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E-raamat: Many-Body Methods for Atoms and Molecules

(Indian Institute of Astrophysics, Bangalore, India),
  • Formaat: 256 pages
  • Ilmumisaeg: 17-Feb-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781315356334
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Many-Body Methods for Atoms and MoleculesSuurem pilt
  • Formaat: 256 pages
  • Ilmumisaeg: 17-Feb-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781315356334
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Brings Readers from the Threshold to the Frontier of Modern Research

Many-Body Methods for Atoms and Molecules addresses two major classes of theories of electron correlation: the many-body perturbation theory and coupled cluster methods. It discusses the issues related to the formal development and consequent numerical implementation of the methods from the standpoint of a practicing theoretician. The book will enable readers to understand the future development of state-of-the-art multi-reference coupled cluster methods as well as their perturbative counterparts.

The book begins with an introduction to the issues relevant to the development of correlated methods in general. It next gives a formally rigorous treatment of aspects that pave the foundation toward the theoretical development of methods capable of tackling problems of electronic correlation. The authors go on to cover perturbation theory first in a fundamental way and then in the multi-reference context. They also describe the idea of state-specific theories, Fock space-based multi-reference coupled cluster methods, and basic issues of the single-reference coupled cluster method. The book concludes with state-of-the-art methods of modern electronic structure.
List of Figures
xi
List of Tables
xiii
Preface xv
1 Introduction
1(22)
1.1 Background
1(2)
1.2 Born-Oppenheimer approximation
3(3)
1.3 Approximate methods
6(2)
1.3.1 Variational method: Linear variation principle
6(2)
1.4 Independent particle model
8(7)
1.4.1 Hartree product
8(1)
1.4.2 Slater determinant
9(1)
1.4.3 Slater's rule
10(1)
1.4.4 Hartree--Fock method
11(2)
1.4.5 Hartree--Fock--Roothan method
13(1)
1.4.6 Brillouin's theorem
14(1)
1.4.7 Koopmans' theorem
14(1)
1.5 Configuration interaction
15(4)
1.6 Electron correlation
19(1)
1.7 Size extensivity and consistency
20(3)
2 Occupation Number Representation
23(26)
2.1 Background
23(1)
2.2 Creation and annihilation operators
24(4)
2.3 Occupation number representation of operators
28(1)
2.4 Evaluation of matrix elements
29(2)
2.4.1 Number operators
29(1)
2.4.2 Overlap matrix elements
29(1)
2.4.3 Matrix elements between vacuum states
30(1)
2.5 Normal order product of ordinary operators
31(3)
2.5.1 Wick's theorem for ordinary operators
32(2)
2.6 Hole-particle formalism and Fermi vacuum
34(2)
2.7 Evaluation of Hamiltonian elements between reference states
36(1)
2.8 Normal order product for a Fermi vacuum
37(3)
2.9 Normal product form of quantum mechanical operators
40(4)
2.9.1 Evaluation of matrix elements between states
43(1)
2.9.2 Vacuum expectation value of composite operators
44(1)
2.10 Graphical representation of normal product operators
44(5)
3 Perturbation Theory
49(24)
3.1 Background
49(1)
3.2 Rayleigh--Schrodinger perturbation theory: Traditional approach
50(6)
3.2.1 Systematic derivation of order by order perturbation expansion
50(3)
3.2.2 Wigner's (2n + 1) rule
53(1)
3.2.3 Hylleraas variation principle
54(2)
3.3 Projection operator based formulation of perturbation theory
56(2)
3.4 Brillouin--Wigner perturbation theory
58(1)
3.5 Rayleigh--Schrodinger perturbation theory
59(2)
3.6 Wave operator based formulation of Rayleigh--Schrodinger perturbation theory
61(3)
3.7 Choice of zero-order Hamiltonian Ho
64(1)
3.8 Intruder state problems in Rayleigh-Schrodinger perturbation theory
65(4)
3.9 Comparison of Brillouin--Wigner and Rayleigh-Schrodinger perturbation theories
69(4)
4 Multireference Perturbation Theory
73(34)
4.1 Introduction
73(2)
4.2 Choice of Fermi vacuum and the hole-particle states
75(3)
4.3 Multiconfiguration self-consistent field method
78(3)
4.4 Improved virtual orbital complete active space configuration method
81(2)
4.4.1 Closed-shell ground state
81(1)
4.4.2 Restricted open-shell doublet state
