Vibronic Research Articles

Spin-Orbit-Lattice Entangled State in A_{2}MgReO_{6} (A=Ca, Sr, Ba) Revealed by Resonant Inelastic X-Ray Scattering.

The 5d^{1} ordered double perovskites present an exotic playground for studying novel multipolar physics due to large spin-orbit coupling. We present Re L_{3} edge resonant inelastic x-ray scattering (RIXS) results that reveal the presence of the dynamic Jahn-Teller effect in the A_{2}MgReO_{6} (A=Ca, Sr, Ba) family of 5d^{1} double perovskites. The spin-orbit excitations in these materials show a strongly asymmetric line shape and exhibit substantial temperature dependence, indicating that they are dressed with lattice vibrations. Our experimental results are explained quantitatively through a RIXS calculation based on a spin-orbit-lattice entangled electronic ground state with the dynamic Jahn-Teller effect taken into consideration. We find that the spin-orbit-lattice entangled state is robust against magnetic and structural phase transitions as well as against significant static Jahn-Teller distortions. Our results illustrate the importance of including vibronic coupling for a complete description of the ground state physics of 5d^{1} double perovskites.

Constant-roll inflation with non-minimally derivative coupling

We investigate the constant-roll inflation with non-minimally kinetic coupling to the Einstein tensor. With the slow-roll parameter ηϕ=−ϕ̈/(Hϕ̇) being a constant, we calculate the power spectra for scalar and tensor perturbations, and derive the expressions for the scalar spectral tilt n s , the tensor spectral tilt n T , and the tensor-to-scalar ratio r. We find that the expressions for n s are different with different ordering of taking the derivative of the scalar power spectrum with respect to the scale k and the horizon crossing condition c s k = aH in the constant-roll inflation, the consistency relation r = − 8n T does not hold if ∣η ϕ ∣ is not small, and the duality of the tensor-to-scalar ratio between the slow-roll inflation and ultra-slow-roll inflation does not exist in inflationary models with non-minimally derivative coupling. The result offers a fresh perspective on the understanding of the inflationary models with non-minimally derivative coupling and is helpful for the production of scalar induced gravitational waves in the framework of ultra-slow-roll inflation with non-minimally derivative coupling.

Theory for proton-coupled energy transfer.

In the recently discovered proton-coupled energy transfer (PCEnT) mechanism, the transfer of electronic excitation energy between donor and acceptor chromophores is coupled to a proton transfer reaction. Herein, we develop a general theory for PCEnT and derive an analytical expression for the nonadiabatic PCEnT rate constant. This theory treats the transferring hydrogen nucleus quantum mechanically and describes the PCEnT process in terms of nonadiabatic transitions between reactant and product electron-proton vibronic states. The rate constant is expressed as a summation over these vibronic states, and the contribution of each pair of vibronic states depends on the square of the vibronic coupling as well as the spectral convolution integral, which can be viewed as a generalization of the Förster-type spectral overlap integral for vibronic rather than electronic states. The convolution integral also accounts for the common vibrational modes shared by the donor and acceptor chromophores for intramolecular PCEnT. We apply this theory to model systems to investigate the key features of PCEnT processes. The excited vibronic states can contribute significantly to the total PCEnT rate constant, and the common modes can either slow down or speed up the process. Because the pairs of vibronic states that contribute the most to the PCEnT rate constant may correspond to spectroscopically dark states, PCEnT could occur even when there is no apparent overlap between the donor emission and acceptor absorption spectra. This theory will assist in the interpretation of experimental data and will guide the design of additional PCEnT systems.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics.

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Simulation and interpretation of zinc and nitrogen dopants induced defect emissions in monoclinic gallium oxide

Zinc (Zn) and nitrogen (N) are potential acceptor dopants for inducing visible emissions and p-type conductivity in monoclinic gallium oxide (β-Ga2O3), however, the poor understanding of these dopants and their recombination process severely limited the optoelectronic applications. Here, we investigate the zinc (Zn) and nitrogen (N) dopants-induced intraband states and the broadening of defect emission bands due to vibronic coupling of highly transparent β-Ga2O3 films through chemical and optical analyses, as well as density function theory. Incorporating Zn and N in β-Ga2O3 shifts the valence band edge towards the Fermi level and introduces band tail states above the valence band maximum. The emission band from pure β-Ga2O3 becomes significantly broad with the incorporation of Zn and N resulting in two additional emission bands: green luminescence (GL) and red luminescence (RL) along with the characteristic ultraviolet luminescence (UVL) and blue luminescence (BL) of pristine β-Ga2O3. Furthermore, the defect states responsible for these UVL, BL, GL, and RL emissions and their phonon coupling strengths are estimated by simulating the spectral line shape of these emission bands using the configuration coordinate model. The simulation results indicate that the Zn and N dopants-induced intraband states are responsible for the GL, and RL bands. These intraband states are acceptors, which provide p-type conductivity in β-Ga2O3 film.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface.

