I was reviewing many electron computational methods recently and got a bit confused about relation between different approaches. In particular in what is essential elemental difference between Hartree-Fock (HF) and tight binding (TB) for example? It could be stupid question, sorry, I am not that deeply familiar with theory. And just for note I am physisist more than chemist. I know that HF is more general method not essentially relying on LCAO approximation. But say we mainly use LCAO for HF anyway in most cases. In TB the hamiltonian matrix elements $H_{ij}$ are mainly used from some tabulated values or fitting with experimental data. This is good for speedy calculations. But can we just use LCAO orbitals and calculate matrix elements analytically using general manybody hamiltonian? Will not it become HF method essentially?


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