Delocalization of Quasiparticle Moiré States in Twisted Bilayer hBN.

Twisted bilayers host many emergent phenomena in which the electronic excitations (quasiparticles, QPs) are closely intertwined with the local stacking order. By inspecting twisted hexagonal boron nitride (t-hBN), we show that nonlocal long-range interactions in large twisted systems cannot be reliably described by the local (high-symmetry) stacking and that the band gap variation (typically associated with the moiré excitonic potential) shows multiple minima with variable depth depending on the twist angle. We investigate twist angles of 2.45°, 2.88°, 3.48°, and 5.09° using the GW approximation together with stochastic compression to analyze the QP state interactions. We find that band-edge QP hybridization is suppressed for intermediate angles that exhibit two distinct local minima in the moiré potential (at AA region and saddle point (SP)) which become degenerate for the largest system (2.45°).

Influence of Carboxylic Acid Structure on the Kinetics of Polyurethane Foam Acidolysis to Recycled Polyol.

Closed-loop recycling of plastics is needed to bridge the gap between the material demands imposed by a growing global population and the depletion of nonrenewable petroleum feedstocks. Here, we examine chemical recycling of polyurethane foams (PUFs), the sixth most produced polymer in the world, through PUF acidolysis via dicarboxylic acids (DCAs) to release recyclable polyols. Acidolysis enables recycling of the polyol component of PUFs to high-quality materials, and while the influence of DCA structure on recycled PUF quality has been reported, there are no reports that examine the influence of DCA structure on the kinetics of polyol release. Here, we develop quantitative relationships between DCA structure and PUF acidolysis function for ∼10 different DCA reagents. PUF acidolysis kinetics were quantified with ∼1 s time resolution using the rate of carbon dioxide (CO2) gas generation, which is shown to occur concomitantly with polyol release. Pseudo-zeroth-order rate constants were measured as a function of DCA composition, reaction temperature, and DCA concentration, and apparent activation barriers were extracted. Our findings demonstrate that DCA carboxyl group proximity and phase of transport are descriptors of PUF acidolysis rates, rather than expected descriptors like pK a. DCAs with closer proximity acid groups exhibited faster PUF acidolysis rate constants. Furthermore, a shrinking core mechanism effectively describes the kinetic functional form of the kinetics of PUF acidolysis by DCAs. Measurements of acidolysis kinetics for model PUF (M-PUF) and end-of-life PUF (EOL PUF) confirm the applicability of our analysis to postconsumer materials. This work provides insights into the physical and chemical mechanisms controlling acidolysis, which can facilitate the development of efficient closed-loop PUF chemical recycling schemes.

Polyurethane Foam Chemical Recycling: Fast Acidolysis with Maleic Acid and Full Recovery of Polyol.

Chemical recycling of polyurethane (PU) waste is essential to displace the need for virgin polyol production and enable sustainable PU production. Currently, less than 20% of PU waste is downcycled through rebinding to lower value products than the original PU. Chemical recycling of PU waste often requires significant input of materials like solvents and slow reaction rates. Here, we report the fast (<10 min) and solvent-free acidolysis of a model toluene diisocyanate (TDI)-based flexible polyurethane foam (PUF) at <200 °C using maleic acid (MA) with a recovery of recycled polyol (repolyol) in 95% isolated yield. After workup (hydrolysis of repolyl ester and separations), the repolyol exhibits favorable physical properties that are comparable to the virgin polyol; these include 54.1 mg KOH/g OH number and 624 cSt viscosity. Overall, 80% by weight of the input PUF is isolated into two clean-cut fractions containing the repolyol and toluene diamine (TDA). Finally, end-of-life (EOL) mattress PUF waste is recycled successfully with high recovery of repolyol using MA acidolysis. The solvent-free and fast acidolysis with MA demonstrated in this work with both model and EOL PUF provides a potential pathway for sustainable and closed-loop PU production.

Vapor-Phase Dicarboxylic Acids and Anhydrides Drive Depolymerization of Polyurethanes.

Polyurethane (PU) is the sixth most used plastic in the world. Because many PU derived materials are thermosets and the monomers are valuable, chemical recycling to recover the polyol component is the most viable pathway to utilizing postconsumer PU waste in a closed-loop fashion. Acidolysis is an effective method to recover polyol from PU waste. Previous studies of PU acidolysis rely on the use of dicarboxylic acid (DCA) in high temperature reactions (>200 °C) in the liquid phase and result in unwanted byproducts, high energy consumption, complex separations of excess organic acid, and an overall process that is difficult to scale up. In this work, we demonstrate selective PU acidolysis with DCA vapor to release polyol at temperatures below the melting points of the DCAs (<150 °C). Notably, acidolysis with DCA vapor adheres to the principles of green chemistry and prevents in part esterification of the polyol product, eliminating the need for additional hydrolysis/processing to obtain the desired product. The methodology was successfully applied to a commercial PU foam (PUF) postconsumer waste.

