Spin-Multiplet Components and Energy Splittings by Multistate Density Functional Theory

Abstract

Kohn-Sham density functional theory has been tremendously successful in chemistry and physics. Yet, it is unable to describe the energy degeneracy of spin-multiplet components with any approximate functional. This work features two contributions. (1) We present a multistate density functional theory (MSDFT) to represent spin-multiplet components and to determine multiplet energies. MSDFT is a hybrid approach, taking advantage of both wave function theory and density functional theory. Thus, the wave functions, electron densities and energy density-functionals for ground and excited states and for different components are treated on the same footing. The method is illustrated on valence excitations of atoms and molecules. (2) Importantly, a key result is that for cases in which the high-spin components can be determined separately by Kohn-Sham density functional theory, the transition density functional in MSDFT (which describes electronic coupling) can be defined rigorously. The numerical results may be explored to design and optimize transition density functionals for configuration coupling in multiconfigurational DFT.

Figure 1

Interaction diagram illustrating electronic coupling among the three determinant configurations for the excited 2s¹2p² configuration of boron atom.

Figure 2

Computed adiabatic and vertical excitation energies of CH₂ at the four adiabatic geometries. The PBE0 exchange-correlation functional is used in multistate density functional theory along with the aug-cc-pVQZ basis set. Geometries were optimized using FCI/TZ2P from ref .

Scheme 1

Structures of α-2, α-3, and α-4-Didehydrotuluene (DHT)