Density Functional Theory (DFT) is a mainstay for those studying in-silico molecules or materials. It works well, is performant, and advances in XC functionals will probably make it even more useful and powerful. However, there have been for some time what are called semi-empirical methods that are not as accurate but are much faster and can provide a good initial idea of the electronic structure of a material. They are called semi-empirical because the inner workings are parameterized rather than derived from first principles. This, in essence, makes them fast, but with the downside that they aren't as transferable to other materials or structures, and their formalism may restrict the description of certain electronic effects.
Tight-binding is one such method. It is based on the LCAO approximation where atomic orbitals remain localized on their parent atoms, and molecular/crystal orbitals are constructed as linear combinations of these atomic orbitals. The method uses a minimal atomic orbital basis set and is straightforward to implement for describing electronic structure of molecules and materials. While accuracy is typically lower than DFT, it can be quite effective for certain material classes.
Why is TB a semi-empirical method? Because it has parameters that are fit to data, specifically the hopping integrals between atomic orbitals. These integrals describe electronic interactions between atoms and are determined by fitting to experimental data or higher-level calculations. The hopping integrals are used to construct the Hamiltonian matrix, which is then diagonalized to obtain electronic structure through the secular equation.
Since atomic orbitals are localized on atomic positions, tight-binding works well for molecules, clusters, and materials where electrons form localized chemical bonds, such as semiconductors. However, it is less effective for metals where the minimal atomic orbital basis inadequately describes metallic bonding1 or where strong electron-correlation effects are important.
I've personally never used tight-binding methods extensively, but they can be very useful for the right material or chemical system. However, I believe their traditional limitations are beginning to change, allowing for broader applicability.
A General-Purpose Extended Tight-Binding Calculator
The team behind g-xTB [1] is the Stefan Grimme Lab, which is well-known and deeply respected in computational chemistry. Their motivation for g-xTB is driven by the goal to close the cost-accuracy gap between semi-empirical tight-binding and hybrid-DFT methods without sacrificing speed. The older GFN2-xTB approaches tried to address this by adding dispersion and hydrogen-bonding corrections onto a minimal basis. Ultimately, however, GFN2-xTB aligned more closely with GGA-DFT, lacked Fock exchange, and retained the limitations inherent in rigid atomic orbitals. The idea behind g-xTB is to overcome these limitations and cover most of the periodic table, aiming for DFT-level accuracy at tight-binding speed, enabling calculations involving reaction thermochemistry, excited states, and more.
g-xTB Advancements
Some key areas in which g-xTB advances tight-binding theory are:
- Increased flexibility due to an atom-in-molecule adaptive q-vSZP basis.
- A refined Hamiltonian incorporating range-separated Fock exchange.
- An explicit first-order term and extensions up to the fourth order in the charge-fluctuation series.
- Charge-dependent Pauli-penetration repulsion.
- Streamlined atomic-correction potentials that address basis shortcomings.
Importantly, every element from H to Lr is covered by a single parameter set trained on 32,000 diverse data points, including "mindless" molecules. This significantly enhances usability.
Outcomes
It appears that g-xTB achieves DFT-level accuracy at tight-binding speed. Across GMTKN55, g-xTB reduces GFN2-xTB’s WTMAD-2 from 25.0 to 9.3 kcal mol⁻¹, matching low-cost hybrid composites while running only about 40% slower than GFN2-xTB and approximately 2,400 times faster than B3LYP-D4 on a 2,000-atom complex—at least according to my understanding of the paper's metrics. The authors also highlight that reaction barriers, spin-state gaps, transition-metal thermochemistry, and large biomolecular zwitterions are now tractable without SCF failures. This gives users a robust drop-in replacement for GFNn-xTB and, in many screening and dynamics workflows, a viable substitute for mid-tier DFT calculations.
Usage
The authors have released a Linux binary, which is usable if you set up your input files and parameter paths correctly.
To simplify things, I decided to create an ASE wrapper [2] for the g-xTB calculator. This is a fairly common and straightforward task in ASE. Existing calculator wrappers for other tight-binding codes might work if environment variables are adjusted correctly, but I preferred to write the file parsers from scratch (it goes quickly these days π).
Since the wrapper won't be regularly maintained and given that the g-xTB binary will eventually be implemented in a more mainstream TB framework, I decided to keep it as a git repo you can clone and install:
python -m venv .venv
source .venv/bin/activate
git clone --recursive https://github.com/stefanbringuier/g-xtb-ase
pip install g-xtb-ase/
Warning
Direct pip installation via git+... isn't supported because pip doesn't handle git submodules. You must clone with --recursive to get the required g-xTB binary and parameter files.
To import the calculator object:
from gxtb_ase import GxTB
...
atoms.calc = GxTB(charge=0, spin=0)
What can you do with it?
You can use it like any other ASE calculator to get total energies and forces (stress not yet supported):
from ase.build import molecule
from gxtb_ase import GxTB
atoms = molecule("H2O")
atoms.calc = GxTB(charge=0)
energy = atoms.get_potential_energy()
forces = atoms.get_forces()
This is useful for geometry optimizations or molecular dynamics (MD). For example, running 3 water molecules in MD at 25 °C for 10 ps with g-xTB takes about 45 minutes on a single CPU. However, I'm unsure how accurate structural details (e.g., RDF or structure factors) compare to other methods.
A nice feature of tight-binding methods is their ability to calculate atomic charges, allowing you to analyze charge transfer, bond orders, bond formation/breakage, and dipole moments in response to external fields.
The wrapper doesn't currently extract electronic structure details, but these are available in the log files.
Web App
I built a backend API using FastAPI and quickly assembled a front end. Compute resources are limited, so large molecules or heavy usage might cause crashes, but water or methane tests should work fine. IR and thermochemistry calculations are also supported.
Expect crashes & bugs
The API and front end are hosted on Render and Netlify, respectively, using their free tiers, limiting resources and uptime. The web app isn't fully unit-tested, so expect potential bugs or app crashes.
Here is an example using it to get the optimized (limited steps) geometry for a simple linear molecule, hydrogen cyanide, and then using that to get the IR spectrum and thermochemistry.
 |
| Figure 1. Hydrogen cyanide structure, IR, and thermochemistry using g-xTB web app |
The agreement is overall pretty good with the IR and thermochemistry, although the heat-capacity is way off but could be a conversion/bug issue in the web app. As of now I think g-xTB can only be used for molecules as I don't see how with the format you specify PBC and a cell, but maybe I'm missing something.
Footnotes
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See Jellium Model or Uniform Electron Gas where the electrons behave like a fluid/gas and those models are useful for understanding the effect of placing a positive charge in them to create a metal. ↩
References
[1] T. Froitzheim, M. MΓΌller, A. Hansen, S. Grimme, g-xTB: A General-Purpose Extended Tight-Binding Electronic Structure Method For the Elements H to Lr (Z=1–103), (2025). https://doi.org/10.26434/chemrxiv-2025-bjxvt.
[2] S Bringuier, ASE Wrapper for g-xTB, 2025. https://github.com/stefanbringuier/g-xtb-ase
