Left–right and dynamic correlation

Within density functional theory, it is natural to separate the correlation energy into two parts: left–right correlation and dynamic correlation. Left–right correlation arises from the exchange part of functionals, and dynamic correlation arises from the correlation part of functionals. We examine the nature of these correlation energies as molecules are distorted. We observe that such a natural separation is not possible using the methods of quantum chemistry. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Highly efficient synthesis of triazolo[1,2-a]indazole-triones and novel spiro triazolo[1,2-a]indazole-tetraones under solvent-free conditions

A new, convenient, and high yielding procedure for the synthesis of triazolo[1,2-a]indazole-triones by the condensation reaction between dimedone, aryl aldehydes, and ueazoles in the presence of a catalytic amount of sulfonated polyethylene glycol (PEG-SO₃H) as a highly stable and reusable eco-friendly degradable polymeric catalyst is described under solvent-free conditions. This procedure has also been applied successfully for the synthesis of novel spiro triazolo[1,2-a]indazole-tetraones.     

Upper and Lower Bound States for Zero Dimensional Space in Scalar Quantum Field Theory

International Journal of Theoretical Physics - The varational method with the Hamiltonian formalism of quantum field theory (QFT) is used to study the bound state for scalar particle and...     

Four-Body Bound-States Systems in Relativistic Scalar Quantum Field Theory: Variational Basis-State Approach

The variational method within the Hamiltonian formalism of quantum field theory has been used in order to investigate the effect of virtual pairs for four-body scalar systems consisting of two particles and two antiparticles of the same mass. The scalar particles and antiparticles interact via a massive or massless mediating scalar field. The ground state energy solutions of Fock-space variational trial states (\(|N{\bar {N}}N{\bar {N}}{ \rangle }+|N{\bar {N}}N{\bar {N}}N{\bar {N}\rangle }\)) of the relativistic wave equations have been studied. We have compared these results with the previous work of four-body system (variational trial states of the form \(|N{ \bar {N}}N{\bar {N}}{\rangle }\)) and we have shown that the inclusion of virtual pairs has a noticeable effect at low coupling and at high coupling the energy of the system is changed by an important amount. In other words, the calculations show that the inclusion of virtual pairs augments the binding energy of the four-body system by a substantial amount at strong coupling. This study can pave the way for some new ideas in order to investigate the effect of virtual pairs, for example, for a bound-states quark-antiquark or tetraquark systems in future.     

Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition

In this work the combined finite difference and spectral methods have been proposed for the numerical solution of the one‐dimensional wave equation with an integral condition. The time variable is approximated using a finite difference scheme. But the spectral method is employed for discretizing the space variable. The main idea behind this approach is that we can get high‐order results. The new method is used for two test problems and the numerical results are obtained to support our theoretical expectations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Kinetic investigation of aquation of some Fe(II) Schiff base amino acid complexes

Kinetics of aquation of some Fe(II) Schiff base amino acid complexes was followed spectrophotometrically. The Schiff base ligands were derived from salicylaldehyde and isoleucine, leucine, serine, methionine, tryptophan, or histidine. The reaction was studied in aqueous media, aqua–propanol mixtures, and in the presence of different concentrations of KBr. Moreover, the activation parameters were calculated and discussed for structures and other physical properties observed. The reaction was acid catalyzed and the general rate equation was suggested as follows: rate = k_obs [complex], where k_obs = k₂ [H⁺]. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 372–379, 2010