Dynamics of recombination via conical intersection in a semiconductor nanocrystal

Subpicosecond Dynamics of Rydberg Excitons Produced from Ultraviolet Excitation of Neutral Cuprite (Cu2O)n Clusters, n < 13

The ultrafast dynamics of subnanometer neutral cuprite clusters (Cu2O)n, n < 13, are examined with pump probe spectroscopy. Upon absorption of an ultraviolet (400 nm) photon, all clusters exhibit a subpicosecond lifetime that we attribute to carrier recombination. Density functional theory (DFT) shows a change in the structural motif between small planar clusters and three-dimensional structures at n = 4. This transition is accompanied by a change in the excited state relaxation behavior, marking the onset for which lifetimes increase gradually with size. Time-dependent DFT calculations show that the excited state lifetimes align with calculated topological parameters and charge carrier delocalization associated with the formation of Rydberg excitons. Terminal Cu atoms are found to be important for the production of Rydberg excitons at the lowest optically allowed excited state. Upon excitation, the electron resides on terminal Cu atoms and the hole becomes delocalized across the remainder of the cluster.

Theoretical Understanding on the Facilitated Photoisomerization of a Carbonyl Supported Borane System

Boron compound BOMes2 containing an internal B-O bond undergoes highly efficient photoisomerization, followed by sequential structural transformations, resulting in a rare eight-membered B, O-heterocycle (S. Wang, et al. Org. Lett. 2019, 21, 5285-5289). In this work, the detailed reaction mechanisms of such a unique carbonyl-supported tetracoordinate boron system in the first excited singlet (S1 ) state and the ground (S0 ) state were investigated by using the complete active space self-consistent field and its second-order perturbation (MS-CASPT2//CASSCF) method combined with time-dependent density functional theory (TD-DFT). Moreover, an imine-substituted tetracoordinated organic boron system (BNMes2 ) was selected for comparative study to explore the intrinsic reasons for the difference in reactivity between the two types of compounds. Steric factor was found to influence the photoisomerization activity of BNMes2 and BOMes2 . These results rationalize the experimental observations and can provide helpful insights into understanding the excited-state dynamics of heteroatom-doped tetracoordinate organoboron compounds, which facilitates the rational design of boron-based materials with superior photoresponsive performances.

Nonadiabatic Potential Energy Surfaces for a Molecule on a Surface as Found by Constrained Complete Active Space Theory

In order to study electron-transfer mediated chemical processes on a metal surface, one requires not one but two potential energy surfaces (one ground state and one excited state) as in Marcus theory. In this letter, we report that a novel, dynamically weighted, state-averaged constrained CASSCF(2,2) (DW-SA-cCASSCF(2,2)) can produce such surfaces for the Anderson impurity model. Both ground and excited state potentials are smooth, they incorporate states with a charge transfer character, and the accuracy of the ground state surface can be verified for some model problems by renormalization group theory. Future development of gradients and nonadiabatic derivative couplings should allow for the study of nonadiabatic dynamics for molecules near metal surfaces.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Tuning the photodynamics of sub-nanometer neutral chromium oxide clusters through sequential oxidation

Sub-nanometer neutral chromium oxide clusters were produced in the gas phase through laser ablation and their low-lying excited state lifetimes were measured using femtosecond pump-probe spectroscopy. Time-dependent density functional theory calculations relate the trends in experimental lifetimes to the cluster's electronic structure. The photoexcited (CrO₂)_n (n < 5) cluster transients with the absence of up to four O atoms (Cr_nO_2n-x, x < 5) exhibit a ∼30 fs and sub-ps lifetime, attributed to instantaneous metallic e-e scattering and vibrationally mediated charge carrier relaxation, respectively. A long-lived (>2 ps) response is found in both small and clusters with low O content, indicating that terminal CrO bonds facilitate efficient excited state relaxation. The ∼30 fs transient signal fraction grows nearly linearly with oxidation, matching the amount of O-2p to Cr-3d charge transfer character of the photoexcitation and suggesting a gradual transition between semiconducting and metallic behavior in chromium oxide clusters at the molecular level. The results presented herein suggest that the photocatalytic properties of chromium oxides can be tunable based on size and oxidation.