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

Low spin solutions of higher spin gravity: BPST instanton

Higher spin gravities do not have a low energy limit where higher-spin fields decouple from gravity. Nevertheless, it is possible to construct fine-tuned exact solutions that activate low-spin fields without sourcing the higher-spin fields. We show that BPST (Belavin-Polyakov-Schwartz-Tyupkin) instanton is an exact solution of Chiral Higher Spin Gravity, i.e. it is also a solution of the holographic dual of Chern-Simons matter theories. This gives an example of a low-spin solution. The instanton sources the opposite helicity spin-one field and a scalar field. We derive an Effective Field Theory that describes the coupling between an instanton and the other two fields, whose action starts with the Chalmers-Siegel action and has certain higher derivative couplings.

Inter-Oligomer Interaction Influence on Photoluminescence in Cis-Polyacetylene Semiconductor Materials.

Semiconducting conjugated polymers (CPs) are pivotal in advancing organic electronics, offering tunable properties for solar cells and field-effect transistors. Here, we carry out first-principle calculations to study individual cis-polyacetylene (cis-PA) oligomers and their ensembles. The ground electronic structures are obtained using density functional theory (DFT), and excited state dynamics are explored by computing nonadiabatic couplings (NACs) between electronic and nuclear degrees of freedom. We compute the nonradiative relaxation of charge carriers and photoluminescence (PL) using the Redfield theory. Our findings show that electrons relax faster than holes. The ensemble of oligomers shows faster relaxation compared to the single oligomer. The calculated PL spectra show features from both interband and intraband transitions. The ensemble shows broader line widths, redshift of transition energies, and lower intensities compared to the single oligomer. This comparative study suggests that the dispersion forces and orbital hybridizations between chains are the leading contributors to the variation in PL. It provides insights into the fundamental behaviors of CPs and the molecular-level understanding for the design of more efficient optoelectronic devices.

Modeling of collision-induced excitation and quenching of atomic nitrogen

Excited atomic nitrogen atoms play an important role in plasma formation in hypersonic shock-waves, as happens during spacecraft reentry and other high velocity vehicle applications. In this study, we have thoroughly studied collision induced excitation associated with two colliding nitrogen atoms in the N(4S), N(2D), and N(2P) states at collision energies up to 6 eV, using time-independent scattering calculations to determine cross sections and temperature-dependent rate coefficients. The calculations are based on potential curves and couplings determined in earlier multireference configuration interaction calculations with large basis sets, and the results are in good agreement with experiments where comparisons are possible. To properly consider the spin–orbit coupling matrix, we have developed a scaling method for treating transitions between different fine-structure components that only require calculations with two coupled states, and with this, we define accurate degeneracy factors for determining cross sections and rate coefficients that include all states. The results indicate that both spin–orbit and derivative coupling effects can play important roles in collisional excitation and quenching, and that although derivative coupling is always much stronger than spin–orbit, there are many transitions where only spin–orbit can contribute. As part of this, we identify two distinct pathways associated with N(2P) relaxation and one Auger-like mechanism leading to two N(2D) that could be important at high temperatures.

Gravity with spacetime torsion

The duality between a higher-curvature f(R) gravity model and a scalar-tensor theory helps to bring out the role of the additional degree of freedom originating from the higher-derivative terms in the gravity action. Such a degree of freedom which appears as a scalar field has been shown to have multiple implications in the cosmological/astrophysical scenario. The present work proposes a novel generalization to this correspondence between f(R) gravity and a dual scalar-tensor theory when the affine connection is considered to have an antisymmetric part. It turns out that the f(R) action in the presence of spacetime torsion can be recast to a coupled scalar-tensor theory with a 2-rank massless antisymmetric tensor field in the Einstein frame, where the scalar field gets coupled with the antisymmetric field through derivative coupling(s).

