We show that nucleation occurs via atom clustering, in tandem with host evolution, revealing the participation of surface defects and host lattice restructuring in trapping Ir atoms to initiate nanoparticle formation and growth. These insights provide a theoretical platform and practical recommendations to further the development of highly functional and broadly applicable exsolvable materials.In exsolution, nanoparticles form by emerging from oxide hosts by application of redox driving forces, leading to transformative advances in stability, activity, and efficiency over deposition techniques, and resulting in a wide range of new opportunities for catalytic, energy and net-zero-related technologies. However, the mechanism of exsolved nanoparticle nucleation and perovskite structural evolution, has, to date, remained unclear. Herein, we shed light on this elusive process by following in real time Ir nanoparticle emergence from a SrTiO The separation of nanoparticles from oxide hosts by exsolution forms the basis for catalytic and energy-related applications. Here, the authors elucidate the multistep mechanism of exsolution at perovskite surfaces by combining real-time electron microscopy and computational methods. In recent years, the method has attracted widespread attention as it allows for the “in situ” generation of metal or alloy NPs4 with uniform size and distribution, with increased stability during operational conditions when compared to more traditional deposition techniques. This is due to the unique characteristic of “socketing” into the host crystal lattice, whereby exsolved NPs partially submerge into the surface of the host oxide, circumventing the deleterious agglomeration and coking common in deposited systems which reduce catalytic activity6. However, many questions remain regarding the mechanism of the nucleation and growth of exsolved NPs, and the rearrangement of the host oxide crystal structure during the controlled reduction of such systems, which, if solved, would dramatically improve structural control of exsolved materials, enable concept rationalisation, and lead to enhanced functional properties.Recent developments in the field of nanomaterials have seen the emergence of a new “bottom-up” synthesis approach termed “exsolution”. Instead of decorating a support material with catalytically active nanoparticles (NPs), as in conventional “top-down” processes, the catalytic metal is incorporated as an ion in an oxide support during synthesis, to then diffuse to the host surface when the material is heat-treated in reducing conditions14 have been performed to gain insights into the exsolution mechanism, capturing the first stages of NP exsolution, where a sub-nanometre metal cluster nucleates before subsequently growing into a socketed NP, is extremely challenging, as reported in recent isothermal literature9. Visualising exsolving NPs during the initial atomic nucleation stage using a slow heating rate, as opposed to isothermal experiments, would slow down the process and allow the real-time observation of the first stages of NP exsolution. However, previous attempts at such studies have, to date, been unsuccessful.Although recent in situ/operando studies3 (STO) model structure in ultra-high vacuum (UHV), overcoming previous challenges, by applying in situ high-resolution high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM). We observe atomic diffusion, nucleation sites, the evolution of the host crystal structure, and evidence of defects and, using computational simulations, ascribe their role in the early stages of nucleation. To investigate the phenomena observed during the evolution of the crystal structure of the host perovskite at lower temperatures we employ a machine-learning (ML) approach, which reveals that the evolution of a reconstruction at the surface of the monitored region prior to nucleation contributes to initiate the mechanism. These observations are combined to reveal the fundamental whole process of NP exsolution.Here, we provide atomic-scale, real-time insight in the early stages of nucleation and exsolution of Ir NPs from a stoichiometric Ir-doped SrTiO15, Ir-doped SrTiO3 (details in ‘Methods’); SrTiO3 has frequently been utilized as a host system for exsolution as it adopts the ABO3 perovskite structure, which facilitates incorporation of dopants and defects18, enabling a vast space of doped systems with different degrees of exsolution and functional properties. We identified and monitored the position of Ir dopant atoms in the lattice before in situ exsolution by low-temperature imaging, which confirmed that Ir atoms substituted for Ti atoms in the SrTiO3 cubic lattice , ex situ X-ray photoelectron spectroscopy (XPS) characterisation showed Ir present in the 3+ oxidation state in the as-synthesized sample15. Density Functional Theory (DFT)-based thermodynamic analysis confirmed that experimental synthesis conditions  favour the Ir3+ ions pair at Ti sites, and hence predicted the conditions when Ir3+ is stabilised over Ir4+  SrO-terminated SrTiO3 surface: an ideal (non-defective) region  in Fig. Sr”; scenario ii) in Fig. Sr”; scenario iii) in Fig. 3+ ion only interacting with one O2− ion and the larger Ir-surface distances shown in the height profile .Figure Sr” suggests that the vacancy acts as a “trapping” site, as the required kinetic energy to overcome such energy barrier would be unlikely even at ≈1300 K. Once a mobile Ir ion has been trapped at a surface Sr vacancy, the surface becomes scenario iii. The complicated energy profile in Fig. 3+ ions causes significant surface reconstruction. Additional structural images extracted from selected simulation positions  the high calculated energy barrier (≈5 eV) for the Ir ion to move away from the V3+ ion over ideal STO surfaces will be trapped if the ion meets a Sr vacancy. These trapped ions can then pair with other moving Ir ions, mediated by surrounding O, and are likely to become initial nucleation sites for further Ir cluster growth and reduction  within the measured temperature range. This confirmed that the growth of the nucleating clusters occurred by incorporation of further Ir atoms diffusing throughout the bulk and the surface of the material due to the increasing number of surface oxygen and A-site vacancies formed, also recently suggested on other systems23. The sub-nanometre clusters initially do not have a crystalline structure  at the surface creates structural inhomogeneities, lowering the surface energy on such regions compared to flat surfaces, and resulting in preferential sites for nucleation23. The direct evidence confirms for the first time that NP migration can be expected during early stages of exsolution, and that socketing, the main characteristic of exsolved NPs, occurs at a later stage.Another type of mobility was also observed from 825 °C involving already formed surface NPs Fig. . During Following the evolution of a ≈[301] Ir-doped STO surface from 400 to 700 °C, we observed the emergence of extra diffractogram spots in the fast Fourier transforms (FFTs) of the STEM images starting after a 2 h dwell at 700 °C  should show superlattice spots or elongated streaks depending on the degree of ordering29. To further investigate the structural changes generating the superlattice spots we employed a ML sliding FFT approach with matrix factorization31 (described in ‘Methods’), as superstructures are more easily visible within the Fourier domain than in real space, due to the intrinsic noise of STEM images. Figure When comparing the two HAADF-STEM images, the presence of the sub-nm Ir clusters found only after the dwell at 700 °C might be suspected to generate the extra spots, however, when investigating specific cluster areas, only the main perovskite signals were found , the distinct morphology and faceting, their number and density evolution over temperature, and the similar environment conditions to Sr-vacancy engineered systems34, make this unlikely. Furthermore, previous ex situ XPS characterization on this system showed presence of Sr surface deficiency15, further corroborating our interpretation of the results in Fig. Another structural feature, the clustering of defects, is evident in the host crystal in the in situ-monitored areas from 400–1100 °C  analysis of the pedestals confirmed their compositional identity with the host perovskite  mechanism38. Here, the matrix in the vapour phase condenses on the surface of a catalyst NP, to redeposit and epitaxially grow into a nanowire. As nanowires can only be grown where large droplets  are present39, we propose that a similar mechanism is occurring at this stage of exsolution. Specifically, if the NP is smaller than the critical radius necessary to achieve steady-state growth of the nanowire, then further growth is not possible, leading to the formation of pyramidal base structures supporting the metal NPs on the host surface39. In our system, the highly dilute amount of Ir employed (0.5%) justifies the size of the exsolved NPs (≤7 nm), potentially explaining the pyramidal base growth observed. The lack of sufficient Ir supply does not allow to reach the catalyst supersaturation necessary for nanowire growth, which therefore cannot be induced40, resulting in the pyramidal bases, or exsolved particles sockets. As further supporting evidence, when exsolving from a higher-doped (5% Ir) STO sample, larger NPs were obtained (≤15 nm), with supporting pedestals of the biggest NPs resembling nanowires  for the achievement of tailored exsolved NPs, with precise control over population, size, and morphology.0.005Ti0.995O3 perovskite was synthesized following a modified solid-state method15. High-purity SrCO3 , TiO2 , IrO2  reagents mixed in stoichiometric ratios and hand-ground in an agate mortar for 30 min were pressed into pellets and calcined at 1000 °C for 12 h in air (≈0.2 bar pO2), after which the pellets were ground into powder, which was mixed for 30 min, pelletised, and sintered at 1340 °C for 12 h in air. In situ STEM heating experiments were performed using an aberration-corrected Nion UltraSTEM100 STEM microscope combined with a Protochips Fusion MEMS-based heating stage. Specimen preparation was carried out by suspending the as-synthesised powder into high-purity 2-propanol followed by ultra-sonication (≈30 min). The samples were then drop-cast onto Protochips heating microchips then baked overnight at 80 °C in vacuum to eliminate any source of contamination prior to the in situ experiments. Imaging was performed at 100 kV voltage with a convergence semi-angle of 31 mrad, probe current of 0.5 nA and under ultra-high vacuum (10−9 Torr). For all the experiments, the samples were first imaged at RT and at 400 °C to evaluate sample stability, which also ensured atomic position retainment and no exsolution occurring at low temperatures in the instrument environment. To separate the potential effect of continuous electron irradiation or beam damage coupling with the observed phenomena, and of the electron beam as an additional driving factor in exsolution, images were also acquired on at least three comparison areas for each sample, to evaluate whether beam-induced effect could be disregarded when imaging in HR-STEM mode41. STEM micrographs of several control areas captured at target temperatures ranging from 725–1100 °C are reported in Supplementary Fig. SrIr3 sample heated under 10−9 Torr vacuum from room temperature to 1100 °C, temperature at which we observed full emergence of Ir nanoparticles when reducing ex situ15. The in situ experiments were performed with heating rates of 1 °C min−1, 2 °C min−1, or 5 °C min−1. Micrographs were analysed using a Gatan Digital Micrograph and a background subtraction algorithm filtering  level of theory with the Vienna ab initio Simulation Package (VASP)46. The projector augmented wave (PAW) pseudopotential-based basis sets supplied in the VASP package were used with an energy cut-off value of 600 eV in these simulations. A 2 × 2 × 2 Monkhorst-Pack k-point mesh was used to sample the reciprocal space. The electronic cycle convergence criterion was set to be 10−6 eV, and the structural convergence criterion used was 0.01 eV Å−1. Spin polarization was also included. Antiferromagnetic (AFM) ordering was assumed when there were two Ir atoms present in the model, as testing suggested that AFM ordering gives lower energy.The host supercell used for simulation was a 3 × 3 × 3 SrTiO48 to achieve better energy description. Based on the linear combination of atomic orbitals (LCAO) method, double-zeta valence polarised (DZVP) atomic basis sets were used coupled with core pseudopotentials obtained on the CRYSTAL17 website. The Coulombic and exchange series were summed to the cut-off thresholds of 7, 7, 7, 9 and 30 as detailed in the CRYSTAL17 manual48. A slightly denser Monkhorst-Pack k-point mesh of 3 × 3 × 3 was used in the HSE06-based calculations to obtain better accuracy. The convergence criterion was set to be 10−7 Hartree. Spin polarisations were accounted for in the same manner as the VASP calculations.These relaxed structures were then refined with the hybrid HSE06 functional using CRYSTAL173 supercells with periodicity only in the x and y directions and top two unit-cell layers allowed to relax, while the other two unit-cell layers held fixed, representing the bulk. The surface calculations were carried out as implemented in GULP49. The cut-off range was 10 Å. The Ir3+–O2− pair potential was custom-fitted against DFT relaxed surface slabs of Ir doped SrTiO3 (fitting details in the 50. An Ir3+ ion was dragged through the region highlighted by the blue box in Supplementary Fig. Pair-potential-based surface scans were performed on slab models made of 3 × 3 × 4 SrTiOFor the N-FINDR analysis, the abundances were further constrained such that they sum to 1, i.e., Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary InformationSupplementary Movie 1Supplementary Movie 2Reporting Summary


Understanding the molecular interactions that drive peptidefoldingis crucial to chemistry and biology. In this study, we analyzed therole of CO···CO tetrel bonding (TtB) interactions inthe folding mechanism of three different peptides , which exhibit a different propensity to fold in an α helixmotif. To achieve this goal, we used both a recently developed Bayesianinference approach (MELDxMD) and Quantum Mechanics (QM) calculationsat the RI-MP2/def2-TZVP level of theory. These techniques allowedus to study the folding process and to evaluate the strength of theCO···CO TtBs as well as the synergies between TtBsand hydrogen-bonding (HB) interactions. We believe that the resultsderived from our study will be helpful for those scientists workingin computational biology, peptide chemistry, and structural biology. Thewide range of functional groups of different sizes for each residue and the large number ofaccessible backbone conformations make them suitable to bind at siteswhere other molecules  cannot. Therefore,interest in pharmaceutical applications has steadily increased thedevelopment of peptide-based drugs, with several blockbusters suchas Trulicity (diabetes) or Copaxone (multiple sclerosis) on the market.6 However, the large flexibility also raises somelimitations: many peptides are intrinsically disordered in their freeform7 and fold upon interacting with acomplementary molecule . Many of suchinteractions are transient, with low binding affinities and rapidoff-rates, thus limiting their experimental characterization and computationalprediction.8 In addition, their shorterlength, compared to a protein, limits the amount of stabilizing intramolecularinteractions. In this regard, some sequences are designed to increasethe propensity for a particular conformation . However, even these might have populations below40% in solution. Many stabilizing forces, such as backbone hydrogenbonding to adopt secondary structure elements, can already be satisfiedin solution with water molecules. The hydrophobic effect (desolvation)is often not enough to drive the peptide to stable conformations.9Peptides are versatile molecules withapplications in biology,10 In principle, we should be able to treat peptides as programmablemolecules to accomplish self-assembly behavior or to identify peptidesthat bind with high affinity. However, computational tools based onforce fields and other energy functions often lack the accuracy neededto study systems that lie at the edge of stability. Successful programmingof peptides typically involves exploiting repeating patterns for self-assemblyand, in cases of binding, maintaining the side chains responsiblefor interaction while increasing the propensity to adopt a secondarystructure .12In the presence of a binding partner, interactionsthrough thebackbone and side chains with the second molecule can lead to stableconformations (known as folding upon binding).13 The p53 epitope is intrinsicallydisordered and adopts a helical conformation upon binding MDM2 andthe homologous MDMX14.10 MDM2 has a deephydrophobic cavity, where three hydrophobic residues  from the peptide anchor themselves, adopting a helicalconformation upon binding. Peptides pDIQ and ATSP have been proposedas potential inhibitors of the MDM2 protein since they retain thesame interaction pattern while changing the sequence to increase helicity,therefore mimicking the p53-MDM2 binding mode. Concretely, peptidepDIQ14 adopts high populations of helicalconformation states in its free form. At the same time, the ATSP peptide11 incorporates a chemical staple through a non-naturalamino acid sequence to further increase helicity and uses an additionalnon-natural amino acid for anchoring during the binding event (Cba26).The p53-MDM2 interactionis an important cancer target, where inhibitingthe interaction would allow p53 to remain free in the cell and triggerapoptosis.15 Particularly, we have focused our attentionon intramolecular interactions involving CO groups from the peptidebackbone. This type of noncovalent force involves the interactionbetween a lone pair of electrons from an oxygen atom and the antibondingπ orbital of a subsequent carbonyl group in the ground state,and previous studies have demonstrated its abundance and importancein protein folding and functionality.18 This interaction canalso be described as a Tetrel bond .21 Tetrel bonds (TtBs), which typically involve a σ-holelocated on an element from group IV and a Lewis base, were theoreticallydescribed by the groups of Frontera19 andArunan in 2013.20 From these initial studies,several computational and experimental works have analyzed the physicalnature of the interaction as well as its impact in the fields of supramolecularchemistry,22 crystal engineering,25 and biology.28In this study, we have combined classical and quantum mechanicscalculations to analyze the folding patterns of p53, pDIQ, and ATSPpeptides and the different backbone interactions that stabilize helicalstates beyond the well-known 1 → 4 hydrogen bonding (HB).30 early manifested inthe work of Burgi and Dunitz, and the proper spatial distributionof substituents to make it sterically accessible to a Lewis base.Since carbonyl groups are crucial components of protein and peptidebackbones, we were interested in analyzing the impact of π-holeTtBs in the folding mechanism of p53, pDIQ, and ATSP peptides , which increasesupon descending in the group. Consequently, the electropositive regionof the σ–hole increases if the EWG–Tt bond (EWG= electron-withdrawing group) is more polarized, resulting in a strengtheningof the noncovalent interactions (NCI). Second, another way to polarizethe EWG–Tt bond is by increasing the electron-withdrawing abilityof EWG. Therefore, the combination of heavy elements and strong EWGincreases the positive potential and size of the σ–hole,thus reinforcing the NCI (by increasing the contribution of electrostatics).In this regard, carbonyl groups typically exhibit a depletion of electrostaticpotential above and below the molecular plane, which corresponds tothe presence of a π-holeides see 1.31 and performed a series of MELDxMD (modelingby employing limited data x molecular dDynamics) simulations using“free” p53, pDIQ, and ATSP peptides, which shed lighton differences in their binding mechanisms. In addition, using quantummechanics (QM) calculations at the B3LYP/def2-SVP level of theory,we identified several CO···CO TtBs that contributeto the stabilization of the backbone structure and quantifed themusing Quantum Theory of Atoms in Molecules (QTAIM) and Noncovalent Interactions plot (NCIplot) analyses.In addition, we conducted a comparative study with the X-ray crystalstructures of the three selected peptides to discuss the ability tosample these interactions during binding with current force fields(FF). Finally, using small model systems, we performed an ab initiostudy (RI-MP2/def2-TZVP level of theory), which allowed us to evaluatethe strength of the interaction as well as the cooperativity betweentetrel and hydrogen-bonding interactions.To achieve that, we built on our previous successof identifyingprotein–peptide-bound states involving p53, pDIQ, and ATSPWe believe that characterizingand understanding these interactionsis of general interest to understand the molecular recognition andaggregation phenomena since the finely tuned balance of energeticand entropic contributions in peptides results in small perturbations(or inaccuracies) that easily shift equilibrium distributions, resultingin the difference between accurate and erroneous predictions. We expectthat the results gathered herein will be of interest to those scientistsworking in the field of computational biology  as well as to structuralbiologists .33 The process samples multiple binding andunbinding events in which the peptides transition from unfolded statesto helical states in the proximity of the binding site.31 As expected, peptides that had a higher degreeof helicity (ATSP > PDIQ > p53) had higher populations of helicalconformations in the replica exchange ensemble.The MDM2-p53 system has been widelysimulated using MD approaches due to its biological relevance, especiallyin cancer. The p53 peptide epitope binds the homologous MDM2 and MDMXproteins by anchoring three hydrophobic residues in a hydrophobiccleft in either protein. For the three residues to satisfy the geometricalrequirements of the cleft, the peptide adopts a helical conformation,whereas in its unbound form, it is intrinsically disordered. Thoughmany peptides bind both proteins, the hydrophobic cleft is deeperin MDM2, leading to higher binding affinities. Peptide inhibitor designstrategies have focused on either increasing the hydrophobic interactions in the cleft or increasing thehelicity of the peptide . Most simulationstudies have focused on the p53-MDM2 interaction around the boundconformation or described the binding process of only p53 due to thecomputational expense of binding simulations. We have previously usedan enhanced sampling approach , in agreement with experiments,it is of good quality to predict the folding of the peptide when itis in proximity to MDM2 (71% population for the highest cluster).We thus only use the information to favor multiple events in whichthe peptide is brought close to the protein binding site. Using thenative contacts in the complex as guiding information trivially identifiesthe bound conformation but misses important details about the bindingprocess. We found that creating a list of possible restraints betweenthe hydrophobic anchoring residues in the peptide and the hydrophobicresidues in the protein binding site favored a more extensive samplingof different peptide orientations, binding modes, and peptide conformations.Through the MELD approach, the peptide samples multiple binding/unbindingevents, leading to (1) identification of the binding pocket and (2)recovering structures of the complex in good agreement with experimentalstructures see 2.We simulated the binding of the native p53 peptideas well as twopeptides with higher affinity (pDIQ and ATSP)  on a series of noncovalent complexesto study in detail the CO···CO TtB interaction. Toachieve this, we used compound 1 (consisting of a cyclicamide) and compound 7 (composed of a bifurcated hydrogenbond (HB) complex between compound 1 and a urea molecule)to evaluate the synergistic effect between both TtB and HB interactions.In addition, we used CO, CH3CN, CH2O, and O(CH3)2 as electron-rich moieties (see We startedthe QM study by performing ties see 4.3 and 5) to moderate (complexes 9 and 12). Interestingly, complexes 8 to 12 achieved larger interaction energy values than complexes 2 to 6, thus pointing to a reinforcement of the TtB dueto the formation of a prior bifurcated HB complex. In addition, forCO involving complexes 2 and 3, the