Nonadiabatic Dynamics Algorithms with Only Potential Energies and Gradients: Curvature-Driven Coherent Switching with Decay of Mixing and Curvature-Driven Trajectory Surface Hopping

Direct dynamics by mixed quantum-classical nonadiabatic methods is an important tool for understanding processes involving multiple electronic states. Very often, the computational bottleneck of such direct simulation comes from electronic structure theory. For example, at every time step of a trajectory, nonadiabatic dynamics requires potential energy surfaces, their gradients, and the matrix elements coupling the surfaces. The need for the couplings can be alleviated by employing the time derivatives of the wave functions, which can be evaluated from overlaps of electronic wave functions at successive time steps. However, evaluation of overlap integrals is still expensive for large systems. In addition, for electronic structure methods for which the wave functions or the coupling matrix elements are not available, nonadiabatic dynamics algorithms become inapplicable. In this work, building on recent work by Baeck and An, we propose new nonadiabatic dynamics algorithms that only require adiabatic potential energies and their gradients. The new methods are named curvature-driven coherent switching with decay of mixing (κCSDM) and curvature-driven trajectory surface hopping (κTSH). We show how powerful these new methods are in terms of computation time and accuracy as compared to previous mixed quantum-classical nonadiabatic dynamics algorithms. The lowering of the computational cost will allow longer nonadiabatic trajectories and greater ensemble averaging to be affordable, and the ability to calculate the dynamics without electronic structure coupling matrix elements extends the dynamics capability to new classes of electronic structure methods.

Effect of oxidation on excited state dynamics of neutral TinO2n-x (n < 10, x < 4) clusters

Excited state lifetimes of neutral titanium oxide clusters (Ti_nO_2n-x, n < 10, x < 4) were measured using a sequence of 400 nm pump and 800 nm probe femtosecond laser pulses. Despite large differences in electronic properties between the closed shell stoichiometric Ti_nO_2n clusters and the suboxide Ti_nO_2n-x (x = 1-3) clusters, the transient responses for all clusters contain a fast response of 35 fs followed by a sub-picosecond (ps) excited state lifetime. In this non-scalable size regime, subtle changes in the sub-ps lifetimes are attributed to variations in the coordination of Ti atoms and localization of charge carriers following UV photoexcitation. In general, clusters exhibit longer lifetimes with increased size and also with the addition of O atoms. This suggests that the removal of O atoms develops stronger Ti-Ti interactions as the system transitions from a semiconducting character to a fast metallic electronic relaxation mechanism.

Vibronic Excitons and Conical Intersections in Semiconductor Quantum Dots

Surface defects and organic surface-capping ligands affect the photoluminescence properties of semiconductor quantum dots (QDs) by altering the rates of competing nonradiative relaxation processes. In this study, broadband two-dimensional electronic spectroscopy reveals that absorption of light by QDs prepares vibronic excitons, excited states derived from quantum coherent mixing of the core electronic and ligand vibrational states. Rapidly damped coherent wavepacket motions of the ligands are observed during hot-carrier cooling, with vibronic coherence transferred to the photoluminescent state. These findings suggest a many-electron, molecular theory for the electronic structure of QDs, which is supported by calculations of the structures of conical intersections between the exciton potential surfaces of a small ammonia-passivated model CdSe nanoparticle.

Increased Excited State Metallicity in Neutral Cr2On Clusters (n < 5) upon Sequential Oxidation

Excited state lifetimes of neutral Cr₂O_n (n < 5) clusters were measured using femtosecond pump-probe spectroscopy. Density functional theory calculations reveal that the excited state dynamics are correlated with changes in the cluster's electronic structure with increasing oxidation. Upon absorption of a UV (400 nm) photon, the clusters exhibit features attributed to three separate relaxation processes. All clusters exhibit similar subpicosecond lifetimes, attributed to vibrational relaxation. However, the ∼30 fs transient signal fraction grows linearly with oxidation, matching the amount of O to Cr charge transfer character of the photoexcitation and highlighting a gradual transition between semiconducting and metallic behavior at the molecular level. A long-lived (>2.5 ps) response is recorded only in clusters with significant d-electron character, suggesting that adiabatic relaxation back to the ground state is efficient in heavily oxidized clusters, due to the presence of terminal O atoms. The simple picture of sequential oxidation of Cr₂O_n reveals a linear variation in the contributions of each relaxation component to the total transient signals, therefore opening possibilities for the design of new molecular spintronic materials.

