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Hess’ law requires modified mathematical rules for information entropy of interdependent chemical reactions 赫斯定律要求对相互依存的化学反应的信息熵数学规则进行修改
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-23 DOI: 10.1007/s10910-023-01566-5
Denis Sh. Sabirov, Alexandra D. Zimina, Alina A. Tukhbatullina
{"title":"Hess’ law requires modified mathematical rules for information entropy of interdependent chemical reactions","authors":"Denis Sh. Sabirov, Alexandra D. Zimina, Alina A. Tukhbatullina","doi":"10.1007/s10910-023-01566-5","DOIUrl":"https://doi.org/10.1007/s10910-023-01566-5","url":null,"abstract":"<p>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.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Physicochemical significance of ChemDraw and Dragon computed parameters: correlation studies in the sets with aliphatic and aromatic substituents ChemDraw 和 Dragon 计算参数的物理化学意义：脂肪族和芳香族取代基组的相关研究
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-18 DOI: 10.1007/s10910-023-01558-5
{"title":"Physicochemical significance of ChemDraw and Dragon computed parameters: correlation studies in the sets with aliphatic and aromatic substituents","authors":"","doi":"10.1007/s10910-023-01558-5","DOIUrl":"https://doi.org/10.1007/s10910-023-01558-5","url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inductive proof of Borchardt’s theorem 博尔哈特定理的归纳证明
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-10 DOI: 10.1007/s10910-023-01561-w
Andy A. Chavez, Alec P. Adam, Paul W. Ayers, Ramón Alain Miranda-Quintana
{"title":"Inductive proof of Borchardt’s theorem","authors":"Andy A. Chavez, Alec P. Adam, Paul W. Ayers, Ramón Alain Miranda-Quintana","doi":"10.1007/s10910-023-01561-w","DOIUrl":"https://doi.org/10.1007/s10910-023-01561-w","url":null,"abstract":"<p>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.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues 解决量子化学问题的极为有效且成本低廉的两步十四阶相位拟合方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-10 DOI: 10.1007/s10910-023-01560-x
Marina A. Medvedeva, T. E. Simos
{"title":"An exceedingly effective and inexpensive two-step, fourteenth-order phase-fitting method for solving quantum chemical issues","authors":"Marina A. Medvedeva, T. E. Simos","doi":"10.1007/s10910-023-01560-x","DOIUrl":"https://doi.org/10.1007/s10910-023-01560-x","url":null,"abstract":"<p>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 <b>economical method</b>, maximizes algebraic order (<i>AOR</i>) while minimizing function evaluations (<i>FEvs</i>). Equation <i>PF</i>5<i>DPFN</i>142<i>SPS</i> describes the unique method. An infinitely periodic <b>P-Stable</b> 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 <i>economic algorithm</i> because each step of the new method only costs 5<i>FEvs</i> to carry out. This helps us to improve our existing condition significantly by achieving an <i>AOR</i> of 14.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Slow invariant manifold assessment for efficient production of H2SO4 by SO2: a computational approach 利用二氧化硫高效生产 H2SO4 的慢速不变量流形评估：一种计算方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-10 DOI: 10.1007/s10910-023-01565-6
Shuguang Li, Faisal Sultan, Muhammad Yaseen, Muhammad Shahzad, El-Sayed M. Sherif
{"title":"Slow invariant manifold assessment for efficient production of H2SO4 by SO2: a computational approach","authors":"Shuguang Li, Faisal Sultan, Muhammad Yaseen, Muhammad Shahzad, El-Sayed M. Sherif","doi":"10.1007/s10910-023-01565-6","DOIUrl":"https://doi.org/10.1007/s10910-023-01565-6","url":null,"abstract":"<p>Sulfur dioxide (SO<sub>2</sub>) belongs to the highly reactive group of gases familiar as “Oxides of Sulfur”. SO<sub>2</sub> 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 SO<sub>2</sub> 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 H<sub>2</sub>SO<sub>4</sub> 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 SO<sub>2</sub> and H<sub>2</sub>SO<sub>4</sub>. SO<sub>2</sub> 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.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139423173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy 外部（非均匀）磁场和共线交换相关能下的混合自旋密度 Kohn-Sham 密度泛函理论的谱近似方案
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-08 DOI: 10.1007/s10910-023-01557-6
{"title":"Spectral approximation scheme for a hybrid, spin-density Kohn–Sham density-functional theory in an external (nonuniform) magnetic field and a collinear exchange-correlation energy","authors":"","doi":"10.1007/s10910-023-01557-6","DOIUrl":"https://doi.org/10.1007/s10910-023-01557-6","url":null,"abstract":"<h3>Abstract</h3> <p>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&quot; the latter Hamiltonian.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139412352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An implicit scheme for time-fractional coupled generalized Burgers’ equation 时间分数耦合广义布尔格斯方程的隐式方案
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-06 DOI: 10.1007/s10910-023-01559-4
J. Vigo-Aguiar, Reetika Chawla, Devendra Kumar, Tapas Mazumdar