82(1)
4.5 Classification of perturbative methods
83(1)
4.6 Formal multireference perturbation theory for complete model space
84(8)
4.6.1 Order by order expansion of the wave operator
87(4)
4.6.2 Linked cluster theorem
91(1)
4.7 Multireference perturbation theory for incomplete model space
92(5)
4.8 Intermediate Hamiltonian methods
97(3)
4.8.1 Generalized degenerate perturbation theory
99(1)
4.9 Effective valence shell Hamiltonian method
100(7)
5 State-Specific Perturbation Theory
107(14)
5.1 Background
107(2)
5.2 Multireference Moller--Plesset second-order perturbation theory
109(4)
5.3 Multiconfiguration quasi-degenerate perturbation theory
113(1)
5.4 Complete active space second-order perturbation theory
114(4)
5.4.1 General formulation
114(3)
5.4.2 Connection with effective Hamiltonian based method
117(1)
5.5 Multistate complete active space second-order perturbation theory
118(3)
6 Coupled Cluster Method
121(30)
6.1 Introduction
121(1)
6.2 Single-reference coupled cluster method
122(2)
6.3 Separability
124(1)
6.4 Relation with full configuration interaction method
125(2)
6.5 Coupled cluster equation for doubles and singles-doubles approximations
127(6)
6.5.1 Coupled cluster doubles method
127(4)
6.5.2 Coupled cluster singles-doubles method
131(2)
6.6 Evaluation of the matrix elements for coupled cluster doubles equations
133(7)
6.6.1 Evaluation of correlation energy matrix elements
139(1)
6.7 Diagrammatic representation of coupled cluster doubles matrix elements
140(7)
6.7.1 Generation of coupled cluster diagrams
140(5)
6.7.2 Diagram rules and evaluation of matrix elements
145(2)
6.8 Emergence of many-body perturbation theory from CC method
147(2)
6.9 Other variants of CC theory
149(2)
7 Fock Space Multireference Coupled Cluster Method
151(36)
7.1 Background
151(2)
7.2 Choice of wave operator for multireference systems
153(2)
7.3 Connectivity of the effective Hamiltonian
155(1)
7.4 Fock space coupled cluster theory for energy difference
156(7)
7.4.1 Hierarchical generation of coupled cluster equations
160(2)
7.4.2 Quadratic nature of Fock space coupled cluster equations
162(1)
7.5 Systematic generation of cluster equations for various valence sectors
163(9)
7.5.1 Coupled cluster equations for the (1,0) valence sector
163(2)
7.5.2 Coupled cluster equations for the (0,1) valence sector
165(2)
7.5.3 Coupled cluster equations for the (1,1) valence sector
167(5)
7.6 Equation of motion coupled cluster method
172(3)
7.7 Relationship between FSMRCC and EOMCC
175(3)
7.8 Numerical examples
178(2)
7.8.1 Ionization potential of Be I and Na I isoelectronic sequence
178(1)
7.8.2 Ionization potential of Yb I
179(1)
7.9 Intermediate Hamiltonian based multireference coupled cluster theory
180(7)
7.9.1 Similarity transformation based formulation
182(2)
7.9.2 Eigenvalue independent partitioning based coupled cluster formulation
184(3)
8 Hilbert Space Coupled Cluster Theory
187(30)
8.1 Introduction
187(1)
8.2 State universal multireference coupled cluster theory
188(4)
8.2.1 State universal multireference perturbation theory
190(2)
8.3 Development of state-specific theories
192(25)
8.3.1 State-specific Brillouin-Wigner multireference coupled cluster theory
193(2)
8.3.2 State specific MkMRCC theory
195(2)
8.3.3 State-specific multireference perturbation theory
197(20)
Index 217
Dr. Rajat Kumar Chaudhuri is a professor at the Indian Institute of Astrophysics. His research interests lie at the interface of chemistry and physics with principal areas of focus on the development and applications of ab initio theories of atomic and molecular systems and theoretical spectroscopy. He has published over 150 scientific articles in the realm of theoretical chemistry.

Dr. Sudip Kumar Chattopadhyay is a professor of chemistry at the Indian Institute of Engineering Science and Technology, where he teaches basic and advanced quantum mechanics and quantum chemistry. His research interests include the development of electronic structure theories and their application to problems of broad chemical interest. He has also been working in the field of chemical dynamics in condensed phases. Dr. Chattopadhyay has published over 100 articles in journals of international repute
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