A-Site Cation Influence on the Structural and Optical Evolution of Ultrathin Lead Halide Perovskite Nanoplatelets.

Imposing quantum confinement has the potential to significantly modulate both the structural and optical parameters of interest in many material systems. In this work, we investigate strongly confined ultrathin perovskite nanoplatelets APbBr3. We compare the all-inorganic and hybrid compositions with the A-sites cesium and formamidinium, respectively. Compared to each other and their bulk counterparts, the materials show significant differences in variable-temperature structural and optical evolution. We quantify and correlate structural asymmetry with the excitonic transition energy, spectral purity, and emission rate. Negative thermal expansion, structural and photoluminescence asymmetry, photoluminescence full width at half-maximum, and splitting between bright and dark excitonic levels are found to be reduced in the hybrid composition. This work provides composition- and structure-based mechanisms for engineering of the excitons in these materials.

Mechanism of Enhanced Triplet-Triplet Upconversion in Organic Molecules.

We use time-dependent density functional theory (TDDFT) to investigate the mechanism of efficient triplet-triplet upconversion (TTU) in certain organic materials. In particular, we focus on materials where some singlets are generated in a two-step spin-nonconserving process (T1 + T1 → T2 → S1). For this mechanism to contribute significantly, the intersystem crossing (ISC) from the high-lying triplet to the singlet (T2 → S1) must outcompete the internal conversion (IC) to the low-lying triplet (T2 → T1). By considering multiple families of materials, we show that the T2 → S1 ISC can be enhanced in a number of ways: the substitution of electron-donating (ED) and electron-withdrawing (EW) groups at appropriate positions; the substitution of bulky groups that distort the molecular geometry; and the substitution of heavy atoms that enhance the spin-orbit coupling (SOC). In the first two cases, the enhancements are consistent with El-Sayed's rule in that rapid T2 → S1 ISC requires significant differences in the characters of the S1 and the T2 wavefunctions. Together, these effects enable a wide tunability of T2 → S1 ISC rates over at least 5 orders of magnitude. Meanwhile, the T2 → T1 IC is inhibited in these systems due to the large T2 - T1 energy gap >0.5 eV, which entails a high energy barrier to the T2 → T1 IC and the prediction of a slow rate regardless of the substituents or the presence of heavy atoms. In this way, tuning the T2 → S1 ISC appears to provide an effective strategy to achieve systematic improvement of TTU materials.

Synthesis of Zwitterionic CsPbBr3 Nanocrystals with Controlled Anisotropy using Surface-Selective Ligand Pairs.

Mechanistic studies of the morphology of lead halide perovskite nanocrystals (LHP-NCs) are hampered by a lack of generalizable suitable synthetic strategies and ligand systems. Here, the synthesis of zwitterionic CsPbBr3 NCs is presented with controlled anisotropy using a proposed "surface-selective ligand pairs" strategy. Such a strategy provides a platform to systematically study the binding affinity of capping ligand pairs and the resulting LHP morphologies. By using zwitterionic ligands (ZwL) with varying structures, majority ZwL-capped LHP NCs with controlled morphology are obtained, including anisotropic nanoplatelets and nanorods, for the first time. Combining experiments with density functional theory calculations, factors that govern the ligand binding on the different surface facets of LHP-NCs are revealed, including the steric bulkiness of the ligand, the number of binding sites, and the charge distance between binding moieties. This study provides guidance for the further exploration of anisotropic LHP-NCs.

Periodic Bootstrap Embedding.

Bootstrap embedding (BE) is a recently developed electronic structure method that has shown great success at treating electron correlation in molecules. Here, we extend BE to treat surfaces and solids where the wave function is represented in periodic boundary conditions using reciprocal space sums (i.e., k-point sampling). The major benefit of this approach is that the resulting fragment Hamiltonians carry no explicit dependence on the reciprocal space sums, allowing one to apply traditional nonperiodic electronic structure codes to the fragments even though the entire system requires careful consideration of periodic boundary conditions. Using coupled cluster singles and doubles (CCSD) as an example method to solve the fragment Hamiltonians, we present minimal basis set CCSD-in-HF results on 1D conducting polymers. We show that periodic BE-CCSD can typically recover ∼99.9% of the electron correlation energy. We further demonstrate that periodic BE-CCSD is feasible even for complex donor-acceptor polymers of interest to organic solar cells─despite the fact that the monomers are sufficiently large that even a Γ-point periodic CCSD calculation is prohibitive. We conclude that BE is a promising new tool for applying molecular electronic structure tools to solids and interfaces.

