內容簡介
It is traditional for quantum theory of molecular systems (molecular quantum chemistry) to describe the properties of a many-atom system on the grounds of in- teratomic interactions applying the linear combination of atomic orbitals (LCAO) approximation in the electronic-structure calculations. The basis of the theory of the electronic structure of solids is the periodicity of the crystalline potential and Bloch- type one-electron states, in the majority of cases approximated by a linear combina- tion of plane waves (LCPW). In a quantum chemistry of solids the LCAO approach is extended to periodic systems and modified in such a way that the periodicity of the potential is correctly taken into account, but the language traditional for chemistry is used when the interatornic interaction is analyzed to explain the properties of the crystalline solids. At first, the quantum chemistry of solids was considered simply as the energy-band theory or the theory of the chemical bond in tetrahedral semi-conductors . From the beginning of the 1970s the use of powerful computer codes has become a common practice in molecular quantum chemistry to predict many properties of molecules in the first-principles LCAO calculations. In the condensed-matter studies the accurate description of the system at an atomic scale was much less advanced .
內頁插圖
目錄
part i theory
1 introduction
2 space groups and crystalline structures
2.1 translation and point symmetry of cryst&lz;
2.1.1 symmetry of molecules and crystals: similarities and differences
2.1.2 translation symmetry of crystals. point symmetry of bravais lattices. crystal class
2.2 space groups
2.2.1 space groups of brawis lattices. symmorphic and nonsymmorphic space groups
2.2.2 three-periodic space groups
2.2.3 site symmetry in crystals. wyckoff positions
2.3 crystalline structures
2.3.1 crystal-structure types. structure information for computer codes
2.3.2 cubic structures: diamond, rocksalt, fluorite, zincblende, cesium chloride, cubic perovskite
2.3.3 tetragonoj structures: rutile, anatase and la~cuo4
2.3.4 orthorhombic structures: lamno3 and yba2cuso?
2.3.5 hexagonal and trigonal structures: graphite, wurtzite, corundum and scmno3
3 symmetry and localization of crystalline orbitals
3.1 translation and space symmetry of crystalline orbitals.bloch functions
3.1.1 symmetry of molecular and crystalline orbitals
3.1.2 irreducible representations of translation group. brillouin zone
3.1.3 stars of wavevectors. little groups. fhll representations of space groups
3.1.4 small representations of a little group. projective representations of point groups
3.2 site symmetry and induced representations of space groups
3.2.1 induced representations of point groups. localized molecular orbitals
3.2.2 induced representations of space groups in q-basis
3.2.3 induced representations of space groups in k-basis.band representations
3.2.4 simple and composite induced representations
3.2.5 simple induced representations for cubic space groups ok, and
3.2.6 symmetry of atomic and crystalline orbitals in mgo, si and srzro3 crystals
3.3 symmetry of localized crystalline orbitals. wannier functions
3.3.1 symmetry of localized orbitals and band representations of space groups
3.3.2 localization criteria in wannier-function generation
3.3.3 localized orbitals for valence bands: lcao approximation
3.3.4 variational method of localized wannier-function generation on the base of bloch functions
4 hartree-fock lcao method for periodic systems
4.1 one-electron approximation for crystals
4.1.1 one-electron and one-determinant approximations for molecules and crystals
4.1.2 symmetry of the one-electron approximation hamiltonian
4.1.3 restricted and unrestricted hartree-fock lcao methods for molecules
4.1.4 specific features of the hartree-fock method for a cyclic model of a crystal
4.1.5 restricted hartree-fock lcao method for crystals
4.1.6 unrestricted and restricted open-shell hartree-fock methods for crystals
4.2 special points of brillouin zone
4.2.1 superceus of three-dimensional bravais lattices
4.2.2 special points of brillouin-zone generating
4.2.3 modification of the monkhorst-pack special-points meshes
4.3 density matrix of crystals in the hartree-fock method
4.3.1 properites of the one-electron density matrix of a crystal
4.3.2 the one-electron density matrix of the crystal in the lcao approximation
4.3.3 interpolation procedure for constructing an approximate density matrix for periodic systems
5 electron correlations in molecules and crystals
5.1 electron correlations in molecules: post-hartree-fock methods
5.1.1 what is the electron correlation ?
5.1.2 configuration interaction and multi-configuration self-consistent field methods
5.1.3 coupled-cluster methods
5.1.4 many-electron perturbation theory
5.1.5 local electron-correlation methods
5.2 incremental scheme for local correlation in periodic systems
5.2.1 weak and strong electron-correlation
5.2.2 method of incfements: ground state
5.2.3 method of increments: valence-band structure and bandgap
5.3 atomic orbital laplace-transformed mp2 theory for periodic systems
5.3.1 laplace mp2 for periodic systems: unit-cell correlation energy
5.3.2 laplace mp2 for periodic systems:bandgap
5.4 local mp2 electron-correlation method for nonconducting crystals
5.4.1 local mp2 equations for periodic systems
5.4.2 fitted wannier functions for periodic local correlation methods
5.4.3 symmetry exploitation in local mp2 method for periodic systems
6 semiempirical lcao methods for molecules and periodic systems
6.1 extended h/ickel and mulliken-r/idenberg approximations
6.1.1 nonself-consistent extended h/ickel-tight-binding method
6.1.2 iterative mulliken-r/idenberg method for crystals
6.2 zero-differential overlap approximations for molecules and crystals
6.2.1 zero-differential overlap apl~roximations for molecules
6.2.2 complete and intermediate neglect of differential overlap for crystals
6.3 zero-differential overlap approximation in cyclic-cluster model
6.3.1 symmetry of cyclic-cluster model of perfect crystal
6.3.2 semiempirical lcao methods in cyclic-cluster model
6.3.3 implementation of the cyclic-clnster model in msindo and hartree-fock lcao methods
7 kohn-sham lcao method for periodic systems
7.1 foundations of the density-functional theory
7.1.1 the basic formulation of the density-functional theory
7.1.2 the kohn-sham single-particle equations
7.1.3 exchange and correlation functionals in the local density approximation
7.1.4 beyond the local density approximation
7.1.5 the pair density. orbital-dependent exchange-correlation functionals
7.2 density-functional lcao methods for solids
7.2.1 implementation of kohn-sham lcao method in crystals calculations
7.2.2 linear-scaling dft lcao methods for solids
7.2.3 heyd-scnseria-ernzerhof screened coulomb hybrid functional
7.2.4 are molecular exchange-correlation functionals transferable to crystals?
7.2.5 density-functional methods for strongly correlated systems: sic dft and dft+u approaches part ii applications
basis sets and pseudopotentlals in periodic lcao calculations
8.1 basis sets in the electron-structure calculations of crystals
8.1.1 plane waves and atomic-like basis sets. slater-type functions
8.1.2 molecular basis sets of gaussian-type functions
8.1.3 molecular basis sets adaptation for periodic systems
8.2 nonrelativistic effective core potentials and valence basis sets
8.2.1 effective core potentials: theoretical grounds
8.2.2 gaussian form of effective core potentials and valence basis sets in periodic lcao calculations
8.2.3 separable embedding potential
8.3 relativistic effective core potentials and valence basis sets
8.3.1 relativistic electronic structure theory: dirac-hartree-fock and dirac-kohn-sham methods for molecules
8.3.2 relativistic effective core potentials
8.3.3 one-center restoration of electronic structure in the core region
8.3.4 basis sets for relativistic calculations of molecules
8.3.5 relativistic lcao methods for periodic systems lcao calculations of perfect-crystal properties
9.1 theoretical analysis of chemical bonding in crystals
9.1.1 local properties of electronic structure in lcao hf and dft methods for crystals and post-hf methods for molecules
9.1.2 chemical bonding in cyclic-cluster model: local properties of composite crystalline oxides
9.1.3 chemical bonding in titanium oxides: periodic and molecular-crystalline approaches
9.1.4 wannier-type atomic functions and chemical bonding in crystals
9.1.5 the localized wannier functions for valence bands: chemical bonding in crystalline oxides
9.1.6 projection technique for population analysis of atomic orbitals. comparison of different methods of the chemical- bonding description in crystals
