# Molecular orbital energies prediction with ML algorithms

In the recent years, computational chemistry community has focused on Machine Learning algorithms to predict molecular properties. Unfortunately, many of the authors of such papers are not chemists, and hence, there are little explanation on chemical aspects of this type of works.

One well known problem is to predict different properties of QM9 dataset given their atom features. The properties include HOMO/LUMO orbital energies, atomization energies, etc. The inputs include type of heavy atoms in the molecule, type of their bonds, type of atom hybridization, etc. You can see a complete list in the following tables

The question is how the inputs are related to the outputs. For example, I understand that HOMO\LUMO energies are solutions of the electronic Schrödinger equation. But which one of the inputs features affects these? I appreciate it if someone can expand on which ones affect frontier molecular energies. Thanks!

• The interpretation of the how the features lead to a given output is a problem with any machine learning prediction. We can make some sort of hand-wavy arguments about why certain features might influence orbital energies, how much a given feature influences an output is entirely dependent on the structure of the model. Particularly for neural networks, where there are a number of layers between features and output, it is difficult to tease out what features are most important. – Tyberius Sep 18 '19 at 16:20
• Thanks for the comment, @Tyberius. Well said. The "hand-wavy arguments about why certain features might influence orbital energies" is what I'm looking for. – Blade Sep 18 '19 at 16:30
• Fundamentally, molecular properties are determined by the atoms, their type, their positions (which includes the chemical environment of each atom) and the number of electrons (total charge). Most of your mentioned features actually try to describe the chemical environment by classifying different structural patterns (e.g. closest neighbors, bond type). Change any of that and you will get different orbital energies. Of course some changes have a larger influence than others. Answering this question is essentially what chemistry is all about. Which makes your question a very broad one ... – Feodoran Sep 19 '19 at 17:42
• One a side note: orbital energies are not solutions to the electronic Schrödinger equation! They are more like intermediate results. – Feodoran Sep 19 '19 at 17:43
• Thanks @Feodoran. By nature, I agree that the question is a broad one, but, I hope that I made it clear that I'm looking for one liner answers such as yours. (Not one-line, but one paragraph! :D) – Blade Sep 19 '19 at 17:58

As several comments have mentioned, interpreting a machine learning method can often be difficult. Outside the question of machine learning, I think your question centers around "what would I want to know to roughly predict HOMO / LUMO energies?"

Unfortunately QM9 isn't very diverse chemically, but if we think from a general qualitative molecular orbital picture (e.g., building up diatomic molecules), you want to know:

• Number of valence electrons (i.e., which orbitals are filled)
• Atom type (which tells you valence electrons and atomic orbital energies)
• Type of bond (e.g., single sigma bonds clearly will yield different MO energies than pi bonds)
• Conjugation - conjugated and aromatic systems will have different MO energies than plain sigma-bonded species
• Bond distances (from the Coulomb repulsion which encodes a distance $$1/r$$)

Given the above information, it's fairly easy to sketch out MO diagrams for $$\ce{O2}$$ or $$\ce{HOH}$$ so one can imagine that they're important for a machine learning algorithm too.

Now how do you know if they actually matter to the ML model?

One easy way is to drop one of the descriptors and retrain the model. Does it get worse? How much?

There are statistical techniques to give you some insight as well. For example, one can use LASSO to drop factors from the input representation that don't have much effect. You can also look at simple statistical correlation between input factors. I'd guess that "Atom Type" and "Atomic Number" are probably highly correlated with each other and only one is truly necessary.. but that's just a guess.

• Thanks, @Geoff Hutchison! Just a note for future readers that I found atom Hybridization to have the highest impact on the quality of prediction, followed by hydrogen neighbor count. Among the bond features also, Conjugation has high impact. – Blade Sep 23 '19 at 16:14
• Makes a lot of sense - IMHO it's important to think critically about ML methods including "what would I want to know as a human" in addition to automated methods. – Geoff Hutchison Sep 23 '19 at 21:13
• BTW, if you want a different data set, you might want to check PubChemQC pubchemqc.riken.jp and doi.org/10.1021/acs.jcim.7b00083 – Geoff Hutchison Sep 23 '19 at 21:14