Hot Carrier Dynamics at Ligated Silicon(111) Surfaces: A Computational Study

We provide a case-study for thermal grafting of benzenediazonium bromide onto a hydrogenated Si(111) surface using ab initio molecular dynamics (AIMD) calculations. A sequence of reaction steps is identified in the AIMD trajectory, including the loss of N₂ from the diazonium salt, proton transfer from the surface to the bromide ion that eliminates HBr, and deposition of the phenyl group onto the surface. We next assess the influence of the phenyl groups on photophysics of hydrogen-terminated Si(111) slabs. The nonadiabatic couplings necessary for a description of the excited-state dynamics are calculated by combining ab initio electronic structures and reduced density matrix formalism with Redfield theory. The phenyl-terminated slab shows reduced nonradiative relaxation and recombination rates of hot charge carriers in comparison with the hydrogen-terminated slab. Altogether, our results provide atomistic insights revealing that (i) the diazonium salt thermally decomposes at the surface allowing the formation of covalently bonded phenyl group, and (ii) the coverage of phenyl groups on the surface slows down charge carrier cooling driven by electron-phonon interactions, which increases photoluminescence efficiency at the near-infrared spectral region.

Oscillation in Excited State Lifetimes with Size of Sub-nanometer Neutral (TiO2)n Clusters Observed with Ultrafast Pump-Probe Spectroscopy

Neutral titanium oxide clusters of up to 1 nm in diameter (TiO₂)_n, with n < 10, are produced in a laser vaporization source and subsequently ionized by a sequence of femtosecond laser pulses. Using a 400 nm pump and 800 nm probe lasers, the excited state lifetimes of neutral (TiO₂)_n clusters are measured. All clusters exhibit a rapid relaxation lifetime of ∼35 fs, followed by a sub-picosecond lifetime that we attribute to carrier recombination. The excited state lifetimes oscillate with size, with even-numbered clusters possessing longer lifetimes. Density functional theory calculations show the excited state lifetimes are correlated with charge carrier localization or polaron-like formation in the excited states of neutral clusters. Thus, structural rigidity is suggested as a feature for extending excited state lifetimes in titania materials.

Hot Electron Cooling in Silicon Nanoclusters via Landau-Zener Nonadiabatic Molecular Dynamics: Size Dependence and Role of Surface Termination

We develop a new express methodology for modeling excited-state dynamics occurring in dense manifolds of electronic states in atomistic systems. The approach leverages a modified Landau-Zener formula, the neglect of a back-reaction approximation, and the highly efficient density functional tight-binding method. We study the hot electron dynamics in a series of H- and F-terminated silicon nanocrystals (NCs) containing up to several hundred atoms. We explain the slower electron cooling dynamics in F-terminated NCs by the larger energy gaps between the adjacent electronic states in these systems as well as their slower fluctuations. We conclude that both the mass and chemical identity of the surface termination groups equally influence the electron dynamics, on average. However, the mass effect becomes dominant for higher-energy excitations. We find that the electron decay dynamics in F-terminated NCs has a greater sensitivity to the mass of the surface ligands than do the H-terminated NCs and explain this observation by the details of the electron-phonon coupling in the systems. We find that in the H-terminated NCs, electronic transitions in the cooling process occur predominantly between the surface states, whereas in F-terminated Si NCs, both surface and NC core states are coupled to the nuclear vibrations. We find that electron energy relaxation is accelerated in larger NCs and attribute this effect to the higher densities of states and smaller energy gaps in these systems.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Locality of conical intersections in semiconductor nanomaterials

A predictive theory connecting atomic structure to the rate of recombination would enable the rational design of semiconductor nanomaterials for optoelectronic applications. Recently our group has demonstrated that the theoretical study of conical intersections can serve this purpose. Here we review recent work in this area, focusing on the thesis that low-energy conical intersections in nanomaterials share a common feature: locality. We define a conical intersection as local if (a) the intersecting states differ by the excitation of an electron between spatially local orbitals, and (b) the intersection is accessed when the energies of these orbitals are tuned by local distortions of the geometry. After illustrating the locality of the conical intersection responsible for recombination at dangling bond defects in silicon, we demonstrate the locality of low-energy conical intersections in cases where locality may be a surprise. First, we demonstrate the locality of low-energy self-trapped conical intersections in a pristine silicon nanocrystal, which has no defects that one would expect to serve as the center of a local intersection. Second, we demonstrate that the lowest energy intersection in a silicon system with two neighboring dangling bond defects localizes to a single defect site. We discuss the profound implications of locality for predicting the rate of recombination and suggest that the locality of intersections could be exploited in the experimental study of recombination, where spectroscopic studies of molecular models of defects could provide new insights.