formerachieved a slightly larger interaction energy value , while the opposite behavior wasobserved for CO complexes 8 and 9 .The results are gathered in 4 involvingCH3CN as an electron donor achieved a more favorable interactionenergyvalue compared to complexes 2 and 3; however,complex 10 was weaker than complexes 8 and 9 involving CO. Finally, complex 6 involvingdimethylether achieved a comparable binding energy value to the COinvolving complex 2 and a larger reinforcement of theTtB interaction upon establishment of a HB with the urea molecule. This will be discussed in the “atomsin molecules” (AIM) analysis (see below).On the other hand, complex 1 and 7 . Therefore, since electrostaticsis not favorable in the case of complexes 2 to 6, it is expected that other energy contributions  as well as ancillary interactions  involving the π-system of compound 1 contributed to favorable interaction energy values obtained.On the contrary, in the case of compound 7, the MEP valueobserved over the C atom from the carbonyl group was positive . This is due to the formation of a bifurcated HB with theurea molecule, which withdraws charge from the sp2 O atom.These results are useful to explain (from an electrostatic point ofview) the reinforcement of the interaction energy observed from complexes 2–6 to complexes 8–12.To rationalizethese findings, we computed the molecular electrostaticpotential (MEP) surface of compounds nd 7 see 5. Asnot2 to 6 and 8 to 12 . In addition, ancillary interactions were also denoted by thepresence of one or two BCPs and bond paths connecting the π-systemof the cyclic amide and the lone pairs, π-system, and CH bondsfrom the Lewis base. The presence of these ancillary interactionshelps to rationalize the attractive interaction energy values obtainedfor compounds 2 to 6, as mentioned above.Finally, in complexes 8 to 12, two BCPsand bond paths connect the O atom from the carbonyl moiety to thetwo NH2 groups from the urea molecule, thus characterizinga bifurcated HB interaction.Also, to analyze the interaction from a charge-densityperspective,we performed an AIM and NCIplot analyses of complexes o 12 see 6. As not1 and the urea molecule exhibited a dark blue isosurface betweenthe O and N–H groups, which denotes the presence of a strongand attractive interaction, as expected.Lastly, the NCIplot analyses of the TtB complexesstudied hereinshowed a greenish isosurface located between the electron-rich moleculeand the cyclic amide, which accounts for the presence and weak natureof the interaction. Also, the HBs established between compound 2 to 6 and the value of thedensity that characterizes the TtB interaction (ρ × 100)(see r = 0.98),which remarks that the ρ values are good predictors of the TtBstrength, in line with other noncovalent interactions.34 The presence of these additional contacts provokesan overestimation of the TtB strength if the value of ρ is usedas TtB energy predictor by means of the equation of ancillary values in ancillary is large is 12, whichis not used in the regression plot. Our next step was to interpolatethe ρ × 100 values obtained from the intramolecular CO···COTtB interactions exhibited by the three different peptides to estimatethe strength of the interaction.Lastly, with the purposeof transferring our observations in smallmodels to the entire peptide structure, we carried out a graphic representationof the relationship between the MP2 BSSE-corrected interaction energiesof complexes 100)see 7. AsnotTo provideevidence regarding the nature and strength of the CO···COTtB studied herein, we built a theoretical model focusing on the peptide’sbackbone, which allowed us to analyze the main noncovalent interactions(NCIs) responsible for the formation of the α helix motif.c0 to c2) related to ATSP peptide. As noticed in all threeclusters, the peptide structure is stabilized by several CO···COTtBs, which assist in the global stabilization of the ensemble. Theseare mainly located at opposite sides of the peptide chain in clusters c0 (c0–1 and c0–3) and c2 (c2–1 and c2–2), while in thecase of c1, only one TtB interaction was found at oneside of the peptide. Also, c0 exhibits a TtB in the middleof the structure (c0–2).In c0 and c2, two main CO···COTtBs were found, involving the same residues in both clusters (c0–1/c2–1–2JH-MK8 and c0–3/c2–2–PHE-0EH). Interestingly,these two TtBs were the ones that presented the narrowest distancedistributions in the MELD ensembles, thus indicating that TtBs participatein the most explored conformations along the course of the MELDxMDtrajectory, likely acting as pincers that assist in holding the helicalconformation in ATSP. Also, the carbonyl groups involved in the TtBsbelong to the aromatic key residues for protein binding ,thus remarking the importance of this interaction to stabilize thehelical structure of the peptide when binding MDM2 protein. Besides,cluster c0 also presented another TtB interaction (c0–2), which was not carried over into cluster c1. This TtB involved residues TRP-ALA, which also exhibiteda narrowed distribution along the course of the MELD trajectory. Onthe other hand, only one TtB was observed in cluster c1 (2JH-MK8), likely pointing to HBs as the main driving force of thisα helix conformation.For clusters c0 to c2 are gathered in c0 and c2), the c0–1 TtB exhibited a stronger TtB interaction than the c0–3 TtB . However, the opposite was observed when comparing c2 cluster TtBs , thus likely indicating that the stabilization effect ofthe TtBs varies along the MELDxMD trajectory at both sides of thepeptide.Interestingly, while the strengthof the TtB established in allclusters seemed of similar magnitude , the computation of the intramolecular CO···COinteractions provided an estimation of the variation of its strengthalong these top 3 clusters from the MELDXMD trajectory. In this regard,the interaction energies regarding the TtBs present in clusters c0–1 and c0–3 TtB energies remainedalmost identical when using D3 empirical dispersion correction, while c0–2 increased 0.3 kcal/mol in strength.On the other hand, using a larger basis set (def2-TZVP) resulted inslightly more favorable interaction energy values . Overall, the results were nonsensitive tothe method, the basis set used, or the use of empirical dispersioncorrection parameters. In this regard, we recommend choosing a densityfunctional theory (DFT) functional with proper treatment of electrostatics,since dispersion seems to have little impact on the strength of theTtB complexes studied herein.In order to evaluate the sensitivity of the resultsto the methodor basis set used, we run a short benchmarking on one of the clustersfrom ATSP peptide (c0) using B3LYP (with and without D3 dispersioncorrection) and M06–2X functionals in addition to def2-SVPand def2-TZVP basis sets. As noted in c0 to c4) related to the p53 peptideare shown. As noted, in cluster c0, only one CO···COTtB interaction was found involving residues TRP-LYS, while in thecase of clusters c1, c2, and c3, two TtB interactions involving PHE-SER (c1–1), PRO-GLU (c1–2), LYS-LEU(c2–1), LEU-PRO (c2–2), TRP-LYS (c3–1), and LEU···ASN(c3–2) per cluster were observed.Finally, in cluster c4, only one TtB interaction wasfound involving LYS-LEU residues (c4–1). Interestingly, clusters c0, c1, and c2 exhibited a larger number of TtBs, thus remarking the roleof this interaction as a stabilization source over the course of theMELDxMD trajectory.In c0–1, c2–1, c2–2, and c4–1 exhibited themore favorable TtB energies and assisted in the stabilization andpacking of the central and terminal parts of the peptide structure.On the other hand, clusters c3–1 and c3–2 presented the lowest interactionenergy values of the set, as expected from their respective CO···COdistance values. These results are in line with the intrinsicallydisordered nature of the p53 peptide, which is less prone to foldin an α helix motif compared to the other two cases studied(ATSP and pDIQ).In c0 exhibiting three TtBs); thus, O···Cinteractions play a noticeable role during the folding process regardingthis peptide.In the case of pDIQ peptide see 5, the toc0, three TtBs were observed (c0–1 involving PHE-GLU), , as noted by the greenish isosurfaces located between theCO groups. Interestingly, two of them (c0–1 and c0–3) involved PHEand TRP carbonyl groups, which achieved a narrow distance distributionin c0–3 exhibited the most favorable TtB energy (in agreement withits shorter distance compared to c0–1 and c0–2 clusters), thus beingthe prominent TtB interaction.In c1, the two TtBsobserved implicated PHE-GLU residues(c1–1) and TRP-SER residues (c1–2); thus, these two TtBs were conservedamong the two most populated clusters of the MELDxMD trajectory, remarkingtheir importance since they involve two of the three aromatic keyresidues to achieve protein binding (PHE and TRP). In this case, bothTtBs exhibited a similar strength , being of equal importance in the stabilizationof the pDIQ α helical conformation. Finally, in c2, two TtB interactions were also found, involving HIE-TRP (c2–1) and TRP-TRP (c2–2). In this case, both TtBs were not related to the aromaticresidues that participate in binding but still contributed to theoverall stabilization of this cluster with −1.7 and −1.9kcal/mol, respectively.In c0 as a reference ineach case), in agreement with their respective propensity to forma helical structure. In With the purposeof comparing the structures gathered from the clustering analysisto the experimental binding pose of the three selected peptide families,we carried out a similar analysis using PDBs 4N5T (ATSP), p53 (1YCR),and 3JZQ (pDIQ) see 11. It isProteins and peptides exhibit an exquisitebalance between entropicdriving forces that favor disordered states and stabilizing energeticcontributions that favor well-defined structures. Most proteins lieat the edge of stability, with a net stabilization energy of justa few hydrogen bonds. It is surprising that fixed-charge force fieldmodels are able to reproduce some of the details that lead to stablestructures and folding routes. Here, we find that when driving forcesfavor one particular state (pDIQ and ATPS), the potential of the bindingpartner is enough to drive binding to native-like conformations. Forsystems that lie at the edge of stability, such as the p53-MDM2 system,the force field is enough to sample native-like states in high populationsbut not the highest population cluster. We thus looked at the presenceof a particular type of interactions that has been recently describedin the literature. The presence of the interaction in the differentstates studied cannot indicate that it is a driving force during thefolding process; it is nonetheless interesting to increase our awarenessof nontraditional interactions involved in supramolecular recognition.Additionally, QM calculations shed light on the nature and numberof stabilizing O···C tetrel bonds, being a complementarysource of stability during the α helix formation process ofthe three selected peptide families. Particularly, a short computationalstudy using a cyclic peptide model allowed us to provide new insightsinto the strength, directionality, and synergistic nature of TtB andHB interactions present in these systems. On the other hand, the combinationof AIM and NCIplot techniques was useful to decipher the number andrelative strength of TtB interactions on the top three (for ATSP andpDIQ peptides) and top five (in the case of p53 peptide) most populatedclusters gathered from the MELDxMD trajectory. Finally, we providedan estimation of the strength of these intramolecular TtBs, whichexhibited values that range from weak to moderately strong, with adependence on the peptide family and cluster population. We believethe results from this study will be useful for those scientists workingin the fields of rational drug design, structural biology, and computationalchemistry as well as for expanding the relevance of tetrel bonds amongthe biological community.35 for side chains and ff99SB force field36 for backbone parameters coupled with the GBneck2 implicit solventmodel (igb = 8).37 Simulations of the freepeptides were performed using the Amber package, and MELDxMD bindingsimulations were performed using the OpenMM package with the MELDplugin.38 MELDxMD simulations used 30 replicaswith a one-dimensional H,T-REMD ladder following previous work.32 Cpptraj was used to analyze the ensembles. Clusteringwas