Understanding Nonradiative Recombination through Defect-Induced Conical Intersections

Numerical Equivalence of Diabatic and Adiabatic Representations in Diatomic Molecules

The (time-independent) Schrödinger equation for atomistic systems is solved by using the adiabatic potential energy curves (PECs) and the associated adiabatic approximation. In cases where interactions between electronic states become important, the associated nonadiabatic effects are taken into account via derivative couplings (DDRs), also known as nonadiabatic couplings (NACs). For diatomic molecules, the corresponding PECs in the adiabatic representation are characterized by avoided crossings. The alternative to the adiabatic approach is the diabatic representation obtained via a unitary transformation of the adiabatic states by minimizing the DDRs. For diatomics, the diabatic representation has zero DDR and nondiagonal diabatic couplings ensue. The two representations are fully equivalent and so should be the rovibronic energies and wave functions, which result from the solution of the corresponding Schrödinger equations. We demonstrate (for the first time) the numerical equivalence between the adiabatic and diabatic rovibronic calculations of diatomic molecules using the ab initio curves of yttrium oxide (YO) and carbon monohydride (CH) as examples of two-state systems, where YO is characterized by a strong NAC, while CH has a strong diabatic coupling. Rovibronic energies and wave functions are computed using a new diabatic module implemented in the variational rovibronic code Duo. We show that it is important to include both the diagonal Born-Oppenheimer correction and nondiagonal DDRs. We also show that the convergence of the vibronic energy calculations can strongly depend on the representation of nuclear motion used and that no one representation is best in all cases.

Origin of Vibronic Coherences During Carrier Cooling in Colloidal Quantum Dots

Recent two-dimensional electronic spectroscopy experiments [Tilluck et al. J. Phys. Chem. Lett. 2021, 12 (39), 9677-9683] indicate the creation of coherent vibronic wavepackets in the first femtoseconds of hot carrier cooling in hexadecylamine-passivated CdSe quantum dots. Here we present a quantum chemical study of the origin of these coherences in a CdSe nanocrystal. We find that coherent wavepacket motions along vibrational coordinates with alkylamine character promote nonradiative relaxation through conical intersections between the exciton states of the inorganic core. Electronic excitations in the core are found to pass energy to the vibrations of the ligands via two distinct mechanisms: excitation of core phonon modes that are coupled to the ligand vibrations and direct excitation of ligand vibrations by delocalization of the exciton onto the ligands, both of which naturally arise within a photochemical framework based on many-electron potential energy surfaces. If these findings are demonstrated to be general, vibronic coherences may be leveraged to control photophysical outcomes in colloidal quantum dots.

Semiclassical Multistate Dynamics for Six Coupled 5A' States of O + O2

Dynamics simulations of high-energy O₂-O collisions play an important role in simulating thermal energy content and heat flux in flows around hypersonic vehicles. To carry out such dynamics simulations efficiently requires accurate global potential energy surfaces and (in most algorithms) state couplings for many energetically accessible electronic states. The ability to treat collisions involving many coupled electronic states has been a challenge for decades. Very recently, a new diabatization method, the parametrically managed diabatization by deep neural network (PM-DDNN), has been developed. The PM-DDNN method uses a deep neural network architecture with an activation function parametrically dependent on input data to discover and fit the diabatic potential energy matrix (DPEM) as a function of geometry, and the adiabatic potential energy surfaces are obtained by diagonalization of a small matrix with analytic matrix elements. Here, we applied the PM-DDNN method to the six lowest-energy potential energy surfaces in the ⁵A' manifold of O₃ to perform simultaneous diabatization and fitting; the data are obtained by extended multistate complete-active-space second-order perturbation theory. We then used the adiabatic surfaces for dynamics calculations with three methods: coherent switching with decay of mixing (CSDM), curvature-driven CSDM (κCSDM), and electronically curvature-driven CSDM (eκCSDM). The κCSDM calculations require only adiabatic potential energies and gradients. The three dynamical methods are in good agreement. We then calculated electronically nonadiabatic, electronically inelastic, and dissociative cross sections for seven initial collision energies, five initial vibrational levels, and four initial rotational levels. Trends in the electronically inelastic cross sections as functions of the initial collision energy and vibrational level were rationalized in terms of the coordinate ranges where the gaps between the second and third potential energy surfaces are small.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Direct Nonadiabatic Dynamics of Ammonia with Curvature-Driven Coherent Switching with Decay of Mixing and with Fewest Switches with Time Uncertainty: An Illustration of Population Leaking in Trajectory Surface Hopping Due to Frustrated Hops

