Graphite-like Charge Storage Mechanism in a 2D π-d Conjugated Metal-Organic Framework Revealed by Stepwise Magnetic Monitoring.

Quasi-two-dimensional (2D) fully π-d conjugated metal-organic frameworks (MOFs) have been widely employed as active materials of secondary batteries; however, the origin of their high charge storage capacity is still unknown. Some reports have proposed a mechanism by assuming the formation of multiple radicals on one organic ligand, although there is no firm evidence for such a mechanism, which would run counter to the resonance theory. In this work, we utilized various magnetometric techniques to monitor the formation and concentration of paramagnetic species during the electrochemical process of 2D π-d conjugated Cu-THQ MOF (THQ = tetrahydroxy-1,4-benzoquinone). The spin concentration of the fully reduced (discharged 1.5 V) electrode was estimated to be around only 0.1 spin-1/2 per CuO4 unit, which is much lower than that of the expected "diradical" form. More interestingly, a significant elevation of the temperature-independent paramagnetic term was simultaneously observed, which indicates the presence of delocalized π electrons in this discharged state. Such results were corroborated by first-principles density functional theory calculations and the electrochemically active density of states, which reveal the microscopic mechanism of the charge storage in the Cu-THQ MOF. Hence, a graphite-like charge storage mechanism, where the π-electron band accepts/donates electrons during the charge/discharge process, was suggested to explain the excessive charge storage of Cu-THQ. This graphite-like charge storage mechanism revealed by magnetic studies can be readily generalized to other π-d conjugated MOFs.

Electrochemical hydrogen isotope exchange of amines controlled by alternating current frequency.

Here, we report an electrochemical protocol for hydrogen isotope exchange (HIE) at α-C(sp3)-H amine sites. Tetrahydroisoquinoline and pyrrolidine are selected as two model substrates because of their different proton transfer (PT) and hydrogen atom transfer (HAT) kinetics at the α-C(sp3)-H amine sites, which are utilized to control the HIE reaction outcome at different applied alternating current (AC) frequencies. We found the highest deuterium incorporation for tetrahydroisoquinolines at 0 Hz (i.e., under direct current (DC) electrolysis conditions) and pyrrolidines at 0.5 Hz. Analysis of the product distribution and D isotope incorporation at different frequencies reveals that the HIE of tetrahydroisoquinolines is limited by its slow HAT, whereas the HIE of pyrrolidines is limited by the overoxidation of its α-amino radical intermediates. The AC-frequency-dependent HIE of amines can be potentially used to achieve selective labeling of α-amine sites in one drug molecule, which will significantly impact the pharmaceutical industry.

Charge Transport Across Dynamic Covalent Chemical Bridges.

Relationships between chemical structure and conductivity in ordered polymers (OPs) are difficult to probe using bulk samples. We propose that conductance measurements of appropriate molecular-scale models can reveal trends in electronic coupling(s) between repeat units that may help inform OP design. Here, we apply the scanning tunneling microscope-based break-junction (STM-BJ) method to study transport through single-molecules comprising OP-relevant imine, imidazole, diazaborole, and boronate ester dynamic covalent chemical bridges. Notably, solution-stable boron-based compounds dissociate in situ unless measured under a rigorously inert glovebox atmosphere. We find that junction conductance negatively correlates with the electronegativity difference between bridge atoms, and corroborative first-principles calculations further reveal a different nodal structure in the transmission eigenchannels of boronate ester junctions. This work reaffirms expectations that highly polarized bridge motifs represent poor choices for the construction of OPs with high through-bond conductivity and underscores the utility of glovebox STM-BJ instrumentation for studies of air-sensitive materials.

Electronic Structure of Metallophthalocyanines, MPc (M = Fe, Co, Ni, Cu, Zn, Mg) and Fluorinated MPc.

We compute the electronic structure and optical excitation energies of metal-free and transition-metal phthalocyanines (H2Pc and MPc for M = Fe, Co, Ni, Cu, Zn, Mg) using density functional theory with optimally tuned range-separated hybrid functionals (OT-RSH). We show that the OT-RSH approach provides photoemission spectra in quantitative agreement with experiments as well as optical band gaps within 10% of their experimental values, capturing the interplay of localized d-states and delocalized π-π* states for these organometallic compounds. We examine the tunability of MPcs and H2Pc through fluorination, resulting in quasi-rigid shifts of the molecular orbital energies by up to 0.7 eV. Our comprehensive data set provides a new computational benchmark for gas-phase phthalocyanines, significantly improving upon other density-functional-theory-based approaches.

Quasiparticle electronic structure of phthalocyanine:TMD interfaces from first-principles GW.