performed by using a hierarchical model with epsilon set to twoand using a Cα and Cβ RMSD as a similarity measure. Clustering was doneeither on the peptide alone  or on the protein–peptide complex to identifybound conformations.All simulations werecarried out using the ff14SB force field2 to 6 and 8 to 12 werecomputed at the RI-MP239/def2-TZVP40 level of theory. This level of theory has beendemonstrated to be appropriate for the study of σ-hole interactionsinvolving neutral and charged electron donors.41 The calculations have been performed by using the programTURBOMOLE version 7.0.42 The Cs symmetrypoint group was imposed during the optimization procedure. The bindingenergies were obtained using the supermolecule approximation, whereΔEcomplex = ΔEmonomer1 – ΔEmonomer2. The results were corrected for the basis set superposition errorfollowing the Boys and Bernardi counterpoise method.43 In addition, calculations for the molecular electrostaticpotential (MEP) surfaces and wave function analysis have been carriedout using Gaussian 16 software.44 The Bader’s″atoms in molecules″ theory45 has been used to study the interactions discussed herein by meansof the AIMall calculation package.46 Thewave function analysis has been carried out at the MP2/def2-TZVP levelof theory.The binding energies of complexes Regarding the choice of the computational models,we chose a cyclic amide as a theoretical model of a peptide to imposeCs symmetry with the purpose of obtaining an energy minimum basedon a single CO···CO tetrel bond presenting the minimumnumber of ancillary interactions. On the other hand, the use of aurea molecule as a molecular model allowed us to solely evaluate thecontribution of having a pre-established bifurcated H-bond on thestrength of the CO···CO tetrel bond, without additionalinteractions involved.48/def2-SVP level of theory). The NCIplot50 index allows convenient visualization of both inter and intramolecularinteractions in real space. It plots isosurfaces of the reduced densitygradient (related to |∇|/ρ4/3), which arecolored in agreement with values of the electron density. The NCIcontacts are characterized by the regions of small reduced densitygradient (RDG) at low densities, being mapped in real space by plottingan isosurface of s for a low value of RDG. Besides,the sign of the second eigenvalue of the density Hessian times thedensity is color-mapped onto the isosurfaces, which allows the characterizationof both the strength and (un)favorable nature of the interactions.More precisely, the color scheme is composed of a red–yellow–green–bluescale using red for repulsive (ρcut+)and blue for attractive (ρcut–)NCI interaction density. Weak repulsive and weak attractive interactionsare identified by yellow and green surfaces, respectively.Weused force field-derived structures; therefore, no geometry optimizationwas performed before the calculation of the wave function (B3LYP


However, the available electrolyzers suffer from intrinsic problems, like flooding and salt accumulation, that must be overcome to industrialize the technology. To mitigate flooding and salt precipitation issues, researchers have used super-hydrophobic electrodes based on either expanded polytetrafluoroethylene (ePTFE) gas-diffusion layers (GDL’s), or carbon-based GDL’s with added PTFE. While the PTFE backbone is highly resistant to flooding, the non-conductive nature of PTFE means that without additional current collection the catalyst layer itself is responsible for electron-dispersion, which penalizes system efficiency and stability. In this work, we present operando results that illustrate that the current distribution and electrical potential distribution is far from a uniform distribution in thin catalyst layers (~50 nm) deposited onto ePTFE GDL’s. We then compare the effects of thicker catalyst layers (~500 nm) and a newly developed non-invasive current collector (NICC). The NICC can maintain more uniform current distributions with 10-fold thinner catalyst layers while improving stability towards ethylene (≥ 30%) by approximately two-fold.Electrochemical reduction of CO Electrolysis of carbon dioxide holds great promise in providing a sustainable pathway for hydrocarbon fuels. In this work, the authors show the effect of current distribution on super-hydrophobic electrodes that avoid flooding and present a solution fit for the scale-up of these systems. As a result, research and development efforts are shifting from understanding fundamental reaction mechanisms towards industrial scale-up and practical challenges of electrochemical conversion processes2. Gas diffusion electrodes (GDEs) are now widely used to overcome mass-transport limitations at the cathode, where CO2 is reduced, to perform CO2RR at industrially relevant reaction rates, to yield value-added carbon products4.The electrochemical reduction of carbon dioxide  of the GDE declines  as current flows through the GDL8, and together with precipitation of hygroscopic carbonate salts, enhances flooding of electrolyte into the GDE pore structure. The flooding of GDE pores with liquid electrolyte blocks gas diffusion pathways for CO2, which reduces the availability of CO2 at the electrocatalytic sites and allows the promotion of the HER9.The electrochemical reduction of COons Fig. . First, 2RR operation, researchers have aimed to increase the hydrophobicity of gas-diffusion layers  gas-diffusion layers15. These GDLs consist of a micro-porous layer (MPL) and backing layer (BL). The MPL is made from ePTFE with 250–500 nm fibrils stretched from 1 to 10 μm nodes, whereas the BL is a polymeric support material formed by coarse laminates of polyethylene or polypropylene . In contrast to carbon-based GDE’s which can quickly lose their ability to prevent flooding17, non-conducting PTFE GDE’s maintain hydrophobicity when exposed to sustained electrochemical potentials and moderate hydrostatic pressures. With further modifications, like covering the catalyst layer with ionomers, electrolyzers using ePTFE type GDE’s have then shown the ability to deliver both high stability (>60 h) and selectivity (>80% FE at 1.17 A cm–2) towards multicarbon (C2+) products during CO2RR  has, to our knowledge, never been studied in detail before.However, a caveat of the excellent non-wetting and COGDL Fig. , which iGDL Fig. . As cata2RR, we need to better understand the operando behavior of the electrode—even more so considering that local activity  can have a critical influence on the product distribution observed23. If current distribution is not uniform due to high conductivity resistance in the catalyst layer, the potential applied to the catalyst will vary spatially, jeopardizing the long-term stability and product selectivity. We have shown previously that local heat production (probed by temperature sensing of the electrode’s GDL) is a valid and accurate proxy for an electrode’s activity24. Infrared (IR) thermography then provides a basis of understanding local conditions and electrode behavior during operation of a CO2 electrolyzer.In order to design and assess efficient electrode architecture designs for CO2RR electrolyzer. Using a 1D reaction-diffusion model of the gas-liquid interfaces in the ePTFE and carbon-based electrodes, we show how the GDE structure and operational stability affects the local availability of CO2 in the catalyst layer and the C2+ product selectivity. Then we analyze the current distribution in ePTFE electrodes and examine the deterioration of the thin catalyst layers deposited on the expanded PTFE-layer. Infrared thermographs display poor current density distribution for 50 nm catalyst layers, where the active region is taxed with a current load around 5 times higher than the average. Finally, we showcase a non-invasive current collector (NICC) as an alternative catalyst layer design to improve the current collection and distribution in ePTFE electrodes whilst maintaining C2+ product selectivity.Herein, we use infrared thermography to demonstrate the potential problems of current distribution in ePTFE-based electrodes with thin catalyst layers in a state-of-the-art flow cell CO26. The disadvantage of these electrodes, however, is the flooding of the micro-porous layer. Besides promoting unwanted HER at the micro-porous layer, flooding impedes CO2 transport towards the catalyst layer. Whereas, on an ePTFE electrode, dissolved CO2 reacts directly on the interface of dissolution. A fully flooded micro-porous layer (MPL) poses a considerable barrier of around 20–40 µm between the coordinate of dissolution and the reactive surface, as the alkaline electrolyte will start buffering the reactant before it reaches the catalyst19.Contrary to ePTFE electrodes, carbon GDL’s have the advantage of being conductive −2 along the gas-liquid phase-boundary, we see that the concentration of dissolved CO2 is severely hampered in the flooded carbon MPL case compared to an ePTFE electrode  across the board  and an ePTFE electrode (Sterlitech® Aspire QL822) over time highlights the limitations of the carbon support which is more susceptible to flooding due to electrowetting of the carbon support. Here we used a three-chamber flow cell with 1 M KOH as both the catholyte and anolyte. The carbon-based GDE was sputtered with a 200 nm Cu layer, and the ePTFE electrode with a 500 nm one. For these two different electrodes we then ran constant current densities experiments from −10 mA cm2 then raises questions on the requirements of a catalyst layer. Further, thicker catalyst layers may deplete dissolved CO2 depending on the operating current density or spatial distribution of CO2 under high single-pass conversion conditions11. If a thinner and thicker catalyst layer can achieve similar performance, then less material would be beneficial from a cost and resource perspective. The development of stable, thin catalytic layers would then enable a more efficient CO2RR process. However, a drawback of these thin layers is the limited in-plane current collection in the absence of conductive gas-diffusion layers.The dependence of product selectivity on local availability of CO28. In the conditions at which these electrodes are operated, i.e. high polarization and high reactant availability, these thin films can then lead to disparity of the current distribution across the GDE. This is directly evidenced by an electrochemical impedance spectra (EIS) analysis which shows the comparatively higher ohmic resistance of 50 nm Cu layer (1.1 Ω) vs. 500 nm Cu layer (0.45 Ω) on ePTFE, as well as vs. the pristine carbon-based support (0.6 Ω)  magnetron sputtering (see “Methods”) show a considerably higher current resistivity compared to bulk metals 24. The heat map directly relates to the current distribution profile, hence it offers a powerful proxy to track the current/voltage disparity by cross comparison of GDEs and differing catalyst layers (see the −2), show a uniform temperature distribution on the backbone of catalyst layers for 500 nm and 1 μm thicknesses. The 50 nm layers, on the other hand, display an activity pattern that is centered around the edges of the electrode for –50 and –200 mA·cm−2, where the travel length for electrons from the current collector is much shorter than for the center of the electrode  versus that of higher hydrocarbons, we see that the C1:C2+ selectivity ratio of the 50 nm layer results is close to 2: 3 at −200 mA cm−2, whereas the thicker 500 nm layer has an approximate 1: 35 ratio :CO(aq) ratios32. If we translate the recorded temperatures to a current density value for the observed temperature increases  that facilitated uniform current distributions, such that the effects of significant variations in current density across the electrode were not considered. Further, many prior studies used planar-type electrodes that do not represent the complexity of the three-dimensional, multi-layered porous GDE structures like the ePTFE electrodes presented in this study.A potential consequence of the high degree of spatial temperature variances described in Fig. 42. Ultimately, this means degradation of the catalyst layer is accelerated under alkaline CO2RR conditions. In effect, even the thicker 500 nm Cu layers in this work presented loss of selectivity for C2+-products and increased H2-production rates in a short period 2 scans45. The lower intensity of copper-specific peaks and the presence of the soluble