Lecture 5 Bonds to Bands

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$Low Energy Electron Diffraction and Microscopy$

Correlation DiagramsHomonuclear diatomicsHeteronuclear diatomicsLecture 511Some symmetry considerations• Strength of bond due to:- overlap of wavefunctions in space- inv. prop. to energy difference of non-interacting orbitals- electron + core repulsionsLecture 5126
Extended Hückel Theory - EHT• Quantum chemical approximation technique (semi-empirical)• Study only valence (i.e., bonding )orbitals• Solve the problem with LCAO variational method, but using ideas fromperturbation theory• The initial state orbitals are atomic Slater type orbitals – STOsXi= Arn−1nexp 0 Y( θ,ϕ)• The initial state energies, H iiare taken from experiments or some othercalculations5r−lmLecture 513Extended Hückel Theory - EHT• Intuitive idea is that the strength of a bond, as represented by the offdiagonalmatrix elements Hij, should be proportional to the extent of overlap(Sij) and the mean energy of the interacting orbitals(Hii+Hjj)/2Hii+ HHij= K2• K is an empirical parameter between 1 and 2• Problems:- H ijis not exact- no charge self consistency- H ijincreases with overlap causing system to show minimum energy whenatoms collapse- no core-core repulsionjjSij• But… EHT does usually show qualitative correct trends in an easilyinterpretable mannerLecture 5147
Page 1 and 2: Lecture 55. The Tight-Binding Appro
Page 3 and 4: Linear Combination of Atomic Orbita
Page 5: Definitions• ψ 1is called bondin
Page 10 and 11: Examples(a) E(k) curve showing the
Page 12 and 13: A polymer - linear array of PtH 4 m
Page 14 and 15: Peierls Distortion• Qualitative e

Lecture 5 Bonds to Bands

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