecular dynamics

The structures of intermediates and transition states in rearrangement reactions of nitrone to amide via oxaziridine were calculated at the unrestricted B3LYP level of theory using the 6-31G(d,p) basis set. The same processes were studied by the method of direct molecular dynamics. Both methods reveal two reaction channels from cyclic oxaziridine to amide. One is via the acyclic structure C(O)H2-NH with eclipsed N-H and C-O and then through the intermediate HC(OH)=NH to amide. The other channel, from oxaziridine, is via the structure C(O)H2-NH and then directly to the amide product. © 2002 Elsevier Science B.V. All rights reserved

Application of ESEEM to study the structure of free radicals

Manifestations of the hyperfine interaction of paramagnetic particles in their electron spin echo signal decay were comprehensively discussed. Mechanochemically activated calcium gluconate was studied using electron spin echo modulation phenomenon and electron-nuclear double resonance techniques and quantum-chemical calculations. Three possible structures are obtained for free radicals in calcium gluconate. To specify the structure of radicals, further investigations are needed. © 2008 Springer

Calculation of the structure and nuclear magnetic shielding constants of some H-bonded carbon acid complexes

Electronic and spatial structure of some H-bonded complexes ((HCOOH)(n) (n = 1-4), formic, acrylic acids and their complexes with water and dimethylsulfoxide) were studied by ab initio methods using MP2/RHF//6-31G*, RHF/6-31G* basis sets, and also by using density functional theory (DFT)within the B3LYP approximation. The possibility of formation of chain and cyclic complexes of formic and acrylic acids with dimethylsulfoxide is shown. In a cyclic complex two hydrogen bonds are formed. One is as usually with the O-H bond (S=O···H-O), the other is between the acid carbonyl group and one hydrogen atom of DMSO methyl groups (C-H···O=C). The calculations of nuclear magnetic shielding were carried out within a framework of the coupled Hartree-Fock method using gauge invariant atomic orbitals. Analysis of the results for various basis sets and comparison of the calculated and experimentally obtained chemical shifts show that the calculations predict a significant downfield shift for 1H and 13C nuclei for H-bonded systems. The results of calculations of 17O magnetic shielding constants strongly depend on the used basis set and theoretical approach. (C) 2000 Elsevier Science B. V