Mathematical Methods for Implicit Solvation Models in Quantum Chemistry

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Mathematical Methods for Implicit Solvation Models in Quantum Chemistry by : Chaoyu Quan

Download or read book Mathematical Methods for Implicit Solvation Models in Quantum Chemistry written by Chaoyu Quan and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is devoted to study and improve the mathematical models and methods used in implicit solvation models in quantum chemistry. The manuscript is composed of two parts. In the first part where we analyze the solute-solvent interface, we give, for the first time, a complete characterization of the so-called “smooth” molecular surface, i.e., the solvent excluded surface (SES). Based on this characterization, we develop a piecewise meshing algorithm for different molecular surfaces, especially the SES, using the advancing-front triangulation. Further, it has been pointed out in the literature that the SES-cavity (the region enclosed by the SES) is a more accurate description of the solute cavity. In the second part, we therefore construct an SES-based polarizable continuum model (PCM), in which the dielectric permittivity parameter is continuous. The electrostatic problem of this model involves solving a Poisson equation defined in R3. We then develop a particular Schwarz domain decomposition method where only local equations restricted to balls need to be solved. Finally, the Poisson-Boltzmann solvation model, another implicit solvation model, is also investigated, which takes into account both the dielectric permittivity and the ionic strength of the solvent. A similar Schwarz domain decomposition method is proposed to solve the associated Poisson-Boltzmann equation by solving local equations restricted to balls as it is for the SES-based PCM.

Mathematical Models and Methods for Ab Initio Quantum Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 3642572375
Total Pages : 247 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Mathematical Models and Methods for Ab Initio Quantum Chemistry by : M. Defranceschi

Download or read book Mathematical Models and Methods for Ab Initio Quantum Chemistry written by M. Defranceschi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of the fourth International Conference on Industrial and Applied Mathematics!, we decided to organize a sequence of 4 minisymposia devoted to the mathematical aspects and the numerical aspects of Quantum Chemistry. Our goal was to bring together scientists from different communities, namely mathematicians, experts at numerical analysis and computer science, chemists, just to see whether this heterogeneous set of lecturers can produce a rather homogeneous presentation of the domain to an uninitiated audience. To the best of our knowledgde, nothing of this kind had never been tempted so far. It seemed to us that it was the good time for doing it, both . because the interest of applied mathematicians into the world of computational chemistry has exponentially increased in the past few years, and because the community of chemists feels more and more concerned with the numerical issues. Indeed, in the early years of Quantum Chemistry, the pioneers (Coulson, Mac Weeny, just to quote two of them) used to solve fundamental equations modelling toy systems which could be simply numerically handled in view of their very limited size. The true difficulty arose with the need to model larger systems while possibly taking into account their interaction with their environment. Hand calculations were no longer possible, and computing science came into the picture.

Algebraic Methods in Quantum Chemistry and Physics

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Publisher : CRC Press
ISBN 13 : 100072266X
Total Pages : 284 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis Algebraic Methods in Quantum Chemistry and Physics by : Francisco M. Fernandez

Download or read book Algebraic Methods in Quantum Chemistry and Physics written by Francisco M. Fernandez and published by CRC Press. This book was released on 2020-01-16 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.

Computational Methods in Quantum Chemistry

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Publisher : World Scientific
ISBN 13 : 9789810226114
Total Pages : 264 pages
Book Rating : 4.2/5 (261 download)

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Book Synopsis Computational Methods in Quantum Chemistry by : Ahmed A. Hasanein

Download or read book Computational Methods in Quantum Chemistry written by Ahmed A. Hasanein and published by World Scientific. This book was released on 1996 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: An account, from first principles, of the methods of numerical quantum mechanics. Coverage encompasses formulations and fundamental postulates; the Hamiltonian and angular momentum operators; and approximation of the solutions of the Schroedinger equation

Computational Methods In Quantum Chemistry, Volume 2: Quantum Chemistry

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Publisher : World Scientific
ISBN 13 : 9814499188
Total Pages : 255 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Computational Methods In Quantum Chemistry, Volume 2: Quantum Chemistry by : Myron W Evans

