Machine Learning Basics

The Faculty of Science maintains a list of research presentations that high school classes can choose from when planning a visit. The description of the talk can include links to material the students and use to prepare and keep working on after the visit. So I made a series of video lectures about machine learning and Python for people with no other background than high school level mathematics.

I hope to add more videos/topics as I find the time and I hope this will get some of the students interested in programming and machine learning.



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Planned papers for 2019 - six months in

In January I wrote about the papers I plan to publish in 2019 and made this list:

Submitted
1. Graph-based Genetic Algorithm and Generative Model/Monte Carlo Tree Search for the Exploration of Chemical Space

Probable
2. Screening for energy storage capacity of meta-stable vinylheptafulvenes
3. Testing algorithms for finding the global minimum of drug-like compounds
4. Towards a barrier height benchmark set for biologically relevant systems - part 2
5. SMILES-based genetic algorithms for chemical space exploration

Maybe
6. Further screening of bicyclo[2.2.2]octane-based molecular insulators
7. Screening for electronic properties using a graph-based genetic algorithm
8. Further screening for energy storage capacity of meta-stable vinylheptafulvenes

Six months later the status is:

Accepted

1. Graph-based Genetic Algorithm and Generative Model/Monte Carlo Tree Search for the Exploration of Chemical Space

Probably submitted in 2019

2. High Throughput Virtual Screening of 200 Billion Molecular Solar Heat Battery Candidates

While we could certainly have gotten this version published, we decided to write an even better paper were we screen all 200 billion molecules and make an even better ML-learning model. We're almost done with the additional calculations.

5. SMILES-based genetic algorithms for chemical space exploration

The calculations are basically done (here, here, and here) and I just started working on the paper now.

3. Testing algorithms for finding the global minimum of drug-like compounds

The coding is basically done and I started generating data for a paper, but then decided on working on paper 5. This paper is next.

I think that'll be it for 2019. I went on to the 2nd round for a research center application and had to write a big proposal, so I got behind on paper writing in the Spring. I also decided to spend more time on making excuses :).

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Useful introductory books and blogposts on neural networks

Here's a list of books and blogposts on neural networks and related aspects that I have found particularly useful. In general, I like very simple examples - preferably with python code - to introduce me to a topic.

Books

Make Your Own Neural Network

This book is an excellent place to start. The book explains the basics of NNs and guides you through writing your own 3-layer NN code from scratch and applying it to the MNIST set. The book even introduces you to Python, so this is something virtually anyone can do. My only (minor) complaint is that the code uses classes, which can be quite difficult for beginners to grasp and it not really needed here.

Deep Learning for the Life Sciences: Applying Deep Learning to Genomics, Microscopy, Drug Discovery, and More
This book offers brief and to-the-point descriptions of some of the major classes of NNs, such CNN and RNN in the first chapters and then walks you though many interesting applications using the DeepChem library. This book gets you started using NNs very quickly and is an excellent supplement to the more basic or more theoretical approaches in this list.

Artificial Intelligence Engines: A Tutorial Introduction to the Mathematics of Deep Learning
This is a more formal treatment of deep learning but I still found it (mostly) very readable and there are several useful pseudo-code examples with Python equivalents. The topics are discussed in roughly chronological order, so you also get a good feel for how the NN field developed including major milestones.

Blogposts

Build a Recurrent Neural Network from Scratch in Python – An Essential Read for Data Scientists

This is basically the equivalent of Make Your Own NN but for a RNN applied to a toy problem.

Introduction to Convolutions using Python and Playing with convolutions in Python

Both posts offer some very simple Python examples of what convolution actually means for images.

How to do Deep Learning on Graphs with Graph Convolutional Networks

A very simple Python introduction to graph convolution, which works quite bit differently from image convolution.

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Comparison of SMILES-, DeepSMILES-, SELFIES-, and graph-based genetic algorithms Part 2

This post is a follow up to this post. There are two changes:

In that post I generated the data for the string based methods using my graph-based GA (GB-GA) code interfaced with new, string-based, crossover and mutation code. However, this involves going back and forth between graph and string-based representations which could potentially change the atom order. To make sure that doesn't happen I have now written a stand alone string-based GA code, where strings only are converted to graphs when computing the score and graphs are never converted back to strings.