Efficient Quasiparticle Determination beyond the Diagonal Approximation via Random Compression.

Calculations of excited states in the Green's function formalism often invokes the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. In this paper, we extend the stochastic approaches applied in the many-body perturbation theory and overcome this limitation for large systems in which we are interested in a small subset of states. We separate the problem into a core subspace whose coupling to the remainder of the system environment is stochastically sampled. This method is exemplified on computing hole injection energies into CO2 on an extended gold surface with nearly 3000 electrons. We find that in the extended system the size of the problem can be compressed up to 95% using stochastic sampling. This result provides a way forward for self-consistent stochastic methods and determination of Dyson orbitals in large systems.

Exceptional Spatial Variation of Charge Injection Energies on Plasmonic Surfaces.

Charge injection into a molecule on a metallic interface is a key step in many photoactivated reactions. We employ the many-body perturbation theory and compute the hole and electron injection energies for CO2 molecule on an Au nanoparticle with ∼3,000 electrons and compare it to results for idealized infinite surfaces. We demonstrate a surprisingly large variation of the injection energy barrier depending on the precise molecular position on the surface. Multiple "hot spots," characterized by low energy barriers, arise due to the competition between the plasmonic coupling and the degree of hybridization between the molecule and the substrate. The charge injection barrier to the adsorbate on the nanoparticle surface decreases from the facet edge to the facet center. This finding contrasts with the typical picture in which the electric field enhancement on the nanoparticle edges is considered the most critical factor.

Embedding vertex corrections in GW self-energy: Theory, implementation, and outlook.

The vertex function (Γ) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot GW correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest;" the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing cycle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot GW approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.

Spatial Decay and Limits of Quantum Solute-Solvent Interactions.

Molecular excitations in the liquid-phase environment are renormalized by the surrounding solvent molecules. Herein, we employ the GW approximation to investigate the solvation effects on the ionization energy of phenol in various solvent environments. The electronic effects differ by up to 0.4 eV among the five investigated solvents. This difference depends on both the macroscopic solvent polarizability and the spatial decay of the solvation effects. The latter is probed by separating the electronic subspace and the GW correlation self-energy into fragments. The fragment correlation energy decays with increasing intermolecular distance and vanishes at ∼9 Å, and this pattern is independent of the type of solvent environment. The 9 Å cutoff defines an effective interacting volume within which the ionization energy shift per solvent molecule is proportional to the macroscopic solvent polarizability. Finally, we propose a simple model for computing the ionization energies of molecules in an arbitrary solvent environment.

Reduced Scaling of Optimal Regional Orbital Localization via Sequential Exhaustion of the Single-Particle Space.

Wannier functions have become a powerful tool in the electronic structure calculations of extended systems. The generalized Pipek-Mezey Wannier functions exhibit appealing characteristics (e.g., reaching an optimal localization and the separation of the σ-π orbitals) compared with other schemes. However, when applied to giant nanoscale systems, the orbital localization suffers from a large computational cost overhead if one is interested in localized states in a small fragment of the system. Herein, we present a swift, efficient, and robust approach for obtaining regionally localized orbitals of a subsystem within the generalized Pipek-Mezey scheme. The proposed algorithm introduces a reduced work space and sequentially exhausts the entire orbital space until the convergence of the localization functional. It tackles systems with ∼10000 electrons within 0.5 h with no loss in localization quality compared to the traditional approach. Regionally localized orbitals with a higher extent of localization are obtained via judiciously extending the subsystem's size. Exemplifying on large bulk and a 4 nm wide slab of diamond with an NV- center, we demonstrate the methodology and discuss how the choice of the localization region affects the excitation energy of the defect. Furthermore, we show how the sequential algorithm is easily extended to stochastic methodologies that do not provide individual single-particle eigenstates. It is thus a promising tool to obtain regionally localized states for solving the electronic structure problems of a subsystem embedded in giant condensed systems.

Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory.

