Discussion Overview
The discussion revolves around the applicability of the Linear Combination of Atomic Orbitals (LCAO) method in creating basis sets for tight-binding models and quantum dots. Participants explore the implications of orbital overlap, orthogonality, and the relationship between LCAO and Bloch's Theorem in different contexts, including density functional theory (DFT) and nanostructures.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Homework-related
Main Points Raised
- Some participants question whether the LCAO method implies tight-binding, particularly in cases of appreciable overlap between atomic orbitals, suggesting that orthogonality may not be maintained.
- Others argue that if there is significant overlap, perturbation theory may not be applicable for obtaining eigenstates, referencing texts that assume no overlap.
- One participant mentions using the LCAO approach for metals in DFT simulations with a double-zeta polarized (DZP) basis set, noting that these orbitals are not true quantum mechanical atomic orbitals but rather parametrized forms.
- There is inquiry into whether DZP basis sets can be applied to tight-binding schemes, despite not being atomic orbitals.
- Participants discuss the implications of limited periodicity in quantum dots, questioning whether the wave function of an electron would conform to Bloch's Theorem and whether LCAOs must obey this theorem in tight-binding calculations.
- One response indicates that Bloch's Theorem remains valid under certain crystal symmetries, even in small materials, and mentions its application in interface simulations.
- Concerns are raised about the limitations of DFT simulations, particularly regarding the maximum number of atoms that can be included in input cells.
Areas of Agreement / Disagreement
Participants express differing views on the implications of orbital overlap and the applicability of Bloch's Theorem in the context of quantum dots and tight-binding models. The discussion remains unresolved regarding the extent to which LCAO can be applied under these conditions.
Contextual Notes
Limitations include the dependence on definitions of overlap and orthogonality, as well as the unresolved nature of how LCAO interacts with Bloch's Theorem in non-periodic systems.