Download or read book Computational Methods In Quantum Chemistry, Volume 2: Quantum Chemistry written by Myron W Evans and published by World Scientific. This book was released on 1996-07-04 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive account, from first principles, of the methods of numerical quantum mechanics, beginning with formulations and fundamental postulates. The development continues with that of the Hamiltonian and angular momentum operators, and with methods of approximating the solutions of the Schroedinger equation with variational and perturbation methods.Chapter 3 is a description of the Hartree-Fock self-consistent field method, which is developed systematically for atoms. The Born-Oppenheimer approximation is introduced, and the numerical methods presented one by one thereafter in a logically consistent way that should be accessible to undergraduates. These include LCAO, Hartree-Fock-SCF method for molecules, Roothaan LCAO-MO-SCF method, and electron correlation energy.Chapter 4 is devoted to the more sophisticated computational methods in quantum chemistry, with an introduction to topics that include: the zero differential overlap approximation; Huckel MO theory of conjugated molecules; Pariser-Parr-Pople MO method; extended Huckel theory; neglect of differential overlap methods; invariance in space requirements; CNDO; INDO; NDDO; MINDO; MNDO; AM1; MNDO-PM3; SAM1; SINDO1; CNDO/S; PCILO,Xα; and ab initio methods.This is followed by an introduction to Moller-Plesset perturbation theory of many electrons, and coupled perturbed Hartree Fock theory, with a description of the coupled cluster method. Finally Chapter 5 applies these methods to problems of contemporary interest.The book is designed to be a junior/senior level text in computational quantum mechanics, suitable for undergraduates and graduates in chemistry, physics, computer science, and associated disciplines.

Quasi-Exactly Solvable Models in Quantum Mechanics

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Publisher : CRC Press
ISBN 13 : 1351420321
Total Pages : 480 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Quasi-Exactly Solvable Models in Quantum Mechanics by : A.G Ushveridze

Download or read book Quasi-Exactly Solvable Models in Quantum Mechanics written by A.G Ushveridze and published by CRC Press. This book was released on 2017-07-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.

Conference on Mathematical Methods for Ab Initio Quantum Chemistry

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Conference on Mathematical Methods for Ab Initio Quantum Chemistry by : Patrick Cassam-Chenai

Download or read book Conference on Mathematical Methods for Ab Initio Quantum Chemistry written by Patrick Cassam-Chenai and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Solvation Effects on Molecules and Biomolecules

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Publisher : Springer Science & Business Media
ISBN 13 : 1402082703
Total Pages : 536 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Solvation Effects on Molecules and Biomolecules by : Sylvio Canuto

Download or read book Solvation Effects on Molecules and Biomolecules written by Sylvio Canuto and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an interdisciplinary treatise on the theoretical approach to solvation problems. It describes the essential details of the theoretical methods and places them into the context of modern applications, and hence is of broad interest to theoreticians and experimentalists. The assembly of these modern methods and applications into one volume is a unique contribution to date and gives a broad and ample description of the field in its present stage of development.

Simple Theorems, Proofs, and Derivations in Quantum Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 1475765193
Total Pages : 341 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Simple Theorems, Proofs, and Derivations in Quantum Chemistry by : Istvan Mayer

Download or read book Simple Theorems, Proofs, and Derivations in Quantum Chemistry written by Istvan Mayer and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1983 I have been delivering lectures at Budapest University that are mainly attended by chemistry students who have already studied quantum chem istry in the amount required by the (undergraduate) chemistry curriculum of the University, and wish to acquire deeper insight in the field, possibly in prepara tion of a master's or Ph.D. thesis in theoretical chemistry. In such a situation, I have the freedom to discuss, in detail, a limited number of topics which I feel are important for one reason or another. The exact coverage may vary from year to year, but I usually concentrate on the general principles and theorems and other basic theoretical results which I foresee will retain their importance despite the rapid development of quantum chemistry. I commonly organize my lectures by treating the subject from the begin ning, without referring explicitly to any actual previous knowledge in quantum chemistry-only some familiarity with its goals, approaches and, to a lesser ex tent, techniques is supposed. I concentrate on the formulae and their derivation, assuming the audience essentially understands the reasons for deriving these results. This book is basically derived from the material of my lectures. The spe cial feature, distinguishing it from most other textbooks, is that all results are explicitly proved or derived, and the derivations are presented completely, step by step. True understanding of a theoretical result can be achieved only if one has gone through its derivation.

