Simulating passage through a cascade of conical intersections with collapse-to-a-block molecular dynamics

Trajectory surface hopping (TSH) methods have been widely used for the study of nonadiabatic molecular dynamics. In the present work, the accuracy of two TSH algorithms, Tully's fewest switching algorithm and an algorithm based on the Landau-Zener formula, has been critically evaluated in comparison with exact nonadiabatic quantum dynamics calculations for a model of the photoinduced hydrogen-atom dissociation reaction in phenol. The model consists of three electronic states (S0, 1ππ*, 1πσ*) and two nuclear degrees of freedom (the OH stretching coordinate and CCOH dihedral angle) and displays two successive conical intersections (1ππ*/1πσ* and 1πσ*/S0). Considering instantaneous photoexcitation from different vibrational levels of the S0 state to the 1ππ* state, we examined the time-dependent electronic population dynamics as well as the branching ratio of the two dissociation channels. The results of fully converged trajectory calculations are compared with the results of exact quantum wave-packet calculations. It is found that both TSH algorithms describe the dynamics at the 1πσ*/S0 conical intersection, which is accessed with high excess energy, with good accuracy. The 1ππ*/1πσ* conical intersection, on the other hand, is accessed with little excess energy so tunneling effects as well as wave-packet interference effects which cannot be reproduced with classical trajectory calculations become relevant. Overall, the performance of the fewest-switching and Landau-Zener surface-hopping algorithms for the photodissociation of phenol is very similar. The populations of the adiabatic S1 and S2 states are found to exhibit fast oscillations which reflect nonadiabatic electronic transitions driven by coherent dynamics in the OH stretching mode. These electronic population oscillations are qualitatively reproduced by both TSH algorithms.

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.

The mixed quantum-classical (MQC) molecular dynamics (MD) approaches are extremely important in practice since, with the increase of atomic degrees of freedom, a full quantum mechanical evaluation for molecular dynamics would quickly become intractable. Moreover, in some cases, the nonadiabatic effects are of crucial importance in the proximity of conical intersection of potential energy surfaces (PESs), where the energy separation between different PESs becomes comparable to the nonadiabatic coupling. In the past decades, there has been great interest in developing and improving various nonadiabatic MQC-MD protocols. The widely known nonadiabatic MD proposals include the so-called Ehrenfest or time-dependent-Hartree mean-field approach, the trajectory surface-hopping method, and their mixed scheme. Among the trajectory-based surface hopping methods, the most popular one is Tully's fewest switches surface hopping approach. In this approach, the nonadiabatic dynamics is treated by allowing hops from one PES to another, with the hopping probability determined by a certain artificial hopping algorithm. In our present work, we extend the study of a recent work on the nonadiabatic MQC-MD scheme, which is based on a view that the nonadiabatic MQC-MD actually implies an effective quantum measurement on the electronic states by the classical motion of atoms. The new protocol, say, the quantum trajectory (QT) approach, provides a natural interface between the separate quantum and classical treatments, without invoking artificial surface hopping algorithm. Moreover, it also connects two widely adopted nonadiabatic dynamics methods, the Ehrenfest mean-field theory and the trajectory surface-hopping method. In our present study, we implement further the QT approach to simulate several typical potential-surface models, i.e., including the single avoided crossing, dual avoided crossing, extended coupling, dumbbell and double arch potentials. In particular, we simulate and compare three decoherence rates, which are from different physical considerations, i.e., the frozen Gaussian approximation, energy discrimination and force discrimination. We also design simulation algorithms to properly account for the energy conservation and force direction change associated with the surface hopping. In most cases, we find that the QT results are in good agreement with those from the full quantum dynamics, which is insensitive to the specific form of the decoherence rate. But for the model involving strong quantum interference, like other nonadiabatic MQC-MD schemes, the QT approach cannot give desirable results. Developing better method should be useful for future investigations in this research area.

Photochemical and photophysical properties of cis-stilbene molecule by electronic structure calculations and nonadiabatic surface-hopping dynamics simulations

We introduce an efficient configuration interaction (CI) method for the calculation of mixed quantum and classical nonadiabatic molecular dynamics for multiple electrons. For any given realization of the classical degrees of freedom (e.g., a solvent), the method uses a novel real-space quadrature to efficiently compute the Coulomb and exchange interactions between electrons. We also introduce an approximation whereby the classical molecular dynamics is propagated for several time steps on electronic potential energy surfaces generated using only a particularly important subset of the CI basis states. By only updating the important-states subset periodically, we achieve significant reductions in the computational cost of solving the multielectron quantum problem. We test the real-space quadrature for the cases of two electrons confined in a cubic box with infinitely repulsive walls and two electrons dissolved in liquid water that occupy a single cavity, so-called hydrated dielectrons. We then demonstrate how to perform mixed quantum and classical nonadiabatic dynamics by combining these computational techniques with the mean-field with surface hopping algorithm of Prezhdo and Rossky [J. Chem. Phys. 107, 825 (1997)]. Finally, we illustrate the practicality of the approach to multielectron nonadiabatic dynamics by examining the nonadiabatic relaxation dynamics of both spin singlet and spin triplet hydrated dielectrons following excitation from the ground to the first excited state.