I also had a another look at Brown et al.'s GA code and noticed that they remove duplicates from the population for each generation, which my code didn't. So implemented that as well for both the graph- and string-based methods. In the table below I list the best results, where the original implementation that does not remove duplicates are indicated by a "*".

For GB the removal of duplicates only improves results for celecoxib, where it is now rediscovered 8 times instead of 4. Tiotixene is not rediscovered and troglitazone is only found once with GB-GA, when duplicates are removed.

The new string-based implementation improves results for SMILES and DeepSMILES, with the exception of SMILES for troglitazone, which is discovered once using the old implementation. For SELFIES the new implementation is a little bit worse, but I would say the difference is within the statistical uncertainty. 

GB still tends to outperform string based methods, though they all perform much better than I had expected. Amazingly, DeepSMILES and SELFIES do not appear to offer a clear advantage over SMILES with the exception of troglitazone, where DeepSMILES performs significantly better.

Here are the high scoring molecules found with string based methods. Some of the molecules have radical centers (red boxes) due to misplaced chiral centers.

x



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Comparison of SMILES-, DeepSMILES-, SELFIES-, and graph-based genetic algorithms

This post is a follow up to this post. There are three main changes: 1) I have included Emilie's code in my code, 2) I have extended the implementation to SELFIES, and 3) the initial pool of molecules is now constructed exactly as described by Brown et al. (i.e. we use the 100 highest scoring molecules from ChEMBL, but remove molecules with scores higher than 0.323).

As before, I run the 10 GA searches, each for 1000 generations, and record the overall highest score found and the average high score. If the score is 1.00 I also record the number of times I found it, in parentheses. I also record the CPU time on 8 cores (note that I stop the search once the score is 1.00, so the time is not necessarily for 10 x 1000 generations).

Here are the high scoring molecules found with string based methods

Bottom line, DeepSMILES and SELFIES perform about the same, and both tend to outperform SMILES for rediscovery using GA.


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Comparison of SMILES-, DeepSMILES- and graph-based genetic algorithms

Emilie is wrapping up her bachelor project and writing the report and here are some preliminary results (which are likely to change a bit).

I recently developed a graph-based genetic algorithm that seems to work pretty well. The crossover and mutation code is about 250 lines with a lot of hyperparameters that mainly specify the probabilities of performing different crossovers and mutations.

The question is whether all this was really necessary or could I have gotten away with about 25 lines of code that perform crossover and mutation operations on SMILES strings? For crossover you simply cut two strings at random places and recombine the fragments, e.g. OCC|C and CC|N (where "|" indicates the cut) yield OCCN and CCC and for mutation you simply change one character to another, e.g. CCC becomes C=C.

The potential problem with using SMILES is that one can imagine many scenarios where this wouldn't work, e.g. OC(|C)C and C1C|O1 would yield OC(O1 and C1CC)C, which are not valid SMILES string.  But can you still find molecules with the desired properties using this approach? If so, do the molecules look very different than the ones you find with the graph-based approach? Which approach is more efficient?

And what about the DeepSMILES representation developed by O'Boyle and Dalke? Here, OC(|C)C and C1C|O1 are written as OC|C)C and CC|O3, which would yield OCO3 and CCC)C - both valid DeepSMILES strings.

Finding molecules with specific penalised logP values
We start by looking at what Brown et al. call a "trivial optimisation objective": finding molecules with a particular modified logP values. We use the same Gaussian modifier approach with a standard deviation of 2 logP units and select the initial population from the first 1000 molecules in the ZINC data set (after removing molecules with logP values within 2 units of the target). The mating pool size and mutation rates are 20 and 10%, respectively. The table shows the average number of generations (based on 10 runs) needed to find a molecule with a logP values within 0.01 of the target.

It is clear that a SMILES-based GA has no problems meeting the objective, but that using DeepSMILES is more effective both in terms of number of required generations and CPU time. The latter, because the percentage of valid strings generated by crossover and mutation (the succes rate) is considerably higher for DeepSMILES as expected. For this target there appears to be no real advantage in using graph-based GA.

Rediscovering a molecule
The next target is considerably harder: generating molecules with a Tanimoto similarity of 1.0 with a target molecule (naphthalene, celecoxib, or tiotixene).  A Tanimoto similarity of 1.0 means that each atom has the same bonding pattern out to a certain radius (here 4 bonds), i.e. that the molecules are very, very similar. The population size is 100 and the mating pool size is 200. The initial populations is 100 molecules with the highest Tanimoto scores to the target (but with Tanimoto scores less than 0.323, following Brown et al.) found among the first 50,000 molecules in the ZINC data set.