Mixed quantum-classical nonadiabatic dynamics is a widely used approach to simulate molecular dynamics involving multiple electronic states. There are two main categories of mixed quantum-classical nonadiabatic dynamics algorithms, namely, trajectory surface hopping (TSH) in which the trajectory propagates on a single potential energy surface, interrupted by hops, and self-consistent-potential (SCP) methods, such as semiclassical Ehrenfest, in which propagation occurs on a mean-field surface without hops. In this work, we will illustrate an example of severe population leaking in TSH. We emphasize that such leaking is a combined effect of frustrated hops and long-time simulations that drive the final excited-state population toward zero as a function of time. We further show that such leaking can be alleviated-but not eliminated-by the fewest switches with time uncertainty TSH algorithm (here implemented in the SHARC program); the time uncertainty algorithm slows down the leaking process by a factor of 4.1. The population leaking is not present in coherent switching with decay of mixing (CSDM), which is an SCP method with non-Markovian decoherence included. Another result in this paper is that we find very similar results with the original CSDM algorithm, with time-derivative CSDM (tCSDM), and with curvature-driven CSDM (κCSDM). Not only do we find good agreement for electronically nonadiabatic transition probabilities but also we find good agreement of the norms of the effective nonadiabatic couplings (NACs) that are derived from the curvature-driven time-derivative couplings as implemented in κCSDM with the time-dependent norms of the nonadiabatic coupling vectors computed by state-averaged complete-active-space self-consistent field theory.

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.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Effects of oxygen vacancies on the photoexcited carrier lifetime in rutile TiO2

The photoexcited carrier lifetime in semiconductors plays a crucial role in solar energy conversion processes. The defects or impurities in semiconductors are usually proposed to introduce electron-hole (e-h) recombination centers and consequently reduce the photoexcited carrier lifetime. In this report, we investigate the effects of oxygen vacancies (O_V) on the carrier lifetime in rutile TiO₂, which has important applications in photocatalysis and photovoltaics. It is found that an O_V introduces two excess electrons which form two defect states in the band gap. The lower state is localized on one Ti atom and behaves as a small polaron, and the higher one is a hybrid state contributed by three Ti atoms around the O_V. Both the polaron and hybrid states exhibit strong electron-phonon (e-ph) coupling and their charge distributions become more and more delocalized when the temperature increases from 100 to 700 K. Such strong e-ph coupling and charge delocalization enhance the nonadibatic coupling between the electronic states along the hole relaxation path, where the defect states behave as intermediate states, leading to a distinct acceleration of e-h recombination. Our study provides valuable insights to understand the role of defects on photoexcited carrier lifetime in semiconductors.

CAS without SCF-Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree-Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Finally, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

Nonadiabatic Effects on Defect Diffusion in Silicon-Doped Nanographenes

Single atom impurities in graphene, substitutional silicon defects in particular, have been observed to diffuse under electron beam irradiation. However, the relative importance of elastic and inelastic scattering in facilitating their mobility remains unclear. Here, we employ excited-state electronic structure calculations to explore potential inelastic effects, and find an electronically nonadiabatic excited-state silicon diffusion pathway involving "softened" Si-C bonding that presents an ∼2 eV lower diffusion barrier than the ground-state pathway. Beam-induced transition rates to this state indicate that the excited-state pathway is accessible through irradiation of the defect site. However, even in the limit of fully elastic scattering, upward nonadiabatic transitions are also possible along the diffusion coordinate, increasing the diffusion barrier and further demonstrating the potential for electronic nonadiabaticity to influence beam-induced atomic transformations in materials. We also propose some experimentally testable signatures of such excited-state pathways.

Biological Interfaces, Modulation, and Sensing with Inorganic Nano-Bioelectronic Materials

The last several years have seen a large and increasing interest in scientific developments that combine methods and materials from nanotechnology with questions and applications in bioelectronics. This follows with a number of broader trends: the rapid increase in functionality for materials at the nanoscale; a growing recognition of the importance of electric fields in diverse physiological processes; and continuous improvements in technologies that are naturally complementary with bioelectronics, such as optogenetics. Here, a progress report is provided on several of the most exciting recent developments in this field. The three critical functions of biointerface formation, biological modulation, and biological sensing using newly developed nanoscale materials are considered.

