Computational Techniques in Quantum Chemistry and Molecular Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 9401018154
Total Pages : 570 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Computational Techniques in Quantum Chemistry and Molecular Physics by : Geerd H.F. Diercksen

Download or read book Computational Techniques in Quantum Chemistry and Molecular Physics written by Geerd H.F. Diercksen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the transcripts of the lectures presented at the NATO Advanced study Institute on "Computational Techniques in Quantum Chemistry and Molecular Physics", held at Ramsau, Germany, 4th - 21st Sept. 1974. Quantum theory was developed in the early decades of this century and was first applied to problems in chemistry and molecular physics as early as 1927. It soon emerged however, that it was impossible to con sider any but the simplest systems in any quantita tive detail because of the complexity of Schrodinger's equation which is the basic equation for chemical and molecular physics applications. This remained the si tuation until the development, after 1950, of elec tronic digital computers. It then became possible to attempt approximate solutions of Schrodinger's equa tion for fairly complicated systems, to yield results which were sufficiently accurate to make comparison with experiment meaningful. Starting in the early nineteen sixties in the United States at a few centres with access to good computers an enormous amount of work went into the development and implementation of schemes for approximate solu tions of Schrodinger's equation, particularly the de velopment of the Hartree-Fock self-consistent-field scheme. But it was soon found that the integrals needed for application of the methods to molecular problems are far from trivial to evaluate and cannot be easily approximated.

Handbook of Computational Quantum Chemistry

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Publisher : Courier Corporation
ISBN 13 : 0486443078
Total Pages : 852 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Handbook of Computational Quantum Chemistry by : David B. Cook

Download or read book Handbook of Computational Quantum Chemistry written by David B. Cook and published by Courier Corporation. This book was released on 2005-08-02 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive text provides upper-level undergraduates and graduate students with an accessible introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations. Topics include the Hartree-Fock method; matrix SCF equations; implementation of the closed-shell case; introduction to molecular integrals; and much more. 1998 edition.

Computational Quantum Chemistry

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Publisher : Royal Society of Chemistry
ISBN 13 : 1782625860
Total Pages : 252 pages
Book Rating : 4.7/5 (826 download)

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Book Synopsis Computational Quantum Chemistry by : Joseph J W McDouall

Download or read book Computational Quantum Chemistry written by Joseph J W McDouall and published by Royal Society of Chemistry. This book was released on 2015-11-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Quantum Chemistry presents computational electronic structure theory as practised in terms of ab initio waveform methods and density functional approaches. Getting a full grasp of the field can often prove difficult, since essential topics fall outside of the scope of conventional chemistry education. This professional reference book provides a comprehensive introduction to the field. Postgraduate students and experienced researchers alike will appreciate Joseph McDouall's engaging writing style. The book is divided into five chapters, each providing a major aspect of the field. Electronic structure methods, the computation of molecular properties, methods for analysing the output from computations and the importance of relativistic effects on molecular properties are also discussed. Links to the websites of widely used software packages are provided so that the reader can gain first hand experience of using the techniques described in the book.

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.

New Methods in Computational Quantum Mechanics

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Publisher : John Wiley & Sons
ISBN 13 : 0470142057
Total Pages : 812 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis New Methods in Computational Quantum Mechanics by : Ilya Prigogine