Here it's clear that the graph-based approach offer an advantage over string-based methods, while DeepSMILES only offers an advantage over SMILES in terms of effciency. The Tanimoto score goes from 0 to 1, so the molecules found for the tiotexene search using graph-based GA look significantly more like tiotexene than those found with the string based methods. (When I run celecoxib search I succeed 5/10 times, and we are still trying to find the cause of this difference.)

Finding molecules that absorb at a particular wavelength
Inspired by the study of Tsuda and co-workers, we search for molecules that absorb at 400 and 800 nm. We use Grimme's semiempirical sTDA-xTB method to estimate the absorption wavelength and oscillator strength based on a low energy MMFF-optimised structure. We use a Gaussian(400/800,50) scoring function for the wavelength and a LinearThresholded(0.3) scoring function for the oscillator strength (0.3 is the oscillator strength computed for indigo dye). The population and mating pool sizes are 20 and 40, respectively and the mutation rate is 15%. We select the initial population from the first 1000 molecules in the ZINC data set (after removing molecules with absorption wavelengths within 300 nm of the target). The GA search is stopped if the top-scoring molecule has an absorption wave length within 5 nm of the target value.

It turns out that the find molecules that absorb relatively strongly at 400 and 800 nm is a relatively easy optimisation problem.

Conclusion
If there are very few ways to meet the target then graph-based GA performs better than string-based GA methods, but otherwise not. DeepSMILES-based GA is computationally more efficient than SMILES-based GA in many cases.  It would be interesting to test the newly introduced SELFIES representation.



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Reviews of Graph-based genetic algorithm and generative model/Monte Carlo tree search for the exploration of chemical space

Here are the reviews of my latest paper which just appeared in Chemical Sciences. I submitted the paper December 1, 2018 and got these reviews on January 13, 2019. I resubmitted January 20, and got the final decision on February 8. As usual with Chem. Sci. a very efficient and positive experience. Kudos to Geoff Hutchison for signing the review (and being cool with me sharing it here) and kudos to Chem. Sci. for passing it on to me.

REVIEWER REPORT(S):
Referee: 1

Recommendation: Revisions required

Comments:
The main question of this paper is whether GA-based algorithms perform better than deep-learning. This paper includes interesting comparisons and free-to-use software, which is potentially a good resource for the AI-chemistry community. Yet I have following reservations about this paper.

1) Essentially GA-based method is faster than ML, creating more molecules. The logP computation is extremely fast, allowing GA to create many molecules in a fixed period of time. When simulation takes a longer time (like DFT), it may be beneficial to use more time to design. It is necessary to give a comparison in terms of the number of simulations needed to obtain good molecules. In that case, ML would be better, because it might be creating "high-quality" molecules using more time. Please provide comparisons with this respect.

2) It seems like the author tuned GA parameters such that the molecules are "realistic looking". It would be beneficial to readers if you can elaborate on this aspect. What exactly did you mean by "realistic looking"? Can you quantify somehow?

3) It seems to me that GA crossover parameters are inspired by chemical reactions. Can you claim that GA-based molecules are more synthesizable than deep-learning-based ones?


Referee: 2

Recommendation: Accept

Comments:
The manuscript “Graph-based genetic algorithm and generative model Monte Carlo tree search for the exploration of chemical space” by Jan Jensen is an excellent addition to recent work on using computational methods to generate new molecular compounds for target properties.

I will admit up-front that I am a proponent of GA strategies, so the conclusions were not surprising. I think the work should be published but would like to make some minor suggestions that I think will strongly improve the work.

