Journal of Mathematical Chemistry最新文献

In recent years, oxide-based nano clusters have shown some significant applications in medical sciences, bio sensing, catalysis, and energy storage. Here we have reported the computational study of oxide-based nano clusters X₃O₄ (X = Ti, Fe, Zn) by means of Conceptual Density Functional Theory (CDFT) method. Geometry optimization and frequency computation of these clusters are carried out using the functional B3LYP/LANL2DZ in the DFT framework. Highest Occupied Molecular Orbital (HOMO)–Lowest Unoccupied Molecular Orbital (LUMO) of the clusters are found between 2.019 and 3.570 eV. The global CDFT descriptors viz. hardness, softness, electronegativity, electrophiliicty index and dipole moment are calculated. Result shows that Zn₃O₄ has the maximum stability whereas Fe₃O₄ is highly reactive in nature. Electronegatiivty and electrophilicity index of these clusters decrease from Fe₃O₄ to Zn₃O₄ to Ti₃O₄. Analyses are conducted for the optical characteristics of X₃O₄ nano clusters, comprising their refractive index, dielectric constant, optical electronegativity and IR activity. Refractive index, dielectric constant and range of harmonic frequency increase from Zn₃O₄ to Fe₃O₄ via Ti₃O₄. The estimated bond length, HOMO–LUMO energy gap, refractive index and IR activity of the nano clusters are in agreement with the reported experimental and theoretical results. The physico-chemical properties of X₃O₄ nano clusters indicate their potential applications in biomedical sciences especialy for the treatment of cancer cells.

In this article, we introduce a novel concept called Generalized Transmission Neighbor Indices, building upon established transmission indices. The primary focus is on two variants of these indices, denoted as (TN^1_{(a,b)}(G)) and (TN^2_{(a,b)}(G)), which offer distinct insights into graph connectivity. The first index, (TN^1_{(a,b)}(G)), quantifies the sum of powered vertex neighbor transmissions for connected vertices, while the second, (TN^2_{(a,b)}(G)), calculates the product of powered vertex neighbor transmissions among connected vertices. Our investigation delves into the diverse values of parameters a and b, shedding light on the relationships between these indices and established transmission neighbor-based metrics. Bounds have been computed, and we have also explored the chemical relevance (Quantitative Structure–Property Relationship) in the context of linear monocarboxylic acids.

Laws of physical chemistry such as quantum mechanics, laws of chemical kinetics, and thermodynamics have been employed as a potential tool to generate some converging sum rules. Special emphasis has been given to Rayleigh–Schrödinger perturbation theory and the use of delta function potential to generate a number of sum rules.

The Gray-Scott system describes one of the crucial components of the reaction-diffusion system. Its mathematical model has a couple of non-linear partial differential equations that are challenging to solve numerically. The present study is concerned with the numerical solution of the time-fractional Gray-Scott model in arbitrary-shaped domains utilizing the finite difference approximation and radial basis functions (RBFs) based collocation method for time and space directions, respectively. The patterns are created in the domains that denote the leftover chemical component concentrations at a specific time in the system. We also witness the effects of the time-fractional order ((alpha )) and diffusion constants ((K_u) and (K_v)) on the model. This study asserts that chemical reactions between two substances manifest chaotic and unpredictable behavior. Investigating the influence of time-fractional order introduces an intriguing avenue for exploring novel patterns and behaviors within this context. Furthermore, the proposed algorithm can be used to solve the model and generate novel patterns by altering the parameter values or geometric configurations in any space dimension.

