Nonadiabatic Quantum Dynamics Research Articles

Non-adiabatic direct quantum dynamics using force fields: Toward solvation.

Quantum dynamics simulations are becoming a powerful tool for understanding photo-excited molecules. Their poor scaling, however, means that it is hard to study molecules with more than a few atoms accurately, and a major challenge at the moment is the inclusion of the molecular environment. Here, we present a proof of principle for a way to break the two bottlenecks preventing large but accurate simulations. First, the problem of providing the potential energy surfaces for a general system is addressed by parameterizing a standard force field to reproduce the potential surfaces of the molecule's excited-states, including the all-important vibronic coupling. While not shown here, this would trivially enable the use of an explicit solvent. Second, to help the scaling of the nuclear dynamics propagation, a hierarchy of approximations is introduced to the variational multi-configurational Gaussian method that retains the variational quantum wavepacket description of the key quantum degrees of freedom and uses classical trajectories for the remaining in a quantum mechanics/molecular mechanics like approach. The method is referred to as force field quantum dynamics (FF-QD), and a two-state ππ*/nπ* model of uracil, excited to its lowest bright ππ* state, is used as a test case.

Prolonged Exciton Lifetime Is Achieved in Porphyrin Nanoring by Template Engineering: A Nonadiabatic Tight Binding Approach.

Porphyrin nanoring has been attracting immense attention due to its light harvesting capacity and potential applications in optical, catalysis, sensor, and electronic devices. We demonstrate by nonadiabatic quantum dynamics simulations that the photovoltaic efficiency can be enhanced by template engineering. Altering the hexadentate template (T6) with two tridentate templates (2T3) within the porphyrin ring (P6) cavity accelerated the electron transfer twice and suppressed the electron-hole recombination by nearly three times. The atomistic tight-binding simulation rationalized the dynamics by different localizations of charge of the band edge states, changes in nonadiabatic coupling, alteration in quantum coherence, and involvement of diverse electron-phonon vibrational modes. Further 2T3 templates more strongly hold the P6 ring than T6, reducing the structural fluctuation. As a result, the nonadiabatic coupling becomes weaker and suppresses the carrier recombination. Current atomistic simulation presents a template engineering strategy to enhance the exciton lifetime along with ultrafast charge separation, crucial factors for photovoltaic applications.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using abinitio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.

Visualizing non-adiabatic quantum dynamics and photo-excitation processes on Excel

We offer two Excel modules that students can use to view the real-time spatial evolution of a diatomic molecule's nuclei when two different potential energy curves governing the nucleus motion spatially cross one another or are coupled by a light field. Module 1 comprises three spreadsheets that can be used to view non-adiabatic nuclear dynamics on two crossing nuclear potential energy curves. These curves cross because there is a value of the spatial coordinate where the two curves have the same energy, which results in a non-zero probability of the probability density crossing from one potential curve to the other. Students can view non-adiabatic nuclear dynamics involving two unbounded nuclear potential curves, pre-dissociation with a bound “ionic state” to an unbound covalent state, and quantum tunneling dynamics between two bounded potential curves. Module 2 comprises two spreadsheets that can be used to view the dynamics of the photo-excitation process, i.e., where the absorption of light leads to transitions between two nuclear potentials. Students can model the light-induced transitions between nuclear potentials when the light is provided by both a continuous wave laser and a pulsed laser. These modules are included as the supplementary material and can be run on any computer that supports Excel.

Quantum simulation of conical intersections.

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

The Lack of Triplet Fusion for an Intramolecular Singlet Fission Chromophore: The Expected, the Unexpected, and a Reconciliation.

Singlet fission (SF) has the potential to play a key role in photovoltaics since it generates a larger number of longer-lived triplet excitons after photoabsorption. Intramolecular SF (iSF) is of special interest since it enables tuning of SF efficiency by adjusting interchromophore configuration through covalent interaction. However, as elaborated in the present work, iSF chromophores are doomed to dissatisfy one general thermodynamic criterion for all SF chromophores, intramolecular or not: E(T2) ≥ 2E(T1), and therefore, the fusion of two triplet excitons to one triplet exciton is thermodynamically favorable. In our nonadiabatic quantum dynamics simulation for a model iSF chromophore, this expected fusion does not occur, because of the inefficient intersystem crossing hidden under the cover of internal conversion of the triplet fusion. A reconciliation is achieved between the dissatisfaction of E(T2) ≥ 2E(T1) and the large tetraradical character for general iSF chromophores.

Nuclear-Electronic Orbital Quantum Dynamics of Plasmon-Driven H2 Photodissociation.

Leveraging localized surface plasmon resonances of metal nanoparticles to trigger chemical reactions is a promising approach for heterogeneous catalysis. First-principles modeling of such processes is challenging due to the large number of electrons and electronic excited states as well as the significance of nuclear quantum effects when hydrogen is involved. Herein, the nonadiabatic nuclear-electronic quantum dynamics of plasmon-induced H2 photodissociation near an Al13- cluster is simulated with real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT). This approach propagates the nonequilibrium quantum dynamics of both electrons and protons. The plasmonic oscillations are shown to inject hot electrons into the antibonding orbital of H2, thereby inducing H2 dissociation. The quantum mechanical treatment of the hydrogen nuclei leads to faster H2 photodissociation and slightly larger isotope effects. Analysis of the nonequilibrium electronic density suggests that these findings stem from enhanced excited-state electronic coupling between the plasmonic mode and the H2 antibonding orbital due to proton delocalization or zero-point energy effects. Given the low computational overhead for including nuclear quantum effects with the RT-NEO-TDDFT approach, this work paves the way for simulating nonadiabatic nuclear-electronic quantum dynamics in other plasmonic systems.

Nonradiative Dynamics Induced by Vacancies in Wide-Gap III-Nitrides: Ab Initio Time-Domain Analysis.

Insightful understanding of defect properties and prevention of defect damage are among the biggest issues in the development of photoelectronic devices based on wide-gap III-nitride semiconductors. Here, we have investigated the vacancy-induced carrier nonradiative dynamics in wide-gap III-nitrides (GaN, AlN, and AlxGa1-xN) by ab initio molecular dynamics and nonadiabatic (NA) quantum dynamics simulations since the considerable defect density in epitaxy samples. E-h recombination is hardly affected by Vcation, which created shallow states near the VBM. Our findings demonstrate that VN in AlN creates defect-assisted nonradiative recombination centers and shortens the recombination time (τ) as in the Shockley-Read-Hall (SRH) model. In GaN, VN improves the NA coupling between the CBM and the VBM. Additionally, increasing x in the AlxGa1-xN alloys accelerates nonradiative recombination, which may be an important issue in further improving the IQE of high Al-content AlxGa1-xN alloys. These findings have significant implications for the improvement of wide-gap III-nitrides-based photoelectronic devices.

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

We develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

Spin-vibronic mechanism at work in a luminescent square-planar cyclometalated tridentate Pt(II) complex: absorption and ultrafast photophysics.

The absorption spectrum of [Pt(dpybMe)Cl] (dpyb = 2,6-di-(2-pyridyl)benzene), representative of luminescent halide-substituted tridentate cyclometalated square planar Pt(II) neutral complexes, has been revisited by means of non-adiabatic wavepacket quantum dynamics. The early photophysics has been investigated on the basis of four singlet and five triplet excited states, namely nineteen "spin-orbit states", coupled with both vibronic and spin-orbit couplings, and includes eighteen normal modes. It is shown that in-plane scissoring and rocking normal modes of the cyclometalated tridentate ligand are responsible for the vibronic structure observed at around 400 nm in the experimental spectrum of the complex. The ultrafast decay of [Pt(dpybMe)Cl], within 1 ps, follows a spin-vibronic mechanism governed by excited state electronic characters, spin-orbit, and active tuning mode interplay. Both spin-orbit coupling and Pt(II) coordination sphere stretching modes and in-plane scissoring/rocking of the cyclometalated ligand activate the ultrafast decay within 20 fs of absorption. At longer time-scales (>100 fs) an asynchronous stretching of the Pt-C and Pt-N bonds activates the depopulation of the upper "reservoir" electronic states to populate the two lowest luminescent T1 and T2 electronic states. The in-plane rocking motion of the ligand controls the T1/T2 population exchange which is equilibrated at about 1 ps. Stabilization of the upper non-radiative metal-centered (MC) states by out-of-plane ligand distortion of low frequency is not competitive with the ultrafast spin-vibronic mechanism discovered here for [Pt(dpybMe)Cl]. Modifying the Pt-C covalent bond position and rigidifying the cyclometalated ligand will have a dramatic influence on the spin-vibronic mechanism and consequently on the luminescence properties of this class of molecules.

