Analytic Dipole Moments For Complete Active Space Linearized Pair-Density Functional Theory

The accurate prediction of molecular dipole moments requires high-quality wave functions or electron densities. For systems exhibiting strong electron correlation, multireference methods are essential to reliably describe molecular properties such as dipole moments. We derive and implement analytic expressions for permanent dipole moments of ground and excited states for linearized pair-density functional theory (L- PDFT), starting with state-averaged complete active space wave functions as reference functions. Dipole moments are evaluated via response theory as the first derivative of the L-PDFT energy with respect to an external electric field. We evaluated the performance of L-PDFT for acetylene, phenol, the spiro cation, and benchmarks of 20 aromatic molecules. L-PDFT consistently predicts accurate dipole moments near conical intersections and in regions of strong nuclear-electronic coupling. The ability to produce smooth and accurate dipole surfaces for diverse molecular systems establishes L-PDFT as a promising method for spectroscopic analysis and generating machine- learning potentials.