[Paper Review] Absolutely Localized Projection-Based Embedding for Excited States

Xuelan Wen, Daniel S. Graham+2 more|arXiv (Cornell University)|Sep 26, 2019

Spectroscopy and Quantum Chemical Studies91 references4 citations

TL;DR

This paper introduces an absolutely localized projection-based quantum embedding method for accurately calculating excited states using EOM-CCSD and TDDFT within a DFT environment. By restricting basis functions to only those on atoms in the excited subsystem, the method drastically reduces computational cost while eliminating spurious charge-transfer excitations and enabling systematic improvement toward full-system accuracy.

ABSTRACT

We present a quantum embedding method that allows for the calculation of local excited states embedded in a Kohn-Sham density functional theory (DFT) environment. Projection-based quantum embedding methodologies provide a rigorous framework for performing DFT-in-DFT and wave function in DFT (WF-in-DFT) calculations. The use of absolute localization, where the density of each subsystem is expanded in only the basis functions associated with the atoms of that subsystem, provide improved computationally efficiency for WF-in-DFT calculations by reducing the number of orbitals in the WF calculation. In this work, we extend absolutely localized projection-based quantum embedding to study localized excited states using EOM-CCSD-in-DFT and TDDFT-in-DFT. The embedding results are highly accurate compared to the corresponding canonical EOM-CCSD and TDDFT results on the full system, with TDDFT-in-DFT frequently more accurate than canonical TDDFT. The absolute localization method is shown to eliminate the spurious low-lying excitation energies for charge transfer states and prevent over delocalization of excited states. Additionally, we attempt to recover the environment response caused by the electronic excitations in the high-level subsystem using different schemes and compare their accuracy. Finally, we apply this method to the calculation of the excited state energy of green fluorescent protein and show that we systematically converge to the full system results. Here we demonstrate how this method can be useful in understanding excited states, specifically which chemical moieties polarize to the excitation. This work shows absolutely localized projection-based quantum embedding can treat local electronic excitations accurately, and make computationally expensive WF methods applicable to systems beyond current computational limits.

Motivation & Objective

• To develop a computationally efficient method for calculating localized excited states in large molecular systems.
• To address the limitations of standard TDDFT in describing charge-transfer and Rydberg excitations by embedding high-level wave function methods in a DFT environment.
• To eliminate spurious low-lying excited states caused by basis set delocalization in embedded TDDFT calculations.
• To systematically recover environment polarization effects in excited states and assess their contribution to excitation energy shifts.
• To demonstrate the method's robustness and systematic improvability on complex systems like green fluorescent protein (GFP)

Proposed method

• Employ projection-based quantum embedding using the Huzinaga operator to enforce orthogonality between subsystems and avoid non-additive kinetic energy functionals.
• Apply absolute localization by restricting the wave function expansion to only basis functions centered on atoms in the high-level subsystem, reducing orbital space and computational cost.
• Use EOM-CCSD for high-accuracy excited state calculations in the localized subsystem, with the environment treated at the DFT level.
• Implement TDDFT-in-DFT for efficient excited state calculations with improved accuracy over canonical TDDFT, especially for charge-transfer states.
• Introduce two schemes to recover environment response: a state-average approach and a TDDFT correction, with the latter shown to be accurate and cost-effective.
• Perform systematic embedding calculations by gradually increasing the size of the high-level subsystem to assess convergence and environmental contributions

Experimental results

Research questions

• RQ1 Can absolutely localized projection-based embedding accurately describe localized excited states in large systems using EOM-CCSD and TDDFT?
• RQ2 Does absolute localization eliminate spurious low-lying charge-transfer excitations common in standard TDDFT-in-DFT?
• RQ3 How significant is the contribution of ground-state environment polarization to excitation energy shifts in solvated systems?
• RQ4 Can environment response due to excited-state polarization be accurately recovered using the proposed correction schemes?
• RQ5 To what extent does the method allow for systematic improvement in accuracy with increasing subsystem size?

Key findings

• The absolutely localized embedding method reduces computational cost significantly by limiting the basis to only atoms in the excited subsystem, with minimal loss in accuracy for EOM-CCSD.
• Embedded TDDFT-in-DFT outperforms canonical TDDFT, especially in describing charge-transfer excitations, and eliminates spurious low-lying states due to basis delocalization.
• Ground-state environment polarization accounts for approximately 90% of the solvation-induced excitation energy shift in GFP, with the remaining 10% due to excited-state polarization response.
• The TDDFT correction scheme accurately recovers the excited-state environment response and is computationally viable when the full-system TDDFT cost is small compared to EOM-CCSD.
• Systematic embedding calculations converge robustly to full-system results, with excitation energy shifts remaining consistent regardless of the order in which environmental moieties are included.
• The method successfully identifies the relative importance of chemical moieties—such as water molecules and protein residues—toward the chromophore’s excited state, enabling mechanistic insight into electronic polarization