Andrew F. Zahrt, Yiming Mo, Kakasaheb Y. Nandiwale, Ron Shprints, Esther Heid, and Klavs F. Jensen (2022)

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Important recent papers in computational and theoretical chemistry

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Andrew F. Zahrt, Yiming Mo, Kakasaheb Y. Nandiwale, Ron Shprints, Esther Heid, and Klavs F. Jensen (2022)

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Derek Lowe has highlighted the chemical aspects of this work already, so here I focus on the machine learning, which is pretty interesting. The authors want to predict whether a molecule will react with 4-dicyanobenzene anion after it is oxized at a cathode. They have 141 data points of which 42% show a reaction.

They tested several classification models using Morgan fingerprints as the molecular representation, but got at accuracy of only 60%. The then reasoned that the accuracy could be improved by using DFT features. However, rather than using molecular features they decided to use atomic features from an NBO analysis on the radical cation, neutral, radical anion. The feature vector was then tested on several data sets and shown to perform well.

The question is then how to combine the atomic feature vectors to a molecular representation for the reaction classification. The usual way is graph convolution but that'll require more than 141 data points to optimise. So instead they use graph2vec, which is an unsupervised learning method so it is easy to create arbitrarily large training sets. Graph2vec is analogous to word2vec (or, more accurately, doc2vec) which creates vector representations of words by predicting context in text (i.e. words that often appear close to the word of interest). For graph2vec the context is subgraphs of the input graph.

The graph2vec embedder was then trained on 38k molecules (note that this requires 38k DFT calculations). Using this representation, the accuracy for the reaction classifier increased to 74%, which is a significant improvement compared to Morgan fingerprints. The classifier was then applied to the 38k molecules and 824 were predicted to be reactive. Twenty of these were selected for experimental validation and 16 (80%) were shown to be reactive. That's not a bad hit rate!

I was not aware of graph2vec before reading this paper and it seems like a very promising alternative to graph convolution, especially in the low data regime.

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James Shee, John L. Weber, David R. Reichman, Richard A. Friesner, and Shiwei Zhang (2022)

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Figure 1 from this paper. (c) the authors

This paper highlights a big problem in the field of quantum chemistry and posits that a solution may be right around the corner. The problem is that we still can't routinely predict the thermochemistry of TM-containing compounds with the same degree of accuracy as we can for organic molecules. The main reason is that the former systems often have a high-degree of non-dynamic correlation which means that our CCSD(T) often does not give reliable results. We can model the non-dynamic correlation with CASSCF, but there is no good way to compute the dynamic correlation based on a CASSCF wavefunction. So when different DFT functional results give wildly different predictions for your TM-compound there is no way to tell which method, if any, if the best.

This paper argues that phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) may be the solution to this problem. ph-AFQMC represents the ground state as a stochastic linear combination of Slater determinants mapped as open-ended random walks starting from a trial wavefunction. The method accounts for both non-dynamic and dynamic correlation and the paper argues that chemical accuracy can be achieved with a few hundred random walks, which can be run in parallel and on GPUs.

So what's missing? According to the authors some of the improvements needed include: more efficient ways of reaching the CBS limit, more efficient random walks and a general, automatable protocol to generate optimal trial wave functions. Let's hope these improvements will be made soon, so we can explore a much larger portion of chemical space with confidence.

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Alessandra Toniato, Jan P. Unsleber, Alain C. Vaucher, Thomas Weymuth, Daniel Probst, Teodoro Laino, and Markus Reiher (2022)

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Part of Figure 7 from the paper. (c) The authors 2022. Reproduced under the CC BY NC ND 4.0 license

This is the first paper I have seen on combining automated QM-reaction prediction with ML-based retrosynthesis prediction. The idea itself is simple: for ML-predictions with low confidence (i.e. few examples in the training data) can automated QM-reaction prediction be used to check whether the proposed reaction is feasible, i.e. whether it is the reaction path with the lowest barrier? If so, it could also be used to augment the training data.

The paper considers two examples using the Chemoton 2.0 method: one where the reaction is an elementary reaction and one where there are two steps (the Friedel-Crafts reaction shown above). It works pretty well for the former, but runs into problems for the latter.

One problem for non-elementary reactions is that one can't predict which atoms are chemically active from the overall reaction. Chemoton therefore must consider reactions involving all atom pairs and preferably more pairs of atoms simultaneously. The number of required calculations quickly gets out of hand and the authors conclude that "For such multistep reactions, new methods to identify the individual elementary steps will have to be developed to maintain the exploration within tight bounds, and hence, within reasonable computing time."

However, even when they specify the two elementary steps for the Friedel-Crafts reaction, their method fails to find the second elementary step. The reason for this failure is not clear but could be due to the semiempirical xTB used for efficiency.

So the paper presents an interesting and important challenge to computational chemistry community. I wish more papers did this.