Interfaces formed between monolayer transition metal dichalcogenides and (metallo)phthalocyanine molecules are promising in energy applications and provide a platform for studying mixed-dimensional molecule-semiconductor heterostructures in general. An accurate characterization of the frontier energy level alignment at these interfaces is key in the fundamental understanding of the charge transfer dynamics between the two photon absorbers. Here, we employ the first-principles substrate screening GW approach to quantitatively characterize the quasiparticle electronic structure of a series of interfaces: metal-free phthalocyanine (H2Pc) adsorbed on monolayer MX2 (M = Mo, W; X = S, Se) and zinc phthalocyanine (ZnPc) adsorbed on MoX2 (X = S, Se). Furthermore, we reveal the dielectric screening effect of the commonly used α-quartz (SiO2) substrate on the H2Pc:MoS2 interface using the dielectric embedding GW approach. Our calculations furnish a systematic set of GW results for these interfaces, providing the structure-property relationship across a series of similar systems and benchmarks for future experimental and theoretical studies.

Dielectric embedding GW for weakly coupled molecule-metal interfaces.

Molecule-metal interfaces have a broad range of applications in nanoscale materials science. Accurate characterization of their electronic structures from first-principles is key in understanding material and device properties. The GW approach within many-body perturbation theory is the state-of-the-art and can in principle yield accurate quasiparticle energy levels and interfacial level alignments that are in quantitative agreement with experiments. However, the interfaces are large heterogeneous systems that are currently challenging for first-principles GW calculations. In this work, we develop a GW-based dielectric embedding approach for molecule-metal interfaces, significantly reducing the computational cost of direct GW without sacrificing the accuracy. To be specific, we perform explicit GW calculations only in the simulation cell of the molecular adsorbate, in which the dielectric effect of the metallic substrate is embedded. This is made possible via a real-space truncation of the substrate polarizability and the use of the interface plasma frequency in the adsorbate GW calculation. Here, we focus on the level alignment at weakly coupled molecule-metal interfaces, i.e., the energy difference between a molecular frontier orbital resonance and the substrate Fermi level. We demonstrate our method and assess a few GW-based approximations using two well-studied systems, benzene adsorbed on the Al (111) and on the graphite (0001) surfaces.

Electronically Transparent Au-N Bonds for Molecular Junctions.

We report a series of single-molecule transport measurements carried out in an ionic environment with oligophenylenediamine wires. These molecules exhibit three discrete conducting states accessed by electrochemically modifying the contacts. Transport in these junctions is defined by the oligophenylene backbone, but the conductance is increased by factors of ∼20 and ∼400 when compared to traditional dative junctions. We propose that the higher-conducting states arise from in situ electrochemical conversion of the dative Au←N bond into a new type of Au-N contact. Density functional theory-based transport calculations establish that the new contacts dramatically increase the electronic coupling of the oligophenylene backbone to the Au electrodes, consistent with experimental transport data. The resulting contact resistance is the lowest reported to date; more generally, our work demonstrates a facile method for creating electronically transparent metal-organic interfaces.

Charge transport and rectification in molecular junctions formed with carbon-based electrodes.

Molecular junctions formed using the scanning-tunneling-microscope-based break-junction technique (STM-BJ) have provided unique insight into charge transport at the nanoscale. In most prior work, the same metal, typically Au, Pt, or Ag, is used for both tip and substrate. For such noble metal electrodes, the density of electronic states is approximately constant within a narrow energy window relevant to charge transport. Here, we form molecular junctions using the STM-BJ technique, with an Au metal tip and a microfabricated graphite substrate, and measure the conductance of a series of graphite/amine-terminated oligophenyl/Au molecular junctions. The remarkable mechanical strength of graphite and the single-crystal properties of our substrates allow measurements over few thousand junctions without any change in the surface properties. We show that conductance decays exponentially with molecular backbone length with a decay constant that is essentially the same as that for measurements with two Au electrodes. More importantly, despite the inherent symmetry of the oligophenylamines, we observe rectification in these junctions. State-of-art ab initio conductance calculations are in good agreement with experiment, and explain the rectification. We show that the highly energy-dependent graphite density of states contributes variations in transmission that, when coupled with an asymmetric voltage drop across the junction, leads to the observed rectification. Together, our measurements and calculations show how functionality may emerge from hybrid molecular-scale devices purposefully designed with different electrodes beyond the so-called "wide band limit," opening up the possibility of assembling molecular junctions with dissimilar electrodes using layered 2D materials.

Mapping the Transmission Functions of Single-Molecule Junctions.