Variational Methods in Molecular Modeling

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Publisher : Springer
ISBN 13 : 9811025029
Total Pages : 331 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Variational Methods in Molecular Modeling by : Jianzhong Wu

Download or read book Variational Methods in Molecular Modeling written by Jianzhong Wu and published by Springer. This book was released on 2016-12-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.

Multi-layer Methods for Quantum Chemistry in the Condensed Phase

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Publisher :
ISBN 13 :
Total Pages : 335 pages
Book Rating : 4.:/5 (847 download)

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Book Synopsis Multi-layer Methods for Quantum Chemistry in the Condensed Phase by : Adrian William George Lange

Download or read book Multi-layer Methods for Quantum Chemistry in the Condensed Phase written by Adrian William George Lange and published by . This book was released on 2012 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: We discuss the development and application of a number of theoretical physical models focused on improving our understanding of quantum chemical phenomena in condensed phase environments, especially aqueous solutions. The large number of atoms and molecules present in such systems precludes the application of the most advanced and accurate quantum chemistry theories available due to their exponential growth of required computational power with respect to the number of electrons in a system. As a feasible alternative, we opt to take a "multi-layer" approach, wherein the full chemical system is partitioned into different layers treated with varying levels of approximation, circumventing the exponential scaling computational cost. How this partitioning is performed and applied appropriately is the principal emphasis of this work.

Computational Chemistry

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Publisher : Gulf Professional Publishing
ISBN 13 : 9780444512482
Total Pages : 928 pages
Book Rating : 4.5/5 (124 download)

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Book Synopsis Computational Chemistry by : Philippe G. Ciarlet

Download or read book Computational Chemistry written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aiming to provide the reader with a general overview of the mathematical and numerical techniques used for the simulation of matter at the microscopic scale, this book lays the emphasis on the numerics, but modelling aspects are also addressed. The contributors come from different scientific communities: physics, theoretical chemistry, mathematical analysis, stochastic analysis, numerical analysis, and the text should be suitable for graduate students in mathematics, sciences and engineering and technology.

Essential Computational Modeling in Chemistry

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Publisher : Elsevier
ISBN 13 : 0444537619
Total Pages : 399 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Essential Computational Modeling in Chemistry by : Philippe G. Ciarlet

Download or read book Essential Computational Modeling in Chemistry written by Philippe G. Ciarlet and published by Elsevier. This book was released on 2010-12-07 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essential Computational Modeling in Chemistry presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling in Chemistry Vol. 10(2005). Computational Modeling is an active field of scientific computing at the crossroads between Physics, Chemistry, Applied Mathematics and Computer Science. Sophisticated mathematical models are increasingly complex and extensive computer simulations are on the rise. Numerical Analysis and scientific software have emerged as essential steps for validating mathematical models and simulations based on these models. This guide provides a quick reference of computational methods for use in understanding chemical reactions and how to control them. By demonstrating various computational methods in research, scientists can predict such things as molecular properties. The reference offers a number of techniques and the numerical analysis needed to perform rigorously founded computations. Various viewpoints of methods and applications are available for researchers to chose and experiment with; Numerical analysis and open problems is useful for experimentation; Most commonly used models and techniques for the molecular case is quickly accessible

Single-Ion Solvation

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Publisher : Royal Society of Chemistry
ISBN 13 : 1782624961
Total Pages : 614 pages
Book Rating : 4.7/5 (826 download)

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Book Synopsis Single-Ion Solvation by : Philippe Hunenberger