Bootstrap Embedding on a Quantum Computer.

We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.

Controlled Assembly and Anomalous Thermal Expansion of Ultrathin Cesium Lead Bromide Nanoplatelets.

Quantum confined lead halide perovskite nanoplatelets are anisotropic materials displaying strongly bound excitons with spectrally pure photoluminescence. We report the controlled assembly of CsPbBr3 nanoplatelets through varying the evaporation rate of the dispersion solvent. We confirm the assembly of superlattices in the face-down and edge-up configurations by electron microscopy, as well as X-ray scattering and diffraction. Polarization-resolved spectroscopy shows that superlattices in the edge-up configuration display significantly polarized emission compared to face-down counterparts. Variable-temperature X-ray diffraction of both face-down and edge-up superlattices uncovers a uniaxial negative thermal expansion in ultrathin nanoplatelets, which reconciles the anomalous temperature dependence of the emission energy. Additional structural aspects are investigated by multilayer diffraction fitting, revealing a significant decrease in superlattice order with decreasing temperature, with a concomitant expansion of the organic sublattice and increase of lead halide octahedral tilt.

Lead Halide Perovskite Nanocrystals with Low Inhomogeneous Broadening and High Coherent Fraction through Dicationic Ligand Engineering.

Lead halide perovskite nanocrystals (LHP NCs) are an emerging materials system with broad potential applications, including as emitters of quantum light. We apply design principles aimed at the structural optimization of surface ligand species for CsPbBr3 NCs, leading us to the study of LHP NCs with dicationic quaternary ammonium bromide ligands. Through the selection of linking groups and aliphatic backbones guided by experiments and computational support, we demonstrate consistently narrow photoluminescence line shapes with a full-width-at-half-maximum below 70 meV. We observe bulk-like Stokes shifts throughout our range of particle sizes, from 7 to 16 nm. At cryogenic temperatures, we find sub-200 ps lifetimes, significant photon coherence, and the fraction of photons emitted into the coherent channel increasing markedly to 86%. A 4-fold reduction in inhomogeneous broadening from previous work paves the way for the integration of LHP NC emitters into nanophotonic architectures to enable advanced quantum optical investigation.

It Is a Trap!: The Effect of Self-Healing of Surface Defects on the Excited States of CdSe Nanocrystals.

Colloidal semiconductor nanocrystals have attracted much interest due to their unique optical properties, with applications ranging from displays to biomedical imaging. Nanocrystal optical properties depend on the structure of the surface, where defects can lead to traps. CdSe nanocrystals undergo surface reorganization, or self-healing, to eliminate defects, removing midgap traps from the band structure. However, the effect of this process on the optical spectrum is not well studied. Here, we show that self-healing not only eliminates midgap traps from the band structure but also brightens the spectrum and causes the excitonic states to emerge as the dominant features, in agreement with experimental annealing studies. We find that self-healing can lead to new traps like bonded Se-Se or Cd-Cd dimers, and their behavior is different from that of undercoordinated atom traps. These results suggest that eliminating traps requires a balance of allowing enough surface reorganization to eliminate undercoordinated atoms, but not so much that dimeric traps form.

Converting Commodity Polyolefins to Electronic Materials through Borane-Catalyzed Alkene Isomerization.

Novel approaches to the functionalization of commodity polymers could provide avenues for the synthesis of materials for next-generation electronic devices. Herein, we present a catalytic method for the conversion of common unsaturated polymers such as polybutadiene, polyisoprene, and styrene-butadiene copolymers [e.g., polystyrene-block-polybutadiene-block-polystyrene and poly(styrene-stat-butadiene)] to poly(acetylene) (PA)-based multiblock copolymers with conjugation lengths of up to ∼20, making them potentially suitable for electronics applications. Additionally, we demonstrate the application of this method to the formal conversion of polyethylene─the most widely produced thermoplastic─into PA-containing multiblock materials.

