Particle-Particle RPA和RPA梯度优化在数值原子轨道框架下的实现
发布时间：2022-01-20 10:11
The first-principle methods are used to calculate the ground-state energy of many-electron systems,where the exchange-correlation part of total energy is approximated.The random phase approximation（RPA）is one of the method for computing the ground-state correlation energy.In this thesis,we present a comparative study of particle-hole and particle-particle channels of RPA for molecular dissociations of different bonding types.We introduced a direct particle-particle RPA scheme,in analogy to the d...
【文章来源】：中国科学技术大学安徽省 211工程院校 985工程院校
【文章页数】：135 页
【学位级别】：博士
【文章目录】：
Declaration
Acknowledgements
Abstract
Chapter1 Introduction
1.1 An Overview of First-Principle Methods
1.2 Non-relativistic Approximation
1.3 Born-Oppenheimer Approximation
1.4 The Independent Particle Model
1.5 Methods for Ground State Calculations
1.5.1 Hartree Fock and Wave Function Methods
1.5.2 Post SCF Correlation Energy Methods
1.5.3 Kohn-Sham Density Functional Theory
1.5.4 Well-Known Approximations for the Exchange Correlation Energy Functional
Chapter2 Basis Sets
2.1 Atom Centered Localized Basis sets
2.1.1 Numerical Atom Centered Basis sets
2.1.2 Hydrogenic and Λ-functions
2.1.3 Slater-type orbitals (STO)
2.1.4 Gaussian Type Orbitals (GTOs)
2.2 Basis Sets Superposition Error (BSSE)
Chapter3 Random Phase Approximation
3.1 Introduction
3.2 Green Functions
3.3 Particle-Particle Green Function
3.4 Particle-Hole Green Function
3.5 Particle-Hole Random Phase Approximation
3.6 Particle-Particle Random Phase Approximation
Chapter4 Comparing particle-particle and particle-hole random phase approximations
4.1 Implementation Details
4.2 Results and Discussion
4.2.1 Binding Energy Curves for H_2 and H_2~+
4.2.2 Binding Energy Curves for N_2
4.2.3 Binding Energy Curves for HF
4.2.4 Binding Energy Curves for Ar_2
4.3 Binding Energy Curves of H_2 and Ar_2 Based on the PBE Reference
4.4 Numerical Acuracy of Our ppRPA Implementation in FHI-aims
4.5 Conclusion
Chapter5 The Optimized Effective Potential Method
5.1 The Exact Exchange Optimized Effective Potential Method
5.2 The Orbital Dependent Functionals for the Exchange-Correlation Energy
5.3 Optimized Effective Potential Correlation Method
5.4 Computational Details
5.5 Results and Discussion
5.6 Conclusion
Chapter6 Analytical Gradient
6.1 Fundamental Theoritical Framework
6.1.1 Analytical Gradient of Total Energy
6.1.2 The Density Functional Perturbation Theory
6.2 Analytical Gradient of RPA Correlation Energy
6.3 Computational Details
6.4 Results and Discussion
6.5 Conclusion
List of Publications
References
本文编号：3598637
【文章来源】：中国科学技术大学安徽省 211工程院校 985工程院校
【文章页数】：135 页
【学位级别】：博士
【文章目录】：
Declaration
Acknowledgements
Abstract
Chapter1 Introduction
1.1 An Overview of First-Principle Methods
1.2 Non-relativistic Approximation
1.3 Born-Oppenheimer Approximation
1.4 The Independent Particle Model
1.5 Methods for Ground State Calculations
1.5.1 Hartree Fock and Wave Function Methods
1.5.2 Post SCF Correlation Energy Methods
1.5.3 Kohn-Sham Density Functional Theory
1.5.4 Well-Known Approximations for the Exchange Correlation Energy Functional
Chapter2 Basis Sets
2.1 Atom Centered Localized Basis sets
2.1.1 Numerical Atom Centered Basis sets
2.1.2 Hydrogenic and Λ-functions
2.1.3 Slater-type orbitals (STO)
2.1.4 Gaussian Type Orbitals (GTOs)
2.2 Basis Sets Superposition Error (BSSE)
Chapter3 Random Phase Approximation
3.1 Introduction
3.2 Green Functions
3.3 Particle-Particle Green Function
3.4 Particle-Hole Green Function
3.5 Particle-Hole Random Phase Approximation
3.6 Particle-Particle Random Phase Approximation
Chapter4 Comparing particle-particle and particle-hole random phase approximations
4.1 Implementation Details
4.2 Results and Discussion
4.2.1 Binding Energy Curves for H_2 and H_2~+
4.2.2 Binding Energy Curves for N_2
4.2.3 Binding Energy Curves for HF
4.2.4 Binding Energy Curves for Ar_2
4.3 Binding Energy Curves of H_2 and Ar_2 Based on the PBE Reference
4.4 Numerical Acuracy of Our ppRPA Implementation in FHI-aims
4.5 Conclusion
Chapter5 The Optimized Effective Potential Method
5.1 The Exact Exchange Optimized Effective Potential Method
5.2 The Orbital Dependent Functionals for the Exchange-Correlation Energy
5.3 Optimized Effective Potential Correlation Method
5.4 Computational Details
5.5 Results and Discussion
5.6 Conclusion
Chapter6 Analytical Gradient
6.1 Fundamental Theoritical Framework
6.1.1 Analytical Gradient of Total Energy
6.1.2 The Density Functional Perturbation Theory
6.2 Analytical Gradient of RPA Correlation Energy
6.3 Computational Details
6.4 Results and Discussion
6.5 Conclusion
List of Publications
References
本文编号：3598637
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