Reduced Functions and Descriptors for Accurate Electronic Structure
Prediction and Understanding Chemical Bonding

Katarzyna Pernal
Institute of Physics, Lodz University of Technology
katarzyna.pernal@p.lodz.pl

Obtaining complete information for a many-electron system requires in principle solving the Schrödinger equation and finding the many-electron wavefunction. However, this wavefunction is a complex object that is not only difficult to calculate, but also challenging to use as an interpretive tool. It has been known for a long time that reduced one- and two-electron functions are sufficient to describe the energy of a molecule, electron correlation, and provide insight into the bonding pattern and its changes during a chemical reaction or when the molecular system transitions from the ground state to an excited state.

In the presentation, I will first introduce reduced functions: the electron density, one-electron and two-electron reduced density matrices, and on-top pair density. I will demonstrate their relationship with the full wavefunction and discuss modern computational methods for predicting electronic structure that do not rely on the wavefunction and only use the reduced functions.

In the second part of the presentation, I will introduce bonding and electron correlation descriptors that are constructed in real space from the reduced functions. I will demonstrate how these descriptors allow us to gain physical insight into the dispersion energy in van der Waals complexes [1] and the ionic versus covalent character of states and chemical bonds [2].

[1] P. H. Kowalski, A. Krzeminska, K. Pernal, and E. Pastorczak, J. Phys. Chem. A 2022, 126, 1312.

[2] K. Pernal and O.V. Gritsenko, Faraday Discuss., 2020, 224, 333; M. Hapka, K. Pernal, O. V. Gritsenko, J. Phys. Chem. Lett. 2020, 11, 5883.