On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page

Accurate calculation of N1s and C1s core electron binding energies of substituted pyridines. Correlation with basicity and with Hammett substituent constants

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Substituent shifts of the energetics of four related ionization processes of pyridines and benzoic acids (Fig. I) were investigated. The first process is core-electron ionization of gas-phase pyridines (Fig. 1A), while the second concerns gas-phase acid-base reaction between a substituted pyridine and a Conjugated acid (Fig. 1B), and the third and fourth processes are the acid dissociation of substituted benzoic acids in aqueous solution (Fig. 1C and in vacuum (Fig. 1D), respectively. Core-electron binding energies for the first process Were Calculated using density-functional theory with the scheme Delta E-KS (PW86x-PW91c/TZP+C-ret)//HF/6-31G*. Average absolute deviation of calculated core electron binding energy shifts at N atom in Substituted pyridines from experiment was 0.08 eV. The shift at N coincides highly with that at a ring carbon atom. The four shifts corresponding to the four processes shown in Figs. 1A-D correlate strongly with one another. with numerical values fairly close to each other when expressed in unit of electron volts. (C) 2008 Elsevier B.V. All rights reserved.863416993338Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2007/58679-8)]CNPq [300467/2003-6