dxtb —An efficient and fully differentiable framework for extended tight-binding

Marvin Friede, Christian Hölzer, Sebastian Ehlert, and Stefan Grimme (2024)
Highlighted by Jan Jensen



When I first saw this paper on SoMe I was incredibly excited because I first thought it was the release of the long-anticipated g-xTB method (I have a bad habit of reading very superficially and seeing what I want to see). But then I skimmed the abstract, saw my mistake, and promptly forgot about it the paper until I saw Jan-Michael Mewes' recent Bluesky thread.

The paper described a fully differentiable Python-baed PyTorch implementation of GFN1-xTB. In the paper they use it to compute some new molecular properties, but the real strength will be in developing new xTB methods for specific applications, i.e. a physics-based alternative to ML potentials. Jan give an illustrative example of this in his thread.

While this is application is mentioned in the paper it doesn't contain an actual application. It remains to be seen how fiddly the actual retraining will be, compared to MLPs, but the hope it that the bespoke xTB methods will require significantly less training data and be more broadly applicable than MLPs.

That's assuming that g-xTB doesn't solve all our problems, which is very much my expectation based on Grimme's talks about it (but keep in mind that my listenings skills are even worse than by reading skills).

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Semiempirical Hamiltonians learned from data can have accuracy comparable to Density Functional Theory

Frank Hu, Francis He, David J. Yaron (2022) 
Highlighted by Jan Jensen

Figure 7 from the paper. (c) The authors 2022. Reproduced under the BY-NC-ND licence

This paper uses ML techniques and algorithms (specifically PyTorch) to fit DFTB parameters, which results in a semiempirical quantum method (SQM) that has an accuracy similar to DFT. The advantage of such a physics-based method over a pure ML-based is that it is likely to be more transferable and requires much less training data. This should make it much easier to extend to other elements and new molecular properties, such as barriers.

Parameterising SQMs is notoriously difficult as the molecular properties depend exponentially on many of the parameters. As a result, most SQMs used today have parameterised by hand. The paper presents several methodological tricks to automate the fitting.

One is the use of high-order polynomial spline functions to describe how the Hamiltonian elements depend the fitting-parameters. The functions allow the computation of not only of the first derivative needed for back propagation, but also high-order derivatives, which are used for regularisation to avoid overfitting and keeping the parameters physically reasonable. Finally, the SCF and training loops are inverted to that the he charge fluctuations needed for the Fock operator are updated based on the current model parameters every 10 epochs. This enables computationally efficient back propagation during training, which is important because the training set is on the order of 100k.

Another neat feature is that the final model is simply a parameter file (SKF file), which can be read by most DFTB programs. So there is nothing new for the user to implement. However, currently the implementation is only for CNHO.

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OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features

Zhuoran Qiao, Matthew Welborn, Animashree Anandkumar, Frederick R. Manby, Thomas F. Miller III (2020)
Highlighted by Jan Jensen

Figure 4 from the paper. (c) the authors 2020.

This method takes information from a GFN1-xTB calculation as input to a graph-convolution (GC) NN to predict the difference between DFT and GFN1-xTB total energies. In conventional GC the molecule is typically represented by an adjacency matrix (a binary matrix where 1 indicates a bond) and a list of atomic and bond features, such as nuclear charges and bond orders, associated with each node and edge. This approach uses the diagonal and off-diagonal elements of matrices such as Fock, overlap, and density matrices from a GFN1-xTB calculation as node and edge features, respectively. 

The model gets state-of-the-art accuracies for QM9 total energies and the same model also gets excellent results for conformational energies from a different data set. Basically DFT level accuracy at semiempirical cost (it's not clear to me how it can be faster than the underlying GFN1-xTB calculation, but that might be down to different implementation of the GFN1-xTB method).

It's not clear to me weather the method can be used to optimise geometries, and thereby correct any deficiency in GFN1-xTB structures, and it's also not clear whether the code will be made available.

This work is licensed under a Creative Commons Attribution 4.0 International License.