Vibrational Electronic-Thermofield Coupled Cluster (VE-TFCC) Theory for Quantum Simulations of Vibronic Coupling Systems at Thermal Equilibrium.

A vibrational electronic-thermofield coupled cluster (VE-TFCC) approach is developed to calculate thermal properties of non-adiabatic vibronic coupling systems. The thermofield (TF) theory and a mixed linear exponential ansatz based on second-quantized Bosonic construction operators are introduced to propagate the thermal density operator as a "pure state" in the Bogoliubov representation. Through this compact representation of the thermal density operator, the approach is basis-set-free and scales classically (polynomial) as the number of degrees of freedoms (DoF) in the system increases. The VE-TFCC approach is benchmarked with small test models and a real molecular compound (CoF4- anion) against the conventional sum over states (SOS) method and applied to calculate thermochemistry properties of a gas-phase reaction: CoF3 + F- → CoF4-. Results shows that the VE-TFCC approach, in conjunction with vibronic models, provides an effective protocol for calculating thermodynamic properties of vibronic coupling systems.

Healthy Horndeski cosmologies with torsion

We show that the full Horndeski theory with both curvature and torsion can support nonsingular, stable and subluminal cosmological solutions at all times. Thus, with torsion, the usual No-Go theorem that holds in a curved spacetime is avoided. In particular, it is essential to include the nonminimal derivative couplings of the ℒ5 part of the Horndeski action (Gμν ∇ μ ∇ νϕ, and (∇2 ϕ)3). Without the latter a No-Go already impedes the eternal subluminality of nonsingular, stable cosmologies.

Generalized second law for non-minimally coupled matter theories

We establish the generalized second law (GSL) within the framework of higher curvature gravity theories, considering non-minimal couplings in the matter sector. Our proof pertains to the regime of linearized fluctuations around equilibrium black holes, aligning with previous works by Wall and Sarkar. Notably, while prior proofs addressed various gravity theories such as Lovelock theory and higher curvature gravity, they uniformly assumed minimally coupled matter sectors. In this work, we extend the proof of the linearized semi-classical GSL to encompass scenarios involving non-minimal couplings in the matter sector. Our approach involves a proposal for evaluation of the matter path integral in the expectation value of the stress tensor, adopting an effective field theory treatment for the higher derivative couplings. We leverage the recently established outcome regarding the linearized second law in such theories to substantiate our argument.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory.

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Detailed Complementary Consistency: Wave Function Tells Particle How to Hop, Particle Tells Wave Function How to Collapse.

In mixed quantum-classical dynamics, the quantum subsystem can have both wave function and particle-like descriptions. However, they may yield inconsistent results for the expectation value of the same physical quantity. We here propose a novel detailed complementary consistency (DCC) method based on the principle of detailed internal consistency. Namely, the wave function along each trajectory tells the particle how to hop, while the particle tells the wave function how to collapse based on active states in the trajectory ensemble. As benchmarked in a diverse array of representative models with localized nonadiabatic couplings, DCC not only achieves fully consistent results (i.e., identical populations calculated based on wave functions and active states) but also closely reproduces the exact quantum results. Due to the high performance, our new DCC method has great potential to give a consistent and accurate mixed quantum-classical description of general nonadiabatic dynamics after further development.

Light harvesting in purple bacteria does not rely on resonance fine-tuning in peripheral antenna complexes

The ring-like peripheral light-harvesting complex 2 (LH2) expressed by many phototrophic purple bacteria is a popular model system in biological light-harvesting research due to its robustness, small size, and known crystal structure. Furthermore, the availability of structural variants with distinct electronic structures and optical properties has made this group of light harvesters an attractive testing ground for studies of structure–function relationships in biological systems. LH2 is one of several pigment-protein complexes for which a link between functionality and effects such as excitonic coherence and vibronic coupling has been proposed. While a direct connection has not yet been demonstrated, many such interactions are highly sensitive to resonance conditions, and a dependence of intra-complex dynamics on detailed electronic structure might be expected. To gauge the sensitivity of energy-level structure and relaxation dynamics to naturally occurring structural changes, we compare the photo-induced dynamics in two structurally distinct LH2 variants. Using polarization-controlled 2D electronic spectroscopy at cryogenic temperatures, we directly access information on dynamic and static disorder in the complexes. The simultaneous optimal spectral and temporal resolution of these experiments further allows us to characterize the ultrafast energy relaxation, including exciton transport within the complexes. Despite the variations in PPC molecular structure manifesting as clear differences in electronic structure and disorder, the energy-transport and—relaxation dynamics remain remarkably similar. This indicates that the light-harvesting functionality of purple bacteria within a single LH2 complex is highly robust to structural perturbations and likely does not rely on finely tuned electronic- or electron-vibrational resonance conditions.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7–2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8–14 ps, with a significantly inhibited ground state recovery.

