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E-raamat: Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory

(University of Florida), (University of Illinois, Urbana-Champaign)
  • Formaat: PDF+DRM
  • Sari: Cambridge Molecular Science
  • Ilmumisaeg: 06-Aug-2009
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511590870
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Sari: Cambridge Molecular Science
  • Ilmumisaeg: 06-Aug-2009
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511590870

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Describes the mathematical and diagrammatic techniques employed in the popular many-body methods to determine molecular structure, properties and interactions.

Written by two leading experts in the field, this book explores the 'many-body' methods that have become the dominant approach in determining molecular structure, properties and interactions. With a tight focus on the highly popular Many-Body Perturbation Theory (MBPT) and Coupled-Cluster theories (CC), the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed. Using this book the reader will be able to understand, derive and confidently implement relevant algebraic equations for current and even new multi-reference CC methods. Hundreds of diagrams throughout the book enhance reader understanding through visualization of computational procedures and extensive referencing allows further exploration of this evolving area. With an extensive bibliography and detailed index, this book will be suitable for graduates and researchers within quantum chemistry, chemical physics and atomic, molecular and solid-state physics.

Arvustused

'All research groups in theoretical chemistry will want to have this volume in their library; the book will form an essential part of any course on electron correlation.' Professor Nicholas Handy, University of Cambridge

Muu info

This book describes the mathematical and diagrammatic techniques employed in the popular many-body methods to determine molecular structure, properties and interactions.
Preface xi
Introduction
1(17)
Scope
1(1)
Conventions and notation
2(1)
The independent-particle approximation
3(4)
Electron correlation
7(2)
Configuration interaction
9(1)
Motivation
10(1)
Extensivity
11(4)
Disconnected clusters and extensivity
15(3)
Formal perturbation theory
18(36)
Background
18(1)
Classical derivation of Rayleigh-Schrodinger perturbation theory
18(9)
Projection operators
27(2)
General derivation of formal time-independent perturbation theories
29(17)
Similarity transformation derivation of the formal perturbation equations and quasidegenerate PT
46(7)
Other approaches
53(1)
Second quantization
54(36)
Background
54(1)
Creation and annihilation operators
55(12)
Normal products and Wick's theorem
67(4)
Particle-hole formulation
71(4)
Partitioning of the Hamiltonian
75(5)
Normal-product form of the quantum-mechanical operators
80(5)
Generalized time-independent Wick's theorem
85(1)
Evaluation of matrix elements
86(4)
Diagrammatic notation
90(40)
Time ordering
90(1)
Slater determinants
91(1)
One-particle operators
92(19)
Two-particle operators
111(19)
Diagrammatic expansions for perturbation theory
130(35)
Resolvent operator and denominators
130(1)
First-order energy
131(1)
Second-order energy
131(1)
Third-order energy
132(2)
Conjugate diagrams
134(1)
Wave-function diagrams
135(3)
Fourth-order energy
138(14)
Linked-diagram theorem
152(1)
Numerical example
153(3)
Unlinked diagrams and extensivity
156(9)
Proof of the linked-diagram theorem
165(12)
The factorization theorem
165(7)
The linked-diagram theorem
172(5)
Computational aspects of MBPT
177(8)
Techniques of diagram summation
177(3)
Factorization of fourth-order quadruple-excitation diagrams
180(2)
Spin summations
182(3)
Open-shell and quasidegenerate perturbation theory
185(66)
Formal quasidegenerate perturbation theory (QDPT)
185(7)
The Fermi vacuum and the model states
192(2)
Normal-product form of the generalized Bloch equations
194(1)
Diagrammatic notation for QDPT
195(3)
Schematic representation of the generalized Bloch equation
198(5)
Level-shift and wave-operator diagrams
203(24)
Incomplete model space
227(24)
Foundations of coupled-cluster theory
251(41)
Coupled-cluster theory for noninteracting He atoms
251(3)
The coupled-cluster wave function
254(4)
The coupled-cluster doubles (CCD) equations
258(14)
Exponential Ansatz and the linked-diagram theorem of MBPT
272(7)
Diagrammatic derivation of the CCD equations
279(13)
Systematic derivation of the coupled-cluster equations
292(55)
The connected form of the CC equations
292(3)
The general form of CC diagrams
295(2)
Systematic generation of CC diagrams
297(2)
The coupled-cluster singles and doubles (CCSD) equations
299(9)
Coupled-cluster singles, doubles and triples (CCSDT) equations
308(13)
Coupled-cluster singles, doubles, triples and quadruples (CCSDTQ) equations
321(7)
Coupled-cluster effective-Hamiltonian diagrams
328(12)
Results of various CC methods compared with full CI
340(7)
Calculation of properties in coupled-cluster theory
347(59)
Expectation value for a CC wave function
347(5)
Reduced density matrices
352(9)
The response treatment of properties
361(5)
The CC energy functional
366(1)
The Λ equations
367(9)
Effective-Hamiltonian form of the Λ equations
376(5)
Response treatment of the density matrices
381(4)
The perturbed reference function
385(11)
The CC correlation-energy derivative
396(10)
Additional aspects of coupled-cluster theory
406(25)
Spin summations and computational considerations
406(5)
Coupled-cluster theory with an arbitrary single-determinant reference function
411(4)
Generalized many-body perturbation theory
415(3)
Brueckner orbitals and alternative treatments of T
418(4)
Monitoring multiplicities in open-shell coupled-cluster calculations
422(3)
The A and B response matrices from the viewpoint of CCS
425(2)
Noniterative approximations based on the CC energy functional
427(2)
The nature of the solutions of CC equations
429(2)
The equation-of-motion coupled-cluster method for excited, ionized and electron-attached states
431(31)
Introduction
431(1)
The EOM-CC Ansatz
432(5)
Diagrammatic treatment of the EE-EOM-CC equations
437(8)
EOM-CC treatment of ionization and electron attachment
445(4)
EOM-CC treatment of higher-order properties
449(5)
EOM-CC treatment of frequency-dependent properties
454(8)
Multireference coupled-cluster methods
462(34)
Introduction
462(3)
Hilbert-space state-universal MRCC
465(6)
Hilbert-space state-specific MRCC
471(4)
Fock-space valence-universal MRCC
475(15)
Intermediate-Hamiltonian Fock-space MRCC
490(6)
References 496(25)
Author index 521(3)
Subject index 524
Isaiah Shavitt is an Emeritus Professor of Ohio State University, and currently serves as an Adjunct Professor of Chemistry at the University of Illinois at Urbana-Champaign. After receiving his Ph.D. in Theoretical Chemistry from the University of Cambridge in 1957, he went on to teach in the chemistry department of Israel Institute of Technology and serve as a Postdoctoral Fellow in Theoretical Chemistry at the University of Wisconsin and the IBM Watson Laboratory at Columbia University. He is an Elected Member of the International Academy of Quantum Molecular Science, and was awarded the 2000 Morley Medal of the Cleveland Section of the American Chemical Society. Rodney J. Bartlett, the Graduate Research Professor at the Quantum Theory Project, University of Florida, pioneered the development of coupled cluster (CC) theory in quantum chemistry to offer highly accurate solutions of the Schrödinger equation for molecular structure and spectra. He is a Fellow of the International Academy of Quantum Molecular Sciences (1991), the American Physical Society (1986), and the Guggenheim Foundation (1986). He has published over 500 papers and book chapters, presented over 200 invited lectures at major meetings, and received numerous awards.