Revision notes for the Theory of Nanoscale Structures
As this is the first time that this course has been given in its current form I am providing the following notes as a guide to the *type* of question that might arise in the examination.
Prof. NM Harrison.
You should be able to;
Explain why density functional theory is required for large systems ie: why can't the Schroedinger equation be solved exactly ?
Provide a qualitative argument establishing the central idea of density functional theory - that the energy is a unique functional of the total electron density.
Explain the concept of the exchange correlation hole (or pair density matrix) and its relevance for analysing the performance of approximations to DFT.
Explain why the crude local density approximation to DFT works rather well in practice.
Explain how and why the GGA improves on the LDA ?
Explain why the early attempts to improve the LDA by including gradient corrections fail ?
Demonstrate an understanding of why DFT is not directly applicable to excited states.
Provide a qualitative argument explaining the role of self-interaction in DFT and in particular how it affects the eigenvalues and the apparent band gap. How do the Hartree-Fock, LDA, GGA and hybrid-exchange (B3LYP) approximations fit into this picture ?
Explain how molecular dynamics can be used to compute atom trajectories from DFT energy and force calculations.
Explain how molecular dynamics can be used to compute thermodynamics functions.
Demonstrate an understanding of how molecular dynamics can be used to study chemical reactions and comment on its advantages and disadvantages relative to other methods such as mapping the energy surface and using transition state theory.
Demonstrate an understanding of the Pauli exclusion principle its influence on electron delocalisation and the consequences of this for magnetic interactions.
Explain the physical origin of Hund's rules.
Provide a qualitative discussion of the occurrence and nature of the magnetism in transition metals (eg: Fe, Co, Ni) and transition metal oxides (eg: FeO, CoO, NiO).
Give a qualitative discussion of the origin of electronic self-interaction in DFT and its consequences for physical properties including the band gap and magnetic state.
Discuss the vibrational states of water on TiO2 and their explanation in terms of first principles molecular dynamics.
You do not need to be able to;
Reproduce mathematical derivations of the DFT theorems, Hartree-Fock theory or the Kohn Sham equations.