Download or read book New Methods in Computational Quantum Mechanics written by Ilya Prigogine and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of quantum chemistry for the quantitative prediction of molecular properties has long been frustrated by the technical difficulty of carrying out the needed computations. In the last decade there have been substantial advances in the formalism and computer hardware needed to carry out accurate calculations of molecular properties efficiently. These advances have been sufficient to make quantum chemical calculations a reliable tool for the quantitative interpretation of chemical phenomena and a guide to laboratory experiments. However, the success of these recent developments in computational quantum chemistry is not well known outside the community of practitioners. In order to make the larger community of chemical physicists aware of the current state of the subject, this self-contained volume of Advances in Chemical Physics surveys a number of the recent accomplishments in computational quantum chemistry. This stand-alone work presents the cutting edge of research in computational quantum mechanics. Supplemented with more than 150 illustrations, it provides evaluations of a broad range of methods, including: * Quantum Monte Carlo methods in chemistry * Monte Carlo methods for real-time path integration * The Redfield equation in condensed-phase quantum dynamics * Path-integral centroid methods in quantum statistical mechanics and dynamics * Multiconfigurational perturbation theory-applications in electronic spectroscopy * Electronic structure calculations for molecules containing transition metals * And more Contributors to New Methods in Computational Quantum Mechanics KERSTIN ANDERSSON, Department of Theoretical Chemistry, Chemical Center, Sweden DAVID M. CEPERLEY, National Center for Supercomputing Applications and Department of Physics, University of Illinois at Urbana-Champaign, Illinois MICHAEL A. COLLINS, Research School of Chemistry, Australian National University, Canberra, Australia REINHOLD EGGER, Fakultät für Physik, Universität Freiburg, Freiburg, Germany ANTHONY K. FELTS, Department of Chemistry, Columbia University, New York RICHARD A. FRIESNER, Department of Chemistry, Columbia University, New York MARKUS P. FÜLSCHER, Department of Theoretical Chemistry, Chemical Center, Sweden K. M. HO, Ames Laboratory and Department of Physics, Iowa State University, Ames, Iowa C. H. MAK, Department of Chemistry, University of Southern California, Los Angeles, California PER-ÅKE Malmqvist, Department of Theoretical Chemistry, Chemical Center, Sweden MANUELA MERCHán, Departamento de Química Física, Universitat de Valéncia, Spain LUBOS MITAS, National Center for Supercomputing Applications and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Illinois STEFANO OSS, Dipartimento di Fisica, Università di Trento and Istituto Nazionale di Fisica della Materia, Unità di Trento, Italy KRISTINE PIERLOOT, Department of Chemistry, University of Leuven, Belgium W. THOMAS POLLARD, Department of Chemistry, Columbia University, New York BJÖRN O. ROOS, Department of Theoretical Chemistry, Chemical Center, Sweden LUIS SERRANO-ANDRÉS, Department of Theoretical Chemistry, Chemical Center, Sweden PER E. M. SIEGBAHN, Department of Physics, University of Stockholm, Stockholm, Sweden WALTER THIEL, Institut für Organische Chemie, Universität Zürich, Zürich, Switzerland GREGORY A. VOTH, Department of Chemistry, University of Pennsylvania, Pennsylvania C. Z. Wang, Ames Laboratory and Department of Physi

Computational Quantum Chemistry

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Publisher : Elsevier
ISBN 13 : 0128159847
Total Pages : 386 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Computational Quantum Chemistry by : Masoud Soroush

Download or read book Computational Quantum Chemistry written by Masoud Soroush and published by Elsevier. This book was released on 2018-10-16 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Quantum Chemistry: Insights into Polymerization Reactions consolidates extensive research results, couples them with computational quantum chemistry (CQC) methods applicable to polymerization reactions, and presents those results systematically. CQC has advanced polymer reaction engineering considerably for the past two decades. The book puts these advances into perspective. It also allows you to access the most up-to-date research and CQC methods applicable to polymerization reactions in a single volume. The content is rigorous yet accessible to graduate students as well as researchers who need a reference of state-of-the-art CQC methods with polymerization applications. Consolidates more than 10 years of theoretical polymerization reaction research currently scattered across journal articles Accessibly presents CQC methods applicable to polymerization reactions Provides researchers with a one-stop source of the latest theoretical developments in polymer reaction engineering

Computational Quantum Chemistry

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Publisher : CRC Press
ISBN 13 : 100034469X
Total Pages : 715 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Computational Quantum Chemistry by : Ram Yatan Prasad

Download or read book Computational Quantum Chemistry written by Ram Yatan Prasad and published by CRC Press. This book was released on 2021-03-10 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Quantum Chemistry, Second Edition, is an extremely useful tool for teaching and research alike. It stipulates information in an accessible manner for scientific investigators, researchers and entrepreneurs. The book supplies an overview of the field and explains the fundamental underlying principles. It also gives the knowledge of numerous comparisons of different methods. The book consists of a wider range of applications in each chapter. It also provides a number of references which will be useful for academic and industrial researchers. It includes a large number of worked-out examples and unsolved problems for enhancing the computational skill of the users. Features Includes comprehensive coverage of most essential basic concepts Achieves greater clarity with improved planning of topics and is reader-friendly Deals with the mathematical techniques which will help readers to more efficient problem solving Explains a structured approach for mathematical derivations A reference book for academicians and scientific investigators Ram Yatan Prasad, PhD, DSc (India), DSc (hc) Colombo, is a Professor of Chemistry and former Vice Chancellor of S.K.M University, Jharkhand, India. Pranita, PhD, DSc (hc) Sri Lanka, FICS, is an Assistant Professor of Chemistry at Vinoba Bhave University, India.

