Journal of Physical and Theoretical Chemistry
Volume:12 Issue: 3, Autumn 2015

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalent to solving its related variational problem. The objective of this paper is to describe themajor direct methods that have been developed over the years for solving these types of problems. Inthis paper we focus on using orthogonal polynomials and triangular functions as basis functions. Eachmethod needs computing operational matrices and some other parameters which are presented aswell. Several numerical examples are then included to demonstrate the accuracy and applicability ofthe reviewed methods. Computational concerns are then discussed to provide a guideline to thepreferred and the most accurate method.

It is well known that the chemical behavior of a compound is dependent upon the structure of itsmolecules. Quantitative structure – activity relationship (QSAR) studies and quantitative structure –property relationship (QSPR) studies are active areas of chemical research that focus on the nature ofthis dependency. Topological indices are the numerical value associated with chemical constitutionpurporting for correlation of chemical structure with various physical properties, chemical reactivityor biological activity. Graph theory is a delightful playground for the exploration of proof techniquesin Discrete Mathematics and its results have applications in many areas of sciences. One of the usefulindices for examination of structure- property relationship is Randic' index. In this study isrepresented the relationship between the Randic', Balaban and Szeged indices and Harary numbers tothe octanol-water partition coefficient (logP) of monocarboxylic acids (C2- C20) are established, andthen, some useful topological indices for examination of the structure- property relationship arepresented.

The use of appropriate level of theories for studying weak van der Waal interactions such as 8-8stacking interactions of aromatic molecules has been an important aspect, since the high levelmethods have limitations for application to large molecules. The differences in the stacking energiesof various aromatic molecular structures are found significant. It is also very important for identifyingthe most favored stacked models of aniline and some of the p-substituted aniline molecules. Theeffect of basis set in the stacking energies of MP2 calculations is small. The values for HF and MP2level of theories calculate less electron correlation energy whereas CCSD (T) methods may be usedfor the calculation of better electron correlation energy. The moderately accurate calculations, MP2level of theories were found feasible for most of the simple aromatic systems such as benzene,pyridine, aniline etc. In our studies, it has been investigated by using MP2 and DFT methods, to studythe 8-8 stacking interaction energies for the minimized stacked models of aniline and some psubstitutedaniline systems.

The acidity constants (pKa) of thirty four (34) ;-substituted carboxylic acids in aqueous solution havebeen calculated using conductor-like polarizable continuum (C-PCM) solvation model. The gasphaseenergies at the Density Functional Theory (DFT-MPW1PW91) and solvation energies atHartree Fock (HF) are combined to estimate the pKa values which are very close to the experimentalvalues where, and the root-mean-square error (rmse) is less than 0.9. In addition, the pKa valuespredicted by Multilinear Regression (MLR), Principle Components Regression (PCR) and PartialLeast Square Regression (PLSR) methods showed an excellent correlation to the experimental valueswhere the root-mean-square error (rmse) decreases from 0.9 to 0.293, 0.326 and 0.319 respectively.Furthermore, the rmse of pKa values found less than 0.3 when the solvation models of some powerfulelectron withdrawing substituted acids are employed at the level of MPW1PW91 theory. Thecomputation by different regression methods showed reasonably a better calculation of pKa valuesthrough the lower root-mean-square errors (rmse).

In this study, the geometries of the [SiNinHn]q and [SiCunHn]q clusters, (n = 4,5,6 and q = 0,+1,-1) complexes have been optimized to form complexes with four, five and six planar and nonplanarsubstituents, with negative, neutral or positive atomic charge, using Density FunctionalTheory (DFT) at B3LYP/6-311+G (3df, p) computational level and then their thermodynamicstability were investigated by studying the obtained smallest vibrational frequencies andbinding energy.

A sensitive and selective solid phase extraction procedure for the determination of traces of Cd(II),Zn(II) and Ag(I) ions has been developed. An alumina-sodium dodecyl sulfate (SDS) coated on with2,3 Di Hydro 2,3 para tolyl Qinazoline (1 H)- 4 one (DPTQO). The influences of the analyticalparameters including pH and sample volume were investigated. Common coexisting ions did notinterfere on the separation and determination of analytes under study. The adsorbed analytes weredesorbed by using 6mL of 4 mol L1 nitric acid. The responses are linear 0.02–0.85 g mL-1 for Cd2+ion 0.01–0.90 g mL-1 for Zn2+ and 0.02–0.92 g mL-1for Ag+ detection limit for Cd(II), Zn(II) andAg(I) ions were found to be 1.4, 1.3 and1.12 (ng mL-1), respectively. It was found that the recoveryfor Cd2+, Zn2+and Ag+ ions were 97.7, 98.2 and 98.0 with RSD of 1.9, 1.8 and 1.7. It was alsoobserved that recovery for repeated recovery on the same solid phase not varies more than 3%. Thepresented procedure was successfully applied for determination of analytes in radiology wastewater,amalgam, natural water and blood samples.

The stacking mechanism of the 1H-4H proton transfer in 4-pyridone, 4-pyridinthione and p-aminopyridineare constructed. For quantitative description of this process by means of the quamtumchemicalmethod density functional theory (DFT) the activation energy (<E#), reaction energy (<E)and tautomeric equilibrium constant (KT) has been calculated. The results of calculations have shown,that the values of the energetical and kinetical characteristics, from the point of view of chemicalreactions, in reasonable limits varies, that allows one to make the conclusion in favour of competenceof the offered stacking mechanism for the 1H-4H proton transfer in pyridine derivatives. It is a newone-stage synchronous and unique mechanism for the 1H-4H proton transfer.