Suppression of Electron-Hole Recombination by Intrinsic Defects in 2D Monoelemental Material

The Shockley-Read-Hall (SRH) model, in which the deep trap defect states in the band gap are proposed as nonradiative electron-hole (e-h) recombination centers, has been widely used to describe the nonradiative e-h recombination through the defects in semiconductor. By using the ab initio nonadiabatic molecular dynamics method, we find that the SRH model fails to describe the e-h recombination behavior for defects in 2D monoelemental material such as monolayer black phosphorus (BP). Through the investigation of three intrinsic defects with shallow and deep defect states in monolayer BP, it is found that, surprisingly, none of these defects significantly accelerates the e-h recombination. Further analysis shows that because monolayer BP is a monoelemental material, the distinct impurity phonon, which often induces fast e-h recombination, is not formed. Moreover, because of the flexibility of 2D material, the defects scatter the phonons present in pristine BP, generating multiple modes with lower frequencies compared with the pristine BP, which further suppresses the e-h recombination. We propose that the conclusion can be extended to other monoelemental 2D materials, which is important guidance for the future design of functional semiconductors.

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.

A discontinuous basis enables numerically exact solution of the Schrödinger equation around conical intersections in the adiabatic representation

Solving the vibrational Schrödinger equation in the neighborhood of conical intersections in the adiabatic representation is a challenge. At the intersection point, first- and second-derivative nonadiabatic coupling matrix elements become singular, with the singularity in the second-derivative coupling (diagonal Born-Oppenheimer correction) being non-integrable. These singularities result from discontinuities in the vibronic functions associated with the individual adiabatic states, and our group has recently argued that these divergent matrix elements cancel when discontinuous adiabatic vibronic functions sum to a continuous total nonadiabatic wave function. Here we describe the realization of this concept: a novel scheme for the numerically exact solution of the Schrödinger equation in the adiabatic representation. Our approach is based on a basis containing functions that are discontinuous at the intersection point. We demonstrate that the individual adiabatic nuclear wave functions are themselves discontinuous at the intersection point. This proves that discontinuous basis functions are essential to any tractable method that solves the Schrödinger equation around conical intersections in the adiabatic representation with high numerical precision. We establish that our method provides numerically exact results by comparison to reference calculations performed in the diabatic representation. In addition, we quantify the energetic error associated with constraining the density to be zero at the intersection point, a natural approximation. Prospects for extending the present treatment of a two-dimensional model to systems of higher dimensionality are discussed.

Unraveling Photodimerization of Cyclohexasilane from Molecular Dynamics Studies

Photoinduced reactions of a pair of cyclohexasilane (CHS) monomers are explored by time-dependent excited-state molecular dynamics (TDESMD) calculations. In TDESMD trajectories, one observes vivid reaction events including dimerization and fragmentation. A general reaction pathway is identified as (i) ring-opening formation of a dimer, (ii) rearrangement induced by bond breaking, and (iii) decomposition through the elimination of small fragments. The identified pathway supports the chemistry proposed for the fabrication of silicon-based materials using CHS as a precursor. In addition, we find dimers have smaller HOMO-LUMO gaps and exhibit a red shift and line-width broadening in the computed photoluminescence spectra compared with a pair of CHS monomers.

Dynamics of recombination via conical intersection in a semiconductor nanocrystal

Conical intersections are well known to introduce nonradiative decay pathways in molecules, but have only recently been implicated in nonradiative recombination processes in materials. Here we apply excited state ab initio molecular dynamics simulations based on a multireference description of the electronic structure to defective silicon nanocrystals up to 1.7 nm in diameter to search for accessible nonradiative recombination pathways. Dangling bond defects are found to induce conical intersections between the ground and first excited electronic states of five systems of various sizes. These defect-induced conical intersections are accessible at energies that are in the visible range (2.4-2.7 eV) and very weakly dependent on particle size. The dynamic simulations suggest that these intersections are accessed 40-60 fs after creation of a defect-localized excitation. This ultrafast recombination is attributed to the fact that Jahn-Teller distortion on the first excited state drives the defect directly towards a conical intersection with the ground electronic state.