9.2 electron properties of crystals in lcao methods
9.2.1 one-electron properties: band structure, density of states, electron momentum density
9.2.2 magnetic structure of metal oxides in lcao methods: magnetic phases of lamnos and scmno3 crystals
9.3 total energy and related observables in lcao methods for solids
9.3.1 equilibrium structure and cohesive energy
9.3.2 bulk modulus, elastic constants and phase stability of solids: lcao ab-initio calculations
9.3.3 lattice dynamics and lcao calculations of vibrational frequencies
10 modeling and lcao calculations of point defects in crystals
10.1 symmetry and models of defective crystals
10.1.1 point defects in solids and their models
10.1.2 symmetry of supercell model of defective crystals
10.1.3 supercell and cyclic-clnster models of neutral and charged point defects
10.1.4 molecular-cluster models of defective solids
10.2 point defects in binary oxides
10.2.1 oxygen interstitials in magnesium oxide: supercell lcao calculations
10.2.2 neutral and charged oxygen vacancy in a1203 crystal: supercell and cyclic-clnster calculations
10.2.3 supercell modeling of metal-doped rutile tio2
10.3 point defects in perovskites
10.3.1 oxygen vacancy in srtio3
10.3.2 superceu model of fe-doped srtio3
10.3.3 modeling of solid solutions of lacsrl-cmno3
11 surface modeling in lcao calculations of metal oxides
11.1 diperiodic space groups and slab models of surfaces
11.1.1 diperiodic (layer) space groups
11.1.2 oxide-surface types and stability
11.1.3 single- and periodic-slab models of mgo and tio2 surfaces
11.2 surface lcao calculations on tio2 and sno2
11.2.1 cluster models of (110) tio2
11.2.2 adsorption of water on the tio2 (rutile) (110) surface: comparison of periodic lcao-pw and embedded-cluster lcao calculations
11.2.3 single-slab lcao calculations of bare and hydroxylated sno2 surfaces
11.3 slab models of srtio3, srgro3 and lamno3 surfaces
11.3.1 hybrid hf-dft comparative study of srzro3 and srtio3 (001) surface properties
11.3.2 f center on the srtio3 (001) surface
11.3.3 slab models of lamno3 surfaces
a matrices of the symmetrical supercell transformations of 14 three-dimensional bravais lattices breciprocal matrices of the symmetric supercell transformations of the three cubic bravais lattices c computer programs for periodic calculations in basis of localized orbitals
references
index
前言/序言
《量子化學與材料探索:從基礎到前沿》 本書將帶領讀者深入探索量子化學的迷人世界,並揭示其在理解和設計新型材料方麵的強大力量。本書旨在為那些對物質微觀結構及其性質背後的量子力學原理感興趣的學生、研究人員及工程師提供一個全麵而深入的導論。我們將從量子力學的基本概念齣發,逐步構建起理解原子、分子和固體行為所需的理論框架。 核心概念的循序漸進: 本書的起點是量子化學的基石——薛定諤方程。我們將詳細闡述其物理意義,並介紹求解該方程的各種方法,包括近似方法的原理與應用。讀者將學習到如何利用量子力學來描述電子在原子和分子中的行為,理解原子軌道的概念,以及原子軌道如何組閤形成分子軌道。 從分子到晶體: 本書將重點關注如何將量子化學的原理應用於周期性體係,即晶體。我們將詳細介紹綫性組閤原子軌道(LCAO)方法,這是一種在第一性原理計算中廣泛應用的近似方法。通過LCAO方法,我們可以構建齣描述固體中電子波函數的基組,並進一步計算其能量和性質。 第一性原理計算的精髓: “第一性原理”計算意味著我們僅依賴於基本的物理常數和量子力學原理,而不引入任何經驗參數。本書將深入探討實現這一目標的關鍵技術,包括: 哈特裏-福剋(Hartree-Fock, HF)方法: 這是最早的自洽場(SCF)方法之一,它將多電子波函數近似為單電子波函數的斯萊特行列式。我們將詳細介紹HF方法的原理、優缺點以及其在固體計算中的局限性。 密度泛函理論(Density Functional Theory, DFT): 作為當前應用最廣泛的第一性原理計算方法,DFT將電子體係的能量視為電子密度的一個泛函。本書將深入剖析DFT的核心概念,包括 Hohenberg-Kohn定理、Kohn-Sham方程,並重點介紹各種交換-關聯泛函的性質、適用範圍和發展趨勢。我們將詳細闡述如何利用DFT來計算晶體的電子結構、能量、力以及各種激發態性質。 超越HF和DFT的方法: 為瞭更精確地描述電子關聯效應,本書還將介紹一些更高級的計算方法,如微擾理論(如MPn方法)和耦閤簇(Coupled Cluster, CC)理論,並討論它們在固體量子化學計算中的潛在應用和挑戰。 晶體結構與性質的連接: 本書將重點關注第一性原理計算如何為我們揭示晶體的結構與性質之間的深刻聯係。我們將學習如何: 計算電子能帶結構: 繪製電子在布裏淵區內的能量隨動量變化的麯綫,從而理解材料的導電性、光學性質和磁性等。 計算態密度(Density of States, DOS): 分析不同能量的電子在體係中齣現的可能性,這對於理解材料的光學吸收、電荷傳輸以及化學反應活性至關重要。 計算晶格動力學: 研究晶體中原子振動的模式(聲子),這直接影響材料的熱容、熱導率以及超導電性等。 計算彈性常數和機械性能: 瞭解材料在受力時的形變行為,預測其強度、硬度和韌性。 計算化學勢和相穩定性: 預測不同化學組分在特定條件下的穩定存在形式,指導材料的閤成與相變研究。 研究錶麵與界麵性質: 探討晶體錶麵和不同晶體之間界麵的電子結構和化學反應活性,這對於催化、傳感器和半導體器件的設計至關重要。 實際應用與前沿展望: 本書的最後部分將著眼於第一性原理計算在現代材料科學研究中的廣泛應用,包括但不限於: 新能源材料: 如鋰離子電池材料、太陽能電池材料、催化劑等。 半導體與電子材料: 探索新型半導體材料的電子特性,設計高性能電子器件。 磁性材料: 理解和設計具有特定磁學行為的材料。 超導材料: 探索高溫超導的微觀機製。 二維材料: 如石墨烯、過渡金屬二硫化物(TMDs)等新型二維材料的電子和光學性質。 本書不僅提供理論知識,還將引導讀者瞭解實際的計算軟件和工作流程,使讀者能夠獨立進行相關的理論計算和數據分析。通過本書的學習,讀者將能夠運用量子化學的第一性原理方法,更深入地理解物質的本質,並為設計和發現具有革命性性能的新材料提供強大的理論工具。