A gallery of real crystal structures¶

You’ll learn: the one shared pattern behind vibe-qc’s real-crystal example set — nine structure types, each run at RHF, B3LYP, and PBE — so you can adapt any of them as a starting point for your own material.

This page is a map, not a derivation: for a full first-principles walkthrough of why periodic Gaussian-basis SCF needs pob-TZVP, IBZ k-mesh reduction, and how to read band structure/DOS/orbital cubes off the result, see Why solid-state calculations use pob-TZVP and the deep single-system walkthrough, Solid-state walkthrough: LiH rocksalt with pob-TZVP. This page instead surveys the other nine real structures in examples/periodic/, which have no tutorial coverage today, and shows the pattern once so you don’t have to read all ~27 nearly-identical scripts to find it.

The shared pattern¶

Every script in the gallery below follows the same shape: a lattice matrix and fractional-feeling Cartesian positions in Å, converted to bohr, built into a PeriodicSystem, and run at Γ through the native GDF route:

from pathlib import Path
import numpy as np
from vibeqc import Atom, BasisSet, PeriodicSystem, run_periodic_job

ANG2BOHR = 1.0 / 0.529177210903

CELL_ANG = [[3.567, 0.0, 0.0], [0.0, 3.567, 0.0], [0.0, 0.0, 3.567]]
ATOM_DATA = [('C', [0.0, 0.0, 0.0]), ('C', [2.67525, 0.89175, 1.7835]), ...]

cell_bohr = np.array(CELL_ANG, dtype=float) * ANG2BOHR
Z_BY_SYM = {"C": 6, ...}   # every script carries its own small lookup
atoms = [Atom(Z_BY_SYM[sym], [x * ANG2BOHR for x in pos])
         for sym, pos in ATOM_DATA]

system = PeriodicSystem(3, cell_bohr, atoms)
basis = BasisSet(system.unit_cell_molecule(), "pob-tzvp")

run_periodic_job(
    system, basis,
    method="RHF",                 # or method="RKS", functional="b3lyp" / "pbe"
    output=Path(__file__).with_suffix(""),
    use_diis=True,
    fmixing_percent=30.0,         # mirrors CRYSTAL's default FMIXING
    max_iter=80,
    conv_tol_energy=1e-7,
)

fmixing_percent=30.0 is there deliberately: it mirrors CRYSTAL’s default Fock/KS-matrix mixing, which is part of why these scripts’ comments describe cross-checking against CRYSTAL14/PySCF references. The route underneath is the native Γ-point GDF driver (run_rhf_periodic_gamma_gdf / its RKS sibling) — see Choosing a periodic method if you need a different route (multi-k, BIPOLE, GPW/GAPW).

The nine structures¶

Each has its own directory under examples/periodic/ with RHF, RKS-B3LYP, and RKS-PBE variants sharing the pattern above (lattice parameters below are the actual values each script’s CELL_ANG uses — verified by reading the scripts, not looked up separately):

Structure	Type	Cell (Å)	Basis
`C-diamond`	Diamond cubic carbon	cubic a = 3.567	pob-TZVP
`Si-diamond`	Diamond cubic silicon	cubic a = 5.431	pob-TZVP
`NaCl-rocksalt`	Rocksalt (NaCl-type)	cubic a = 5.64	pob-TZVP
`MgO-rocksalt`	Rocksalt (NaCl-type)	cubic a = 4.21 (2-atom primitive)	pob-TZVP + a separate sto-3g Γ target
`Ne-fcc`	FCC solid neon	cubic a = 4.43	pob-TZVP
`SiO2-alpha-quartz`	α-quartz	trigonal, a = 4.9134, c = 5.4052	pob-TZVP
`TiO2-rutile`	Rutile	tetragonal, a = 4.5937, c = 2.9587	pob-TZVP
`ZnO-wurtzite`	Wurtzite	hexagonal, a = 3.2495, c = 5.2069	pob-TZVP
`Al2O3-corundum`	α-corundum, space group R-3c (#167)	hexagonal, a = 4.7589, c = 12.991	sto-3g (RHF only)

(LiH-rocksalt also lives in this directory with the same three-method pattern, but gets its own deep walkthrough — see Solid-state walkthrough: LiH rocksalt with pob-TZVP instead of repeating it here.)

Two structures don’t quite follow the plain pattern above:

MgO-rocksalt additionally ships a CRYSTAL14 side-by-side comparison: MgO-rocksalt-RHF-pobtzvp-mp8-gdf.py builds the same 2-atom FCC primitive cell CRYSTAL14 uses internally and runs it on an 8x8x8 k-mesh through the native multi-k GDF backend end to end, reporting the SCF energy, HOMO/LUMO gap, and IBZ-expansion metadata. A matching .d12 CRYSTAL14 input and a README-crystal14-parity.md sit in the same directory for the actual parity comparison.
Al2O3-corundum uses ASE’s ase.spacegroup.crystal to build the 12 Al + 18 O conventional cell from the space group and Wyckoff parameters directly (R-3c, a = 4.7589 Å, c = 12.991 Å, from Springer Materials entry sd_1400479) rather than hand-listing atom positions — worth a look if you want to build a structure from its space group instead of pasting fractional coordinates by hand. It also only has an RHF/sto-3g variant, no B3LYP/PBE siblings.

Adapting one for your own material¶

The fastest path to a new structure: copy the closest existing script (same structure type, if one matches), replace CELL_ANG and ATOM_DATA with your own lattice and basis, and keep everything else. If your basis isn’t pob-TZVP-covered for an element you need, see Why solid-state calculations use pob-TZVP for when a molecular basis is still safe to use instead.

Next¶

Why solid-state calculations use pob-TZVP for the basis theory these scripts all depend on.
Solid-state walkthrough: LiH rocksalt with pob-TZVP for the deep single-system version of this pattern: k-mesh convergence, band structure, DOS, and orbital cubes.
Choosing a periodic method for GDF vs. BIPOLE vs. GPW/GAPW, if Γ-point GDF isn’t the right route for your system.