hydroxide species suggest that copper mainly detaches from the surface by dissolution in the basic electrolyte. This is further confirmed by Cu LMM scans, which show the presence of a metallic underlayer for pristine samples46. This metallic underlayer is preserved in the 500 nm Cu sample, but missing in the 50 nm sample 18. An analysis of the used sample showed little remnants of copper on the surface close to the center of the electrode, which could be fully oxidized. The increased difficulty in acquiring these later images also confirms the reduction in electrical conductivity of used 50 nm samples. While 500 nm samples show a minor degradation after running . This contrast in detachment is confirmed by AFM scans we performed on 50 nm Cu ePTFE electrodes and 200 nm Cu carbon electrodes  from the current collector leading to chemical oxidation and dissolution of the copper species. Conversely, the areas that remain electrically connected near the perimeter of the electrode would experience accelerated deterioration due to the increased share of the local current density carbonate salts.Previously developed electrodes using these super-hydrophobic backbones have overcome current collection issues simply by applying a rather thick sandwiching layer consisting of carbon nano-particles (C-NPs) and a graphite coating on top57. By segmenting an area into smaller current collection channels, the ohmic resistance experienced by current traveling in-plane is greatly reduced. To illustrate the comparative conductance of different copper film thicknesses, we measured the ohmic drop of a 1 µm Cu film using a 2-electrode probe showing a 9-fold reduced resistivity for the 1 µm vs 50 nm thin films  is widespread in the manufacture of photovoltaic semiconductors. Here, a thin busbar of (most commonly) silver collects current generated by the semi-conductor upon exposure to sunlightMaking use of deposition masks, we sputtered 1 µm thick copper busbars on a 50 nm Cu/ePTFE electrode to fabricate non-invasive current collectors (NICCs) for our electrode architecture  at constant potential during extended periods (4 hrs. max.), resulted in the ethylene selectivity displayed in Fig. 18, the mass loadings of copper in this work are orders of magnitude lower (0.112 mgCu cm−2 for a 50 nm Cu/NICC electrode versus ~ 2 mgCu cm−2). This observation is supported by 7-h constant potential measurements comparing (i) a 1 µm Cu electrode, (ii) a 200 nm Cu/NICC electrodes, and (iii) a 500 nm Cu sample  at different scan rates between −0.3 and 0.3 V vs. Ag/AgCl. The capacitance analysis of the NICC design shows a noticeable increase against its 50 nm counterpart  electrode. To examine the prospect of using the ePTFE and copper busbar approach for larger electrodes, we assessed the busbar dimensions required for a 20 cm by 20 cm (400 cm2) electrode to maintain an identical voltage drop from the exterior current collector to the center of the electrode. These calculations are shown in the The demonstrations in this work were on a 2.25 cm by 2.25 cm  and only taken out before assembly of the electrolyzer cell. NICCs were sputtered using a slit-mask with 0.3 mm wide, 1 µm thick Cu slits along the entire width of the pre-sputtered 50 nm ePTFE GDE.Copper metallic layers were deposited directly on the ePTFE  or carbon-based GDLs (Sigracet® 38BB) by DC magnetron sputtering at a pressure of 3 µbar. By regulating the power applied and the time of exposure, we were able to regulate the thickness of the catalytic layer. After deposition, the electrodes were stored in a glovebox (<0.1 ppm O2 Titanium Anode Block). Around this anode block, we designed and printed a catholyte flow-chamber with a reference electrode port (ø = 1.75 mm) and a similar gas-chamber, with matching gaskets as sealants  foam as the anode, and Sustainion® X37-50 anionic exchange membranes (AEMs). Electrolyte was flown pumping the electrolyte and sucking the anolyte, as to generate a pressure delta across the membrane. This avoided expansion of the membrane in the catholyte compartment and accumulation of O2 (±2.25 by 2.25 cm square), with an Edmund Optics® uncoated sapphire window . Temperature values acquired with the camera were corrected by the compound transmittance of the sapphire window and the emissivity of the polypropylene backing of the ePTFE electrodes. Measurements were performed under a light-shielding blanket to avoid contamination of signals with external reflections on the camera lens.Thermal images of the backbone of the electrode were acquired using a FLIR SC7650 camera system, using the windowed electrolyzer. The camera was equipped with a fixed focal length of 25 mm and acquired images at a framerate of 1 fps with a total resolution of 640 by 512 pixels, operated by commercial ALTAIR® software. The total scanned area of the electrode was 5 cmElectrochemical routines were applied using either a Princeton Applied Research® Parstat 4000  or MC-1000  in a three-electrode configuration. Gas-flow to the electrolyzer was controlled by a Bronkhorst® mass-flow controller. Electrolyte was pumped using two separate peristaltic pumps and two sets of pressure dampeners, to alleviate the cyclic pressure spikes of the peristaltic motion. All three fluid channels were regulated through a back-pressure regulator (BPR), which controlled pressure for each stream independently, and measured live mass flowrate for the gaseous product stream. This stream was circulated through a liquid trap and a proprietary liquid detector to avoid liquid injections to the in-line gas-chromatographer . Before reaching this GC, a valve regulated pressure spikes to avoid disruption of the backpressure after each injection. Liquid product samples were collected periodically in duplicate from the catholyte beaker using a needle and were stored in air-tight vials at 5 °C to avoid evaporation of volatile species. These samples were then analyzed in batch using an Agilent Technologies® 1260 Infinity II HPLC.−2 at a rate of –1 mA cm−2 s−1. Product distribution studies were acquired either at increasing fixed current densities or at fixed working electrode potential (without i·R feedback correction). Capacitance measurements were performed on all three different architectures by cycling the electrodes from −0.3 to +0.3 V vs. Ag/AgCl, collecting the average charging current over a non-Nernstian region for the anodic swing at increasing scan-rates . The value for capacitance was extracted as the slope of the linearization of charging current over scan-rate.Polarization curves were applied by a galvanodynamic swing from 0 to –300 mA cmPristine and post-operation samples of both carbon and ePTFE GDE’s were stored in a glovebox before characterization. Scanning electron microscopy (SEM) was performed on a JOEL JSM-7001F and FEI Nova NanoSEM 450 instruments. To improve image quality, the surfaces of GDE were cleaned using an Evactron 25 De-Contaminator RF Plasma Cleaning System, and the ePTFE GDEs were coated with a Pt film (~5 nm) using a Quorum Q150T Metal Coater. One more plasma cleaning was conducted after the coating process. In addition to this, a fresh cross-section of GDE was obtained by breaking the sample in liquid nitrogen before the general sample preparation.−9 mbar. Resulting scans were averaged after 10 measurements .XPS spectra were collected using a Thermo Scientific® K-alpha spectrometer using an Al Kα monochromator. For all measurements  the spot size was 400 µm, the pass energy 50 eV and the step-size 0.10 eV, while the base pressure of the analysis chamber was 2·10Supplementary InformationPeer Review File


We find that chalcogen defectsand the graphene interface radically alter the optical propertiesof the transition-metal dichalcogenide in the heterobilayer, due toa combination of dielectric screening and the many-body nature ofdefect-induced intralayer and interlayer optical transitions. By analyzingthe intrinsic radiative rates of the subgap excitonic features, weshow that while defects introduce low-lying optical transitions, resultingin excitons with non-negligible oscillator strength, they decreasethe optical response of the pristine-like transition-metal dichalcogenideintralayer excitons. Our findings relate excitonic features with interfacedesign for defect engineering in photovoltaic and transport applications.Associating atomic vacancies to excited-state transportphenomenain two-dimensional semiconductors demands a detailed understandingof the exciton transitions involved. We study the effect of such defectson the electronic and optical properties of WS Therefore,and due to the defect’s ubiquitous nature, a microscopic understandingof the emergent electronic and excitonic properties of TMDC–graphene(Gr) heterobilayers in the presence of vacancies is interesting fordynamic modeling of optoelectronic devices and applications.The electronic and optical properties of layered TMDCs andtheirheterostructures are sensitive to the potential created by defects.2–Gr and MoS2–Gr heterobilayerswith monatomic chalcogen vacancies. We employ a GW-BSE approach56 to compute the many-body electronic properties and optical characteristicsand find that due to the combination of screening and strong opticalhybridization, absorption resonances of well-known pristine TMDC excitonsare strongly quenched in the heterostructure, resulting in substantiallyaltered absorbance properties compared to the pristine TMDC–Grheterobilayer or defected TMDC without graphene. These pristine-likeTMDC “A” and “B” peaks are largely reduceddue to the mixing of the optical transitions with both graphene anddefect electronic states, and the electron–hole transitionsdetermining their excitonic composition are fundamentally altered.This manifests also in a strong reduction of the excitonic bindingenergy for the excitons composing those absorption peaks. In addition,Fermi-level alignment of the defect transition levels and the magnitudeof the spin–orbit interaction, determined by the choice ofTMDC, lead to substantial changes in the heterostructure optical properties.We obtain the intrinsic radiative rates for excitons with the largestbinding energy, which create strongly mixed subgap resonances andshow that the associated inverse rates are comparable to those calculatedfor pristine TMDC monolayers.In this work, we investigate the electronic and optical propertiesof WS2 (respectively MoS2) and 5 × 5 graphene elementarycells; see Supporting Information (SI).We consider a vacancy concentration of ∼3%, corresponding toan isolated monoatomic sulfur vacancy per supercell, located at theopposite side of the graphene layer with sufficiently small interactionsbetween defect sites at neighboring periodic replicas of the supercell.17 We first perform a geometry optimization ofthe supercell atomic positions, keeping the supercell volume constant(see ref (SI). This optimization reduces the nearest-neighborbonds close to the vacancy (which shrinks and strains the TMDC lattice)as well as the interlayer distance between the TMDC and the graphenelayer. Using DFT as a starting point , we perform a one-shot GW (G0W0) calculation for each TMDC–Gr heterobilayer . 