Does the LCAO Method Create Basis Sets for Tight-Binding and Quantum Dots?

[Modey3]

Hello,

Haven't been here in a while. Does the Linear Combination of Atomic Orbitals (LCAO) method of developing a basis set imply tight-binding ? Is there a way of using this basis set for not so tigtly bound (there is appreciable overlap) atomic orbitals and still maintain orthagonality between the atomic orbitals, which is required for a basis set representing the lattice wavefuntion ? I'm leaning towards no, but maybe somebody else has other information.

Best Regards

Modey3

 

[inha]

I'd lean to no aswell. If you have appreciative overlap you can't really use perturbation theory to get the eigenstates. A couple of texts I checked also assumed that there's no overlap at all.

 

[marlon]

Is there a way of using this basis set for not so tigtly bound (there is appreciable overlap) atomic orbitals and still maintain orthagonality between the atomic orbitals, which is required for a basis set representing the lattice wavefuntion ?
Modey3

One can even use the LCAO approach to study metals like Ta. I am currently doing such DFT simulations where i use a DZP basis set to describe the electronic wavefunctions. Keep in mind that these orbitals are NOT really the QM atomic orbitals. They contain parametrisations that arise from the DFT formalism. Check the Vanderbilt website for more info.

marlon

 

[Modey3]

Thanks Marlon,

DZP basis sets are new to me (I just started learning about Ab Initio modeling). Are they only used to provide the basis sets for DFT , or can they be applied to tight-binding schemes even though they arn't atomic orbitals.

This is a little off topic. When studying quantum dots that have limited periodicity. Is it true that the wave function of an electron will not have the form dictated by Blochs Theorem? When one does tight binding calculations for quantum dots do we throw out the requirement that the LCAOs for each orbital (s,p etc..) obey Blochs Theorem? I'm still trying to learn the subtle difference in doing bulk and nanostructure calculations.

Regards

Modey3

 

[marlon]

Thanks Marlon,

DZP basis sets are new to me (I just started learning about Ab Initio modeling). Are they only used to provide the basis sets for DFT , or can they be applied to tight-binding schemes even though they arn't atomic orbitals.

Yes ofcourse. These basis sets contain parameters that you can change. By changing them you acquire wavefunctions that resemble the atomic orbitals at hand while keeping the computational effort "low".

This is a little off topic. When studying quantum dots that have limited periodicity. Is it true that the wave function of an electron will not have the form dictated by Blochs Theorem? When one does tight binding calculations for quantum dots do we throw out the requirement that the LCAOs for each orbital (s,p etc..) obey Blochs Theorem? I'm still trying to learn the subtle difference in doing bulk and nanostructure calculations.

Regards

Modey3

The Bloch Theorem is valid due to the atomic/crystal structure of the material at hand. Even if the material is very small, Blochwaves can still be used as long as there is certain crystal symmetry.

For example, Bloch waves are used in interface simulations of a metal gate and a high k material. The magnitude of such a system is in the nanometer range (ie the thickness). Keep in mind that with DFT, one can only simulate input cells containing 200 atoms at maximum !

regards
marlon