Efficient Random Phase Approximation for Diradicals

TL;DR

This paper introduces an efficient RPA-based model for predicting singlet-triplet gaps in diradical molecules, showing reasonable accuracy compared to advanced quantum chemistry methods.

Contribution

It develops a simplified, analytically solvable RPA model for diradicals that improves parameter estimation in two-orbital systems.

Findings

Average relative difference of 40% with NEVPT2 predictions.

Better than 20% accuracy for molecules with small singlet-triplet splitting.

Model effectively accounts for doubly occupied and empty orbitals.

Abstract

We apply the analytically solvable model of two electrons in two orbitals to diradical molecules, characterized by two unpaired electrons. The effect of the doubly occupied and empty orbitals is taken into account by means of random phase approximation (RPA). We show that in the static limit the direct RPA leads to the renormalization of the parameters of the two-orbital model. We test our model by comparing its predictions for the singlet-triplet splitting with the results from multi-reference CASSCF and NEVPT2 simulations for a set of ten molecules. We find that, for the whole set, the average relative difference between the singlet-triplet gaps predicted by the RPA-corrected two-orbital model and by NEVPT2 is about 40%. For the five molecules with the smallest singlet-triplet splitting the accuracy is better than 20%.