Tensor Numerical Methods in Quantum Chemistry

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110391376
Total Pages : 343 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Tensor Numerical Methods in Quantum Chemistry by : Venera Khoromskaia

Download or read book Tensor Numerical Methods in Quantum Chemistry written by Venera Khoromskaia and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.

Computational Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 0306483912
Total Pages : 474 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Computational Chemistry by : Errol G. Lewars

Download or read book Computational Chemistry written by Errol G. Lewars and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational chemistry has become extremely important in the last decade, being widely used in academic and industrial research. Yet there have been few books designed to teach the subject to nonspecialists. Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics is an invaluable tool for teaching and researchers alike. The book provides an overview of the field, explains the basic underlying theory at a meaningful level that is not beyond beginners, and it gives numerous comparisons of different methods with one another and with experiment. The following concepts are illustrated and their possibilities and limitations are given: - potential energy surfaces; - simple and extended Hückel methods; - ab initio, AM1 and related semiempirical methods; - density functional theory (DFT). Topics are placed in a historical context, adding interest to them and removing much of their apparently arbitrary aspect. The large number of references, to all significant topics mentioned, should make this book useful not only to undergraduates but also to graduate students and academic and industrial researchers.

Linear-Scaling Techniques in Computational Chemistry and Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 9048128536
Total Pages : 522 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Linear-Scaling Techniques in Computational Chemistry and Physics by : Robert Zaleśny

Download or read book Linear-Scaling Techniques in Computational Chemistry and Physics written by Robert Zaleśny and published by Springer Science & Business Media. This book was released on 2011-03-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Linear-Scaling Techniques in Computational Chemistry and Physics" summarizes recent progresses in linear-scaling techniques and their applications in chemistry and physics. In order to meet the needs of a broad community of chemists and physicists, the book focuses on recent advances that extended the scope of possible exploitations of the theory. The first chapter provides an overview of the present state of the linear-scaling methodologies and their applications, outlining hot topics in this field, and pointing to expected developments in the near future. This general introduction is then followed by several review chapters written by experts who substantially contributed to recent developments in this field. The purpose of this book is to review, in a systematic manner, recent developments in linear-scaling methods and their applications in computational chemistry and physics. Great emphasis is put on the theoretical aspects of linear-scaling methods. This book serves as a handbook for theoreticians, who are involved in the development of new efficient computational methods as well as for scientists, who are using the tools of computational chemistry and physics in their research.

Computational Methods in Catalysis and Materials Science

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Publisher : John Wiley & Sons
ISBN 13 : 3527802665
Total Pages : 475 pages
Book Rating : 4.5/5 (278 download)

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Book Synopsis Computational Methods in Catalysis and Materials Science by : Rutger A. van Santen

Download or read book Computational Methods in Catalysis and Materials Science written by Rutger A. van Santen and published by John Wiley & Sons. This book was released on 2015-11-19 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide describes the basic computational methodologies for catalysis and materials science at an introductory level, presenting the methods with relevant applications, such as spectroscopic properties, chemical reactivity and transport properties of catalytically interesting materials. Edited and authored by internationally recognized scientists, the text provides examples that may be considered and followed as state-of-the art.

Computational Organic Chemistry

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Publisher : John Wiley & Sons
ISBN 13 : 1118291921
Total Pages : 653 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Computational Organic Chemistry by : Steven M. Bachrach

