Journal of Mathematical Chemistry最新文献

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Closed-form representations of the Coulomb integral over hydrogenic orbitals 氢轨道上库仑积分的封闭形式表示
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-07 DOI: 10.1007/s10910-025-01734-9
Balakrishnan Viswanathan, Darien DeWolf
{"title":"Closed-form representations of the Coulomb integral over hydrogenic orbitals","authors":"Balakrishnan Viswanathan,&nbsp;Darien DeWolf","doi":"10.1007/s10910-025-01734-9","DOIUrl":"10.1007/s10910-025-01734-9","url":null,"abstract":"<div><p>The theory of atomic structure is conceptually built on hydrogen-like orbitals and computed using Slater or Gaussian orbitals, owing to the relative difficulty of computing integrals concerning the hydrogenic orbitals. The optimal set of hydrogenic orbitals in an atom is obtained by minimizing the energy with respect to the orbitals. The Coulomb integral is difficult to compute due to the inverse distance relationship. In this paper, we evaluate the Coulomb integral and its derivative using two expressions for the inverse distance: the Laplace expression and the Legendre expression. The two expressions for inverse distance are similar and yield different integral forms. The Laplace expression yields the Coulomb integral as a sum of hypergeometric functions while the Legendre expression yields a compact polynomial form. The derivative of the Coulomb integral (computed using both forms) with respect to the decay constant is also provided.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1523 - 1550"},"PeriodicalIF":1.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073579","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
Low-order efficient Adams–Bashforth–Moulton methods for first-order IVPs with oscillating solutions 具有振荡解的一阶ivp的低阶有效Adams-Bashforth-Moulton方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-05-06 DOI: 10.1007/s10910-025-01727-8
Chia-Liang Lin, Theodore E. Simos
{"title":"Low-order efficient Adams–Bashforth–Moulton methods for first-order IVPs with oscillating solutions","authors":"Chia-Liang Lin,&nbsp;Theodore E. Simos","doi":"10.1007/s10910-025-01727-8","DOIUrl":"10.1007/s10910-025-01727-8","url":null,"abstract":"<div><p>The methodology for calculating the phase-lag and amplification-factor for both explicit and implicit multistep methods for first-order differential equations was recently developed by one of the authors. The objective of this study is to develop low-order Adams–Bashforth–Moulton predictor–corrector algorithms that eradicate phase-lag, amplification-factor. The stability regions of the newly established methodologies will also be highlighted. Furthermore, we will examine our results from numerical experiments employing the newly developed approaches.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1496 - 1522"},"PeriodicalIF":1.7,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073751","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 efficient approximation algorithm for the nonlinear reaction: diffusion equations in an electro catalytic thin film models using Hosoya polynomials 非线性反应扩散方程的有效逼近算法:电催化薄膜模型的细谷多项式
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-26 DOI: 10.1007/s10910-025-01728-7
M. Bhuvaneswari, V. Vinoba, G. Hariharan
{"title":"An efficient approximation algorithm for the nonlinear reaction: diffusion equations in an electro catalytic thin film models using Hosoya polynomials","authors":"M. Bhuvaneswari,&nbsp;V. Vinoba,&nbsp;G. Hariharan","doi":"10.1007/s10910-025-01728-7","DOIUrl":"10.1007/s10910-025-01728-7","url":null,"abstract":"<div><p>The paper discusses a mathematical model for non-Michaelis–Menten kinetics, which involves a substrate forming a complex with the immobilized catalyst. A new Hosoya polynomial approximation method (HPAM) is applied for solving the reaction–diffusion equations. Analytical expressions are established to the nonlinear reaction–diffusion equation arising in electro catalytic thin film with an arbitrary shape models using the Hosoya polynomials. The main idea of the proposed research work is that the nonlinear reaction–diffusion problems are converted into a system of algebraic equations using the Hosoya polynomials. Analytical expressions for substrate concentration profiles are derived in closed and simplified forms for various geometries (planar, cylindrical, and spherical), along with the corresponding steady-state amperometric current response. The proposed results are validated with the other available results. Moreover, the utility of HPAM is investigated to be simple, straight forward, efficient and flexible. Also, the paper examines how different parameters influence the substrate concentration in the above models.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1475 - 1495"},"PeriodicalIF":1.7,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074189","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
Correction to: Linear forms in logarithms and the mathematical method of diophantine equations: applications in chemistry and physics 修正:对数的线性形式和丢番图方程的数学方法:在化学和物理中的应用
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-22 DOI: 10.1007/s10910-025-01722-z
Pagdame Tiebekabe, Ismaïla Diouf
{"title":"Correction to: Linear forms in logarithms and the mathematical method of diophantine equations: applications in chemistry and physics","authors":"Pagdame Tiebekabe,&nbsp;Ismaïla Diouf","doi":"10.1007/s10910-025-01722-z","DOIUrl":"10.1007/s10910-025-01722-z","url":null,"abstract":"","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1551 - 1553"},"PeriodicalIF":1.7,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074039","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
