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
- 01What Is a Group?12m
- 02Symmetry Groups in Action15m
- 03Representations and Matrices18m
- 04Character Tables15m
- 05Reducible and Irreducible Representations18m
- 06The Great Orthogonality Theorem20m
- 07Direct Products and Selection Rules15m
- 08Double Groups and Spin18m
- 09Symmetry-Adapted Basis Functions15m
- 10Group Theory in VASP Output12m
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
- 01The Band-Gap Problem and Why DFT Needs Help18m
- 02Hartree–Fock Exchange Recap18m
- 03Self-Interaction Error in DFT15m
- 04Hybrid Functionals: PBE0, B3LYP, HSE0620m
- 05Range-Separated Hybrids — HSE in Detail18m
- 06Iterative Diagonalization: Davidson and RMM-DIIS22m
- 07Density Mixing: Pulay, Broyden, and Kerker18m
- 08Direct Minimization and Preconditioning15m
- 09Computational Cost and Acceleration of Hybrid DFT15m
- 10Running Hybrid DFT in VASP18m
VASP Project— Mn:CdSe simulation from scratch.
VASP in Practice — Mn:CdSe Simulation
Complete VASP workflow from structure setup to publication-quality results for Mn-doped CdSe quantum dots
- 01VASP Input Files Overview15m
- 02Building the CdSe Supercell18m
- 03Convergence Testing15m
- 04Structural Relaxation15m
- 05Mn Doping: Substitutional Defects18m
- 06Spin-Polarized Calculations18m
- 07Band Structure and DOS Analysis20m
- 08Optical Properties Calculation15m
- 09Post-Processing and Visualization15m
- 10Publication-Quality Results12m
Where the book lands in practice.
VASP in Practice — Mn:CdSe Simulation
Complete VASP workflow from structure setup to publication-quality results for Mn-doped CdSe quantum dots
Open chapter70 sections. Begin with one.
Chapter 1 — The Architecture of Crystals — Real Space — is where every reader starts.