Linearized Pair-Density Functional Theory

20 February 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multi-state PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.


Electronic Structure
Pair-Density Functional Theory
Excited States

Supplementary materials

Supporting Information: Linearized Pair-Density Functional Theory
Structure coordinates, absolute energies for PES scans, LiH ground-state potential energy curve, L-PDFT Hamiltonian coupling elements for the spiro cation, acetylene ground and excited-state potential energy curves. This information is available free of charge.


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