Accurate predictions of charge excitation energies of molecules in the disordered condensed phase are central to the chemical reactivity, stability, and optoelectronic properties of molecules and critically depend on the specific environment. Herein, we develop a stochastic GW method for calculating these charge excitation energies. The approach employs maximally localized electronic states to define the electronic subspace of a molecule and the rest of the system, both of which are randomly sampled. We test the method on three solute-solvent systems: phenol, thymine, and phenylalanine in water. The results are in excellent agreement with the previous high-level calculations and available experimental data. The stochastic calculations for supercells containing up to 1000 electrons representing the solvated systems are inexpensive and require ≤1000 central processing unit hrs. We find that the coupling with the environment accounts for ∼40% of the total correlation energy. The solvent-to-solute feedback mechanism incorporated in the molecular correlation term causes up to 0.6 eV destabilization of the quasiparticle energy. Simulated photo-emission spectra exhibit red shifts, state-degeneracy lifting, and lifetime shortening. Our method provides an efficient approach for an accurate study of excitations of large molecules in realistic condensed phase environments.

Are multi-quasiparticle interactions important in molecular ionization?

Photo-emission spectroscopy directly probes individual electronic states, ranging from single excitations to high-energy satellites, which simultaneously represent multiple quasiparticles (QPs) and encode information about electronic correlation. The first-principles description of the spectra requires an efficient and accurate treatment of all many-body effects. This is especially challenging for inner valence excitations where the single QP picture breaks down. Here, we provide the full valence spectra of small closed-shell molecules, exploring the independent and interacting quasiparticle regimes, computed with the fully correlated adaptive sampling configuration interaction method. We critically compare these results to calculations with the many-body perturbation theory, based on the GW and vertex corrected GWΓ approaches. The latter explicitly accounts for two-QP quantum interactions, which have often been neglected. We demonstrate that for molecular systems, the vertex correction universally improves the theoretical spectra, and it is crucial for the accurate prediction of QPs as well as capturing the rich satellite structures of high-energy excitations. GWΓ offers a unified description across all relevant energy scales. Our results suggest that the multi-QP regime corresponds to dynamical correlations, which can be described via perturbation theory.

Decomposition and embedding in the stochastic GW self-energy.

We present two new developments for computing excited state energies within the GW approximation. First, calculations of the Green's function and the screened Coulomb interaction are decomposed into two parts: one is deterministic, while the other relies on stochastic sampling. Second, this separation allows constructing a subspace self-energy, which contains dynamic correlation from only a particular (spatial or energetic) region of interest. The methodology is exemplified on large-scale simulations of nitrogen-vacancy states in a periodic hBN monolayer and hBN-graphene heterostructure. We demonstrate that the deterministic embedding of strongly localized states significantly reduces statistical errors, and the computational cost decreases by more than an order of magnitude. The computed subspace self-energy unveils how interfacial couplings affect electronic correlations and identifies contributions to excited-state lifetimes. While the embedding is necessary for the proper treatment of impurity states, the decomposition yields new physical insight into quantum phenomena in heterogeneous systems.

Quasiparticles and Band Structures in Organized Nanostructures of Donor-Acceptor Copolymers.

The performance of organic semiconductor devices is linked to highly ordered nanostructures of self-assembled molecules and polymers. Many-body perturbation theory is employed to study the excited states in bulk copolymers. The results show that acceptors in the polymer scaffold introduce a, hitherto unrecognized, conduction impurity band that leads to electron localization. The donor states are responsible for the formation of conjugated bands, which are only mildly perturbed by the presence of the acceptors. Along the polymer axis, the nonlocal electronic correlations among copolymer strands hinder efficient band transport, which is, however, strongly enhanced across individual chains. Holes are most effectively transported along the π-π stacking, while electrons in the impurity band follow the edge-to-edge directions. The copolymers exhibit regions with inverted transport polarity, in which electrons and holes are efficiently transported in mutually orthogonal directions.

Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene.

We implement stochastic many-body perturbation theory for systems with 2D periodic boundary conditions. The method is used to compute quasiparticle excitations in twisted bilayer phosphorene. Excitation energies are studied using stochastic [Formula: see text] and partially self-consistent [Formula: see text] approaches. The approach is inexpensive; it is used to study twisted systems with unit cells containing >2700 atoms (>13 500 valence electrons), which corresponds to a minimum twisting angle of [Formula: see text] [Formula: see text]. Twisted bilayers exhibit band splitting, increased localization and formation of localized Moiré impurity states, as documented by band-structure unfolding. Structural changes in twisted structures lift band degeneracies. Energies of the impurity states vary with the twisting angle due to an interplay between non-local exchange and polarization effects. The mechanisms of quasiparticle energy (de)stabilization due to twisting are likely applicable to a wide range of low-dimensional Moiré superstructures.

Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies.

New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: G0W0, G0W0tc, and G0W0tcΓX. All three methods are formulated in the time domain, and the latter two incorporate nonlocal vertex corrections. In the case of G0W0tcΓX, the vertex corrections are included both in the screened Coulomb interaction and in the expression for the self-energy. The implementation of the three approximations is verified by comparison to deterministic results for a set of small molecules. The performance of the fully stochastic implementation is tested on acene molecules, C60 and PC60BM. The vertex correction appears crucial for the description of unoccupied states. Unlike conventional (deterministic) approaches, all three stochastic methods scale linearly with the number of electrons.

Stochastic time-dependent DFT with optimally tuned range-separated hybrids: Application to excitonic effects in large phosphorene sheets.

We develop a stochastic approach to time-dependent density functional theory with optimally tuned range-separated hybrids containing nonlocal exchange, for calculating optical spectra. The attractive electron-hole interaction, which leads to the formation of excitons, is included through a time-dependent linear-response technique with a nonlocal exchange interaction which is computed very efficiently through a stochastic scheme. The method is inexpensive and scales quadratically with the number of electrons, at almost the same (low) cost of time dependent Kohn-Sham with local functionals. Our results are in excellent agreement with experimental data, and the efficiency of the approach is demonstrated on large finite phosphorene sheets containing up to 1958 valence electrons.

Simple eigenvalue-self-consistent Δ ¯ G W 0 .

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ ¯ G W 0 , can be trivially implemented at zero additional cost for large scale one-shot G 0 W 0 calculations. The method significantly improves one-shot G 0 W 0 and for large systems is very accurate. Δ ¯ G W 0 is similar in spirit to evGW 0 where the self-consistency is only applied on the eigenvalues entering Green's function, while both W and the eigenvectors of Green's function are held fixed. Δ ¯ G W 0 further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent G 0 W 0 self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-GW approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of Δ ¯ G W 0 increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and evGW 0 to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches evGW 0 quite well and both methods are in good agreement with the experiment.

Exploring Oxidation State-Dependent Selectivity in Polymerization of Cyclic Esters and Carbonates with Zinc(II) Complexes.

Neutral zinc alkoxide complexes show high activity toward the ring-opening polymerization of cyclic esters and carbonates, to generate biodegradable plastics applicable in several areas. Herein, we use a ferrocene-chelating heteroscorpionate complex in redox-switchable polymerization reactions, and we show that it is a moderately active catalyst for the ring-opening polymerization of L-lactide, ɛ-caprolactone, trimethylene carbonate, and δ-valerolactone. Uniquely for this type of catalyst, the oxidized complex has a similar polymerization activity as the corresponding reduced compound, but displays significantly different rates of reaction in the case of trimethylene carbonate and δ-valerolactone. Investigations of the oxidized compound suggest the presence of an organic radical rather than an Fe(III) complex. Electronic structure and density functional theory (DFT) calculations were performed to support the proposed electronic states of the catalytic complex and to help explain the observed reactivity differences. The catalyst was also compared with a monomeric phenoxide complex to show the influence of the phosphine-zinc interaction on catalytic properties.

Effects of symmetry breaking on the translation-rotation eigenstates of H2, HF, and H2O inside the fullerene C60.

Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

Thermal Equilibration Controls H-Bonding and the Vertical Detachment Energy of Water Cluster Anions.

One of the outstanding puzzles in the photoelectron spectroscopy of water anion clusters, which serve as precursors to the hydrated electron, is that the excess electron has multiple vertical detachment energies (VDEs), with different groups seeing different distributions of VDEs. We have studied the photoelectron spectroscopy of water cluster anions using simulation techniques designed to mimic the different ways that water cluster anions are produced experimentally. Our simulations take advantage of density functional theory-based Born-Oppenheimer molecular dynamics with an optimally tuned range-separated hybrid functional that is shown to give outstanding accuracy for calculating electron binding energies for this system. We find that our simulations are able to accurately reproduce the experimentally observed VDEs for cluster anions of different sizes, with different VDE distributions observed depending on how the water cluster anions are prepared. For cluster anion sizes up to 20 water molecules, we see that the excess electron always resides on the surface of the cluster and that the different discrete VDEs result from the discrete number of hydrogen bonds made to the electron by water molecules on the surface. Clusters that are less thermally equilibrated have surface waters that tend to make single H-bonds to the electron, resulting in lower VDEs, while clusters that are more thermally equilibrated have surface waters that prefer to make two H-bonds to the electron, resulting in higher VDEs.