In the Born-Oppenheimer approximation for molecular dynamics as generalized by Born and Huang, nuclei move on multiple potential-energy surfaces corresponding to different electronic states. These surfaces may intersect at a point in the nuclear coordinates with the topology of a double cone. These conical intersections have important consequences for the dynamics. When an adiabatic electronic wave function is transported around a closed loop in nuclear coordinate space that encloses a conical intersection point, it acquires an additional geometric, or Berry, phase. The Schr\"odinger equation for nuclear motion must be modified accordingly. A conical intersection also permits efficient nonadiabatic transitions between potential-energy surfaces. Most examples of the geometric phase in molecular dynamics have been in situations in which a molecular point-group symmetry required the electronic degeneracy and the consequent conical intersection. Similarly, it has been commonly assumed that the conical intersections facilitating nonadiabatic transitions were largely symmetry driven. However, conical intersections also occur in the absence of any symmetry considerations. This review discusses computational tools for finding and characterizing the conical intersections in such systems. Because these purely accidental intersections are difficult to anticipate, they may occur more frequently than previously thought and in unexpected situations, making the geometric phase effect and the occurrence of efficient nonadiabatic transitions more commonplace phenomena. [S0034-6861(96)00404-7]

The H-atom photodissociationreaction from the pyridinyl radical (C5H5NH) via the low-lying πσ* excited electronic state is investigated by nonadiabatic time-dependent quantum wave-packet dynamics calculations. A model comprising three electronic states and three nuclear coordinates has been constructed using ab initio multi-configurational self-consistent-field and multi-reference perturbation theory methods. Two conical intersections among the three lowest electronic states have been characterized in the framework of the linear vibronic-coupling model. Time-dependent wave-packet simulations have been performed using the multi-configuration time-dependent Hartree method. The population dynamics of the diabatic and adiabatic electronic states and the time-dependent dissociation behavior are analyzed for various vibrational initial conditions. The results provide detailed mechanistic insight into the photoinduced H-atom dissociation process from a hypervalent aromatic radical and show that an efficient dissociationreaction through two conical intersections is possible.

The primal definition of first-order non-adiabatic couplings among electronic states relies on the knowledge of how electronic wavefunctions vary with nuclear coordinates. However, the non-adiabatic coupling between two electronic states can be obtained in the vicinity of a conical intersection from energies only, as this vector spans the branching plane along which degeneracy is lifted to first order. The gradient difference and derivative coupling are responsible of the two-dimensional cusp of a conical intersection between both potential-energy surfaces and can be identified to the non-trivial eigenvectors of the second derivative of the square energy difference, as first pointed out in Köppel and Schubert [Mol. Phys. 104(5-7), 1069 (2006)]. Such quantities can always be computed in principle for the cost of two numerical Hessians in the worst-case scenario. Analytic-derivative techniques may help in terms of accuracy and efficiency but also raise potential traps due to singularities and ill-defined derivatives at degeneracies. We compare here two approaches, one fully numerical, the other semianalytic, where analytic gradients are available but Hessians are not, and investigate their respective conditions of applicability. Benzene and 3-hydroxychromone are used as illustrative application cases. It is shown that non-adiabatic couplings can thus be estimated with decent accuracy in regions of significant size around conical intersections. This procedure is robust and could be useful in the context of on-the-fly non-adiabatic dynamics or be used for producing model representations of intersecting potential energy surfaces with complete obviation of the electronic wavefunctions.

Chapter 10 - Enzymatic recognition of radiation-produced oxidative DNA lesion. Molecular dynamics approach

Analog quantum simulators, which efficiently represent model systems, have the potential to provide new insight toward naturally occurring phenomena beyond the capabilities of classical computers. Incorporating dissipation as a resource unlocks a wider range of out-of-equilibrium processes such as chemical reactions. Here, we operate a hybrid qubit-oscillator circuit quantum electrodynamics simulator and model nonadiabatic molecular dynamics through a conical intersection. We identify dephasing of the electronic qubit as the mechanism that drives wave-packet branching when the corresponding oscillator undergoes large amplitude motion. Furthermore, we directly observe enhanced branching when the wave-packet passes through the conical intersection. Thus, the forces that influence a chemical reaction can be viewed from the perspective of measurement backaction in quantum mechanics—there is an effective measurement-induced dephasing rate that depends on the position of the wave packet relative to the conical intersection. Our results set the groundwork for more complex simulations of chemical dynamics using quantum simulators, offering deeper insight into the role of dissipation in determining macroscopic quantities of interest such as the quantum yield of a chemical reaction.5 MoreReceived 16 May 2022Revised 1 November 2022Accepted 19 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011008Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum information processing with continuous variablesQuantum simulationQuantum Information

