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Author: John Avery Publisher: World Scientific ISBN: 9814350478 Category : Science Languages : en Pages : 239
Book Description
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians.
Author: John Avery Publisher: World Scientific ISBN: 9814350478 Category : Science Languages : en Pages : 239
Book Description
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians.
Author: John Avery Publisher: World Scientific ISBN: 981435046X Category : Science Languages : en Pages : 239
Book Description
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a many-particle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetry-adapted basis functions. The conventional method for generating symmetry-adapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetry-adapted basis sets automatically with computer techniques. The method has a wide range of applicability, and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians.
Author: John Scales Avery Publisher: World Scientific ISBN: 9814478016 Category : Science Languages : en Pages : 258
Book Description
This book describes the generalized Sturmian method, which offers a fresh approach to the calculation of atomic spectra. Generalized Sturmians are isoenergetic solutions to an approximate many-electron Schrödinger equation with a weighted potential. The weighting factors are chosen in such a way as to make all of the solutions correspond to a given energy. The advantage of such an isoenergetic basis set is that every basis function has the correct turning point behavior needed for efficient synthesis of the wave function.The book also discusses methods for automatic generation of symmetry-adapted basis sets. Calculations using the generalized Sturmian method are presented and compared with experimental results from the NIST database. The relationship of Sturmians to harmonic polynomials and hyperspherical harmonics is also described. Methods for treating angular functions and angular integrals by means of harmonic projection are discussed, and these methods are shown to be especially useful for relativistic calculations. A final chapter discusses application of the generalized Sturmian method to the calculation of molecular spectra.
Author: Sergey Yurchenko Publisher: CRC Press ISBN: 1498761208 Category : Science Languages : en Pages : 206
Book Description
This book provides a detailed description of the modern variational methods available for solving the nuclear motion Schrödinger equation to enable accurate theoretical spectroscopy of polyatomic molecules. These methods are currently used to provide important molecular data for spectroscopic studies of atmospheres of astronomical objects including solar and extrasolar planets as well as cool stars. This book has collected descriptions of quantum mechanical methods into one cohesive text, making the information more accessible to the scientific community, especially for young researchers, who would like to devote their scientific career to the field of computational molecular physics. The book addresses key aspects of the high-accuracy computational spectroscopy of the medium size polyatomic molecules. It aims to describe numerical algorithms for the construction and solution of the nuclear motion Schrödinger equations with the central idea of the modern computational spectroscopy of polyatomic molecules to include the construction of the complex kinetic energy operators (KEO) into the computation process of the numerical pipeline by evaluating the corresponding coefficients of KEO derivatives on-the-fly. The book details key aspects of variational solutions of the nuclear motion Schrödinger equations targeting high accuracy, including construction of rotational and vibrational basis functions, coordinate choice, molecular symmetry as well as of intensity calculations and refinement of potential energy functions. The goal of this book is to show how to build an accurate spectroscopic computational protocol in a pure numerical manner of a general black-box type algorithm. This book will be a valuable resource for researchers, both experts and not experts, working in the area of the computational and experimental spectroscopy; PhD students and early-career spectroscopists who would like to learn basics of the modern variational methods in the field of computational spectroscopy. It will also appeal to astrophysicists and atmospheric physicists who would like to assess data and perform calculations themselves. Key features: Supported by the latest research and based on the state-of-the-art computational methods in high-accuracy computational spectroscopy of molecules. Authored by an authority in the field. Accessible to both experts and non-experts working in the area of computational and experimental spectroscopy, in addition to graduate students.
Author: Jochen Autschbach Publisher: Oxford University Press, USA ISBN: 0190920807 Category : Science Languages : en Pages : 756
Book Description
"Quantum Theory for Chemical Applications (QTCA) Quantum theory, or more specifically, quantum mechanics is endlessly fascinating, curious & strange, and often considered to be difficult to learn. It is true that quantum mechanics is a mathematical theory. Its scope, its predictions, the wisdom we gain from its results, all these become fully clear only in the context of the relevant equations and calculations. But the study of quantum mechanics is definitely worth the effort, and - as I like to tell my students- it is not rocket science"--
Author: Peter W. Atkins Publisher: Oxford University Press ISBN: 0199541426 Category : Science Languages : en Pages : 552
Book Description
This text unravels those fundamental physical principles which explain how all matter behaves. It takes us from the foundations of quantum mechanics, through quantum models of atomic, molecular, and electronic structure, and on to discussions of spectroscopy, and the electronic and magnetic properties of molecules.
Author: D. R. Yarkony Publisher: World Scientific ISBN: 9812832114 Category : Science Languages : en Pages : 785
Book Description
Modern Electronic Structure Theory provides a didactically oriented description of the latest computational techniques in electronic structure theory and their impact in several areas of chemistry. The book is aimed at first year graduate students or college seniors considering graduate study in computational chemistry, or researchers who wish to acquire a wider knowledge of this field.
Author: John R. Sabin Publisher: Elsevier ISBN: 0080458211 Category : Science Languages : en Pages : 341
Book Description
Advances in Quantum Chemistry presents surveys of current developments in this rapidly developing field that falls between the historically established areas of mathematics, physics, chemistry, and biology. With invited reviews written by leading international researchers, each presenting new results, it provides a single vehicle for following progress in this interdisciplinary area. This volume continues the tradition with high quality and thorough reviews of various aspects of quantum chemistry. It contains a variety of topics that include an extended and in depth discussion on the calculation of analytical first derivatives of the energy in a similarity transformed equation of motion couples cluster method.
Author: Pavlo O. Dral Publisher: Elsevier ISBN: 0323886043 Category : Science Languages : en Pages : 702
Book Description
Quantum chemistry is simulating atomistic systems according to the laws of quantum mechanics, and such simulations are essential for our understanding of the world and for technological progress. Machine learning revolutionizes quantum chemistry by increasing simulation speed and accuracy and obtaining new insights. However, for nonspecialists, learning about this vast field is a formidable challenge. Quantum Chemistry in the Age of Machine Learning covers this exciting field in detail, ranging from basic concepts to comprehensive methodological details to providing detailed codes and hands-on tutorials. Such an approach helps readers get a quick overview of existing techniques and provides an opportunity to learn the intricacies and inner workings of state-of-the-art methods. The book describes the underlying concepts of machine learning and quantum chemistry, machine learning potentials and learning of other quantum chemical properties, machine learning-improved quantum chemical methods, analysis of Big Data from simulations, and materials design with machine learning. Drawing on the expertise of a team of specialist contributors, this book serves as a valuable guide for both aspiring beginners and specialists in this exciting field. - Compiles advances of machine learning in quantum chemistry across different areas into a single resource - Provides insights into the underlying concepts of machine learning techniques that are relevant to quantum chemistry - Describes, in detail, the current state-of-the-art machine learning-based methods in quantum chemistry
Author: John Avery
Author: John Avery
Author: John Avery
Author: John Scales Avery
Author: Sergey Yurchenko
Author: Jochen Autschbach
Author: Peter W. Atkins
Author: D. R. Yarkony
Author: John R. Sabin
Author: Harry Theo Jonkman
Author: Pavlo O. Dral