{"title":"An implicit scheme for time-fractional coupled generalized Burgers’ equation","authors":"J. Vigo-Aguiar, Reetika Chawla, Devendra Kumar, Tapas Mazumdar","doi":"10.1007/s10910-023-01559-4","DOIUrl":"https://doi.org/10.1007/s10910-023-01559-4","url":null,"abstract":"<p>This article presents an efficient implicit spline-based numerical technique to solve the time-fractional generalized coupled Burgers’ equation. The time-fractional derivative is considered in the Caputo sense. The time discretization of the fractional derivative is discussed using the quadrature formula. The quasilinearization process is used to linearize this non-linear problem. In this work, the formulation of the numerical scheme is broadly discussed using cubic B-spline functions. The stability of the proposed method is proved theoretically through Von-Neumann analysis. The reliability and efficiency are demonstrated by numerical experiments that validate theoretical results via tables and plots.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139376642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An alternative approach to normalizing the Coulomb $$R_{n ell }(r)$$ radial solutions 对库仑 $$R_{n ell }(r)$$ 径向解进行归一化的另一种方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2024-01-04 DOI: 10.1007/s10910-023-01562-9
B. Cameron Reed, Gregory L. Bason
{"title":"An alternative approach to normalizing the Coulomb $$R_{n ell }(r)$$ radial solutions","authors":"B. Cameron Reed, Gregory L. Bason","doi":"10.1007/s10910-023-01562-9","DOIUrl":"https://doi.org/10.1007/s10910-023-01562-9","url":null,"abstract":"<p>The normalization of the radial functions <span>(R_{n ell }(r))</span> for the solution of Schrödinger’s equation for the Coulomb potential usually proceeds by appealing to the properties of Associated Laguerre polynomials. In this paper we show how to effect the normalization directly from the overall form of the solution and the recursion relation for its series part. Our approach should be applicable to similar problems, such as the harmonic oscillator, and can serve to offer students an alternate method of establishing fully-normalized wavefunctions without invoking the properties of special functions.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic 纯粹四分法和用概率演化理论求解常微分方程，同时用精确算术计算系数
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2023-12-30 DOI: 10.1007/s10910-023-01563-8
Coşar Gözükırmızı
{"title":"Pure quadratization and solution of ordinary differential equations by probabilistic evolution theory with concurrent computation of coefficients using exact arithmetic","authors":"Coşar Gözükırmızı","doi":"10.1007/s10910-023-01563-8","DOIUrl":"https://doi.org/10.1007/s10910-023-01563-8","url":null,"abstract":"<p>Probabilistic evolution theory provides a promising method for the solution of ordinary differential equations with multinomial right hand side functions. In this work, the solution by probabilistic evolution theory is implemented in C++ programming language. A novel algorithm for concurrent computation of the coefficients of the series expansion is designed and implemented. Using the program, approximate solutions for different ordinary differential equations are obtained and the results are compared to results of certain prominent methods for numerical solution of ordinary differential equations.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139064566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optical solutions to the truncated M-fractional Schrödinger–KdV equation via an analytical method 通过分析方法求得截断 M 分数薛定谔-KdV 方程的光学解
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2023-12-23 DOI: 10.1007/s10910-023-01554-9
{"title":"Optical solutions to the truncated M-fractional Schrödinger–KdV equation via an analytical method","authors":"","doi":"10.1007/s10910-023-01554-9","DOIUrl":"https://doi.org/10.1007/s10910-023-01554-9","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we will use the exp<span> <span>((-Phi (eta )))</span> </span>-expansion method to obtain the solitonic wave solution in the sense of the truncated M-fractional Schrödinger–KdV equation. The provided equation is converted into an ordinary differential equation using the appropriate wave transformation. Standard waveform shapes are determined, such as hyperbolic, exponential, dark, bright, rational, plane, and combo bright-dark soliton. We create 2D, density, and contour graphs of the solutions using consistent parametric values to examine the physical characteristics of the constructed solitons. Using Wolfram Mathematica, the newly created solutions are verified by inserting them back into the model under consideration. The suggested method and results can also be used to analyze high-order fractional models found in fields such as optics, hydrodynamics, plasma, wave theory, and others.</p>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139022373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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