固体量子化学

作者简介

《固体量子化学:晶体的原子轨道线性组合第一性原理计算方法》全面系统地介绍了计算周期系统电子结构的原子轨道线性组合（LCAO）第一性原理计算方法。全书内容分为两部分。第一部分介绍了周期系统中原子轨道线性组合方法的基本理论，Hartree—Fock LCAO方法，基于密度泛涵理论的LCAO方法等。作者在晶体的局域化轨道基础上讨论了周期系统的电子关联效应，还讲解了如何利用LCAO方法进行周期系统的化学键分析等。第二部分讨论了应用原子轨道线性组合方法计算体材料的性质，包括磁有序和晶体结构优化。此外还介绍了利用该方法计算非金属固体中的点缺陷和晶体表面电子结构等。《固体量子化学:晶体的原子轨道线性组合第一性原理计算方法》内容全面，讲解清楚，简单易懂，对计算凝聚态物理和量子化学领域的物理学家和研究生来讲，是一本非常难得的理想教材和入门读物。目次：第一部分：理论；（1）简介；（2）空间群和晶体结构；（3）晶体轨道的对称性和局域化；（4）周期系统的Hartree–Fock LCAO方法；（5）分子和晶体中的电子关联；（6）分子和周期系统中的半经验LCAO方法；（7）周期系统中的Kohn–Sham LCAO方法；第二部分：应用；（8）周期性LCAO计算中的基础集和赝势；（9）理想晶体性质的LCAO计算；（10）具有点缺陷的晶体的模型化和LCAO计算；（11）金属氧化物LCAO计算中的表面模型化；附录；参考文献；索引。

书籍目录

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

编辑推荐

《固体量子化学:晶体的原子轨道线性组合第一性原理计算方法》适合凝聚态物理、材料科学和量子化学等专业的高年级本科生、研究生和相关专业的科研人员参考阅读。

内容概要

作者：(俄罗斯)叶瓦列斯托夫(R.A.Evarestov)

章节摘录

版权页：   插图：   2.1 Translation and Point Symmetry of Crystals 2.1.1 Symmetry of Molecules and Crystals: Similarities and DifferencesMolecules consist of positively charged nuclei and negatively charged electrons movingaround them.If the translations and rotations of a molecule as a whole are excluded,then the motion of the nuclei,except for some special cases,consists of small vibrations about their equilibrium positions.Orthogonal operations(rotations throughsymmetry axes,reflections in symmetry planes and their combinations) that transform the equilibrium configuration of the nuclei of a molecule into itself are called thesymmetry operations of the molecule.They form a group F of molecular symmetry.Molecules represent systems from finite(sometimes very large) numbers of atoms,andtheir symmetry is described by so-called point groups of symmetry.In a molecule it isalways possible to so choose the origin of coordinates that it remains fixed under alloperations of symmetry.All the symmetry elements(axes,planes,inversion center)are supposed to intersect in the origin chosen.The point symmetry of a molecule isdefined by the symmetry of an arrangement of atoms forming it but the origin ofcoordinates chosen is not necessarily occupied by an atom. In modern computer codes for quantum-chemical calculations of molecules thepoint group of symmetry is found automatically when the atomic coordinates aregiven.In this case,the point group of symmetry is only used for the classification ofelectronic states of a molecule,particularly for knowledge of the degeneracy of theone-electron energy levels.To make this classification one needs to use tables of irreducible representations of point groups.The latter are given both in books[13-15]and on an Internet site[16]Calculation of the electronic structure of a crystal(forwhich a macroscopic sample contains 1023 atoms) is practically impossible without the knowledge of at least the translation symmetry group.The latter allows thesmallest possible set of atoms included in the so-called primitive unit cell to be considered.However,the classification of the crystalline electron and phonon states requiresknowledge of the full symmetry group of a crystal(space group).The structure of theirreducible representations of the space groups is essentially more complicated anduse of existing tables[17]or the site[16]requires knowledge of at least the basics of space-group theory.

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