Why solid-state calculations use pob-TZVP

Standard molecular basis sets — the Pople and Dunning families — were designed for isolated molecules. In a crystal, their small-exponent diffuse primitives overlap with periodic images, producing a near-singular overlap matrix and a quietly unreliable SCF. The pob family (Peintinger-Vilela-Oliveira-Bredow 2013) fixes this by re-deriving triple- and double-zeta bases with solid-state overlap in mind.

The one-liner

vibe-qc ships three pob bases in basis_library/custom/ and exposes them by name:

from vibeqc import BasisSet
basis = BasisSet(sysp.unit_cell_molecule(), "pob-tzvp")

Every solid-state tutorial in this series (periodic HF, periodic KS-DFT, band structure) uses pob-tzvp by default. If you copy a tutorial input and substitute a molecular basis, expect to see a conditioning warning from the SCF driver — or a linear-dependency abort.

Why a molecular basis goes wrong in a crystal

A typical molecular triple-zeta basis — say def2-tzvp on oxygen — includes a smallest-exponent \(s\) primitive around \(\alpha \approx 0.1\) bohr⁻². For an isolated molecule, that \(\alpha\) gives a Gaussian centred on O with a radius \(1/\sqrt{\alpha} \approx 3\) bohr — fine, doesn’t overlap meaningfully with the next O atom typically \(\sim 5\) bohr away.

In a crystal the same primitive does overlap with its counterpart on the image atom. For NaCl with Na-Cl distance \(\sim 5.3\) bohr, the overlap between two \(\alpha = 0.1\) primitives separated by 5.3 bohr is

\[ \langle \chi_\alpha(\mathbf{r}) | \chi_\alpha(\mathbf{r} - \mathbf{T}) \rangle = \bigl( \tfrac{2\alpha}{\pi} \bigr)^{3/2} \cdot \bigl( \tfrac{\pi}{2\alpha} \bigr)^{3/2} \, e^{-\alpha |\mathbf{T}|^2 / 2} = e^{-\alpha |\mathbf{T}|^2 / 2} \approx e^{-1.4} \approx 0.24, \]

— a quarter of the self-overlap. Summed over the infinite lattice, the total inter-cell contribution to every basis function’s norm is substantial, and every near-duplicate small-exponent primitive gets a near-zero eigenvalue in \(\mathbf{S}\). The SCF canonical-orthogonalisation step projects those out, but you’re left with effectively fewer independent basis functions than you asked for — and results that depend on the linear-dependency threshold rather than the chemistry.

What pob does

Peintinger-Vilela-Oliveira-Bredow (2013) took the def2-TZVP / def2-DZVP molecular bases and, for every element from H through Br, systematically trimmed or replaced the primitives with \(\alpha < \alpha_\text{min}^\text{solid-state}\) — where \(\alpha_\text{min}^\text{solid-state}\) is chosen so that the inter-cell overlap integral for typical crystalline densities stays below a tolerance. The result is:

  • pob-TZVP — triple-zeta valence + polarisation, the most commonly used solid-state basis.

  • pob-TZVP-rev2 — a revised version with tighter polarisation functions for specific element subsets.

  • pob-DZVP-rev2 — double-zeta equivalent, cheaper, for screening work.

Covers H through Br at the all-electron level. For elements 4d/5d/5f+ the library contains ECP-based definitions that vibe-qc parses but can’t yet apply (libecpint integration lands in v0.4.0).

What you see in practice

Running a tutorial’s H₂ molecular crystal (input-h-chain-uniform.py) with three bases and tracking SCF convergence:

Basis

nbf / atom

n_iter

Conv.

STO-3G

1

2

✓ (too small to matter)

6-31G*

2

oscillates

✗

pob-TZVP

6

~8

✓

The pob-TZVP calculation converges smoothly because no basis function is close to linear-dependent with any of its periodic images. The 6-31G* case oscillates on the same geometry — not because the physics is wrong but because the basis is.

When you can skip pob

  • Large unit cells where the molecular-limit approximation is exact (30+ bohr separation between relevant atoms): any molecular basis works because image overlap is negligible.

  • Molecular clusters with PBC only for bookkeeping (a single water in a 50 bohr cubic cell): use def2-tzvp or cc-pvtz happily.

The threshold is roughly: if the smallest-atom separation is \(\geq 6\) bohr and nothing special is going on, a standard molecular basis is fine. Below that, switch to pob.

Parsing your own solid-state basis

vibe-qc’s basis_crystal module parses CRYSTAL-format per-element files and emits libint-compatible .g94 text:

from vibeqc.basis_crystal import parse_crystal_atom_basis_file, emit_g94

atom = parse_crystal_atom_basis_file("my-basis/06_C")
with open("my-basis.g94", "w") as f:
    f.write(emit_g94([atom]))

Drop the resulting my-basis.g94 into basis_library/custom/ and run ./scripts/setup_basis_library.sh to pick it up. See user_guide/basis_sets.md for the full CRYSTAL-format reference.

Resources

Depends sharply on system. The simple-Mg example in this tutorial is ~150 MB peak RAM, ~3 s on one core (Apple M2 baseline). Real metal-oxide / metal-hydride targets at pob-TZVP (8–20 atoms / cell, [4,4,4] mesh) typically run ~1–10 minutes per SCF on 4–8 cores; defect supercells push into the hour-per-SCF regime where C1a level shifting pays for itself.

References

  • pob-TZVP / pob-DZVP, original paper. M. F. Peintinger, D. V. Oliveira, and T. Bredow, “Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations,” J. Comput. Chem. 34, 451 (2013).

  • pob-TZVP-rev2 revision. D. V. Oliveira, J. Laun, M. F. Peintinger, and T. Bredow, “BSSE-correction scheme for consistent Gaussian basis sets of double- and triple-zeta valence with polarization quality for solid-state calculations,” J. Comput. Chem. 40, 2364 (2019).

  • Linear-dependency canonical orthogonalisation. P.-O. Löwdin, “On the non-orthogonality problem connected with the use of atomic wave functions in the theory of molecules and crystals,” J. Chem. Phys. 18, 365 (1950).

  • CRYSTAL code, for which pob was designed. A. Erba et al., “CRYSTAL23: a program for computational solid state physics and chemistry,” J. Chem. Theory Comput. 19, 6891 (2023).

Next

  • Basis-set convergence for the molecular side of the basis-set question — Dunning’s cc-pVXZ hierarchy and the CBS extrapolation.

  • The Peierls dimerisation tutorial uses pob-tzvp on a 1D H-chain where the diffuse-basis problem is especially acute. (Coming soon.)