Nonadiabatic quantum dynamics of the charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+).

Nonadiabatic quantum dynamics of the charge transfer (CT) reaction H+ + NO(X2Π) → H + NO+(X1Σ+) is investigated on a new diabatic potential energy matrix (PEM) including the 12A' and 22A' states of HNO+/HON+ at the multireference configuration interaction level with Davidson correction using a large basis set. The diabatization of the two coupled states was achieved by the adiabatic-to-diabatic transformation with a mixing angle and the final diabatic PEM was obtained by fitting each matrix element separately using a three-dimensional cubic spline interpolation including more than 22 000 ab initio points. The reaction was found to be dominated by the resonances supported by the double well associated with HNO+ and HON+ species, manifested by the oscillatory structures in the reaction probabilities and product rotational distributions. The product vibrational states were highly excited due to the large exothermicity of the reaction. Consistent with the complex-forming mechanism, the differential cross sections (DCSs) were found to be dominated by the forward and backward scatterings. A clear forward bias in the vibrational state resolved DCSs suggests that the non-statistical behavior of the reaction mainly comes from the low vibrational states of the product. In addition, the rate constants of the reaction in the temperature range from 50 to 500 K were computed for the first time and found to be in fairly good agreement with the available experimental results at 300 K. In particular, compared to other reactions involving neutral species in this system including N, O, and H atoms, such a CT reaction was found to be much more reactive, which has rate constants more than thirty times larger.

Quasiclassical approaches to the generalized quantum master equation.

The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin-boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite.

Efficient Frozen Gaussian Sampling algorithms for nonadiabatic quantum dynamics at metal surfaces

In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm for simulating nonadiabatic quantum dynamics at metal surfaces with a continuous spectrum. This method consists of a Monte-Carlo algorithm for sampling the initial wave packets on the phase space and a surface-hopping type stochastic time propagation scheme for the wave packets. We prove that to reach a certain accuracy threshold, the sample size required is independent of both the semiclassical parameter ε and the number of metal orbitals N, which makes it one of the most promising methods to study the nonadiabatic dynamics. The algorithm and its convergence properties are also validated numerically. Furthermore, we carry out numerical experiments including exploring the nuclei dynamics, electron transfer and finite-temperature effects, and demonstrate that our method captures the physics which can not be captured by classical surface hopping trajectories.

Non-adiabatic mapping dynamics in the phase space of the SU(N) Lie group.

We present the rigorous theoretical framework of the generalized spin mapping representation for non-adiabatic dynamics. Our work is based upon a new mapping formalism recently introduced by Runeson and Richardson [J. Chem. Phys. 152, 084110 (2020)], which uses the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space. Following this interesting idea, the Stratonovich-Weyl transform is used to map an operator in the Hilbert space to a continuous function on the SU(N) Lie group, i.e., a smooth manifold which is a phase space of continuous variables. We further use the Wigner representation to describe the nuclear degrees of freedom and derive an exact expression of the time-correlation function as well as the exact quantum Liouvillian for the non-adiabatic system. Making the linearization approximation, this exact Liouvillian is reduced to the Liouvillian of several recently proposed methods, and the performance of this linearized method is tested using non-adiabatic models. We envision that the theoretical work presented here provides a rigorous and unified framework to formally derive non-adiabatic quantum dynamics approaches with continuous variables and connects the previous methods in a clear and concise manner.

Dynamical free energy based model for quantum decision making

We propose a quantum-mechanical framework to describe the dynamics of human decision making, where the interactions between the open quantum system of decision makers and its surrounding environment at given temperature are relevantly taken into account. The temporal evolution of quantum system is described in terms of the time-dependent density matrix, from which we can evaluate those thermodynamic functions such as internal energy, (von Neumann) entropy and (Helmholtz) free energy. In this study we rely on the symmetrical quasi-classical (SQC) windowing approach to numerically solve the non-adiabatic quantum dynamics. We then consider the Hamiltonians to formulate the Prisoner’s Dilemma (PD) problem and calculate the population dynamics of the quantum states of two players’ decisions, where some quantum coherence or interference effects are observed. The evaluated free energy tends to decrease toward the thermodynamic equilibrium value, thus driving the dynamics of quantum system between the Nash equilibrium and Pareto optimum states. The calculated entropy often shows a tendency of temporal decrease, thus indicating the emergence of order in the quantum system. We have also applied the present scheme to the issue of the violation of the sure thing principle and found its occurrence through explicit numerical simulations for the PD problem. The present study may provide a theoretical basis to connect the dynamics of quantum decision making to the free energy principle in cognitive science.