59 GW quasi-particle corrections increase the gap inboth systems, qualitatively, conserving the DFT picture for theseheterobilayers.17 There are four spin–orbitsplit defect states shifted upon the GW calculation to higher energywith respect to the Fermi level. Far from the Fermi level, we findthe valence band splitting due to spin–orbit interaction tobe ∼460 meV for WS2–Gr and 150 meV for MoS2–Gr, which is consistent with 425 ± 18 and 170± 2 meV obtained from high-resolution ARPES measurements.26 The dielectric screening also shifts the pairof occupied defect states to lower energies (by ∼400–450meV for WS2–Gr and ∼400 meV for MoS2–Gr). Simultaneously, the pristine-like band gap of WS2 increases from 1.69 eV at the DFT level to 2.20 eV at theGW level. Similarly, the pristine-like band gap of MoS2–Gr changes from 1.73 to 2.19 eV. These values reflect a significantrenormalization of the TMDC band gaps compared to the monolayer case,as expected due to the quasi-metallic character of graphene with GWcorrections including image charge effects.59 Our GW results are in agreement with previous calculations witha reported band gap reduction of ∼300–350 meV60 compared to each pristine counterpart.58 They are also consistent with the experimental values of the quasi-particleband gap found in MoS2–Gr heterostructures, reportedto be ∼2.0–2.2 eV,62 and in WS2–Gr, which is in the range ∼2.0–2.3 eV.64We employ a commensurate supercellcomposed of 4 × 4 WS2–Gr and MoS2–Gr heterobilayersusing theBethe–Salpeter equation55 within the Tamm–Dancoffapproximation (see the SI). We show in 2–Gr as well as its decompositioninto intralayer graphene, intralayer TMDC, and interlayer contributions(see the SI for the case of MoS2–Gr). At low optical energies, intralayer graphene electron–holeexcitonic features are found to be the most prominent. Graphene electronicintraband transitions  are known to dominate this regime,65 which is marked by a dashed gray rectangle.The resonant peaks are a consequence of the finite k-gridsampling of the graphene Dirac cone, and therefore, the absorptionin this region is actually continuous in the dense grid limit. Inthe high infrared spectral range, excitonic peaks corresponding tointerlayer graphene–defect and graphene–pristine opticaltransitions appear at higher energies while graphene intralayer contributionsbecome less relevant. At optical energies ≳2.0 eV, intralayerTMDC contributions  become the dominantfeatures of the spectrum over the interlayer contributions. Out ofall optical transitions sampled for the examined k-gridand energy range, 0.4% belong to intralayer graphene, while 62% correspondto intralayer TMDC transitions, with the remaining 37% representinga large degree of interlayer mixing.Next, we examine the excitonic properties of defectedWS71 This limit is represented by a dashed horizontal line in 2 in the absence of graphene.28 To furthervalidate our findings, we compare the absorbance spectra of WS2–Gr with and without vacancies. We observe that, unlikethe defected heterostructure, the absorbance of the pristine heterobilayeroscillates around the graphene limit in that energy range, supportingour previous conclusion. In the visible range , experiments on WS2 have reported a red shift and asignificant reduction of the exciton peak area upon graphene stacking.72 These effects are typically attributed to both changes in the dielectricenvironment upon the heterostructure formation and possible interfacialcharge transfer.73 Our results demonstratethat within the exciton basis set, optical transitions at both layersmix already upon light absorption. In defected WS2–Grheterobilayers, we observe a reduction of the strength of the pristine-likeTMDC resonances in addition to the substantial interlayer mixing inthe subgap optical region dominated by transitions to the defect states.This effect is attributed to the strong optical mixing of TMDC andgraphene, which results in additional interlayer optical transitions.These occur within the pristine gap at many different k-points due to the dispersive nature of the Dirac cone and yielda redistribution of the oscillator strength from the original pristinetransitions to the defects. These combined effects of the grapheneand vacancies quench the pristine-like “A” and “B”resonances75 and also broaden them.41 As a consequence, they are no longer as dominantin the spectrum. Moreover, the composition of the absorption peaks,clearly defined at ∼2.2, ∼2.4, and ∼2.7 eV, alsochanges drastically compared to the expectation for the pristine ordefected TMDC monolayers (see the SI).The spectral absorbance of graphene for infraredlight is almostconstant at 2.4%.76). Each excitonic state, |ΨS⟩, defined by its wave function amplitude ASvck and energy ΩS, isrepresented by a column of dots whose area is proportional to ∑vk |AvckS|2, for each electronband (c), and ∑ck|AvckS|2, for each hole band (v). The colorof the dot represents the layer from which c or fromwhich v the transitions occur. We observe intralayergraphene optical transitions in the low energy region (≲0.5eV), while excitonic resonances with interlayer character appear onlyabove 0.5 eV. The dispersive nature of graphene can be seen from theincrease in the conduction band number of graphene with energy. Asexpected, the quenched high-energy resonances show significant contributionof mixed TMDC and graphene optical transitions; thus, although theyappear in similar positions, they no longer possess true “A”and “B” characters (see the SI). We note that while the increase of the dielectric screening bythe surrounding media and the reduction of the absorbance is expected,64 here the effect is further pronounced due tothe electron–hole defect and nondefect mixing in the subgapregion.To further understand this effect, we show in 2 and 0.3–0.7 eV forWS2 pristine “A” excitons.78 Theoretical predictions give 0.6 eV for MoS2 and 0.2 eV for WS2 pristine “B” excitons.75 In 2–Gr (see the SI for MoS2–Gr). The binding energy is computedfrom the energy difference between the free and bound electron-holepairs composing each exciton (see SI). For excitons in the opticalregion where the pristine “A” and “B”resonances would be expected, we observe that excitons have substantiallylower binding energies compared to the pristine or encapsulated counterparts,as well as substantially smaller oscillator strengths. We attributethis to a redistribution of the oscillator strength due to the combinedeffect of substantial hybridization of the defect and nondefect electron–holetransitions with graphene, as well as the small binding propertiesof excitons in graphene resulting from its quasi-metallic nature atlow energies. Importantly, we also find excitons (with oscillatorstrength in the range 10–2–1.0 a.u.) in theoptical region 1.5–2.0 eV with a binding energy comparableto that of pristine excitons in the absence of a graphene layer. Theseexcitons result from intralayer optical transitions to defect statesand interlayer graphene–defect transitions. To gain insightinto the nature of these excitons, we show in k-space distribution fora representative case marked by a circle in k-space. The right-hand side of k-points, supporting our analysis that this exciton is formedby a combination of defect–defect (notably at K̅), graphene–valence,and graphene–defect transitions (for the k-pointnoted as k*).The binding energy of the exciton quantifies how stronglyboundthe electrons and holes participating in the excitation are. Intralayergraphene excitonic features have vanishing small binding energies 81 We considerthe inverse rate, which scales as γS–1 ≔ τS ≈ ΩS/μS. This rate accounts only forpart of the radiative line width, as other contributions, e.g. electron–phononand exciton–phonon terms, are not included, and is useful toevaluate the significance of the oscillator strength. Our analysisreveals that the inverse rates for the excitons with binding >50meVcan be as large as τS ≈ 0.1ps for both heterobilayers. However, depending on the oscillator strength,they can be shorter, even as small as τS ≈ 0.1 fs for MoS2–Gr (see the SI). Intralayer graphene excitonic features,which have significantly small binding, have substantially largerintrinsic rates due to their large optical transition dipole. Darkinterlayer excitons with large binding have larger inverse rates,as large as ∼100 ps for WS2–Gr, due to thesmaller oscillator strength. For pristine WS2–Grbright “A” and “B” excitons in the TMDClayer, τS can be even shorter, essentiallydue to the increased oscillator strength  which yields τS ≈ 10–4–10–5 fs. We note that compared to pristine TMDCs,80 graphene adsorption has a strong impact on τS, which only become comparable again to thepristine ones in the presence of defects due to the strong excitonhybridization of the graphene and the subgap vacancy-related features.Furthermore, charge transfer times of photocarriers at TMDC–grapheneinterfaces,83 where single-particle defect tunneling is understood to be the dominatingcoherent transport channel,17 can be of a similarorder of magnitude. In this scenario, defects slow down coherent chargetransfer due to relatively small interlayer tunneling. Interestingly,in the presence of graphene, defects optically enhance transitionsassociated with them, resulting in excitons with significantly higheroscillator strength, compared to the reduced oscillator strength ofthe original pristine-like “A” and “B”TMDC excitons.Finally, we relate our findings to the intrinsicradiative decayrates of zero-momentum excitons, which can be computed from the GW-BSEoscillator strength and excitation energy.2–Gr and MoS2–Gr heterobilayerswith chalcogen vacancies by employing first-principles many-body perturbationtheory. We find that strong hybridization of the defect states withgraphene gives rise to subgap features, which manifest as strong resonancesin the optical absorbance spectrum, while quenching the “A”and “B” pristine exciton peaks originally coming fromintralayer TMDC transitions. These altered absorption features maybe used to extend the functionality in the infrared of solar cells.We have analyzed the stability of the excitons and found a strongreduction of the binding energy for those TMDC excitons, while stronglyhybridized interlayer and defect-dominated excitons have binding energiesup to ∼250 meV. We computed the intrinsic radiative decay rateof these excitons and found inverse rates of up to 0.1 ps. Overall,our results demonstrate how point-like defects can be used to designoptical features in graphene-based van der Waals heterostructures,where excitons inherit properties from two well-distinct layers ina nontrivial way, pointing to the relevance of a first-principlesunderstanding of many-body effects in the description of these systemsfor transport and potential optoelectronic applications.In conclusion, we have studied the electronicand optical propertiesof WS


Combining probe photon energy-resolved coherent phonon spectroscopy measurements with model Hamiltonian calculations, we show that the dynamical transition is manifested through anomalies in the temperature, pump excitation fluence, and probe photon energy dependence of the strongly coupled phonon. With this procedure, we introduce a general pathway to uncover hidden multipolar ordered states and to control their re-orientation on ultrashort timescales.Ultrafast laser excitation provides a means to transiently realize long-range ordered electronic states of matter that are hidden in thermal equilibrium. Recently, this approach has unveiled a variety of thermally inaccessible ordered states in strongly correlated materials, including charge density wave, ferroelectric, magnetic, and intertwined charge-orbital ordered states. However, more exotic hidden states exhibiting higher multipolar ordering remain elusive owing to the challenge of directly manipulating and detecting them with light. Here we demonstrate a method to induce a dynamical transition from a thermally allowed to a thermally forbidden spin-orbit entangled quadrupolar ordered state in Ca Ultrafast laser excitation can generate metastable states in quantum materials, with no counterpart in equilibrium. Here the authors demonstrate a transient quadrupolar ordered state in Ca2RuO4 single crystals via excitation of a phonon mode coupled to the order parameter. More exotic symmetry broken states that exhibit ordering of higher electronic multipole moments are prevalent in strongly interacting electron systems, notably the f- and heavy d-electron based materials17. However, because multipolar ordered states are challenging to directly manipulate and to detect using conventional techniques, experimental demonstrations of light-induced transitions between their equilibrium and hidden counterparts remain elusive.Photo-excited quantum materials can be transiently steered away from their ground state. Targeting nearby local minima in their potential energy landscapes may then reveal ordered states that are thermally inaccessible. This strategy has been adopted to drive dynamical transitions from structurald-electron orbital polarized state as a representative example, which is described by an electric quadrupolar order parameter. Consider the general structural building block of a transition metal oxide, consisting of an oxygen octahedral cage surrounding a central transition metal ion with electrons occupying the t2g levels . Above the critical temperature for quadrupolar order (QO), the system is characterized by a harmonic lattice Hamiltonian B > 0 is a constant and γ runs over the orthornormal eigenmodes Qγ of the octahedral complex. The potential energy