- On page 2, the number of non-H atoms is described coming “from a distribution with a mean 39.15 and a standard deviation of 3.50” - this is a number without a unit. Based on the article, I think it should read “a mean of 39.15 atoms, with standard deviation of 3.50 atoms”
- The last paragraph on page 3 is perhaps a bit technical for the Chemical Science audience, discussing “leaf parallelization” and “leaf nodes.” I think the whole paragraph needs to be written for a general audience (i.e., not someone implementing a MCTS code) or moved to the supporting information. The code is, after all, open source and available.
- The penalized logP score could be described better. From the text, the penalty for “unrealistically large rings” was not described.
- The J(m) scores in Table 2 could perhaps be a bit expanded. For example, my assumption is that the SA scores and/or ring penalities may be higher in some methods than others. I think it would be useful to add columns for the raw logP, SA, and penalty scores - if not in the text then in the supporting information.
- The results and discussion could benefit from a figure indicating the rate of improvement with generations for the GA methods and/or the GB-GM-MCTS methods. We have, for example, shown that GA methods show high rate of improvement in early generations, but finding beneficial mutations slows over time. This would likely explain why the lower mutation rate shows better performance in this work - and moreover suggest an “early stop” (e.g., are all 50 generations needed for this problem?)
- Similarly, I find it strange that the author didn’t try longer runs or attempt to find an optimal mutation rate for the GA, particularly if the CPU time is so short.
- The caption for Table 3 includes a typo - I believe “BG-GM” should read “GB-GM”
- The conclusions suggest that the GB-GA approach “can traverse a relatively large distance in chemical space” - the author should really use similarity scores (e.g., a Tanimoto coefficient using ECFP fingerprints or similar) to quantify this - again, the discussion could be expanded.

Overall, I think it’s a great addition to the discussion on optimization of molecular structures for properties.

-Geoff Hutchison, University of Pittsburgh

Screening for large energy storage capacity of meta-stable dihydroazulenes Part 3

This is a follow up to this post, which was a follow up to this post. Briefly, we (that is to say Mads) have computed $\Delta E_{rxn}$ and $\Delta E^\ddagger$ for about 32,500 molecules using xTB and PM3 respectively. We can afford to do a reasonably careful (DFT/TZV) study on at most 50 molecules, so the next question is how to identify the top 50 candidates. In other words to what extent can we trust the conformational search and the xTB and PM3 energies?

In my last post we saw that the xTB and PM3 energies can be trusted well enough and this post we'll see that the conformational search also can be trusted.

Conformational search
The xTB storage energy calculation is based on the lowest energy DHA and VHF structures found by optimisations of $5+5n_{rot}$ geometries generated using RDKit. The plot above shows a comparison of this approach to one where we generated all conformers by systematically rotating each rotateable bond by $\pm 120^\circ$ for a subset of 100 molecules. It is clear that the $5+5n_{rot}$-approach works really well for most molecules (including the 20 with high storage energy) and, if anything, overestimates the storage energy (i.e. at worst we will have som false positives).

From 35,588 to 41 to 6 to ?? candidates

The fact that we can trust the storage energies reasonably well means that we can proceed with the 41 molecules I identified in the previous post. As a first step we optimised the geometries at the DFT level and as expected most of the molecules have barriers that are too low. But 6 of them still look promising, so the next step is to perform a systematic conformer search using xTB (just to be safe) and then re-optimise all structures with energies close to the xTB minimum with DFT. Stay tuned ... with fingers crossed.

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Screening for large energy storage capacity of meta-stable dihydroazulene Part 2

This is a follow up to this post. Briefly, we have computed $\Delta E_{rxn}$ and $\Delta E^\ddagger$ for about 32,500 molecules using xTB and PM3 respectively. We can afford to do a reasonably careful (DFT/TZV) study on at most 50 molecules, so the next question is how to identify the top 50 candidates. In other words to what extent can we trust the conformational search and the xTB and PM3 energies?

To try to answer the latter question we (i.e. Mads) randomly chose 20, 60, and 20 molecules with high, medium, and low xTB-$\Delta E_{rxn}$ values and recomputed $\Delta E_{rxn}$ at the M06-2X/6-31G(d) level of theory using the lowest xTB-energy DHA and VHF structures as starting geometries. The results are shown below

The vertical and and horizontal lines denote $\Delta E_{rxn}$ and $\Delta E^\ddagger$, respectively, for an experimentally characterised "reference" compound that we want to improve upon, i.e. we are looking for compounds that have larger $\Delta E_{rxn}$ and $\Delta E^\ddagger$ values. $\Delta E_{rxn}$ should ideally be at least 5 kcal/mol higher than the reference (but in general as large as possible) and $\Delta E^\ddagger$ should be at least 2 kcal/mol higher than the reference, but anything higher than that is not necessarily better. The half life depends very sensitively on the barrier, and is hard to compute accurately, so we have to be careful about excluding molecules with high storage capacity in cases where the barrier is close to the reference.

