Crystallography, Electronic Structure & VASP
From Crystal Symmetry to Mn-Doped Quantum Dot Simulations
Master crystal symmetry, reciprocal space, and electronic structure theory. Build toward Mn-doped CdSe quantum dot simulations using VASP from first principles.
Real Space— Crystal lattices, symmetry, and space groups.
The Architecture of Crystals — Real Space
Lattice vectors, unit cells, Bravais lattices, symmetry operations, point groups, space groups, and supercell construction
Group Theory— Representations, characters, and selection rules.
Mathematics of Symmetry — Group Theory Essentials
Group axioms, representations, character tables, direct products, and selection rules for crystallography
Reciprocal Space— Brillouin zones, diffraction, and k-points.
Reciprocal Space and Diffraction
Reciprocal lattice, Brillouin zones, structure factors, diffraction theory, and k-point sampling
Quantum Theory— DFT, pseudopotentials, and SCF.
Quantum Mechanics for Solids
Free electron model, nearly free electrons, tight binding, DFT foundations, and exchange-correlation functionals
Electronic Structure— Bands, DOS, optics, and defects.
Electronic Structure and Properties
Band structures, DOS, optical properties, magnetic ordering, spin-orbit coupling, and defect physics
- 01Band Structure Fundamentals15m
- 02Density of States12m
- 03Metals, Semiconductors, and Insulators15m
- 04Effective Mass and Carrier Transport18m
- 05Optical Properties from DFT15m
- 06Magnetic Ordering and Spin18m
- 07Spin-Orbit Coupling15m
- 08Defects and Doping18m
- 09Quantum Confinement in Nanocrystals15m
- 10Beyond DFT: GW and Hybrid Functionals20m
Hybrid Functionals & Algorithms— Beyond LDA/GGA — exact exchange, HSE06, and the iterative machinery of DFT codes.
Hybrid Functionals and DFT Algorithms
Self-interaction error, Hartree–Fock exchange, hybrid functionals (PBE0, B3LYP, HSE06), iterative diagonalization, density mixing, and the algorithmic machinery behind modern DFT codes
39 sections. Begin with one.
Chapter 1 — The Architecture of Crystals — Real Space — is where every reader starts.
In progress — 39 of 70 lessons published
31 more sections are still being written and are not part of this count.