One-Shot Trajectory Learning of Open Quantum Systems Dynamics.

Nonadiabatic quantum dynamics is important for understanding light-harvesting processes, but its propagation with traditional methods can be rather expensive. Here we present a one-shot trajectory learning approach that allows us to directly make an ultrafast prediction of the entire trajectory of the reduced density matrix for a new set of such simulation parameters as temperature and reorganization energy. The whole 10-ps-long propagation takes 70 ms as we demonstrate on the comparatively large quantum system, the Fenna-Matthews-Olsen (FMO) complex. Our approach also significantly reduces time and memory requirements for training.

Tunneling dynamics of an oscillating universe model

Quasiclassical methods for non-adiabatic quantum dynamics can reveal new features of quantum effects, such as tunneling evolution, that are harder to analyze in standard treatments based on wave functions of stationary states. Here, these methods are applied to an oscillating universe model introduced recently. Our quasiclassical treatment correctly describes several expected features of tunneling states, in particular just before and after tunneling into a trapped region where a model universe may oscillate through many cycles of collapse and expansion. As a new result, the oscillating dynamics is found to be much less regular than in the classical description, revealing a succession of cycles with varying maximal volume even when the matter ingredients and their parameters do not change.

Non-adiabatic quantum dynamics of tribovoltaic effects at sliding metal–semiconductor interfaces

Recent experiments observe electric current generation at sliding metal–semiconductor interfaces. Here, we present a detailed theoretical study on how electric voltage is generated at such a sliding interface. Our study is based on a two-band Anderson–Holstein model, where we solve the coupled electron–phonon dynamics using a surface hopping method. We show that the high local temperature induced by mechanical motion at the interfaces can lead to electron–hole pair generation through electron–phonon couplings. We quantify the efficiency of electron–hole generation as well as electric voltage as a function of local temperatures and semiconductor bandgaps. We find that increasing the local temperatures can lead to higher electron–hole generation and electric voltage. Furthermore, we find that there is a turnover for the electric voltage as a function of the bandgap. Such an observation is in agreement with the experimental results. Our study offers a theoretical framework to understand tribovoltaic effects from a quantum mechanical point of view, and our approach can be used to quantitatively simulate realistic sliding metal–semiconductor junctions.

A Photochemical Reaction in Different Theoretical Representations

The Born–Oppenheimer picture has forged our representation and interpretation of photochemical processes, from photoexcitation down to the passage through a conical intersection, a funnel connecting different electronic states. In this work, we analyze a full in silico photochemical experiment, from the explicit electronic excitation by a laser pulse to the formation of photoproducts following a nonradiative decay through a conical intersection, by contrasting the picture offered by Born–Oppenheimer and that proposed by the exact factorization. The exact factorization offers an alternative understanding of photochemistry that does not rely on concepts such as electronic states, nonadiabatic couplings, and conical intersections. On the basis of nonadiabatic quantum dynamics performed for a two-state 2D model system, this work allows us to compare Born–Oppenheimer and exact factorization for (i) an explicit photoexcitation with and without the Condon approximation, (ii) the passage of a nuclear wavepacket through a conical intersection, (iii) the formation of excited stationary states in the Franck–Condon region, and (iv) the use of classical and quantum trajectories in the exact factorization picture to capture nonadiabatic processes triggered by a laser pulse.

Universal nonadiabatic energy pumping in a quasiperiodically driven extended system

The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower dimensional time-dependent system maps into a higher dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Different than most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one dimensional chain driven by two frequencies, which maps into a gapless Weyl semimetal in synthetic dimension. Based on analytical reasoning and numerical simulations, we found the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically found such behaviors are robust against a considerable amount of spatial disorder.