Exact solution of Schrödinger equation for Pseudoharmonic potential

Exact solution of Schr?dinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov–Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of ℓ and n with n ≤ 5 for some diatomic molecules.      

Molecular and crystal structure of 2-{(<Emphasis Type="Italic">E</Emphasis>)-[(4-Methylphenyl)imino]methyl}-4-nitrophenol: A redetermination

The crystal structure of the title compound, C₁₄H₁₂N₂O₃, was recently determined as a mixture of its neutral (OH containing) and zwitterionic (NH containing) forms, in a 0.60 (4): 0.40 (4) ratio using the X-ray determination. In this study, the title compound has been characterized by FT-IR and X-ray diffraction. The redetermination showed that the title compound has only enol (OH) form because of lack of the NH stretching vibration in FT-IR spectrum. In addition, the molecular structure and tautomerism of the title compound have been discussed.     

Probabilistic evolution theory for the solution of explicit autonomous ordinary differential equations: squarified telescope matrices

Probabilistic evolution theory (PREVTH) is used for the solution of initial value problems of first order explicit autonomous ordinary differential equation sets with second degree multinomial right hand side functions. It is an approximation method based on Kronecker power series: a rewriting of multivariate Taylor series using matrices having certain flexible parameters. Kronecker power series have matrices which are called telescope matrices: \(n \times n^{j+1}\) matrices where j is the index of summation. The additive terms of each telescope matrix is formed through Kronecker product from both sides by Kronecker powers of identity matrices. Recently, squarification is proposed in order to avoid the growing of the matrices in size at each additive term of the series. This paper explains the squarification procedure: the procedure used in order to avoid Kronecker multiplications within PREVTH so that the sizes of the matrices do not grow and so that the amount of necessary computation is reduced. The recursion between squarified matrices is also given. As a numerical application, the solution of a Hénon–Heiles system is provided.     

Efficient global optimization of reactive force‐field parameters

Reactive force fields make low‐cost simulations of chemical reactions possible. However, optimizing them for a given chemical system is difficult and time‐consuming. We present a high‐performance implementation of global force‐field parameter optimization, which delivers parameter sets of the same quality with much less effort and in far less time than before, and also offers excellent parallel scaling. We demonstrate these features with example applications targeting the ReaxFF force field. © 2015 Wiley Periodicals, Inc.     

Fermionic approach to soliton equations

In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the τ-function for charged free fermions in terms of determinants. Examples of how to get soliton, rational and dromion solutions from τ-functions for the various soliton equations are given.     

On asymptotically equivalent difference sequences with respect to a modulus function

This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence and Δ ^m -lacunary strongly summable with respect to a modulus f. Using this definitions we have proved the (f, Δ ^m )-asymptotically equivalence and Δ ^m -lacunary statistical asymptotically equivalence analogues of theorems of Tripathy and Et (Stud Univ Babe?-Bolyai Math (1):119–130, 2005) and Çolak’s theorems (Filomat 17:9–14, 2003).     

Combined experimental and computational modeling studies on 4‐[(2‐hydroxy‐3‐methylbenzylidene) amino]‐1,5‐dimethyl‐2‐phenyl‐1,2‐dihydro‐3H‐pyrazol‐3‐one

The Schiff base compound, 4‐[(2‐hydroxy‐3‐methylbenzylidene)amino]‐1,5‐dimethyl‐2‐phenyl‐1,2‐dihydro‐3H‐pyrazol‐3‐one, has been synthesized and characterized by IR, UV–vis, and X‐ray single‐crystal determination. Molecular geometry from X‐ray experiment of the title compound in the ground state have been compared using the density functional method (B3LYP) with 6‐31G(d,p) basis set. Calculated results show that density functional theory (DFT) can well reproduce the structure of the title compound. The energetic behavior of the title compound in solvent media has been examined using B3LYP method with the 6‐31G(d,p) basis set by applying the Onsager and the polarizable continuum model (PCM). The results obtained with these methods reveal that the PCM method provided more stable structure than Onsager's method. By using TD‐DFT method, electronic absorption spectra of the title compound have been predicted and a good agreement with the TD‐DFT method and the experimental one is determined. The predicted nonlinear optical properties of the title compound are much greater than ones of urea. In addition, DFT calculations of the title compound, molecular electrostatic potential and NBO analysis were performed at B3LYP/6‐31G(d,p) level of theory. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A novel one-pot, three-component reaction for the synthesis of isocoumarin-condensed pyrazoles

The one-pot, three-component reaction of substituted homophthalic anhydrides with hydrazine in DMF as solvent and reactant, at reflux temperature, afforded isochromeno[3,4-c]pyrazole-5(2H)-one derivatives in high yields. The mechanism and roles of the substrates were investigated and it was found that cyclic hydrazides were formed as intermediates.     

Fluctuation free multivariate integration based logarithmic HDMR in multivariate function representation

This paper focuses on the Logarithmic High Dimensional Model Representation (Logarithmic HDMR) method which is a divide–and–conquer algorithm developed for multivariate function representation in terms of less-variate functions to reduce both the mathematical and the computational complexities. The main purpose of this work is to bypass the evaluation of N–tuple integrations appearing in Logarithmic HDMR by using the features of a new theorem named as Fluctuationlessness Approximation Theorem. This theorem can be used to evaluate the complicated integral structures of any scientific problem whose values can not be easily obtained analytically and it brings an approximation to the values of these integrals with the help of the matrix representation of functions. The Fluctuation Free Multivariate Integration Based Logarithmic HDMR method gives us the ability of reducing the complexity of the scientific problems of chemistry, physics, mathematics and engineering. A number of numerical implementations are also given at the end of the paper to show the performance of this new method.