Download or read book Computational Organic Chemistry written by Steven M. Bachrach and published by John Wiley & Sons. This book was released on 2014-04-07 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition demonstrates how computational chemistry continues to shed new light on organic chemistry The Second Edition of author Steven Bachrach’s highly acclaimed Computational Organic Chemistry reflects the tremendous advances in computational methods since the publication of the First Edition, explaining how these advances have shaped our current understanding of organic chemistry. Readers familiar with the First Edition will discover new and revised material in all chapters, including new case studies and examples. There’s also a new chapter dedicated to computational enzymology that demonstrates how principles of quantum mechanics applied to organic reactions can be extended to biological systems. Computational Organic Chemistry covers a broad range of problems and challenges in organic chemistry where computational chemistry has played a significant role in developing new theories or where it has provided additional evidence to support experimentally derived insights. Readers do not have to be experts in quantum mechanics. The first chapter of the book introduces all of the major theoretical concepts and definitions of quantum mechanics followed by a chapter dedicated to computed spectral properties and structure identification. Next, the book covers: Fundamentals of organic chemistry Pericyclic reactions Diradicals and carbenes Organic reactions of anions Solution-phase organic chemistry Organic reaction dynamics The final chapter offers new computational approaches to understand enzymes. The book features interviews with preeminent computational chemists, underscoring the role of collaboration in developing new science. Three of these interviews are new to this edition. Readers interested in exploring individual topics in greater depth should turn to the book’s ancillary website www.comporgchem.com, which offers updates and supporting information. Plus, every cited article that is available in electronic form is listed with a link to the article.

Introduction to Computational Chemistry

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Publisher : John Wiley & Sons
ISBN 13 : 1118825950
Total Pages : 1056 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Introduction to Computational Chemistry by : Frank Jensen

Download or read book Introduction to Computational Chemistry written by Frank Jensen and published by John Wiley & Sons. This book was released on 2016-12-14 with total page 1056 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Computational Chemistry 3rd Edition provides a comprehensive account of the fundamental principles underlying different computational methods. Fully revised and updated throughout to reflect important method developments and improvements since publication of the previous edition, this timely update includes the following significant revisions and new topics: Polarizable force fields Tight-binding DFT More extensive DFT functionals, excited states and time dependent molecular properties Accelerated Molecular Dynamics methods Tensor decomposition methods Cluster analysis Reduced scaling and reduced prefactor methods Additional information is available at: www.wiley.com/go/jensen/computationalchemistry3

Computational Chemistry of Solid State Materials

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Publisher : John Wiley & Sons
ISBN 13 : 3527612297
Total Pages : 300 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Computational Chemistry of Solid State Materials by : Richard Dronskowski

Download or read book Computational Chemistry of Solid State Materials written by Richard Dronskowski and published by John Wiley & Sons. This book was released on 2008-01-08 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present both classical and quantum-chemical approaches to computational methods, incorporating the many new developments in this field from the last few years. Written especially for "non"-theoretical readers in a readily comprehensible and implemental style, it includes numerous practical examples of varying degrees of difficulty. Similarly, the use of mathematical equations is reduced to a minimum, focusing only on those important for experimentalists. Backed by many extensive tables containing detailed data for direct use in the calculations, this is the ideal companion for all those wishing to improve their work in solid state research.

Computational Methods in Chemistry

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Publisher : Springer Science & Business Media
ISBN 13 : 1468437283
Total Pages : 337 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Computational Methods in Chemistry by : Joachim Bargon

Download or read book Computational Methods in Chemistry written by Joachim Bargon and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers collected in this volume were presented at an international symposium on Computational Methods in Chemistry. This symposium was sponsored by IBM Germany and was held September 17-19, 1979, in Bad Neuenahr, West Germany. According to Graham Richards [Nature 278, 507 (1979)] the "Third Age of Quantum Chemistry" has started-;-where the results of quantum chemical calculations have become so accurate and reliable that they can guide the experimentalists in their search for the unknown. The particular example highlighted by Richards was the suc cessful prediction and subsequent identification of the relative energies, transition probabilities and geometries of the lowest triplet states of acetylene. The theoretical predictions were based chiefly upon the work of three groups: Kammer [Chern. Phys. Lett. ~, 529 (1970)] had made qualitatively correct predictions; Demoulin [Chern. Phys. 11, 329 (1975)] had calculated the potential energy curves for the two lowest triplet states (3 and 3 ) of B A acetylene; and Wetmore and Schaefer III [J. Chern. Phys. ~~ 1648 (1978)] had determined the geometries of the cis (3B and ~A ) and the trans (3B and 3A ) isomers of these two sta~es. Inua 2 2 guided search, Wendt, Hunziker and Hippler [J. Chern. PHys. 70, 4044 (1979)] succeeded in finding the predicted near infrared absorption of the cis triplet acetylene (no corresponding absorp tion for the trans form was found, which is in agreement with theory), and the resolved structure of the spectrum confirmed the predicted geometries conclusively.

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.