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 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

　　It is traditional for quantum theory of molecular systems（molecular quantum chemistry） to describe the properties of amany-atom system on the grounds of in- teratomic interactionsapplying the linear combination of atomic orbitals （LCAO）approximation in the electronic-structure calculations. The basisof the theory of the electronic structure of solids is theperiodicity of the crystalline potential and Bloch- typeone-electron states， in the majority of cases approximated by alinear combina- tion of plane waves （LCPW）. In a quantum chemistryof solids the LCAO approach is extended to periodic systems andmodified in such a way that the periodicity of the potential iscorrectly taken into account， but the language traditional forchemistry is used when the interatornic interaction is analyzed toexplain the properties of the crystalline solids. At first， thequantum chemistry of solids was considered simply as theenergy-band theory　or the theory of the chemical bond intetrahedral semi-conductors . From the beginning of the 1970s theuse of powerful computer codes has become a common practice inmolecular quantum chemistry to predict many properties of moleculesin the first-principles LCAO calculations. In the condensed-matterstudies the accurate de*ion of the system at an atomic scalewas much less advanced .

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 anddifferences

2.1.2 translation symmetry of crystals. point symmetry of bravaislattices. crystal class

2.2 space groups

2.2.1 space groups of brawis lattices. symmorphic and nonsymmorphicspace 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 computercodes

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.blochfunctions

3.1.1 symmetry of molecular and crystalline orbitals

3.1.2 irreducible representations of translation group. brillouinzone

3.1.3 stars of wavevectors. little groups. fhll representations ofspace groups

3.1.4 small representations of a little group. projectiverepresentations of point groups

3.2 site symmetry and induced representations of space groups

3.2.1 induced representations of point groups. localized molecularorbitals

3.2.2 induced representations of space groups in q-basis

3.2.3 induced representations of space groups in k-basis.bandrepresentations

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 andsrzro3 crystals

3.3 symmetry of localized crystalline orbitals. wannierfunctions

3.3.1 symmetry of localized orbitals and band representations ofspace groups

3.3.2 localization criteria in wannier-function generation

3.3.3 localized orbitals for valence bands: lcaoapproximation

3.3.4 variational method of localized wannier-function generationon 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 moleculesand crystals

4.1.2 symmetry of the one-electron approximation hamiltonian

4.1.3 restricted and unrestricted hartree-fock lcao methods formolecules

4.1.4 specific features of the hartree-fock method for a cyclicmodel of a crystal

4.1.5 restricted hartree-fock lcao method for crystals

4.1.6 unrestricted and restricted open-shell hartree-fock methodsfor 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-pointsmeshes

4.3 density matrix of crystals in the hartree-fock method

4.3.1 properites of the one-electron density matrix of acrystal

4.3.2 the one-electron density matrix of the crystal in the lcaoapproximation

4.3.3 interpolation procedure for constructing an approximatedensity matrix for periodic systems

5 electron correlations in molecules and crystals

5.1 electron correlations in molecules: post-hartree-fockmethods

5.1.1 what is the electron correlation ?

5.1.2 configuration interaction and multi-configurationself-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 periodicsystems

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 andbandgap

5.3 atomic orbital laplace-transformed mp2 theory for periodicsystems

5.3.1 laplace mp2 for periodic systems: unit-cell correlationenergy

5.3.2 laplace mp2 for periodic systems:bandgap

5.4 local mp2 electron-correlation method for nonconductingcrystals

5.4.1 local mp2 equations for periodic systems

5.4.2 fitted wannier functions for periodic local correlationmethods

5.4.3 symmetry exploitation in local mp2 method for periodicsystems

6 semiempirical lcao methods for molecules and periodicsystems

6.1 extended h/ickel and mulliken-r/idenberg approximations

6.1.1 nonself-consistent extended h/ickel-tight-bindingmethod

6.1.2 iterative mulliken-r/idenberg method for crystals

6.2 zero-differential overlap approximations for molecules andcrystals

6.2.1 zero-differential overlap apl~roximations for molecules

6.2.2 complete and intermediate neglect of differential overlap forcrystals

6.3 zero-differential overlap approximation in cyclic-clustermodel

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 andhartree-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 densityapproximation

7.1.4 beyond the local density approximation

7.1.5 the pair density. orbital-dependent exchange-correlationfunctionals

7.2 density-functional lcao methods for solids

7.2.1 implementation of kohn-sham lcao method in crystalscalculations

7.2.2 linear-scaling dft lcao methods for solids

7.2.3 heyd-scnseria-ernzerhof screened coulomb hybridfunctional

7.2.4 are molecular exchange-correlation functionals transferableto 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 ofcrystals

8.1.1 plane waves and atomic-like basis sets. slater-typefunctions

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 basissets

8.2.1 effective core potentials: theoretical grounds

8.2.2 gaussian form of effective core potentials and valence basissets in periodic lcao calculations

8.2.3 separable embedding potential

8.3 relativistic effective core potentials and valence basissets

8.3.1 relativistic electronic structure theory: dirac-hartree-fockand dirac-kohn-sham methods for molecules

8.3.2 relativistic effective core potentials

8.3.3 one-center restoration of electronic structure in the coreregion

8.3.4 basis sets for relativistic calculations of molecules

8.3.5 relativistic lcao methods for periodic systems lcaocalculations 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 dftmethods for crystals and post-hf methods for molecules

9.1.2 chemical bonding in cyclic-cluster model: local properties ofcomposite crystalline oxides

9.1.3 chemical bonding in titanium oxides: periodic andmolecular-crystalline approaches

9.1.4 wannier-type atomic functions and chemical bonding incrystals

9.1.5 the localized wannier functions for valence bands: chemicalbonding in crystalline oxides

9.1.6 projection technique for population analysis of atomicorbitals. comparison of different methods of the chemical- bondingdescription 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: magneticphases of lamnos and scmno3 crystals

9.3 total energy and related observables in lcao methods forsolids

9.3.1 equilibrium structure and cohesive energy

9.3.2 bulk modulus, elastic constants and phase stability ofsolids: lcao ab-initio calculations

9.3.3 lattice dynamics and lcao calculations of vibrationalfrequencies

10 modeling and lcao calculations of point defects incrystals

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 chargedpoint 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 lcaocalculations

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 tio2surfaces

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 lcaocalculations

11.2.3 single-slab lcao calculations of bare and hydroxylated sno2surfaces

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 14three-dimensional bravais lattices breciprocal matrices of thesymmetric supercell transformations of the three cubic bravaislattices c computer programs for periodic calculations in basis oflocalized orbitals

references

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