surface (PES) is a parabola with its minimum corresponding to a state with zero orbital polarization and zero octahedral distortion  orbital occupation and Qθ < 0 (Qθ > 0).Here we exploit the intrinsic coupling of a multipolar order parameter to lattice degree of freedom as a route both to impart and to detect a dynamical transition into a hidden state. We illustrate the general principle using a mentclass2pt{minimmentclass2pt{minimQθ phonon coordinate, the system can in principle overcome the potential barrier once a critical phonon amplitude is exceeded, allowing the system to transiently access the hidden state  dependence of the quadrupolar order coupled phonon (QOCP) amplitude will exhibit an anomaly: in contrast to an ordinary uncoupled phonon whose amplitude continues to increase linearly with F  and spin (S = 1) angular momenta of the two t2g holes combine into an ionic ground state with total angular momentum (pseudospin) J = 021. However, inter-atomic superexchange interactions condense J = 1 spin-orbit excitons and drive the system into an antiferromagnetic state below a Néel temperature TN = 110 K22. In a temperature window between TN and TQO= 260 K, the system is reported to realize a spin-nematic state characterized by an electric quadrupolar order parameter, which is a spin-orbit coupled analog of an orbital ordered state23  was tuned well below the low temperature Mott gap ( ~ 0.6 eV) and far away from phonon resonances (Supplementary Note 5)27, allowing fluences up to 30 mJ/cm2 to be reached. We found that the amplitudes of different coherent phonon modes vary strongly with probe photon energy. Therefore, we scanned the probe photon energy from 0.5 eV to 2.1 eV, covering the dxy → dxz/yz and the dxz/yz → dxz/yz absorption peaks near 1 eV and 2 eV, respectively29, in order to capture a large set of modes.To search for signatures of a coherent phonon-induced hidden QO state, we performed pump fluence-dependent coherent phonon spectroscopy measurements on CaT = 80 K and F = 15 mJ/cm2 are displayed in Fig. 30. Upon subtracting the background term 33. To this end, we can construct a microscopic Hamiltonian for Ca2RuO4: Qθ and Qϵ modes. To capture multi-orbital electronic interactions within the JH is the intra-atomic Hund’s exchange, U is the intra-orbital Coulomb interaction, 34. We also add a SOC term λ is the coupling strength, which endows the QO with spin-orbit entangled character. By performing exact diagonalization of the Hamiltonian 2RuO4, we obtain the PES as a function of the two Eg eigenmodes of the octahedron (Qθ and Qϵ). For T < TQO, the PES exhibits three minima  and solve for the system dynamics following an impulsive Gaussian pulse matching our experimental pump envelope , the system can then either directly relax to the local minimum, or continue to temporally oscillate back and forth between the global and local minima before eventually settling into one of them. We calculated the temporal trajectory of  for different fluences  between 0.5 and 1.3 eV that is attributed predominantly to the dxy → dxz/yz transition, and another peak (β) between 1.3 and 2.1 eV that is attributed predominantly to the dxz/yz → dxz/yz transition29. A probe photon energy tuned to the α-peak is expected to be particularly sensitive to tetragonal distortions (Qθ) because this mode modulates the energy splitting between the dxy and dxz/yz levels , because this mode lifts the degeneracy of the dxz/yz bands and modulates their splitting. Since the eigenvector of the QOCP mode at 3.7 THz has a finite projection along both the Qθ and Qϵ coordinates, our model predicts that the deviation from linear fluence scaling above Fc observed for the 3.7 THz mode should be much more pronounced when the probe is tuned to the β-peak than when it is tuned to the α-peak  direction immediately before the experiment to obtain a fresh and smooth surface. The whole sample was then kept in high vacuum with pressure lower than 10−7 torr.High-quality plate-like single-crystal Cadxy → dxz/yz transition. To probe resonant with dxz/yz → dxz/yz transition, the remaining small portion of the 800 nm light and the second harmonic of the OPA light produced by BBO crystal are used. Our probe energy can thus scan from 0.5 eV to 2.1 eV. Si and InGaAs photodiodes are utilized as the photo-detectors. The fluence of the pump is tunable from 0 to 35 mJ/cm2, above which thermal damage may occur as shown by a steady decrease of static reflectivity. The polarizations of the pump and the probe pulses were set to be perpendicular to each other, but both are parallel to the nearly isotropic [001] plane of the crystal.The sample temperature was fixed at 80 K without further notification. In the experimental setup, a Ti:sapphire amplified laser operating at 1 kHz generates 800 nm pulses with 40 fs time duration. Most of the power seeds two optical parametric amplifiers (OPAs) with individually tunable near infrared light ranging from 1200 to 2400 nm with a duration of 80 fs. One of the two OPAs pumps a differential frequency generator (DFG) and produces midinfrared light centered around 4000 nm with 100 fs time duration, which is used as the pump. The other OPA is used as a wavelength-tunable probe resonant with 2RuO4 consists of four terms, and the detailed discussion on the cooperative SOC and JT effect can be found in Supplementary Note A comprehensive low energy microscopic model of Caλ is the SOC constant, g is the JT coupling constant, B is the elastic lattice energy determined by the QOCP frequency, JH is the intra-atomic Hund’s coupling, and U is the Hubbard intra-orbital Coulomb interaction. Qθ and Qϵ . Based on the experimental observations  functionals along with fully-relativistic Optimized Norm-Conserving Vanderbilt Pseudopotentials (ONCVPSP). The crystal structure of Ca2RuO4 was obtained using the 90 K data from ref. 24. For self-consistency, the energy cutoff and grid density are converged with respect to total energy, with wavefunction cutoff of 50 Ry and a 6 × 6 × 3 Monkhorst-Pack grid as final values. For electronic structure calculations, an additional non-self-consistent calculation was performed at higher k-mesh of 9 × 9 × 4. Following ref. 30, we included collinear spin polarization and DFT + U with U = 3.5 eV. Simulations of the optical spectrum used the Epsilon.x code to smooth out numerical instabilities (interband smearing). We used the Phonopy package to calculate the phonon eigenmodes and frequencies under the frozen-phonon approximation using a 2 × 2 × 1 supercell, allowing for dimensions > 10 Å along each axis40. We analyzed the effect of the 3.7 and 5.7 THz phonon modes with atomic displacements on the order of 0.01 Å for oxygen atoms and 0.1 Å for calcium atoms to avoid nonlinear effects.The optical conductivity spectra in the presence of specific lattice distortions were calculated from first principles using density functional theory (DFT) as implemented in the Quantum ESPRESSO packageSupplementary InformationPeer Review FileSource Data


Bilayer materials made of 2D monolayers are emerging as new systems creating diverse opportunities for basic research and applications in optoelectronics, thermoelectrics, and topological science among others. Herein, we present a computational bilayer materials dataset containing 760 structures with their structural, electronic, and transport properties. Different stacking patterns of each bilayer have been framed by analyzing their monolayer symmetries. Density functional theory calculations including van der Waals interactions are carried out for each stacking pattern to evaluate the corresponding ground states, which are correctly identified for experimentally synthesized transition metal dichalcogenides, graphene, boron nitride, and silicene. Binding energies and interlayer charge transfer are evaluated to analyze the interlayer coupling strength. Our dataset can be used for materials screening and data-assisted modeling for desired thermoelectric or optoelectronic applications. Starting with graphene10, layered materials and their heterostructures have been the source of emergent phenomena coupling their electronic, optical, thermal, and mechanical response with nontrivial topology. For example, hexagonal honeycomb materials can host valley Hall effect and quantum anomalous Hall effect providing a platform to study dissipation-less valleytronics11. Layered materials with broken inversion symmetry could lead to k-valley-dependent contrasted circular dichroism, enabling valley optical selection rules12. Different substrate environments can provide substantial Rashba effect, making it possible to design spintronics devices such as spin-field effect transistors13.Monolayered materials have attracted considerable research interest in science and technology due to their inherent novel properties compared to their bulk counterparts. Systems, such as transition metal dichalcogenides (TMDs)15. Recent large scale simulations predict over 4000 2D materials with different chemical compositions and lattice space groups16. Some of them have been synthesized such as transition metal dichalcogenides (TMDs)17, hexagonal boron nitride (hBN)18, graphene19, MSe2 21, ZrS222, TiS223, MoSSe24 and so on, while others are waiting to be realized in the laboratory.Layered materials are typically composed of chemically inert monolayers that can be organized to make various multilayer composites. In addition to individual layers, systems that consist of finite number of identical monolayers or heterostructures made of layers with different chemical compositions give rise to new subfields in science and technology. The diversity is practically limitless given the ever increasing library of layered materials26. In particular, the semimetallic behavior of graphene limits its application in the next-generation device application; however, its bilayer has a tunable band gap via external electric fields, enabling its device applications27. On the other hand, various types of stacking patterns in bilayers could offer a platform to study different novel phenomena, including magneto-electric coupled multiferroics effect28, different optical response30, topology31, magnetism32, and Rashba spin-splitting33. Besides, different twisting angles of monolayers can exhibit moiré patterns resulting in many intriguing properties, such as Mott insulating behavior34, topological superconducting state35, tunable band gaps36, and light-matter interactions37 providing an opportunity to study twistronics in a large class of bilayers.In addition to their monolayer phase, bilayers constitute a separate subset of 2D materials whose different stacking patterns and interlayer interactions become additional sources of new physics16. We consider monolayers with hexagonal and square type lattices with various stackings obtained by rotating or sliding the top layer against the bottom layer as dictated by the symmetry of each monolayer. Besides, many of the different stacking patterns can be viewed as variations of the AA and AB bilayer orientations for bilayer graphene38. For each of the constructed 760 bilayers, the energetically most stable configuration is reported together with several electronic and transport properties. By calculating the density of states (DOS) and band structures, energy gaps in the 0≤Eg < 6 eV are found, further highlighting the role of spin orbit coupling (SOC). Lattice parameters, interlayer separations, van der Waals coupling, and charge transfer are also calculated to generate data driven information of interlayer effects in bilayers. Additionally, calculated Seebeck coefficient, electrical conductivity, and effective band structure masses provide the foundation for a transport database39 properties of 2D materials. The reported data gives valuable information for screening and identifying materials with targeted properties as well as a set of descriptors to be used in future statistical models based on data mining and machine learning methods41.In this study, we report high throughput Density Functional Theory (DFT) calculations of van der Waals bilayer materials, composed of chemically inert dynamically stable nonmagnetic monolayers as reported in the C2DB database site42, where we consider non-magnetic and dynamically stable monolayers for further screening. The breakdown of the stoichiometry, group symmetry, and the corresponding number