Charge transport phenomena in single-molecule junctions are often dominated by tunneling, with a transmission function dictating the probability that electrons or holes tunnel through the junction. Here, we present a new and simple technique for measuring the transmission functions of molecular junctions in the coherent tunneling limit, over an energy range of 1.5 eV around the Fermi energy. We create molecular junctions in an ionic environment with electrodes having different exposed areas, which results in the formation of electric double layers of dissimilar density on the two electrodes. This allows us to electrostatically shift the molecular resonance relative to the junction Fermi levels in a manner that depends on the sign of the applied bias, enabling us to map out the junction's transmission function and determine the dominant orbital for charge transport in the molecular junction. We demonstrate this technique using two groups of molecules: one group having molecular resonance energies relatively far from EF and one group having molecular resonance energies within the accessible bias window. Our results compare well with previous electrochemical gating data and with transmission functions computed from first principles. Furthermore, with the second group of molecules, we are able to examine the behavior of a molecular junction as a resonance shifts into the bias window. This work provides a new, experimentally simple route for exploring the fundamentals of charge transport at the nanoscale.

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.

Control of single-molecule junction conductance of porphyrins via a transition-metal center.

Using scanning tunneling microscope break-junction experiments and a new first-principles approach to conductance calculations, we report and explain low-bias charge transport behavior of four types of metal-porphyrin-gold molecular junctions. A nonequilibrium Green's function approach based on self-energy corrected density functional theory and optimally tuned range-separated hybrid functionals is developed and used to understand experimental trends quantitatively. Importantly, due to the localized d states of the porphyrin molecules, hybrid functionals are essential for explaining measurements; standard semilocal functionals yield qualitatively incorrect results. Comparing directly with experiments, we show that the conductance can change by nearly a factor of 2 when different metal cations are used, counter to trends expected from gas-phase ionization energies which are relatively unchanged with the metal center. Our work explains the sensitivity of the porphyrin conductance with the metal center via a detailed and quantitative portrait of the interface electronic structure and provides a new framework for understanding transport quantitatively in complex junctions involving molecules with localized d states of relevance to light harvesting and energy conversion.

Communication: energy-dependent resonance broadening in symmetric and asymmetric molecular junctions from an ab initio non-equilibrium Green's function approach.

The electronic structure of organic-inorganic interfaces often features resonances originating from discrete molecular orbitals coupled to continuum lead states. An example is molecular junction, individual molecules bridging electrodes, where the shape and peak energy of such resonances dictate junction conductance, thermopower, I-V characteristics, and related transport properties. In molecular junctions where off-resonance coherent tunneling dominates transport, resonance peaks in the transmission function are often assumed to be Lorentzian functions with an energy-independent broadening parameter Γ. Here we define a new energy-dependent resonance broadening function, Γ(E), based on diagonalization of non-Hermitian matrices, which can describe resonances of a more complex, non-Lorentzian nature and can be decomposed into components associated with the left and right leads, respectively. We compute this quantity via an ab initio non-equilibrium Green's function (NEGF) approach based on density functional theory (DFT) for both symmetric and asymmetric molecular junctions, and show that our definition of Γ(E), when combined with Breit-Wigner formula, reproduces the transmission calculated from DFT-NEGF. Through a series of examples, we illustrate how this approach can shed new light on experiments and understanding of junction transport properties in terms of molecular orbitals.

Generalized Substrate Screening GW for Covalently Bonded Interfaces.

An accurate description of the interfacial quasiparticle electronic structure is key to the design of heterogeneous materials. While the first-principles GW approach is state-of-the-art, the computational cost is high for large interface systems. This has led to the substrate screening GW approach for weakly coupled interfaces, which breaks down for covalently bonded interfaces. In this work, we present the generalized substrate screening GW approach, based on the following two considerations: (i) the contribution of the interfacial covalent bond to the polarizability can be efficiently calculated with a low energy cutoff; (ii) the contribution of the deprotonated adsorbate to the interface polarizability can be well approximated by that of the protonated molecule. Our approach is exemplified using interfaces formed between benzene-1,4-dithiol (BDT) and Au(111), which feature the widely used Au-S bonds in experiments. Our work provides a robust and simple scheme for accurate and efficient GW calculations of covalently bonded interfaces.

Robust binding between secondary amines and Au electrodes.

While primary amines are one of the most widely used linker groups for forming single-molecule junctions, it remains elusive whether and how the substitution of one hydrogen in a primary amine with a methyl group (secondary amine) can alter its functional properties as a linker group. Here we show that a robust binding between a secondary amine and an Au electrode is absent with the use of a non-coated Au tip and is achieved when in contact with a wax-coated Au tip, which we propose is catalyzed by the more frequent formation of Au adatoms in measurements with a wax-coated tip.

Accelerating GW Calculations of Point Defects with the Defect-Patched Screening Approximation.