Exchange controlled triplet fusion in metal-organic frameworks.

Triplet-fusion-based photon upconversion holds promise for a wide range of applications, from photovoltaics to bioimaging. The efficiency of triplet fusion, however, is fundamentally limited in conventional molecular and polymeric systems by its spin dependence. Here, we show that the inherent tailorability of metal-organic frameworks (MOFs), combined with their highly porous but ordered structure, minimizes intertriplet exchange coupling and engineers effective spin mixing between singlet and quintet triplet-triplet pair states. We demonstrate singlet-quintet coupling in a pyrene-based MOF, NU-1000. An anomalous magnetic field effect is observed from NU-1000 corresponding to an induced resonance between singlet and quintet states that yields an increased fusion rate at room temperature under a relatively low applied magnetic field of 0.14 T. Our results suggest that MOFs offer particular promise for engineering the spin dynamics of multiexcitonic processes and improving their upconversion performance.

Diabatic Valence-Hole States in the C2 Molecule: "Putting Humpty Dumpty Together Again".

Despite the long history of spectroscopic studies of the C2 molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C2 is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions that occur within four symmetry manifolds of excited states of C2 (1Πg, 3Πg, 1Σu+ , and 3Σu+ ). The key concept of our model is the existence of two "valence-hole" configurations, 2σg22σu11πu33σg2 for 1,3Πg states and 2σg22σu11πu43σg1 for 1,3Σu+ states, that are derived from 3σg ← 2σu electron promotion. The lowest-energy state from each of the four C2 symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s22p2 + 2s2p3 separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the global electronic structure and unimolecular dynamics of C2.

Machine learning dynamic correlation in chemical kinetics.

Lattice models are a useful tool to simulate the kinetics of surface reactions. Since it is expensive to propagate the probabilities of the entire lattice configurations, it is practical to consider the occupation probabilities of a typical site or a cluster of sites instead. This amounts to a moment closure approximation of the chemical master equation. Unfortunately, simple closures, such as the mean-field and the pair approximation (PA), exhibit weaknesses in systems with significant long-range correlation. In this paper, we show that machine learning (ML) can be used to construct accurate moment closures in chemical kinetics using the lattice Lotka-Volterra model as a model system. We trained feedforward neural networks on kinetic Monte Carlo (KMC) results at select values of rate constants and initial conditions. Given the same level of input as PA, the ML moment closure (MLMC) gave accurate predictions of the instantaneous three-site occupation probabilities. Solving the kinetic equations in conjunction with MLMC gave drastic improvements in the simulated dynamics and descriptions of the dynamical regimes throughout the parameter space. In this way, MLMC is a promising tool to interpolate KMC simulations or construct pretrained closures that would enable researchers to extract useful insight at a fraction of the computational cost.

Resolving the Triexciton Recombination Pathway in CdSe/CdS Nanocrystals through State-Specific Correlation Measurements.

As luminescence applications of colloidal semiconductor nanocrystals push toward higher excitation flux conditions, there is an increased need to both understand and potentially control emission from multiexciton states. We develop a spectrally resolved correlation method to study the triply excited state that enables direct measurements of the recombination pathway for the triexciton, rather than relying on indirect extraction of rates. We demonstrate that, for core-shell CdSe-CdS nanocrystals, triexciton emission arises exclusively from the band-edge S-like state. Time-dependent density functional theory and extended particle-in-a-sphere calculations demonstrate that reduced carrier overlap induced by the core-shell heterostructure can account for the lack of emission observed from the P-like state. These results provide a potential avenue for the control of nanocrystal luminescence, where core-shell heterostructures can be leveraged to control carrier separation and therefore maintain emission color purity over a broader range of excitation fluxes.

Maximizing TADF via Conformational Optimization.

