[PDF] Development And Applications Of Direct Methods For Electron Correlation Calculations eBook

Author : Petr Carsky
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 18,28 MB
Release : 2012-12-06
Category : Science
ISBN : 3642931405

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Until recently quantum chemical ab initio calculations were re stricted to atoms and very small molecules. As late as in 1960 Allen l and Karo stated : "Almost all of our ab initio experience derives from diatomic LCAO calculations ••• N and we have found in the litera ture "approximately eighty calculations, three-fourths of which are for diatomic molecules ••• There are approximately twenty ab initio calculations for molecules with more than two atoms, but there is a decided dividing line between the existing diatomic and polyatomic wave functions. Confidence in the satisfactory evaluation of the many -center two-electron integrals is very much less than for the diatom ic case". Among the noted twenty calculations, SiH was the largest 4 molecule treated. In most cases a minimal basis set was used and the many-center two-electron integrals were calculated in an approximate way. Under these circumstances the ab initio calculations could hard ly provide useful chemical information. It is therefore no wonder that the dominating role in the field of chemical applications was played by semiempirical and empirical methods. The situation changed essentially in the next decade. The problem of many-center integrals was solved, efficient and sophisticated computer programs were devel oped, basis sets suitable for a given type of problem were suggested, and, meanwhile, a considerable amount of results has been accumulated which serve as a valuable comparative material. The progress was of course inseparable from the development and availability of computers.

Author :
Publisher : Academic Press
Page : 354 pages
File Size : 10,89 MB
Release : 2021-09-28
Category : Science
ISBN : 0128235470

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Advances in Quantum Chemistry presents surveys of current topics in this rapidly developing field one that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. It features detailed reviews written by leading international researchers. In this volume the readers are presented with an exciting combination of themes. Presents surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry and biology Features detailed reviews written by leading international researchers

Author : Frank Jensen
Publisher : John Wiley & Sons
Page : 1056 pages
File Size : 33,78 MB
Release : 2016-12-14
Category : Science
ISBN : 1118825950

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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

Author : S. Wilson
Publisher : Courier Corporation
Page : 305 pages
File Size : 29,42 MB
Release : 2014-07-01
Category : Science
ISBN : 0486150224

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Electron correlation effects are of vital significance to the calculation of potential energy curves and surfaces, the study of molecular excitation processes, and in the theory of electron-molecule scattering. This text describes methods for addressing one of theoretical chemistry's central problems, the study of electron correlation effects in molecules. Although the energy associated with electron correlation is a small fraction of the total energy of an atom or molecule, it is of the same order of magnitude as most energies of chemical interest. If the solution of quantum mechanical equations from first principles is to provide an accurate quantitative prediction, reliable techniques for the theoretical determination of the effect of electron correlation on molecular properties are therefore important. To that end, this text explores molecular electronic structure, independent electron models, electron correlation, the linked diagram theorem, group theoretical aspects, the algebraic approximation, and truncation of expansions for expectation values.

Author : Motoi Tobita
Publisher :
Page : pages
File Size : 44,56 MB
Release : 2002
Category :
ISBN :

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ABSTRACT: This dissertation is focused on the development of highly accurate electron-correlation methods for one- and two-dimensional periodic systems. For one-dimensional systems, atomic-orbital based many-body perturbation theory and coupled cluster theory are developed and applied to polyacetylene and lithium-hydride model chain. Use of atomic orbitals instead of conventional crystalline (molecular) orbitals enables us to control runtime and accuracy of the calculation. The gain in the atomic-orbital based coupled cluster method originates from the locality and sparsity of matrices needed in the framework of the theory. Provided, efficient sparse matrix-matrix multiplication routines, we obtain good estimates of the correlation energy much faster than the conventional method for large systems. 90 percent of the correlation energy can be recovered very quickly, and 2 to 3 digit accuracy can be obtained for polymers with relatively simple unit cells such as polyacetylene. The formalism behind the atomic-orbital based coupled cluster theory is applicable for both large molecular systems and periodic systems. Formal aspects of the atomic-orbital based coupled cluster theory are discussed and correspondence between the atomic-orbital based framework and crystalline (molecular) orbital based framework are shown. Two-dimensional code development is based on Hartree-Fock and density functional theories due to the fact that coupled-cluster theory is too costly. Efficient inclusion of the Coulomb effects by the fast multipole method and analytical gradient techniques are the core elements that contribute robustness and computational efficiency for two-dimensional systems. The fast multipole method is an algorithm to include the long-range Coulomb effects for uniform systems with linear-scaling costs for molecular systems and with logarithmic scaling for infinite periodic systems. The analytical gradient technique is a powerful tool when optimized geometries or vibrational frequencies are computed. If optimum geometries or vibrational frequencies are required, then analytical gradients are for all practical purposes, a necessity.

Author : Kenneth L. Bell
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 11,90 MB
Release : 1999-08-31
Category : Science
ISBN : 0306461900

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Professor Philip G. Burke, CBE, FRS formally retired on 30 September 1998. To recognise this occasion some of his colleagues, friends, and former students decided to hold a conference in his honour and to present this volume as a dedication to his enormous contribution to the theoretical atomic physics community. The conference and this volume of the invited talks reflect very closely those areas with which he has mostly been asso- ated and his influence internationally on the development of atomic physics coupled with a parallel growth in supercomputing. Phil’s wide range of interests include electron-atom/molecule collisions, scattering of photons and electrons by molecules adsorbed on surfaces, collisions involving oriented and chiral molecules, and the development of non-perturbative methods for studying multiphoton processes. His devel- ment of the theory associated with such processes has enabled important advances to be made in our understanding of the associated physics, the interpretation of experimental data, has been invaluable in application to fusion processes, and the study of astrophysical plasmas (observed by both ground- and space-based telescopes). We therefore offer this volume as our token of affection and respect to Philip G. Burke, with the hope that it may also fill a gap in the literature in these important fields.

Author : Petr Cársky
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 42,72 MB
Release : 2010-07-03
Category : Science
ISBN : 9048128854

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I feel very honored that I have been asked to write a Foreword to this book. The subject of the book – “Coupled cluster theory” – has been around for about half a century. The basic theory and explicit equations for closed-shell ground states were formulated before 1970. At the beginning of the seventies the rst ab initio calcu- tion were carried out. At that time speed and memory of computers were very limited compared to today’s standards. Moreover, the size of one-electron bases employed was small, so that it was only possible to achieve an orientation in methodical aspects rather than to generate new signi cant results. Extensive use of the coupled-cluster method started at the beginning of the eighties. With the help of more powerful computers the results of coupled-cluster approaches started to yield more and more interesting results of relevance to the interpretation of experimental data. New ideas in methodology kept appearing and computer codes became more and more ef cient. This exciting situation continues to this very day. Remarkably enough, even the - quired equations can now be generated by a computer with the help of symbolic languages. The size of this monograph and the rich variety of articles it contains attests to the usefulness and viability of the couple-cluster formalism for the h- dling of many-electron correlation effects. This represents a vivid testimony of a tremendous work that has been accomplished in coupled-cluster methodology and its exploitation.