There are lots of ways to think about where electrons are in molecules, ranging from plum puddings (whatever those are) to Lewis structures to orbitals. Orbitals, which are computed using quantum mechanics, accurately describe the location of electrons as wave-like probability distributions.

Atomic orbitals are solutions to the quantum mechanics equations governing single atoms, and provide a nice visual representation of the location of electrons within atoms.1

Molecular orbitals, like atomic orbitals, are calculated by solving quantum mechanics equations, and provide a picture of the location and movement of electrons in molecules.

We’re excited to be launching an orbitals workflow in Rowan, which can be used to calculate molecular orbitals as well as electron density, electrostatic potential, atom-centered charges, bond orders, and multipole moments. With this workflow, you can now draw a structure, run a workflow, and view the resulting orbitals and isosurfaces in your browser. We think this will be a super helpful tool to help build intuition around bonding, excited states, and reactivity.

Molecular orbitals can help you understand the conjugation and reactivity of a given system. Orbital surfaces that touch only one atom are called “nonbonding.” Orbitals that touch two atoms are “bonding,” and adding electrons to these orbitals will strengthen the corresponding bonds. If an orbital contains a node (a gap between a red surface and a blue surface) that divides a bond, it is “anti-bonding”; adding electrons to these orbitals will weaken the corresponding bonds. The pictured orbital is a bonding orbital, strengthening benzene’s aromatic bonds.

Isosurfaces

Rowan’s orbitals workflow can also compute the electron density and electrostatic potential of a system.

Electron density isosurfaces (viewed with cutoffs in the range of 0.01–0.05 e/Bohr³) can provide a sense of a molecule’s shape. When viewed with a higher cutoff (0.1–0.15 e/Bohr³), electron density isosurfaces show “bond density,” and areas with higher order bonds will have correspondingly higher volumes.

Electrostatic potential gives us an idea of a molecule’s charge distribution. Areas of negative electrostatic potential correspond to areas that will attract positive charges (electrophiles), while areas of positive electrostatic potential correspond to areas that will attract negative charges (nucleophiles). This electrostatic potential map shows us that faces of this benzene ring are electron rich and would attract a positive charge (or an electrophile).

In open shell systems, orbitals and density are calculated for each spin of electron (α and β). You can view the spin-density surface of a molecule (the difference between α and β electron density), which gives a picture of the location of unpaired electrons.

Bond Orders, Charge, and Multipole Moments

As a part of this same workflow, we’re also adding the ability to view bond orders, atom-centered charges, and multipole moments. Bond order can be useful in gaining insight into aromaticity and bond localization and delocalization—a calculation on ferrocene shows that each C–C bond has a bond order of about 1.28, indicating that the cyclopentadienyl rings are indeed substantially aromatic, and each C–Fe bond has a bond order of 0.47.

Similarly, charges and multipole moments can be used to determine where electron density resides, and can be used as descriptors in QSAR/QSPR models or to parameterize molecular force fields. Right now, Rowan has two bond-order schemes (Wiberg and Mayer) and two charge schemes (Mulliken and Löwdin)—we hope to add more in the future!

Podcast: Can AI improve the current state of molecular simulation?

Abhishaike Mahajan, who writes Owl Posting, recently sat down with Corin Wagen and Ari Wagen to talk about the future of machine learning for molecular simulation. The podcast focuses on neural network potentials—how they’re trained, where we expect them to be useful in the future, how we validate their results, etc.

If you’re interested, you can watch the podcast (or read the transcript) on Substack, Spotify, Apple Podcasts, or YouTube.