A simplified a posteriori error analysis of a second-order difference scheme for a singularly perturbed convection-diffusion problem 奇异摄动对流扩散问题二阶差分格式的简化后验误差分析
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-18 DOI: 10.1007/s10910-025-01729-6
Jian Huang, Zhongdi Cen, Aimin Xu
{"title":"A simplified a posteriori error analysis of a second-order difference scheme for a singularly perturbed convection-diffusion problem","authors":"Jian Huang,&nbsp;Zhongdi Cen,&nbsp;Aimin Xu","doi":"10.1007/s10910-025-01729-6","DOIUrl":"10.1007/s10910-025-01729-6","url":null,"abstract":"<div><p>In this paper a numerical method on a posteriori mesh is presented to solve a second-order singularly perturbed convection-diffusion equation. A second-order three-point difference method is used to discretize the singularly perturbed convection-diffusion equation. A posteriori error analysis involving simple calculations with fewer proof techniques is developed for the second-order three-point difference method on an arbitrary mesh. A solution-adaptive algorithm based on a posteriori error analysis is designed to generate a posteriori mesh and the approximation solution. Numerical experiments verify the second-order uniform convergence of this method.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1461 - 1474"},"PeriodicalIF":1.7,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073880","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
Combinatorics of colorings of Dűrer graph, Dűrer solid in Melencolia I, their heptagonal analogues and antiprisms for all irreducible representations: chirality, dynamics, NMR spectra and enumerations 所有不可约表示的Dűrer图,Dűrer固体Melencolia I及其七面类似物和反棱镜的着色组合:手性,动力学,NMR光谱和枚举
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-16 DOI: 10.1007/s10910-025-01720-1
Krishnan Balasubramanian
{"title":"Combinatorics of colorings of Dűrer graph, Dűrer solid in Melencolia I, their heptagonal analogues and antiprisms for all irreducible representations: chirality, dynamics, NMR spectra and enumerations","authors":"Krishnan Balasubramanian","doi":"10.1007/s10910-025-01720-1","DOIUrl":"10.1007/s10910-025-01720-1","url":null,"abstract":"<div><p>The Dűrer Solid has an art and mathematical history ever since it appeared in Dűrer’s 1514 copper engraving, <i>Melencolia I</i>. The associated truncated triangular trapezohedron is an intriguing structure owing to the symmetry, chirality concepts and combinatorial properties. The heptahedral version corresponds to the generalized Petersen’s graph G(7,2). It is shown that the heptagonal antiprism exhibits interesting combinatorial and chirality properties. The heptagonal bipyramid boron complex has been studied recently, and thus the developed techniques were applied to the multiple-quantum NMR of this complex. These graphs and solids serve as representations in dynamic stereochemistry of fluxional molecules as well as in material and molecular science. We consider symmetry-driven combinatorial-group theory through generating functions for the face, edge and vertex colorings of the title graphs and solids for all irreducible representations of the respective symmetry groups. We demonstrate of our computational-combinatorics techniques with tables of combinatorial numbers for the various colorings of these graphs for all irreducible representations. The chirality of the colorings can be directly inferred from the combinatorial enumerations. Applications to the <sup>10</sup>B and <sup>11</sup>B MQ-NMR and nuclear spin statistics of the heptagonal bipyramid complex are considered.</p><h3>Graphical abstract</h3><div><figure><div><div><picture><img></picture></div></div></figure></div></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1395 - 1446"},"PeriodicalIF":1.7,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073992","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
Simulation of optimal linear control for stabilizing chaotic behavior in a chemical reaction model 稳定化学反应模型混沌行为的最优线性控制仿真
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-16 DOI: 10.1007/s10910-025-01723-y
Henrique Antonio Mendonça Faria, Jorge Manuel Vieira Capela, Fabio Roberto Chavarette
{"title":"Simulation of optimal linear control for stabilizing chaotic behavior in a chemical reaction model","authors":"Henrique Antonio Mendonça Faria,&nbsp;Jorge Manuel Vieira Capela,&nbsp;Fabio Roberto Chavarette","doi":"10.1007/s10910-025-01723-y","DOIUrl":"10.1007/s10910-025-01723-y","url":null,"abstract":"<div><p>Complex dynamical systems, such as multicomponent chemical reactions, can exhibit chaotic behaviour, posing challenges for process control and optimisation. The pursuit of effective control methodologies to stabilise chaotic reaction systems constitutes a broad field of research and application. This study proposes the application of optimal linear control to mitigate chaotic behaviour in a model of four-component chemical reactions within a continuous stirred-tank reactor (CSTR). The methodology involves representing the reaction system through differential equations and minimising the Hamilton–Jacobi-Bellman functional equation via a linear feedback controller based on a Lyapunov function. Numerical simulations validate the methodology’s efficacy, demonstrating the controller’s capacity to transition the system of equations from a chaotic state to a stable periodic regime. The results highlight the potential of optimal linear control for optimising the model of complex chemical processes, thereby opening possibilities for technological applications in specific scenarios. Optimal linear control has proven effective in stabilising the model of the reaction system, presenting itself as a promising tool for the design of industrial processes involving continuous flow reactors. In these reactors, precise control of concentrations is crucial to ensure process quality and safety.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1447 - 1460"},"PeriodicalIF":1.7,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073993","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
