Low-Scaling Many-Body Green's Function Calculations for Molecular Systems via Interacting-Bath Dynamical Embedding Theory

Abstract

We present a molecular extension of our recently proposed Green's function embedding method, interacting-bath dynamical embedding theory (ibDET), for computing charged excitation energies at the $GW$ and EOM-CCSD levels. Starting from atom-centered impurities, we construct bath representations that capture the frequency-dependent entanglement between the impurity and its environment and can be systematically improved via the construction of cluster-specific natural orbitals. Utilizing a $GW$ or coupled-cluster Green's function solver, the self-energy of the full system is assembled from all embedding problems to obtain the interacting Green's function. We show that ibDET provides accurate spectral properties with much reduced cost for a broad range of systems, including conjugated molecules and nanoclusters. Compared with full-system results, the errors in the predicted ionization potentials and electron affinities are around 0.1 eV or smaller, while each embedding problem includes only a small fraction of the total orbital space. This work provides an efficient and scalable framework for computing spectral properties of molecular systems.

Figures (5)

• Figure 1: (a) Illustration of the ibDET approach for molecules. Scaling bottlenecks associated with ibDET integral transformations are given in red. (b) An example of systematically increasing occupied embedding space in BODIPY. Showing the embedding space electron density.
• Figure 2: Silicon nanocluster HF+$GW$ ibDET benchmark. (a,b) HOMO, LUMO quasiparticle energies vs. embedding size, with Hartree-Fock and full $G_0W_0$@HF for reference. (c,d) Extrapolation to the full-space limit with respect to embedding size. Extrapolated values shown on (a) and (b) as a star. The full-space $GW$ HOMO and LUMO are $-8.57$ eV and $-0.50$ eV respectively. (e) ibDET density of states compared against full-space $G_0W_0$@HF.
• Figure 3: Phosphorene nanosheet ibDET HF+$GW$ benchmark. (a) Errors for HOMO and LUMO quasiparticle energies relative to full-space results vs. nanosheet size. Largest nanosheet ($6\times 6$ unit cells, 144 phosphorous atoms) is shown for reference. (b) Log-log plot of key computation timings vs. system size. ibDET is broken down into bath construction (1-PNO construction and integral transformations) and impurity solver steps. Power law fits are shown as dashed lines.
• Figure 4: BODIPY molecule HF+CC ibDET benchmark. (a,b) HOMO, LUMO energies vs. embedding size, with Hartree-Fock and full IP/EA-EOM-CCSD for reference. (c,d) Extrapolation to the full-space limit with respect to embedding size. Extrapolated values shown on (a) and (b) as a star. (e) ibDET-predicted EOM-CCSD density of states overlaid with IP/EA-EOM-CCSD values shown as dashed line. Full-space $G_0W_0$@HF spectrum is also shown for reference. The full-space $GW$ HOMO and LUMO are $-5.89$ eV and $-0.68$ eV respectively.
• Figure 5: Quaterrylene molecule HF+CC ibDET benchmark. (a,b) HOMO, LUMO energies vs. embedding size, with Hartree-Fock and full IP/EA-EOM-CCSD for reference. (c,d) Extrapolation to the full-space limit with respect to embedding size. Extrapolated values are shown on (a) and (b) as a star. The full-space $GW$ HOMO and LUMO are $-5.59$ eV and $-1.25$ eV respectively. The full-space IP/EA-EOM-CCSD HOMO and LUMO are $-5.54$ eV and $-1.38$ eV respectively.