Minimum-Energy Conical Intersections by Compressed Multistate Pair-Density Functional Theory

Compressed multistate pair-density functional theory (CMS-PDFT) is a multistate version of multiconfiguration pair-density functional theory that can capture the correct topology of coupled potential energy surfaces (PESs) around conical intersections. In this work, we develop interstate coupling vectors (ISCs) for CMS-PDFT in the <i>OpenMolcas</i> and <i>PySCF/mrh</i> electronic structure packages. Yet, the main focus of this work is using ISCs to calculate minimum-energy conical intersections (MECIs) by CMS-PDFT. This is performed using the projected constrained optimization method in <i>OpenMolcas</i>, which uses ISCs to restrain the iterations to the conical intersection seam. We optimize the <i>S</i>₁/<i>S</i>₀ MECIs for ethylene, butadiene, and benzene and show that CMS-PDFT gives smooth PESs in the vicinities of the MECIs. Furthermore, the CMS-PDFT MECIs are in good agreement with the MECI calculated by the more expensive XMS-CASPT2 method.