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Frank Hu, Francis He, David J. Yaron (2022)

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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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Paul G. Francoeur, Daniel PeĆ±aherrera, and David R. Koes (2022)

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Parts of Figures 5 and 6. (c) The authors 2022. Reproduced under the CC-BY licence

One approach to active learning is to grow the training set with molecules for which the current model has the highest uncertainties. However, according to this study, this approach does not seem to work for small-molecule pKa prediction where active learning and random selection give the same results (within the relatively high standard deviations) for three different uncertainty estimated.

The authors show that there are molecules in the pool that can increase the initial accuracy drastically, but that the uncertainties don't seem to help identify these molecules. The green curve above is obtained by exhaustively training a new model for every molecule in the pool during each step of the active learning loop and selecting the molecule that gives the largest increase in accuracy for the test set. Note that the accuracy decreases towards the end meaning that including some molecules in the training set diminishes the performance.

The authors offer the following explanation for their observations: "We propose that the reason active learning failed in this pKa prediction task is that all of the molecules are informative."

That's certainly not hard to imagine given the is the small size of the initial training set (50). It would have been very instructive to see the distribution of uncertainties for the initial models. Does every molecule have roughly the same (high) uncertainty? If so, the uncertainties would indeed not be informative.

Also, uncertainties only correlate with (random) errors on average. The authors did try adding molecules in batches, but the batch size was only 10.

It would have been interesting to see the performance if one used the actual error, rather than the uncertainties, to select molecules. That would test the case where uncertainties correlate perfectly with the errors.

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Seunghoon Lee, Joonho Lee, Huanchen Zhai, Yu Tong, Alexander M. Dalzell, Ashutosh Kumar, Phillip Helms, Johnnie Gray, Zhi-Hao Cui, Wenyuan Liu, Michael Kastoryano, Ryan Babbush, John Preskill, David R. Reichman, Earl T. Campbell, Edward F. Valeev, Lin Lin, Garnet Kin-Lic Chan (2022)

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Figure 1 from the paper. (c) 2022 the authors. Reproduced under the CC-BY licence.

Quantum chemical calculations are widely seen as one of quantum computings killer app's. This paper examines the available evidence for this assertion and doesn't find any.

The potential of quantum computing rests on two assumptions: that the cost of quantum computer calculations on chemical systems scales polynomially with system size, while the corresponding calculations on classical computers scale exponentially.

The former assumption is true for the actual quantum "computation" and the latter assertion is true for the Full CI solution. However, this paper suggests that preparing the state for the quantum "computation" may scale exponentially with system size, and that we don't need Full CI accuracy and that chemically accurate methods such as coupled-cluster based method scale polynomially with system size for a given desired accuracy.

The argument for the potential exponential scaling for system preparation is as follows: If you want the energy of the ground state you have to provide a guess at the ground state wavefunction that resembles the exact wavefunction as much as possible. More precisely, the probability of obtaining the ground state energy scales as $S^{-2}$, where S is the overlap between the trial and exact wavefunction. The authors show that $S$ scales exponentially with system size for a series of Fe-S clusters, which suggests an overall exponential dependence for the quantum computations.

The argument for polynomial scaling of chemically accurate quantum chemistry calculations has two parts: "normal" organic molecules and strongly correlated systems.

The former is pretty straight-forward: no one knowledgeable is really arguing that CCSD(T)-level accuracy is insufficient for ligand-protein binding energies and CCSD(T) scales polynomially with system size. So the simple notion of accelerating drug discovery by computing this with quantum computers does not hold water.

However, CCSD(T) does not work for strongly correlated systems and we don't have any real practical alternative for which we can test the scaling. Instead the authors look at simpler model of strongly correlated systems and demonstrate polynomial scaling with system size.

As the authors are carefull to point out, none of this represents a rigorous proof of anything. But it is far from obvious that quantum chemistry is the killer app for quantum computing that most people seem to think it is.

In addition to the paper you can find a very clear lecture on the topic here.

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Wenhao Gao, Tianfan Fu, Jimeng Sun, Connor W. Coley (2022)

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Figure 1 from the paper. (c) The authors 2022. Reproduced under the CC-BY license.

The development of generative models that can find molecules with certain properties has become very popular but there are very few studies that compare them, so it's hard to know what works best. This study compares the performance of 25 different generative models in 23 different optimisation tasks and draws some very interesting conclusions.

None of these methods find the optimum value given an "budget" of 10,000 oracle evaluations and for some tasks the best performance is not exactly impressive. This doesn't bode well for some real life applications where even a few hundred property evaluations are challenging.

Some methods are slower to converge than others, so you might draw completely different conclusions regarding efficiency if you 100,000 oracle evaluations. Similarly, some methods have high variability in performance so you might draw very different conclusions from 1 run compared to 10 runs. This is especially a consideration for problems when you can only afford one run. It might be better to choose a method that performs slightly worse on average but is less variable, rather than risk a bad run from a highly variable method that performs better on average.

The method that performed best overall is one of the oldest methods, published in 2017!

Food for thought

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