Combinatorial S-function method for relativistic spinor states of 5g-row dimers: (E-121)2 to (E-137)2 g行二聚体(E-121)2 ~ (E-137)2相对论旋量态的组合s函数方法
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-15 DOI: 10.1007/s10910-025-01715-y
Krishnan Balasubramanian
{"title":"Combinatorial S-function method for relativistic spinor states of 5g-row dimers: (E-121)2 to (E-137)2","authors":"Krishnan Balasubramanian","doi":"10.1007/s10910-025-01715-y","DOIUrl":"10.1007/s10910-025-01715-y","url":null,"abstract":"<div><p>The electronic states arising from the 5g-row of the periodic table are far less explored compared to other lighter elements in the periodic table. Relativistic effects are extremely large for the 5g-row elements (E-121 to E-138) due to a large nuclear charge approaching the inverse of the fine structure constant. The large relativistic effects result in a molecular spinor nature of the electronic states leading to a substantial mixing of electronic states with different spin multiplicities and differing spatial symmetries. Hence we present the combinatorial enumeration of ω–ω states arising for the 5g-row dimers by employing multinomially-driven symmetric function methods. The combinatorial techniques enumerate all possible ω–ω states originating from the relativistic 2-component molecular spinors for all the 5g-row dimers. There is a combinatorial explosion of electronic states, for example, a 5g-mid-row dimer with 18 electrons exhibits <span>(text{4,537,567,650})</span> terms in the S-functions. The S-functions for the 5g-row dimers are constructed, and from the S-function terms, those that comply with the Pauli exclusion principle result in a large number of relativistic ω–ω states for the 5g-row dimers. We have constructed the combinatorial tables for the relativistic ω–ω states of several 5g-row dimers subsequent to stipulating several conditions imposed on the level of electron excitations so that the combinatorics is manageable. Furthermore we invoke the electron–hole equivalence to mirror the ω–ω states for the remaining dimers of the 5g-row to enumerate them. Consequently, the developed technique enumerates the ω–ω states arising from up to 18 open-shell states without any restrictions making it applicable to numerous ω–ω states with varied quantum numbers.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1352 - 1394"},"PeriodicalIF":1.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073921","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
On the application of the Rayleigh–Ritz method to a projected Hamiltonian Rayleigh-Ritz方法在投影哈密顿量中的应用
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-10 DOI: 10.1007/s10910-025-01725-w
Francisco M. Fernández
{"title":"On the application of the Rayleigh–Ritz method to a projected Hamiltonian","authors":"Francisco M. Fernández","doi":"10.1007/s10910-025-01725-w","DOIUrl":"10.1007/s10910-025-01725-w","url":null,"abstract":"<div><p>We apply the well known Rayleigh–Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh–Ritz variational principle to ensemble states. By means of a toy model we show that the RRM eigenvalues approach to those of the projected Hamiltonian from below in most cases. We also discuss the effect of an energy shift and the projection of the identity operator.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 6","pages":"1343 - 1351"},"PeriodicalIF":1.7,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073838","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
Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step 含可逆一阶后步的两步动力学方程的解析解
IF 1.7 3区 化学
Journal of Mathematical Chemistry Pub Date : 2025-04-08 DOI: 10.1007/s10910-025-01726-9
Rebeka Szabó, Gábor Lente
{"title":"Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first order later step","authors":"Rebeka Szabó,&nbsp;Gábor Lente","doi":"10.1007/s10910-025-01726-9","DOIUrl":"10.1007/s10910-025-01726-9","url":null,"abstract":"<div><p>Analytical solutions for the ordinary differential equations are reported for the kinetics of two-step processes for which the later step is a first order reversible process. The earlier step is always irreversible: zeroth order, first order, second order and third order reactions are considered. For the first and second order cases, a qualitative analysis of the kinetic curves was also carried out and the parametric conditions of finding extrema on all the kinetic curves are explored. It is found that the scheme consisting of a second order or mixed second order earlier reaction and a reversible first order later one may feature a reactant with two extrema on its concentration–time trace. In such cases, the first extremum is always a maximum, and the second one is a minimum.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 5","pages":"1323 - 1341"},"PeriodicalIF":1.7,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10910-025-01726-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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