of monolayers are also given explicitly. A total of 520 monolayers have been examined and schematic representation of those monolayers is provided in Fig. The high throughput computational work flow to build the bilayer materials dataset is shown in Fig. 1X2) 1 T and 2H phases have provided additional adaptability for constructing the Janus-derived bilayers. We framed three distinct bilayers phases as X1AX2-X2AX1 (60 structures), X1AX2-X1AX2 (60 structures), and X2AX1-X1AX2 (60 structures) with X2-X2, X2-X1, and X1-X1 atoms making up the interface region. Accordingly, 760 bilayers with nine different phases have been formulated from the initial 520 monolayers.The symmetries in each monolayer type have been analyzed to generate different bilayer stacking patterns having chemically identical monolayers. These stacking patterns are created by considering an initial interlayer separation of 3.3 Å. Besides the atomic registry dependence, the different surface atoms in the Janus (AXσ/τ), Seebeck coefficient (S), and scaled Power factor (S2σ/τ) within a constant relaxation time approximations τ are also calculated. These data are also provided in our BMDS dataset43.DFT self-consisted calculations are then performed by considering the van der Waals interactions to obtain the relaxed structures of all bilayers. Energies of the stackings in each bilayer type are compared, and the stacking order of the energetically most stable system is identified as the ground state configuration for our bilayer materials dataset (BMDS). Subsequently, electronic structure calculations are carried out to obtain the energy band gaps with and without SOC, the magnitude of the SOC energy, charge transfer between the layers, effective masses at the valence band maxima and conduction band minima of the most stable bilayers. These results are reported in the BMDS. Transport properties, such as the scaled electrical conductivity  have two stacking patterns while finite thick materials have four possible stacking patterns.The construction of the differently stacked bilayers is facilitated by analyzing the crystal symmetries of the constituent monolayers51. The projector-augmented wave (PAW) potentials are used to incorporate the ion-electron interactions in the calculations52. The Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation is adopted to estimate the exchange-correlation potential53. To expand the wavefunctions on a plane-wave basis, a kinetic energy cutoff of 600 eV is used with an energy convergence threshold of 10−6 eV. The structures were relaxed by utilizing a conjugate gradient scheme until each component of Hellmann-Feynman forces on the atoms was less than 0.005 eVÅ−1. A Γ-centered 12 × 12 × 1 Monkhorst-Pack54 k-point grid is considered for sampling the Brillouin Zone. A minimum vacuum layer of 15 Å is taken to avoid interactions with adjacent layers. Electronic band structure and transport properties are calculated by considering the SOC effect. The charge difference between the monolayer and bilayer has been calculated by Bader charge analysis55. The van der Waals interaction in different stacking is approximated by considering the DFT-D3 method with a zero-damping function56. Effective masses of VBM and CBM are calculated using the SUMO PYTHON package57.The stacking configurations for the considered bilayers are calculated using DFT methods as implemented in the Vienna Ab initio Simulation Package (VASP)E1, E2… En are the total DFT energies for all n possible stacking patterns of a given bilayer, as explicitly given in Figs. a and interlayer separation d in terms of number of materials for all nine bilayer sub-classes are shown in Figs. a and d, which can further be compared with the lattice constants a of the monolayers given in Fig. a and b lattice constants is rather small. In most bilayers, a lies within 3–4.5 Å, and this trend is especially pronounced for the 1 T and 2 H Janus (AX1X2) materials where all data is concentrated in that region. We find that six materials, K2Br2, K2Cl2, K2I2, Rb2Br2, Rb2Cl2, and Rb2I2, in the square lattice phase A2X2 (P4/nmm), have much larger bilayer lattice parameters which is consistent with the data for the corresponding monolayers  and the total charge of the monolayer as part of the bilayer structure (subscript sublayer in BL) using the relation,qi is the charge of i-th atom (Mi) and the summation runs over the total number of atomic species in each monolayer class. This is a quantitative measure of the charge redistribution occurring in the bilayer formation as the monolayers are brought together. Data for Δq as a function of the interlayer separation is given in Fig. q in Fig. −2e < Δq < 0.5 × 10−2e range. This is consistent with a weaker interlayer coupling, also discussed earlier in the context of the interlayer separation. Further information can be obtained from the Eg vs Δq correlation displayed in Fig. q for bilayers with Eg ≠ 0, while in metallic systems charge transfer occurs in the entire studied range.Another important property for the interlayer interaction is the charge transfer that occurs upon bringing the two monolayers together. Using Bader charge analysis, here we calculate the charge difference Δκ is also calculated within DFT, and results for κ as a function of the lattice constant are shown in Fig. κ < 25 window shows the distribution of the data for bilayers with smaller dielectric constant. It is found that about 541 bilayers have κ < 25, while 60 systems have κ > 100. Figure κ” and/or large gap dielectric nano-structured materials for the next generation electronic devices61. In addition to large κ responsible for enhanced capacitive coupling, dielectrics with a large band gap are needed to prevent leakage currents between electrodes for successful integration.The dielectric constant ZT = S2σT/κth, where S, σ, T, and κth are the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity, respectively. Materials with higher ZT are sought out for efficient thermoelectric devices. One way to achieve this goal is to look for materials with large values of their power factors S2σ. Using the semi-classical linearized Boltzmann transport theory within the constant relaxation time (τ) approximation  as implemented in the BoltzTraP2 code62, we have calculated S, σ, and S2σ for the energetically most stable bilayers. The simulations are performed with 3240 k-points, which is a dense enough mesh to obtain the transport properties.Transport properties such as electrical conductivity, Seebeck coefficient, and power factor are widely used for evaluating the materials thermoelectric figure of merit S and σ/τ, we obtain the rescaled by the relaxation time power factor. A histogram plot distribution of S2σ/τ for the number of considered bilayers is shown in Fig. 64. These quantities are readily available from DFT calculations, which can help one to assess if a given material may be a potential thermoelectric candidate. In Fig. S and σ/τ values for bilayers with nonzero Eg. One observes that largest σ/τ and S values are found for materials with smaller me and mh, which correlates well with data for 3D bulk materials64.After calculating 43. The figures for the electronic band structure with considering relativistic SOC effect and the transport coefficients at different temperature with varying the chemical potential are also provided in figshare. The description of the columns in the spreadsheet are shown explicitly the Table Our BMDS dataset containing 760 bilayer materials are composed of identical dynamically stable and nonmagnetic monolayers from the C2DB. The reported data contains information for the ground state stacking order of each material. All calculated data for the ground state bilayers are given in a CSV spreadsheet file and it can be found on figshareμ = 0 for insulating bilayers are also reported in the CSV file. Additionally, effective masses at the VBM and CBM for insulating materials are included in the CSV file. Transport properties and effective masses of VBM and CBM are obtained for bilayers with nonzero energy gap. For metallic systems, that block is denoted as “metal”. Note that we considered all reported dynamically stable and nonmagnetic C2DB monolayers, however, some bilayers did not attain a stable interlayer separation, which became quite large or very small during the relaxation process (>8 Å or <1 Å in most cases). Such bilayers are discarded and the reported 760 bilayers are well converged structures. Also, while we considered only nonmagnetic monolayers, 24 bilayers acquired finite magnetic moments (>0.5 μB). Therefore we have added a column for magnetic moment in the CSV file. For these magnetic bilayers, we have reported the spin polarized calculations. We find that all magnetic bilayers are metallic, thus their transport properties are not evaluated.Transport properties, such a Seebeck coefficient, power factor, and conductivity at T = 300 K and https://cmrdb.fysik.dtu.dk/c2db/cmrdb-c2db). First principles calculations are done using DFT methods with included van der Waals interactions. Such an approach is extensively used by the solid state physics and chemistry communities for materials predictions and property investigations. VASP is a premier quantum mechanical software package through which many emerging databases (including C2DB) are built. Each step of our high throughput calculations is checked with stringent convergence criteria. The stacking order of each bilayer is generated by utilizing previously established symmetry based criteria capturing the energetically most stable pattern configurations as reported by numerous references50.For the bilayer dataset presented here, we have taken electronically and dynamically stable nonmagnetic monolayers from the well known C2DB database (Eformation = Ebilayer−2 × Emonolayer, where Emonolayer and Ebilayer are the total energies of monolayer and its corresponding ground state stacked bilayer structures, respectively. Normally, negative formation energy values indicate structural stability of the bilayer. Figure Eformation for the studied materials. All bilayers are found to have negative formation energies, such that −0.7 eV/atom < Eformation < 0 eV/atom. The only exception is the bilayer MgCl2 in the square AX2 phase, for which Eformation = 1.24 eV/atom and it is not explicitly given in Fig. 42 due to the lack of negative phonon modes. Additionally, several studies have shown that many bilayers composed of monolayers from the AX2, AX1X2, AX and A2 classes also have phonon band structure lacking negative modes72 demonstrating a dynamical stability for stacking patterns considered here as well. Although the phonon dispersion is an important factor for the stability of materials, it requires careful examination in terms of type and size of the constructed supercells, different functionals, and/or smearing parameters77. While small differences in bond lengths and angles may not show noticeable differences in the electronic structure, they are detrimental for the phonon band structure. Changes in the interlayer separation, which is closely related to the particular vdW dispersion method, can also have important consequences for the presence or lack of negative phonons of layered materials. We note that the monolayers dynamical stability and the several studies on vdW bilayers are strong indicators for the stability of the bilayer dataset here. The crucial influence of the specific DFT approximations and parameters on the phonon dispersion is materials dependent, thus phonon calculations are not part of this high throughput study.The vast majority of bilayer materials in BMDS have not been studied before. Therefore, we examine their stability by calculating the bilayer formation energy as: 78 for which d = 3–3.5 Å are found.The electronic structure properties of several bilayers have also been studied computationally by others. A comparison of the interlayer distances, band gaps, and stacking pattens of previously reported and calculated here data are shown in Table 43. The dataset can further be expanded by considering bilayers formed of other 2D monolayers with different lattice structures which may or may not host magnetic states.The data for the bilayers BMDS can be accessed directly from the CSV spreadsheet provided in figshareSupplementary Information: High throughput calculations for a dataset of bilayer materials