In mathematical chemistry, a chemical reaction is represented as a transformation of one molecular ensemble into another one, and information entropy is used for quantitative describing changes in the molecular complexity. The information entropy of a chemical reaction is the difference between the values of the ensembles of products and reagents. As is known, the information entropy of molecular ensemble depends on the information entropies of individual molecules and, additionally, on the cooperative entropy, an emergent parameter that reflects uniting the molecules into the ensemble. Accounting this parameter determines the peculiarities of calculating the information entropy for interdependent chemical reactions. In the present study, we have derived a general formula that connects the information entropy of the complex chemical process with the parameters of its elementary stages and demonstrated its work on typical examples of successive, parallel, and conjugated chemical reactions. Notably, the view of the derived formula differs from the equations used when Hess’ law is applied to the thermodynamic parameters of interdependent reactions. The only case when the Hess’ law has the same analytical expression for both information-entropy and thermodynamic parameters is the isomegethic set of chemical reactions, viz. the system of the successive reactions, in which the size of the molecular ensemble remains constant.

Quantitative Structure Activity Relationship (QSAR) requires the use of chemical descriptors which are either empirical or non-empirical. Although the ease of computation of computationally derived parameters such as given by ChemDraw software like CAA, CMA, CSEV and Dragon parameters like Au, Nc, Vs, TIC3, ATS2p etc. are easier to be used in the QSAR studies, but they still lack the biological interpretation as no prior knowledge of their physicochemical significance and their interrelationship is available. Therefore, the QSAR models developed using such parameters may be useful only in prediction of activity but are meaningless in terms of understanding the mode of action of the bioactive molecules. Thus, to fulfil this knowledge gap, and in continuation of our earlier work on physicochemical significance of topological parameters this study has been attempted to understand the empiricism of such computationally derived parameters in terms of their physicochemical significance. Here, we report that most of the ChemDraw and Dragon computed parameters are also best correlated with MR similar to topological parameters.

We provide a (strong) inductive proof of Borchardt’s theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability.

In order to get rid of the phase-lag and its first, second, third, fourth, and fifth derivatives, a phase-fitting method might be applied. The new strategy, called the economical method, maximizes algebraic order (AOR) while minimizing function evaluations (FEvs). Equation PF5DPFN142SPS describes the unique method. An infinitely periodic P-Stable technique is suggested. The proposed method is applicable to numerous problems with periodic and/or oscillatory solutions. In quantum chemistry, this novel approach was used to address the challenging problem of Schrödinger-type coupled differential equations. It is an economic algorithm because each step of the new method only costs 5FEvs to carry out. This helps us to improve our existing condition significantly by achieving an AOR of 14.

Sulfur dioxide (SO₂) belongs to the highly reactive group of gases familiar as “Oxides of Sulfur”. SO₂ has lots of adverse effects on plants, respiratory system and many other environmental issues. Sulfur dioxide is a primary pollutant which is regulated worldwide, due to the combustion of fuel. Different approaches are adopted to economically control the SO₂ in the environment which causes the production of sulfuric acid that is reflected in acid rain. The aim of this study is to investigate the invariant regions and solution pathways for the formation of H₂SO₄ in a multi-step reaction mechanism. The employed Model Reduction Techniques (MRTs) such as Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM) give the solution curves, which functions as a primary approximation to invariant manifold. It is achieved that each chemical specie can be assessed rather than taking the overall mechanism. The new discovery suggests that we could achieve the invariant regions for SO₂ and H₂SO₄. SO₂ emissions, along with emission norms, will be disclosed. The comparison of MRTs is depicted through tabular and graphical representations, while theoretical results are demonstrated through computer simulations using MATLAB.

We provide a mathematical justification of a spectral approximation scheme known as spectral binning for the Kohn–Sham spin density-functional theory in the presence of an external (nonuniform) magnetic field and a collinear exchange-correlation energy term. We use an extended density-only formulation for modeling the magnetic system. No current densities enter the description in this formulation, but the particle density is split into different spin components. By restricting the exchange-correlation energy functional to be of a collinear LSDA form, we prove a series of results which enable us to mathematically justify the spectral binning scheme using the method of Gamma-convergence, in conjunction with auxiliary steps involving recasting the electrostatic potentials, justifying the spectral approximation by making a spectral decomposition of the Hamiltonian and “linearizing" the latter Hamiltonian.