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 .
目錄：
part i theory
1 introduction
2 space groups and crystalline structures
2.1 translation and point symmetry of crystlz
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 hickel and mulliken-ridenberg approximations
6.1.1 nonself-consistent extended hickel-tight-binding
method
6.1.2 iterative mulliken-ridenberg 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
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