Energy Level Alignment at Molecule-Metal Interfaces from an Optimally-Tuned Range-Separated Hybrid Functional

The alignment of the frontier orbital energies of an adsorbed molecule with the substrate Fermi level at metal-organic interfaces is a fundamental observable of significant practical importance in nanoscience and beyond. Typical density functional theory calculations, especially those using local and semi-local functionals, often underestimate level alignment leading to inaccurate electronic structure and charge transport properties. In this work, we develop a new fully self-consistent predictive scheme to accurately compute level alignment at certain classes of complex heterogeneous molecule-metal interfaces based on optimally-tuned range-separated hybrid functionals. Starting from a highly accurate description of the gas-phase electronic structure, our method by construction captures important nonlocal surface polarization effects via tuning of the long-range screened exchange in a range-separated hybrid in a non-empirical and system-specific manner. We implement this functional in a plane-wave code and apply it to several physisorbed and chemisorbed molecule-metal interface systems. Our results are in quantitative agreement with experiments, both the level alignment and work function changes. Our approach constitutes a new practical scheme for accurate and efficient calculations of the electronic structure of molecule-metal interfaces.Comment: 15 pages, 8 figure

Reliable energy level alignment at physisorbed molecule-metal interfaces from density functional theory.

A key quantity for molecule-metal interfaces is the energy level alignment of molecular electronic states with the metallic Fermi level. We develop and apply an efficient theoretical method, based on density functional theory (DFT) that can yield quantitatively accurate energy level alignment information for physisorbed metal-molecule interfaces. The method builds on the "DFT+Σ" approach, grounded in many-body perturbation theory, which introduces an approximate electron self-energy that corrects the level alignment obtained from conventional DFT for missing exchange and correlation effects associated with the gas-phase molecule and substrate polarization. Here, we extend the DFT+Σ approach in two important ways: first, we employ optimally tuned range-separated hybrid functionals to compute the gas-phase term, rather than rely on GW or total energy differences as in prior work; second, we use a nonclassical DFT-determined image-charge plane of the metallic surface to compute the substrate polarization term, rather than the classical DFT-derived image plane used previously. We validate this new approach by a detailed comparison with experimental and theoretical reference data for several prototypical molecule-metal interfaces, where excellent agreement with experiment is achieved: benzene on graphite (0001), and 1,4-benzenediamine, Cu-phthalocyanine, and 3,4,9,10-perylene-tetracarboxylic-dianhydride on Au(111). In particular, we show that the method correctly captures level alignment trends across chemical systems and that it retains its accuracy even for molecules for which conventional DFT suffers from severe self-interaction errors

Magnetic configurations of open-shell molecules on metals: The case of CuPc and CoPc on silver

For nanostructured interfaces between open-shell molecules and metal surfaces that involve charge transfer upon adsorption, the investigation of molecular magnetic properties is an interesting yet difficult task, because in principle different magnetic configurations with distinct properties can be found. Here, we study the magnetic properties of CuPc-Ag and CoPc-Ag interfaces, which constitute interesting test cases because charge is transferred to the initially open-shell Pc molecules upon adsorption. Using hybrid density functional theory, we examine the stability of the various magnetic configurations occurring at these nanoscale interfaces, as well as for the corresponding gas-phase anions, and compare our findings to those of previous experimental studies. For CuPc-Ag, we identify a high-spin triplet configuration as the most likely configuration at the interface, whereas for CoPc-Ag a quenching of the total magnetic moment is found. Interestingly, such quenching is consistent with two distinctly different interfacial electronic configurations. These important differences in the magnetic properties of CuPc and CoPc on Ag are rationalized by variations in the interaction of their central metal atoms with the substrate. Our work facilitates a deeper understanding of the magnetic configuration and interlinked electronic-structure properties of molecule-metal interfaces. Furthermore, it highlights the necessity of an appropriate choice of methodology in tandem with a detailed evaluation of the different emerging magnetic properties

Distinguishing between Charge-Transfer Mechanisms at Organic/Inorganic Interfaces Employing Hybrid Functionals

When modeling inorganic/organic interfaces with density functional theory (DFT), the outcome often depends on the chosen functional. Hybrid functionals, which employ a fraction of Hartree–Fock exchange α, tend to give better results than the more commonly applied semilocal functionals, because they remove or at least mitigate the unphysical electron self-interaction. However, the choice of α is not straightforward, as its effect on observables depends on the physical properties of the investigated system, such as the size of the molecule and the polarizability of the substrate. In this contribution, we demonstrate this impact exemplarily for tetrafluoro-1,4-benzoquinone on semiconducting (copper-I-oxide Cu₂O) and metallic (Cu) substrates and explore how the simulated charge transfer depends on α. We determine the value α* that marks the transition point between spurious over-localization and over-delocalization of charges. This allows us to shed light on the interplay between the value of α* and the physical properties of the interface. We find that on the inert semiconducting substrate, α* strongly depends on surface screening. Furthermore, α has a significant impact on the amount of charge transfer and, in particular, the charge localization. Conversely, for the adsorption on Cu, α affects only the amount of transferred charge, but not its localization, which is a consequence of strong hybridization. Finally, we discuss limitations to the predictive power of DFT for modeling charge transfer at inorganic/organic interfaces and explain why the choice of a “correct” amount of Hartree–Fock exchange is difficult, if not impossible. However, we argue why simulations still provide valuable insights into the charge-transfer mechanism at organic/inorganic interfaces and describe how α can be chosen sensibly to simulate any given system

Quasiparticle Levels at Large Interface Systems from Many-body Perturbation Theory: the XAF-GW method

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 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.Comment: More detailed proof of Add-Chi for hybridized states added in this versio

Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-Particle Spectrum.

We develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons