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| 商品編號： | DCT6055 | |
| 商品名稱： | The hartree-fock method for many-electron problems 出版公司:Tamkang University Press 作者:S.M. Shiau 類型:科學科普-物理 PDF電子書 英文版 | | | 語系版本： | PDF電子書 英文版 | |
| 運行平台： | PDF電子書,沒有任何平台限制,終身使用 | |
| 更新日期： | 2026-05-01 | |
| 光碟片數： | 1片CD光碟 | |
| 銷售價格： | $100元 | |
| 熱門標籤： | 物理
科學科普
hartree
fock
method
many
electron
problems
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The hartree-fock method for many-electron problems 出版公司:Tamkang University Press 作者:S.M. Shiau 類型:科學科普-物理 PDF電子書 英文版
商品資料
作者：S.M. Shiau
出版社：Tamkang University Press
出版年：2017
課程類型：科學科普>物理
檔案格式：PDF
ISBN：9789865608484
書籍簡介
Back ground of the Hartree-Fock method
Introduction
The physical systems, such as atoms, molecules and solids, consist not only of electrons but also of nuclei, and each of these particles moves in the field generated by the others.
The Hartree-Fock (HF) approach is to consider the nuclei as being fixed, and to solve the Schrodinger equation for the electronic system in the field of the static nuclei.
This approach is called the Born-oppenheimer approximation. It remains then to solve for the electronic structure.
The wave functions of the many-electron system have the form of an anti-symmetries product of one-electron wave functions.
This restriction leads to an effective Schrodinger equation for the individual one-electron wave functions (call orbitals) with a potential determined by the orbitals occupied by the other electrons.
The solution to the effective Schrodinger equation must be found iteratively in a self-consistency procedure.
In the variational approach, correlations between the electrons are neglected to some extent.
In particular, the coulomb repulsion between the electrons is represented in an averaged way.
In the HF approach, the effective interaction caused by the fact that the electrons are fermions, obeying Pauli's principle, and want to keep apart if they have the same spin, is included.
HF approximation (neglect the coulomb correlations) is improved by constructing a many-electron state as linear combination of Slater determinants.
These determinants are constructed from the ground state by excitation: the first determinant is the Hartree-Fock ground state and the second one is the first excited state (within the spectrum determined selfconsistently for the ground state) and so on.
The matrix elements of the Hamiltonian between these Slater determinants are calculated and the resulting Hamilton matrix (which has a dimension equal to the number of Slater determinants taken into account) is diagonalized.
The resulting state is then a linear combination of Slater determinants.
章節
1 Back ground of the Hartree - Fock method(第1頁)- 1.1 Introduction(第2頁)
- 1.2 The Born - Oppenheimer approximation and the independent particle method(第3頁)
- 1.3 Many - electron systems and the Slater determinant(第5頁)
- 1.4 Self - consistency and exchange(第8頁)
2 The variational method for the Schrodinger equation(第13頁)- 2.1 Variational calculus(第14頁)
- 2.2 Solution of the generalized eigenvalue problem(第16頁)
- 2.3 Perturbation theory and variational calculus(第17頁)
3 Basis functions(第21頁)- 3.1 Introduction(第22頁)
- 3.2 Closed - and open - shell systems(第22頁)
- 3.3 Bais functions : STO and GTO(第27頁)
4 Theoretical framework - CRYSTAL code(第33頁)- 4.1 Basic equations(第34頁)
- 4.2 Treatment of the Coulomb series(第37頁)
- 4.3 The exchange series(第37頁)
- 4.4 Exploitation of symmetry(第38頁)
- 4.5 Reciprocal space integration(第39頁)
5 Applications and results with CRYSTAL Code for Piezoelectric calculations on ZnO Wurtzite(第41頁)- 5.1 Brief input files and output results(第42頁)
- 5.2 More details of the input file(第45頁)
- 5.3 More details of the output results(第48頁)
References(第220頁)
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