Energy-Conserving Surface Hopping for Auger Processes.

Auger-type processes are ubiquitous in nanoscale materials because quantum confinement enhances Coulomb interactions, and there exist large densities of states. Modeling Auger processes requires the modification of nonadiabatic (NA) molecular dynamics algorithms to include transitions caused by both NA and Coulomb couplings. The system is split into quantum and classical subsystems, e.g., electrons and vibrations, and as a result, energy conservation becomes nontrivial. In surface hopping, an electronic transition induced by NA coupling is accompanied by a classical velocity readjustment to ensure conservation of the total quantum-classical energy. A different treatment is needed for Auger transitions driven by Coulomb interactions. We develop a nonadiabatic molecular dynamics methodology that meticulously differentiates the energy redistribution accompanying hops induced by the NA coupling and the Coulomb interaction and correctly conserves the total energy at each transition. If the transition is driven by a Coulomb interaction, the hop energy is redistributed within the quantum electronic subsystem only. If the transition is NA, the energy is redistributed between the quantum and classical subsystems. Properly maintaining energy conservation for both types of transitions is crucial to generate a correct order of events, obtain accurate transition times, maintain a proper statistical distribution of state populations, and reach thermodynamic equilibrium. We test the method with biexciton annihilation and Auger-assisted hot electron relaxation in a CdSe quantum dot. The sequence of Auger and phonon-driven processes and the calculated time scales are in excellent agreement with the experimental results. The developed approach can be coupled with any surface-hopping method and provides a crucial practical advance to study charge-carrier dynamics in the nanoscale and condensed matter systems.

Optimizing Conical Intersections without Explicit Use of Non-Adiabatic Couplings.

We present two alternative methods for optimizing minimum energy conical intersection (MECI) molecular geometries without knowledge of the derivative coupling (DC). These methods are based on the utilization of Lagrange multipliers: (i) one method uses an approximate calculation of the DC, while the other (ii) do not require the DC. Both methods use the fact that information on the DC is contained in the Hessian of the squared energy difference. Tests done on a set of small molecular systems, in comparison with other methods, show the ability of the proposed methods to optimize MECIs. Finally, we apply the methods to the furimamide molecule, to optimize and characterize its S1/S2 MECI, and to optimizing the S0/S1 MECI of the silver trimer.

An Effective Model for Capturing the Role of Excitonic Interactions in the Wave-Packet Dynamics of DNA Nucleobases

Investigating exciton dynamics within DNA nucleobases is essential for comprehensively understanding how inherent photostability mechanisms function at the molecular level, particularly in the context of life’s resilience to solar radiation. In this paper, we introduce a mathematical model that effectively simulates the photoexcitation and deactivation dynamics of nucleobases within an ultrafast timeframe, particularly focusing on wave-packet dynamics under conditions of strong nonadiabatic coupling. Employing the hierarchy equation of motion, we simulate two-dimensional electronic spectra (2DES) and calibrate our model by comparing it with experimentally obtained spectra. This study also explores the effects of base stacking on the photo-deactivation dynamics in DNA. Our results demonstrate that, while strong excitonic interactions between nucleobases are present, they have a minimal impact on the deactivation dynamics of the wave packet in the electronic excited states. We further observe that the longevity of electronic excited states increases with additional base stacking and pairing, a phenomenon accurately depicted by our excitonic model. This model enables a detailed examination of the wave packet’s motion on electronic excited states and its rapid transition to the ground state. Additionally, using this model, we studied base stacks in DNA hairpins to effectively capture the primary exciton dynamics at a reasonable computational scale. Overall, this work provides a valuable framework for studying exciton dynamics from single nucleobases to complex structures such as DNA hairpins.