Some Integrals for Molecular Properties and Relativistic Effects over Hermite-Gaussian Functions

Formulas for some integrals over Hermite-Gaussian functions occurring in the calculations of the molecular first and second order properties as well as relativistic corrections arising in the Breit hamiltonian are discussed. It is shown that all these molecular properties integrals can be reduced to the integrals already encountered in the minimum energy calculations. More specifically, the one-electron and two-electron integrals involving (l/r1 j)" operator, where j denotes either the coordinates of a nucleus or the coordinates of the electron 2 and n is an integer, are expressed in terms of nuclear attraction and Coulomb repulsion integrals, respectively. Therefore the electric and magnetic properties of molecules can be computed with little additional effort if the Hermite-Gaussian basis set is employed. The same conclusion holds for the matrix elements arising in the pseudo-potential calculations involving the Bonifacic- Huzinaga model potential which in turn give a fair description of the heavy atoms inner-shell electrons. Since the Hermite- Gaussian functions are particularly advantageous for atomic orbitals with higher angular momentum quantum numbers (f, g, h etc.) their use is expected to be preferable in molecules involving heavy atoms. The relativistic effects are of great importance for the latter and it is gratifying that the corresponding integrals over Hermite-Gaussians can be expressed in a closed form

Hermite-Gaussian Expansion of Hydrogenic Orbitals

Hydrogen ls, 2s, 2p, 3s, 3p, 3d, 4s, 4p and 4d (HO) orbitals are expanded in series of Hermite-Gaussian (HG) functions. Adjustable parameters are determined by the integral least-square fit procedure. HG approximation of the fourth degree (HG4) proved particularly good and useful in representing hydrogen AOs. It yields hydrogen (and hydrogen-Iike) orbitals which are more accurately described than the corresponding GTO expansion. Hydrogen type orbitals (HTO) expressed in HG4 bases could be useful in molecular calculations involving heavier atoms because some STO orbi ta ls do not perform well for higher principal quantum numbers. Use of STOs for inner-shells and HOs for outer valence shell electrons in heavy atoms might be advantageous. Both types of atomic orbitals could be well represented by HG functions. HG representation of polarization functions, which play an important role in describing charge redistribution upon formation of chemical bonds and are crucial in treating anions, might be useful too. The HG functions may also serve a purpose in solving the Schrodinger equation in momentum representation and in calculations of the X-ray scattering factors

GRB 081024B and GRB 140402A: two additional short GRBs from binary neutron star mergers

Theoretical and observational evidences have been recently gained for a two-fold classification of short bursts: 1) short gamma-ray flashes (S-GRFs), with isotropic energy $E_{iso}<10^{52}$~erg and no BH formation, and 2) the authentic short gamma-ray bursts (S-GRBs), with isotropic energy $E_{iso}>10^{52}$~erg evidencing a BH formation in the binary neutron star merging process. The signature for the BH formation consists in the on-set of the high energy ($0.1$--$100$~GeV) emission, coeval to the prompt emission, in all S-GRBs. No GeV emission is expected nor observed in the S-GRFs. In this paper we present two additional S-GRBs, GRB 081024B and GRB 140402A, following the already identified S-GRBs, i.e., GRB 090227B, GRB 090510 and GRB 140619B. We also return on the absence of the GeV emission of the S-GRB 090227B, at an angle of $71^{\rm{o}}$ from the \textit{Fermi}-LAT boresight. All the correctly identified S-GRBs correlate to the high energy emission, implying no significant presence of beaming in the GeV emission. The existence of a common power-law behavior in the GeV luminosities, following the BH formation, when measured in the source rest-frame, points to a commonality in the mass and spin of the newly-formed BH in all S-GRBs.Comment: 16 pages, submitted to ApJ, second version addressing the comments by the refere

The microscopic structure of cold aqueous methanol mixtures

The evolution of the micro-segregated structure of aqueous methanol mixtures, in the temperature range 300 K-120 K, is studied with computer simulations, from the static structural point of view. The structural heterogeneity of water is reinforced at lower temperatures, as witnessed by a pre-peak in the oxygen-oxygen structure factor. Water tends to form predominantly chain-like clusters at lower temperatures and smaller concentrations. Methanol domains have essentially the same chain-like cluster structure as the pure liquid at high concentrations and becomes mono- meric at smaller ones. Concentration uctuations decrease with temperature, leading to quasi-ideal Kirkwood-Bu integrals, despite the enhanced molecular interactions, which we interpret as the signature of non-interacting segregated water and methanol clusters. This study throws a new light on the nature of the micro-heterogeneous structure of this mixture: the domain segregation is essentially based on the appearance of linear water clusters, unlike other alcohol aqueous mixtures, such as with propanol or butanol, where the water domains are more bulky.

Hermite-Gaussian Expansion of Hydrogenic Orbitals

Hydrogen ls, 2s, 2p, 3s, 3p, 3d, 4s, 4p and 4d (HO) orbitals are expanded in series of Hermite-Gaussian (HG) functions. Adjustable parameters are determined by the integral least-square fit procedure. HG approximation of the fourth degree (HG4) proved particularly good and useful in representing hydrogen AOs. It yields hydrogen (and hydrogen-Iike) orbitals which are more accurately described than the corresponding GTO expansion. Hydrogen type orbitals (HTO) expressed in HG4 bases could be useful in molecular calculations involving heavier atoms because some STO orbi ta ls do not perform well for higher principal quantum numbers. Use of STOs for inner-shells and HOs for outer valence shell electrons in heavy atoms might be advantageous. Both types of atomic orbitals could be well represented by HG functions. HG representation of polarization functions, which play an important role in describing charge redistribution upon formation of chemical bonds and are crucial in treating anions, might be useful too. The HG functions may also serve a purpose in solving the Schrodinger equation in momentum representation and in calculations of the X-ray scattering factors

Comparison of three methods of DNA extraction from human bones with different degrees of degradation

There is a necessity for deceased identification as a result of many accidents and sometimes bones are the only accessible source of DNA. So far, a universal method that allows for extraction of DNA from materials at different stages of degradation does not exist. The aims of this study were: the comparison of three methods of DNA extraction from bones with different degree of degradation and an evaluation of the usefulness of these methods in forensic genetics. The efficiency of DNA extraction, the degree of extract contamination by polymerase chain reaction (PCR) inhibitors and the possibility of determining the STR loci profile were especially being compared. Nuclear DNA from bones at different states of degradation was isolated using three methods: classical, organic phenol–chloroform extraction, DNA extraction from crystal aggregates and extraction by total demineralisation. Total demineralisation is the best method for most cases of DNA extraction from bones, although it does not provide pure DNA. DNA extraction from aggregates removes inhibitors much better and is also a good method of choice when identity determination of exhumed remains is necessary. In the case of not buried bones (remains found outside) total demineralisation or phenol–chloroform protocols are more efficient for successful DNA extraction