The GW approximation has been widely accepted as an ab initio tool for calculating defect levels with the many-electron effect included. However, the GW simulation cost increases dramatically with the system size, and unfortunately, large supercells are often required to model low-density defects that are experimentally relevant. In this work, we propose to accelerate GW calculations of point defects by reducing the simulation cost of many-electron screening, which is the primary computational bottleneck. The random-phase approximation of many-electron screening is divided into two parts: one is the intrinsic screening, calculated using a unit cell of pristine structures, and the other is the defect-induced screening, calculated using the supercell within a small energy window. Depending on specific defects, one may only need to consider the intrinsic screening or include the defect contribution. This approach avoids the summation of many conduction states of supercells and significantly reduces the simulation cost. We have applied it to calculate various point defects, including neutral and charged defects in two-dimensional and bulk systems with small or large bandgaps. The results are consistent with those from the direct GW simulations. This defect-patched screening approach not only clarifies the roles of defects in many-electron screening but also paves the way to fast screen defect structures/materials for novel applications, including single-photon sources, quantum qubits, and quantum sensors.

Bethe ansatz approach to the Kondo effect within density-functional theory.

Transport through an Anderson junction (two macroscopic electrodes coupled to an Anderson impurity) is dominated by a Kondo peak in the spectral function at zero temperature. We show that the single-particle Kohn-Sham potential of density-functional theory reproduces the linear transport, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculate this potential for all coupling strengths, including the crossover from mean-field behavior to charge quantization caused by the derivative discontinuity. A simple and accurate interpolation formula is also given.

Comparative Study of Covalent and van der Waals CdS Quantum Dot Assemblies from Many-Body Perturbation Theory.

Quantum dot (QD) assemblies are nanostructured networks made from aggregates of QDs and feature improved charge and energy transfer efficiencies compared to discrete QDs. Using first-principles many-body perturbation theory, we systematically compare the electronic and optical properties of two types of CdS QD assemblies that have been experimentally investigated: (i) QD gels, where individual QDs are covalently connected via di- or polysulfide bonds, and (ii) QD nanocrystals, where individual QDs are bound via van der Waals interactions. Our work illustrates how the electronic and optical properties evolve when discrete QDs are assembled into 1D, 2D, and 3D gels and nanocrystals, as well as how the one-body and many-body interactions in these systems impact the trends as the dimensionality of the assembly increases. Furthermore, our work reveals the crucial role of the di- or polysulfide covalent bonds in the localization of the excitons, which highlights the difference between QD gels and QD nanocrystals.

Quasiparticle electronic structure of two-dimensional heterotriangulene-based covalent organic frameworks adsorbed on Au(111).

The modular nature and unique electronic properties of two-dimensional (2D) covalent organic frameworks (COFs) make them an attractive option for applications in catalysis, optoelectronics, and spintronics. The fabrications of such devices often involve interfaces formed between COFs and substrates. In this work, we employ the first-principlesGWapproach to accurately determine the quasiparticle electronic structure of three 2D carbonyl bridged heterotriangulene-based COFs featuring honeycomb-kagome lattice, with their properties ranging from a semi-metal to a wide-gap semiconductor. Moreover, we study the adsorption of these COFs on Au(111) surface and characterize the quasiparticle electronic structure at the heterogeneous COF/Au(111) interfaces. To reduce the computational cost, we apply the recently developed dielectric embeddingGWapproach and show that our results agree with existing experimental measurement on the interfacial energy level alignment. Our calculations illustrate how the many-body dielectric screening at the interface modulates the energies and shapes of the Dirac bands, the effective masses of semiconducting COFs, as well as the Fermi velocity of the semi-metallic COF.

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

Excited-state processes at organic-inorganic interfaces consisting of molecular crystals are essential in energy conversion applications. While advances in experimental methods allow direct observation and detection of exciton transfer across such junctions, a detailed understanding of the underlying excitonic properties due to crystal packing and interface structure is still largely lacking. In this work, we use many-body perturbation theory to study structure-property relations of excitons in molecular crystals upon adsorption on a gold surface. We explore the case of the experimentally-studied octyl perylene diimide (C8-PDI) as a prototypical system, and use the GW and Bethe-Salpeter equation (BSE) approach to quantify the change in quasiparticle and exciton properties due to intermolecular and substrate screening. Our findings provide a close inspection of both local and environmental structural effects dominating the excitation energies and the exciton binding and nature, as well as their modulation upon the metal-organic interface composition.

Adiabatic connection for strictly correlated electrons.

Modern density functional theory (DFT) calculations employ the Kohn-Sham system of noninteracting electrons as a reference, with all complications buried in the exchange-correlation energy (E(XC)). The adiabatic connection formula gives an exact expression for E(XC). We consider DFT calculations that instead employ a reference of strictly correlated electrons. We define a "decorrelation energy" that relates this reference to the real system, and derive the corresponding adiabatic connection formula. We illustrate this theory in three situations, namely, the uniform electron gas, Hooke's atom, and the stretched hydrogen molecule. The adiabatic connection for strictly correlated electrons provides an alternative perspective for understanding DFT and constructing approximate functionals.