Using these criteria I would select 5 points for further study indicated by the red points (let's call them Square, Star, Triangle, Dot, and Diamond). Square is clearly the most promising one with significantly higher $\Delta E_{rxn}$ and $\Delta E^\ddagger$ compared to the reference. The remaining 4 points are chosen because they either have reasonably high $\Delta E_{rxn}$ and $\Delta E^\ddagger$-values  that are only a few kcal/mol below the reference (Triangle and Star) or reasonably high $\Delta E^\ddagger$ and $\Delta E_{rxn}$ that are somewhat (ca 3 kcal/mol) higher than the reference. I'd call the last 4 points pseudo-positives.

The corresponding plot for SQM storage energies and barrier heights is shown above. The good news is that Square is still the clear winner and I would also have picked Star and Triangle for further investigation. However, there are many more points that I also would picked (false pseudo-positives) and Diamond and Dot would not have been picked (false pseudo-negatives).

The false positives are due to PM3 overestimating the barrier, so let's use B3LYP/6-31+G(d)//xTB barriers instead. Square is still the winner, Star would still be picked (but not Triangle), and the false positives are gone. However, the barriers for Dot and Diamond are now so low that they will not be picked (false pseudo-negatives).

Summary and outlook
SQM finds the only true positive (Square). PM3 tends to over estimate the barrier relative to the reference, which leads to false pseudo-positives. xTB tends to underestimate the storage capacity which leads to a few false pseudo-negatives. DFT/PM3 barriers removes the false pseudo-positives but also leads to some false pseudo-negatives.

The above plot shows the molecules with an xTB storage energy that is at least 4 kcal/mol higher than the reference (4 rather than 5 kcal/mol since xTB tends to underestimate the storage energy). The solid line shows the reference barrier and the dotted line lies 2 kcal/mol above that (since PM3 tends to underestimate the barrier). There are 41 points above that line, including good old Square, that we should investigate further and it's probably also good to look at a few more points with very high storage energy and reasonably high barrier.

But all this assumes that we can trust the conformational search so this has to be tested next.

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Open access chemistry publishing options in 2019

Here is an updated list of affordable impact neutral and other select OA publishing options for chemistry

Impact neutral journals
$0 (in 2019) PeerJ chemistry journals. Open peer review. (Disclaimer I am an editor on PeerJ Physical Chemistry)

$425 (normally $850) Results in Chemistry. Closed peer review

$750 ACS Omega (+ ACS membership $166/year). Closed peer review. WARNING: not real OA. You still sign away your copyright to the ACS.

$1000 F1000Research. Open peer review. Bio-related

$1095 PeerJ - Life and Environment. Open peer review. Bio-related. PeerJ also has a membership model, which may be cheaper than the APC.

$1260. Royal Society Open Science.  Open peer review. 

(The RSC manages "the journal’s chemistry section by commissioning articles and overseeing the peer-review process")

$1350 Cogent Chemistry. Has a "pay what you can" policy. Closed peer review.

$1595 PLoS ONE. Closed peer review.

$1790 Scientific Reports. Closed peer review

Free or reasonably priced journals that judge perceived impact

$0 Chemical Science Closed peer review

$0 Beilstein Journal of Organic Chemistry. Closed peer review.

$0 Beilstein Journal of Nanotechnology. Closed peer review.

$0 ACS Central Science. Closed peer review. ($500-1000 for CC-BY, WARNING: not real OA. You still sign away your copyright to the ACS as far as I know) 

$100 Living Journal of Computational Molecular Science. Closed peer review

€500 Chemistry². Closed peer review.

£750 RSC Advances. Closed peer review.


Let me know if I have missed anything.




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Screening for large energy storage capacity of meta-stable dihydroazulenes

Here's a summary of where we are at with Mads project

The Challenge

Dihydroazulenes (DHAs) are promising candidates for storing solar energy as chemical energy, which can be released as thermal energy when needed. The ideal DHA derivative has a large $\Delta H_{rxn}$ and a $\Delta G^{\ddagger}$ that is large enough to give a half life of days to months but low enough so that the energy release can be reduced.  Of course any modification should not affect light adsorption adversely. This presents an interesting optimisation challenge!

