Quasiparticle Levels at Large Interface Systems from Many-Body Perturbation Theory: The XAF-GW Method

Abstract

We present a fully ab initio approach based on many-body perturbation theory in the GW approximation, to compute the quasiparticle levels of large interface systems without significant covalent interactions between the different components of the interface. The only assumption in our approach is that the polarizability matrix (chi) of the interface can be given by the sum of the polarizability matrices of individual components of the interface. We show analytically, using a two-state hybridized model, that this assumption is valid even in the presence of interface hybridization to form bonding and anti-bonding states, up to first order in the overlap matrix elements involved in the hybridization. We validate our approach by showing that the band structure obtained in our method is almost identical to that obtained using a regular GW calculation for bilayer black phosphorus, where interlayer hybridization is significant. Significant savings in computational time and memory are obtained by computing chi only for the smallest sub-unit cell of each component, and expanding (unfolding) the chi matrix to that in the unit cell of the interface. To treat interface hybridization, the full wavefunctions of the interface are used in computing the self-energy.We thus call the method XAF-GW (X: eXpand-chi, A: Add-chi, F: Full wavefunctions).Compared to GW-embedding type approaches in the literature, the XAF-GW approach is not limited to specific screening environments or to non-hybridized interface systems. XAF-GW can also be applied to systems with different dimensionalities, as well as to Moire 2 superlattices such as in twisted bilayers. We illustrate the generality and usefulness of our approach by applying it to self-assembled PTCDA monolayers on Au(111) and Ag(111), and PTCDA monolayers on graphite-supported monolayer WSe2, where good agreement with experiment is obtained.

Exciton Modulation in Perylene-Based Molecular Crystals Upon Formation of a Metal-Organic Interface From Many-Body Perturbation Theory

“…In this approach, the non-interacting polarizability of the interface is approximated by the summation of the separately calculated polarizabilies of the substrate (Au) and adsorbate (C8-PDI), i.e., where and are the polarizabilities associated with the standalone molecular layer and metal substrates, respectively. This approximation holds for systems with weak hybridization between the adsorbate and the substrate ( Liu et al, 2019 ; Xuan et al, 2019 ; Adeniran et al, 2020 ). The goal is to assess the validity of Eq.…”

“…where χ 0 mol and χ 0 sub are the polarizabilities associated with the standalone molecular layer and metal substrates, respectively. This approximation holds for systems with weak hybridization between the adsorbate and the substrate (Liu et al, 2019;Xuan et al, 2019;Adeniran et al, 2020). The goal is to assess the validity of Eq.…”

“…We can infer from these results that there is negligible orbital hybridization at the C8-PDI@Au interface, and that the Au substrate simply provides a dielectric environment that effectively screens the molecular crystal. We expect that the substrate screening approach, based on the additivity of the non-interacting polarizability of the interface (Liu et al, 2019;Xuan et al, 2019), is applicable to other systems without significant orbital hybridization or covalent bonding. We believe this conclusion could help us understand the physical interface where a C8-PDI monolayer in its pristine bulk lattice (rather than the artificial commensurate lattice as we did in this work) is adsorbed on Au (111).…”

Accelerating GW-Based Energy Level Alignment Calculations for Molecule–Metal Interfaces Using a Substrate Screening Approach

“…These methods, often referred to as DFT+Σ, can be accurate in the weak-coupling limit; 11,13,30 but they require the definition of an image-plane 29 and they neglect dynamical effects of the electrode polarizability. Beyond DFT+Σ, recently there have been a number of studies focusing on efficient substrate screening, [31][32][33][34][35][36][37][38][39] especially at interfaces involving two-dimensional materials. The essential idea is that the non-interacting RPA polarizability of the interface can be well approximated by the sum of the non-interacting RPA polarizabilities of each individual components, 31,32,34,39 with the latter further approximated using a variety of approaches.…”

Dielectric screening by 2D substrates

“…We note that the effects of hybridization can be included in our estimate of the HOMO-LUMO gap using more involved methodologies. 25,26 We can further improve our estimation in equation (8) Figure 3. GW π-π* gap of benzene on BN, MoS2 and graphene versus the π-π* gap predicted using Vscr.…”