[Paper Review] Multireference Density Functional Theory for Describing Ground and Excited States with Renormalized Singles

Jiachen Li, Zehua Chen+1 more|arXiv (Cornell University)|Nov 30, 2021

Advanced Chemical Physics Studies4 citations

TL;DR

This paper introduces ppTDA@RS-DFA, a multireference density functional theory method that uses renormalized singles (RS) Hamiltonians to accurately describe ground and excited states in systems with strong static correlation. By incorporating all singles contributions into the particle-particle Tamm-Dancoff approximation (ppTDA) and optimizing the total energy via the optimized effective potential (OEP) method, the approach achieves improved dissociation curves, accurate double bond rotation profiles, and reduced functional dependence in excitation energies, with a favorable O(N⁴) computational scaling.

ABSTRACT

We applied renormalized singles (RS) in the multireference density functional theory (DFT) to calculate accurate energies of ground and excited states. The multireference DFT approach determines the total energy of the $N$-electron system as the sum of the ($N-2$)-electron energy from a density functional approximation (DFA) and the two-electron addition energies from the particle-particle Tamm-Dancoff approximation (ppTDA), naturally including multireference description. The ppTDA@RS-DFA approach uses the RS Hamiltonian capturing all singles contributions in calculating two-electron addition energies, and its total energy is optimized with the optimized effective potential method. It significantly improves the original ppTDA@DFA. For ground states, ppTDA@RS-DFA properly describes dissociation curves tested and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies and largely eliminates the DFA dependence. ppTDA@RS-DFA thus provides an efficient multireference approach to systems with static correlation.

Motivation & Objective

• To develop a multireference DFT approach that accurately describes systems with strong static correlation, such as bond dissociation and double bond rotation.
• To address the limitations of conventional Kohn-Sham DFT and ppRPA@DFA in describing multiconfigurational systems with fractional spin and charge errors.
• To reduce the dependence of excitation energies on the choice of density functional approximation (DFA) in multireference DFT.
• To achieve efficient computational scaling suitable for larger systems by leveraging the active space method and OEP optimization.

Proposed method

• The method decomposes the N-electron system energy into the (N−2)-electron energy from a DFA and two-electron addition energies computed via the particle-particle Tamm-Dancoff approximation (ppTDA).
• The ppTDA equation is solved using a renormalized singles (RS) Hamiltonian that captures all one-body perturbations, improving the description of electron correlation.
• The total energy is optimized using the optimized effective potential (OEP) method, ensuring physical potentials and improved self-consistency over generalized OEP (GOEP).
• The Hxc kernel in the gradient evaluation is reformulated using two-electron integrals via an RI approximation, reducing computational scaling to O(N⁴).
• The active space method is employed to diagonalize the ppTDA matrix in a small subspace, significantly reducing computational cost with a small prefactor.
• The approach is implemented with orbital optimization and tested across ground and excited states using various DFAs.

Experimental results

Research questions

• RQ1 Can the inclusion of renormalized singles in the ppTDA framework improve the description of ground state dissociation curves and bond breaking in multiconfigurational systems?
• RQ2 Does ppTDA@RS-DFA accurately describe the double bond rotation in ethylene, a challenging test for static correlation?
• RQ3 To what extent does ppTDA@RS-DFA reduce the dependence of excitation energies on the choice of density functional approximation (DFA)?
• RQ4 Can the OEP method in ppTDA@RS-DFA produce physically meaningful potentials where standard GOEP fails?
• RQ5 What is the computational scaling of ppTDA@RS-DFA, and can it be efficiently applied to larger systems using active space approximations?

Key findings

• ppTDA@RS-DFA produces accurate dissociation curves for four test systems, correctly capturing spin density symmetry and dissociation energies, outperforming both ppTDA@DFA and conventional KS-DFT.
• The method accurately describes the double bond rotation in ethylene, with correct energy profiles and proper multiconfigurational character.
• Excitation energies for atomic and molecular systems are highly accurate, with significantly reduced dependence on the choice of DFA compared to ppTDA@DFA.
• The OEP method successfully generates physical potentials in most cases, overcoming issues of unphysical potentials in standard GOEP optimizations.
• The computational scaling is O(N⁴), and the active space method reduces the cost of solving the ppTDA equation and computing gradients, enabling application to larger systems.
• The Hxc kernel in the gradient evaluation is reformulated using two-electron integrals via an RI approximation, enabling O(N⁴) scaling instead of O(N⁵) in standard ppTDA@DFA with non-HF functionals.