We present the ab initio Wigner distribution approach for simulation of femtosecond pump–probe and pump–dump signals and the new strategy for tailoring the light pulses that allow for optimal control of ultrafast processes. Our ab initio Wigner distribution approach combines the Wigner–Moyal representation of the vibronic density matrix with the ab initio multistate adiabatic and nonadiabatic molecular dynamics “on the fly” involving ground and excited electronic states. This approach allows for accurate simulations of femtosecond signals based on analytic formulation for systems of moderate complexity taking into account all degrees of freedom. For this purpose the following items are needed: (1) temperature‐dependent ground‐state initial conditions; (2) an ensemble of trajectories for the investigation of the dynamics of the system either on the adiabatic electronic excited state or on both the excited and ground states through nonadiabatic coupling; and (3) either the cationic or neutral ground state for the probing step. The goal of optimal control of femtosecond processes is to tailor pump–dump pulses that drive the system via electronically excited state to the desired ground‐state objective with the maximal yield. For the multidimensional systems this is possible only if the connective pathway between initial state and the objective can be ensured and the optimal pathway can be found. We show that these requirements are fulfilled by introducing the concept of the intermediate target in the excited state. Its role is to select the appropriate parts of energy surfaces at the given time delay between the two pulses, allowing us to reach optimally the objective. We illustrate the scope of our approach on nonstoichiometric halide deficient NanFn−1 clusters, which are characterized by strong ionic bonding and one excess electron. The choice of the systems has been made to determine timescales of different processes in the excited states and apply the new strategy for optimal control. This involves the bond breaking leading to (1) periodic geometric rearrangements such as in the case of Na2F or (2) nonadiabatic radiationless decay through conical intersection between the first excited state and the ground state occurring for Na3F2. In the latter case we optimize and analyze the pump and dump pulses to drive the isomerization process in the Na3F2 cluster to the second isomer by suppressing radiationless transition through conical intersection. The shaped pump–dump pulses serve as guidance for the experimental work in progress. Population of one of the two isomers allows us to establish a molecular switch. Such bimodal type of behavior might provide a basic element for information storage. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Detailed mechanistic understanding of multistep chemical reactions triggered by internal conversion via a conical intersection is a challenging task that emphasizes limitations in theoretical and experimental techniques. Hypothesis-driven methodologies (e.g. characterization of critical points and biased molecular dynamics) are commonly employed to explore chemical space and simulate reaction events. In this contribution, we present a discovery-based, hypothesis-free computational approach based on first principles molecular dynamics to discover and refine the switching mechanism of Donor-Acceptor Stenhouse Adducts (DASAs). Using state-of-the-art graphical processing units-enabled electronic structure calculations we performed in total ~2ns of adiabatic and non-adiabatic ab initio molecular dynamics discovering a) critical intermediates that are involved in the open-to-closed transformation, b) several competing pathways which lower the overall switching yield, and c) key elements for future design strategies. Our dynamics describe the natural evolution of both the nuclear and electronic degrees of freedom that govern the interconversion between DASA ground state intermediates exposing significant elements for the future design strategies of molecular switches.

Interfacial characteristics of polymer nanocomposites represent a crucial aspect to understand their global properties and to evaluate the interaction between nanofillers and matrix. In this work we used a molecular dynamics (MD) approach to characterize the interfacial region at the atomistic scale of graphene-based polymer nanocomposites. Three different polymer matrixes were considered, polylactic acid (PLA), polypropylene (PP) and epoxy resin (EPO), which were reinforced with three types of graphene fillers: pristine graphene (G), graphene oxide (GO) and reduced graphene oxide (rGO). In particular, the compatibility of the nanofillers in polymer matrixes were evaluated in terms of the interaction energy, while the interfacial thermal resistance (Kapitza resistance) between matrices and fillers was calculated with a nonequilibrium molecular dynamics (NEMD) method. Results showed that the oxidation degree plays an important role on the studied properties of the interfacial region. In particular, it was observed that the Kapitza resistance is decreased in the oxidized graphene (GO and rGO), while interaction energy depended on the polarity of the polymer matrix molecules and the contribution of the Coulombic component.

Changes in mechanical properties of copper-silver matrix welded by the iron blade by increasing initial pressure: A molecular dynamics approach

We develop a novel method to simulate analytical nonadiabatic switching probability based on effective coupling and effective collision energy by using only electronic adiabatic potential energy surfaces and its gradients in the case of avoided crossing types of nonadiabatic transitions. In addition, the present method can keep the same time step for computing both on-the-fly trajectory and nonadiabatic transitions accurately. The present method is most useful for localized nonadiabatic transitions induced by conical intersection. We employ the on-the-fly surface hopping algorithm with an ab initio quantum chemistry calculation to demonstrate a dynamic simulation for photoisomerization in azobenzene. Simulated quantum yield and lifetime converge to 0.39 and 53 femtosecond, respectively (0.33 and 0.81 picosecond) for cis-to-trans (trans-to-cis) photoisomerization with up to 800 (600) sampling trajectories. The present results agree well with those of the experiment, as well as results simulated with use of nonadiabatic coupling within Tully's fewest switching method. The present trajectory-based nonadiabatic molecular dynamics free from nonadiabatic coupling greatly enhances the simulation power of molecular dynamics for large complex chemical systems.