We investigate a new strategy to enhance thermally activated delayed fluorescence (TADF) in organic light-emitting diodes (OLEDs). Given that the TADF rate of a molecule depends on its conformation, we hypothesize that there exists a conformation that maximizes the TADF rate. To test this idea, we use time-dependent density functional theory (TDDFT) to simulate the TADF rates of several TADF emitters while varying their geometries in a select subspace of internal coordinates. We find that geometric changes in this subspace can increase the TADF rate up to 3 orders of magnitude with respect to the minimum energy conformation, and the simulated TADF rate can even be brought into the submicrosecond time scales under the right conditions. Furthermore, the TADF rate enhancement can be maintained with a conformational energy that might be within the reach of modern synthetic chemistry. Analyzing the maximum TADF conformation, we extract a number of structural motifs that might provide a useful handle on the TADF rate of a donor-acceptor (DA) system. The incorporation of conformational engineering into the TADF technology could usher in a new paradigm of OLEDs.

Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding.

Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.

Colloidal CdSe nanocrystals are inherently defective.

Colloidal CdSe nanocrystals (NCs) have shown promise in applications ranging from LED displays to medical imaging. Their unique photophysics depend sensitively on the presence or absence of surface defects. Using simulations, we show that CdSe NCs are inherently defective; even for stoichiometric NCs with perfect ligand passivation and no vacancies or defects, we still observe that the low energy spectrum is dominated by dark, surface-associated excitations, which are more numerous in larger NCs. Surface structure analysis shows that the majority of these states involve holes that are localized on two-coordinate Se atoms. As chalcogenide atoms are not passivated by any Lewis base ligand, varying the ligand should not dramatically change the number of dark states, which we confirm by simulating three passivation schemes. Our results have significant implications for understanding CdSe NC photophysics, and suggest that photochemistry and short-range photoinduced charge transfer should be much more facile than previously anticipated.

Understanding the Dipole Moment of Liquid Water from a Self-Attractive Hartree Decomposition.

The dipole moment of a single water molecule in liquid water has been a critical concept for understanding water's dielectric properties. In this work, we investigate the dipole moment of liquid water through a self-attractive Hartree (SAH) decomposition of total electron density computed by density functional theory, on water clusters sampled from ab initio molecular dynamics simulation of bulk water. By adjusting one parameter that controls the degree of density localization, we reveal two distinct pictures of water dipoles that are consistent with bulk dielectric properties: a localized picture with smaller and less polarizable monomer dipoles and a delocalized picture with larger and more polarizable monomer dipoles. We further uncover that the collective dipole-dipole correlation is stronger in the localized picture and is key to connecting individual dipoles with bulk dielectric properties. On the basis of these findings, we suggest considering both individual and collective dipole behaviors when studying the dipole moment of liquid water and propose new design strategies for developing water models.

Bootstrap embedding with an unrestricted mean-field bath.

A suite of quantum embedding methods have recently been developed where the Schmidt decomposition is applied to the full system wavefunction to derive basis states that preserve the entanglement between the fragment and the bath. The quality of these methods can depend heavily on the quality of the initial full system wavefunction. Most of these methods, including bootstrap embedding (BE) [M. Welborn et al; J. Chem. Phys. 145, 074102 (2016)], start from a spin-restricted mean-field wavefunction [call this restricted BE (RBE)]. Given that spin-unrestricted wavefunctions can capture a significant amount of strong correlation at the mean-field level, we suspect that starting from a spin-unrestricted mean-field wavefunction will improve these embedding methods for strongly correlated systems. In this work, BE is generalized to an unrestricted Hartree-Fock bath [call this unrestricted BE (UBE)], and UBE is applied to model hydrogen ring systems. UBE's improved versatility over RBE is utilized to calculate high spin symmetry states that were previously unattainable with RBE. Ionization potentials, electron affinities, and spin-splittings are computed using UBE with accuracy on par with spin-unrestricted coupled cluster singles and doubles. Even for cases where RBE is viable, UBE converges more reliably. We discuss the limitations or weaknesses of each calculation and how improvements to RBE and density matrix embedding theory these past few years can also improve UBE.