advanced-electronic

name	advanced-electronic
description	Advanced Electronic Structure Methods (5 sub-skills: gw-approximation, hubbard-u, spin-orbit-coupling, topological-invariants, van-der-waals)

Advanced Electronic Structure Methods

Beyond-standard-DFT methods for accurate electronic properties in materials where standard GGA/LDA fails qualitatively. These methods address strong correlation, spin-orbit physics, topological classification, quasiparticle energies, and long-range dispersion interactions.

Sub-Skills

Sub-Skill	Directory	Use Case	Key QE / VASP Keywords
DFT+U (Hubbard U)	hubbard-u/	Strongly correlated d/f-electron systems, Mott insulators, transition metal oxides	lda_plus_u, Hubbard_U(i), HUBBARD card, hp.x; VASP: LDAU, LDAUU
Spin-Orbit Coupling	spin-orbit-coupling/	Heavy elements, topological insulators, Rashba splitting, magnetic anisotropy, band inversion	noncolin, lspinorb, FR pseudopotentials; VASP: LSORBIT, LNONCOLLINEAR
Topological Invariants	topological-invariants/	Z2 classification, Wilson loops, Berry phase, Wannier charge centers, topological insulator screening	z2pack, pw2wannier90.x, Wannier90; parity eigenvalues at TRIM
GW Approximation	gw-approximation/	Accurate quasiparticle band gaps, band alignment, comparison with photoemission	Yambo / SternheimerGW interface for QE; VASP: ALGO=GW0, ALGO=scGW
Van der Waals Corrections	van-der-waals/	Layered materials, molecular crystals, adsorption, MOFs	vdw_corr='dft-d3', input_dft='rvv10'; VASP: IVDW, LUSE_VDW

Decision Guide

Does your system have open d or f shells (TM oxides, lanthanides, actinides)?
  YES --> DFT+U (hubbard-u/)
  NO  --> Standard DFT may suffice for ground-state energetics

Does your system contain heavy elements (Z > 50) or involve spin-dependent phenomena?
  YES --> Spin-Orbit Coupling (spin-orbit-coupling/)
  NO  --> Scalar-relativistic pseudopotentials are sufficient

Do you need to classify topological order (Z2, Chern number, surface states)?
  YES --> Topological Invariants (topological-invariants/)
  NO  --> Standard band structure is sufficient

Do you need accurate band gaps (comparison with photoemission/optical data)?
  YES --> GW Approximation (gw-approximation/)
  NO  --> DFT gaps with scissors correction may suffice

Are van der Waals interactions important (layered, molecular, adsorption)?
  YES --> Van der Waals Corrections (van-der-waals/)
  NO  --> Standard DFT is fine

These methods are NOT mutually exclusive. Common combinations include:

• DFT+U + SOC for correlated topological materials (e.g., iridates, SmB6)
• SOC + topological invariants for TI classification (Bi2Se3, Bi2Te3)
• DFT+U + vdW for correlated layered materials (e.g., NiPS3, CrI3)
• GW + SOC for accurate gaps in heavy-element semiconductors

Method Selection

Material Class	Recommended Method(s)	Example Systems
Transition metal oxides	DFT+U	NiO, Fe2O3, LiFePO4, SrTiO3
f-electron compounds	DFT+U (large U)	CeO2, UO2, SmB6
Topological insulators	SOC + topological invariants	Bi2Se3, Bi2Te3, HgTe
Rashba systems	SOC	BiTeI, GeTe, oxide interfaces
Semiconductors (accurate gaps)	GW	Si, GaAs, ZnO, MgO
Layered materials	vdW corrections	graphite, MoS2, h-BN, black P
Molecular crystals	vdW corrections	organic semiconductors, ice
Correlated topological	DFT+U + SOC + Z2	SmB6, pyrochlore iridates
2D magnets	DFT+U + vdW + SOC	CrI3, Fe3GeTe2

General Prerequisites

• Quantum ESPRESSO 7.5 installed (pw.x, pp.x, hp.x, projwfc.x, bands.x)
• For GW: Yambo or SternheimerGW (QE interface) or VASP with GW support
• Fully relativistic pseudopotentials for SOC calculations (PSlibrary _rel or ONCVPSP _FR)
• Wannier90 for topological invariant workflows
• Python packages: pymatgen, ASE, numpy, scipy, matplotlib, z2pack