Download or read book Single-Ion Solvation written by Philippe Hunenberger and published by Royal Society of Chemistry. This book was released on 2015-10-20 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ions are ubiquitous in chemical, technological, ecological and biological processes. Characterizing their role in these processes in the first place requires the evaluation of the thermodynamic parameters associated with the solvation of a given ion. However, due to the constraint of electroneutrality, the involvement of surface effects and the ambiguous connection between microscopic and macroscopic descriptions, the determination of single-ion solvation properties via both experimental and theoretical approaches has turned out to be a very difficult and highly controversial problem. This unique book provides an up-to-date, compact and consistent account of the research field of single-ion solvation thermodynamics that has over one hundred years of history and still remains largely unsolved. By reviewing the various approaches employed to date, establishing the relevant connections between single-ion thermodynamics and electrochemistry, resolving conceptual ambiguities, and giving an exhaustive data compilation (in the context of alkali and halide hydration), this book provides a consistent synthesis, in depth understanding and clarification of a large and sometimes very confusing research field. The book is primarily aimed at researchers (professors, postgraduates, graduates, and industrial researchers) concerned with processes involving ionic solvation properties (these are ubiquitous, eg. in physical/organic/analytical chemistry, electrochemistry, biochemistry, pharmacology, geology, and ecology). Because of the concept definitions and data compilations it contains, it is also a useful reference book to have in a university library. Finally, it may be of general interest to anyone wanting to learn more about ions and solvation. Key features: - discusses both experimental and theoretical approaches, and establishes the connection between them - provides both an account of the past research (covering over one hundred years) and a discussion of current directions (in particular on the theoretical side) - involves a comprehensive reference list of over 2000 citations - employs a very consistent notation (including table of symbols and unambiguous definitions of all introduced quantities) - provides a discussion and clarification of ambiguous concepts (ie. concepts that have not been defined clearly, or have been defined differently by different authors, leading to confusion in past literature) - encompasses an exhaustive data compilation (in the restricted context of alkali and halide hydration), along with recommended values (after critical analysis of this literature data) - is illustrated by a number of synoptic colour figures, that will help the reader to grasp the connections between different concepts in one single picture

Theoretical Chemistry Accounts

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Publisher : Springer Science & Business Media
ISBN 13 : 3662104210
Total Pages : 205 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Theoretical Chemistry Accounts by : Christopher Cramer

Download or read book Theoretical Chemistry Accounts written by Christopher Cramer and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the New Century Issue of the journal "Theroretical Chemistry Accounts" the advisory editors identified papers from the first century of theoretical chemistry and discussed their importance for the twentieth century with an eye towards the twenty-first century. Sixty-six such perspectives are published in the New Century Issue. To make this unique collection available to younger scientists for entertaining reading and re-reading of the original publications, the publisher decided to reprint a special edition of the issue.

An Analysis for Some Methods and Algorithms of Quantum Chemistry

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Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
ISBN 13 : 9783838126074
Total Pages : 136 pages
Book Rating : 4.1/5 (26 download)

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Book Synopsis An Analysis for Some Methods and Algorithms of Quantum Chemistry by : Thorsten Rohwedder

Download or read book An Analysis for Some Methods and Algorithms of Quantum Chemistry written by Thorsten Rohwedder and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2011-05 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the field of ab-initio calculation of theproperties of atoms, molecules and solids, the solution of the electronic Schrodinger equation, an operator eigenvalue equation for the Hamiltonianof the system, plays a major role. Of utmost significance is thelowest eigenvalue of this Hamiltonian, representing the ground state energy of the system.To meet the requirements of the multitude of possibleapplications of the electronic Schrodinger equation, the last decades have seen the development of avariety of different methods designed to approximate the solution of this extremelyhigh-dimensional minimization problem.The present work delivers amathematical analysis for aspects of some of these methods used in the context of quantumchemistry calculation. Three approaches used in the algorithmic treatment ofthe electronic Schrodinger equation are analysed in detail: A "direct minimization" scheme used inHartree-Fock, Kohn-Sham and in CI calculations, the Coupled Cluster method, being of high practicalsignificance in calculations where high accuracy is demanded, and the common acceleration technique DIIS.

Special Issue on Mathematical Methods for Ab Initio Quantum Chemistry

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Publisher :
ISBN 13 :
Total Pages : 229 pages
Book Rating : 4.:/5 (931 download)

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Book Synopsis Special Issue on Mathematical Methods for Ab Initio Quantum Chemistry by : Patrick Cassam-Chenaï

Download or read book Special Issue on Mathematical Methods for Ab Initio Quantum Chemistry written by Patrick Cassam-Chenaï and published by . This book was released on 2012 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: