ChIN简介页:芬兰赫尔辛基大学教学讲义:相对量子化学介绍
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芬兰赫尔辛基大学教学讲义:相对量子化学介绍

【URL】 http://www.chem.helsinki.fi/Education/RQC

【收费情况】 免费

【简介】
     Lecture notes for a introductory course to relativistic quantum chemistry taught at the University of Helsinki.

Lecturer: Prof Pekka Pyykko (tel. 09-191 50171, pyykko@chem.helsinki.fi)
Level: Advanced undergraduate and postgraduate

Index:

Preface
Preface to the 1975 edition
Table of Contents (pages i–iv, 33 kB) version 21.10.2003
All-in-One (pages 1–119, 2.24 MB) version 21.10.2003
LaTeX source file (236 kB)
1 Lorentz Transformations and Lorentz Groups (pages 1–14, 450 kB) version 21.10.2003

1.1 Lorentz transformations
1.1.1 Introduction
1.1.2 Rotations and translations of the four-dimensional space
1.1.3 Lorentz transformations as rotations
1.1.4 Addition of velocities
1.1.5 Perpendicular motion
1.1.6 The relativistic mass transformation
1.1.7 Derivation of E = mc2
1.1.8 Connection between T and p
1.2 Lorentz matrices
1.3 Infinitesimal Lorentz transformations
1.4 The Lorentz group

2 Relativistic Fields (pages 15–20, 61 kB) version 21.10.2003
2.1 Definition
2.2 Scalar fields
2.3 An S = 1 field
2.4 Two-component spinor fields
2.5 Four-component spinor fields

3 Relativistic Wave Equations (pages 21–52, 467 kB) version 21.10.2003
3.1 Klein-Gordon
3.2 Dirac
3.2.1 Why must N >= 4?
3.2.2 Properties of Dirac matrices
3.3 Some properties of the Dirac equation
3.3.1 Solutions with ±E
3.3.2 Inclusion of electromagnetic fields
3.3.3 Free-particle solutions
3.3.4 Probability density
3.4 The Pauli limit
3.5 Central fields
3.5.1 The radial part
3.5.2 Non-relativistic limit
3.6 The Dirac-Coulomb problem
3.7 Virial theorems
3.7.1 Non-relativistic case
3.7.2 Dirac

4 Dirac-Fock (pages 53–70, 234 kB) version 21.10.2003
4.1 The energy expression
4.2 The Dirac-Fock equations
4.2.1 The relativistic Koopmans theorem
4.2.2 Multiconfiguration treatment, a simple example
4.2.3 "Average-of-configuration" treatment
4.3 Numerical solution of the DF equations
4.3.1 Specific features of the DF-OCE method

5 Symmetry (pages 71–86, 572 kB) version 21.10.2003
5.1 Rotation Operators
5.1.1 The Euler angles
5.1.2 Rotation of spherical harmonics
5.1.3 Rotation of |jm> functions
5.1.4 The 2-to-1 homomorphism from SU(2) to SO(3)
5.2 Double groups
5.2.1 Non-relativistic case with spin
5.2.2 Relativistic case
5.2.3 Improper rotations
5.2.4 The Group O(3)
5.2.5 The double group is a symmetry group of the Dirac equation
5.2.6 The Element E
5.2.7 Elements of double groups
5.2.8 Irreducible representations ("irreps")
5.2.9 Classes
5.2.10 Theorem of Opechowski
5.3 Construction of relativistic MO:s
5.3.1 Projection operators
5.3.2 Coupling constant method
5.4 Time reversal
5.4.1 Non-relativistic case
5.4.2 Inclusion of spin
5.4.3 n-electron wave functions
5.4.4 Kramers' theorem
5.4.5 The cases (a), (b) and (c) of Wigner (1932)
5.4.6 Further examples
5.5 Quaternions

6 Molecular Orbital Methods (pages 87–100, 120 kB) version 21.10.2003
6.1 Semi-empirical methods
6.1.1 Extended Hückel methods
6.1.2 Zero Differential Overlap Approximation
6.1.3 Inclusion of Spin-Orbit Splitting
6.1.4 Relativistic Extended Hückel (REX)
6.2 One-electron molecules
6.2.1 The Hamiltonian
6.2.2 Possible coordinate systems
6.2.3 Transformation of the Dirac equation

7 Pseudopotentials (pages 101–104, 61 kB) version 21.10.2003
7.1 Introduction
7.2 A bit of history
7.3 Where to get pseudopotentials

8 On QED (pages 105–112, 600 kB) version 21.10.2003
8.1 Introduction
8.2 Some formulas for vacuum polarization
8.3 Some formulas for self-energy (vacuum fluctuation)

9 On Transformed Hamiltonians (pages 113–119, 96 kB) version 21.10.2003
9.1 General
9.2 The Foldy-Wouthuysen transformation
9.3 The Cowan-Griffin equation
9.4 Douglas-Kroll-Hess
9.5 Zero Order Regular Approximation, ZORA
9.6 Direct Perturbation Theory, DPT
9.7 Further examples
9.7.1 RESC
9.7.2 AMFI

【相关链接】
  课程材料:量子化学讲义 (Quantum Chemistry Lecture Notes)
  量子化学发展史
  Lecture Topics of the Quantum Chemistry at University of Georgia (乔治亚大学提供的量子化学课件)
  量子化学入门
  NIH分子模拟中心:量子化学建模指南


Summary by 储春梅 on 2004-03-02

Last updated by 杨宏伟 on 2004-03-09

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