We asked Mogens Brøndsted Nielsen to come up with a list of substituents and he suggested 40 different substituents and 7 positions, which results in 164 billion different molecules (we chose to interpret the right hand figure more generally). We decided to start by looking at all single and double substitutions, which amounts to 35,588 different molecules. The first question is what level of theory will allow us to screen this many molecules. 

The initial screen

At a minimum we need to compute $\Delta E_{rxn}$ which involves at least a rudimentary conformational search for both reactants and products. We used an approach similar to this study, ($5+5n_{rot}$ RDKit generated start geometries) which results in over 1 million SQM geometry optimisations, but used GFN-xTB instead of PM3 because the former is about 10 times faster.

To find the barriers, we did a 12-point scan along the breaking bond in DHA (out to 3.5Å) starting from the lowest energy DHA conformer. The highest energy structure was then used as a starting point for a TS search using Gaussian and "calcall". We used ORCA for the scan and Gaussian for the TS search, and used PM3 because it is implemented in both programs. We also optimised the lowest VHF structure with PM3 to compute the barrier. We verify the TS by checking whether the imaginary normal mode lies along the reacting bond. This worked in 32,623 cases. The whole thing took roughly 5 days using roughly 250 cores.

Note that this approach finds a TS to cis-VHF, which we assume is in thermal equilibrium with the lower energy trans-VHF form. For both barriers and reaction energies we use the electronic energy differences rather than free energies of activation and reaction enthalpies.

The next step

We can afford to do a reasonably careful (DFT/TZV) study on at most 50 molecules, so the next question is how to identify the top 50 candidates. In other words to what extent can we trust the conformational search and the xTB and PM3 energies? I plan to cover this in a future blog post.

A more efficient initial screen
We now have data with which to test more efficient ways of performing the initial screen:

1. (a) We could perform the conformational search using MMFF and only xTB-optimise the lowest energy DHA and VHF structures.
(b) We could only perform the TS search for molecules with large $ \Delta E_{rxn}$ values.
(c) We could perform the bond-scan with xTB rather than ORCA. 
(d) We could test whether the bond-scan barrier can be used instead of the TS-based barrier.

2. We could test the use ML-based energy functions such as ANI-1 instead of SQM.

3. We could test whether ML can be trained to predict $\Delta E_{rxn}$ and/or $\Delta E^{\ddagger}$ based on the DHA structure.

We'd be very happy to collaborate on this.

Beyond double substitution

No matter how efficient we make the initial screen, screening all 164 billion molecules is simply not feasible. Instead we'll need to use search algorithms such as genetic algorithms or random forest.

Other ideas/comments/questions on this or anything else related to this blogpost are very welcome.

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Planned papers for 2019

A year ago I thought I'd probably publish three papers in 2018:

Accepted
1. Fast and accurate prediction of the regioselectivity of electrophilic aromatic substitution reactions

Probable
2. Random Versus Systematic Errors in Reaction Enthalpies Computed using Semi-empirical and Minimal Basis Set Methods
3. Improving Solvation Energy Predictions using the SMD Solvation Method and Semi-empirical Electronic Structure Methods

Unexpected

4. The Bicyclo[2.2.2]octane Motif: A Class of Saturated Group 14 Quantum Interference Based Single-Molecule Insulators

5. Empirical corrections and pair interaction energies in the fragment molecular orbital method

The end result was five papers. In addition I also published a proposal.

Here's the plan for 2019

Submitted

1. Graph-based Genetic Algorithm and Generative Model/Monte Carlo Tree Search for the Exploration of Chemical Space

Probable

2. Screening for energy storage capacity of meta-stable vinylheptafulvenes

3. Testing algorithms for finding the global minimum of drug-like compounds

4. Towards a barrier height benchmark set for biologically relevant systems - part 2

5. SMILES-based genetic algorithms for chemical space exploration

Maybe

6. Further screening of bicyclo[2.2.2]octane-based molecular insulators

7. Screening for electronic properties using a graph-based genetic algorithm

8. Further screening for energy storage capacity of meta-stable vinylheptafulvenes

I haven't started a draft on any of papers 2-5 so I'm not exactly brimming with confidence that all 4 will make it into print in 2019. However, we have 80-90% of all the data needed to write each paper, and I've blogged a bit about paper 3.

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