Adiabatic Potential Energy Surfaces Research Articles

Significant Isotope Effects from the Nonadiabatic Couplings in the Cl(2P) + HD(v = 0, j = 0) Reaction.

The impact of non-Born-Oppenheimer couplings on the isotopic effects in the reaction of the Cl(2P) atom with the HD (v = 0, j = 0) molecule is investigated with our recently developed nonadiabatic time-independent quantum scattering methods, where the full open-shell characteristics are included in the six-state model, and also with the recently developed two-state model solving by time-independent methods, where part of the open-shell characteristic is included. The same reaction is also calculated with the simple adiabatic model using the lowest adiabatic potential energy surface. Compared with the results from different models, it is found that the reactivity of the Cl + HD → HCl + D channel is significantly overestimated in the adiabatic model. In contrast, the reactivity of the other channel agrees well with the nonadiabatic models. This is due to the van der Waals well in the reactant channel being changed a lot by including the nonadiabatic couplings. These quantum dynamics calculations suggest that sometimes the adiabatic model should be used with caution; otherwise, it may result in significant deviations for some reactions.

Surface Hopping with Reliable Wave Function by Introducing Auxiliary Wave Packets to Trajectory Branching.

It is well-known that the widely utilized fewest switches surface hopping method suffers from the severe overcoherence problem, and thus adiabatic populations calculated by wave functions are generally inferior to those based on active states. More importantly, to achieve a complete description of nonadiabatic dynamics, the density matrix is essential. In this paper, we present an auxiliary branching corrected surface hopping (A-BCSH) method that introduces auxiliary wave packets (WPs) on the adiabatic potential energy surfaces for trajectory branching. Both rapid and gradual separation of WP components on different surfaces are characterized, and thus the correct decoherence time along each trajectory is captured. As demonstrated in the three standard Tully models, A-BCSH exhibits excellent internal consistency. Namely, close adiabatic populations are obtained based on both wave functions and active states. In particular, A-BCSH successfully obtains a reliable time-dependent spatial distribution of the density matrix, which relies only on electronic wave functions. Due to its high performance, our A-BCSH method provides a new and highly promising perspective on further development of more consistent surface hopping with reliable wave function.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2.

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Mutual neutralization in collisions of Li+ with CN.

The mutual neutralization reaction in collisions of Li+ with CN- is a promising candidate for rigorous multi-dimensional ab initio studies of atom-molecule charge transfer processes. The reaction is driven by the non-adiabatic interaction between the lowest two 1A' electronic states at large Li-CN distances, resulting in a large cross section for mutual neutralization. As a first step, the relevant adiabatic potential energy surfaces and non-adiabatic interaction are computed ab initio, and the process is studied quantum mechanically using the vibrational sudden approximation, where the vibrational and rotational motions of the CN molecule are assumed to be frozen during the collision.

Formation Mechanisms of Electronically Excited Nitrogen Molecules from N + N2 and N + N + N Collisions Revealed by Full-Dimensional Potential Energy Surfaces.

This work reports six new full-dimensional adiabatic potential energy surfaces (PESs) of the N3 system (four 4A″ states and two 2A″ states) at the MRCI + Q/AVQZ level of theory that correlated to N2(X1Σg+) + N(4S), N2(X1Σg+) + N(2D), N2(A3Σu+) + N(4S), N2(B3Πg) + N(4S), N2(W3Δu) + N(4S), and N(4S) + N(4S) + N(4S) channels. The neural networks with a proper account of the nuclear permutation invariant symmetry of N3 were employed to fit the PESs based on about 4000 ab initio points. The accuracy of the PESs was validated by excellent agreement on the equilibrium bond length, vertical excitation energy, and dissociation energy with experimental values. Two possible mechanisms of the formation of N2(A) were found. One is that the collision occurs between N2(X) and N(4S) in the 14A″ state, followed by a nonadiabatic transition through the conical intersection with the 24A″ PES, resulting in the formation of the N2(A) + N(4S) product. The other takes place in the collision among three N(4S) atoms in the adiabatic 24A″ state, and then, N2(A) + N(4S) is formed. This is the first systematical research of the N3 system focusing on the formation of the excited states of N2 via both adiabatic and nonadiabatic pathways.

Relaxation processes among adiabatic potential energy surfaces of Tl+ and Au− centers in NaCl crystals

We investigated temperature dependencies of the temporal behaviors of luminescence bands attributed to the radiative transitions from adiabatic potential energy surfaces (APESs) of 1T1g, 3T2u+3Eu, 3T1g, and 3A1u of Tl+ and Au− centers in NaCl crystals. In addition to NaCl:Au−, a luminescence band with the sharp zero-phonon luminescence line was observed in NaCl:Tl+, a strong electron-lattice interaction system. A time-resolved study revealed that this luminescence band with the zero-phonon line in NaCl:Tl + exhibited the decay time of 4.3 ms at low temperatures attributed to the radiative transition from 3A1u APES. The characteristic temperature dependences of the decay time constant and luminescence intensity of the luminescence from the 3T1g and 3A1u APESs were discussed based on a configuration coordinate scheme. The intensities and decay time constants of luminescence bands caused by radiative transitions from the 1T1g, 3T2u+3Eu, 3T1g, and 3A1u APESs changed with temperature through thermally activated nonradiative transitions among APESs. The temperature dependencies of luminescence intensities and decay time constants were analyzed using rate equations that comprise radiative and nonradiative transitions from APESs and among APESs, respectively. The activation energies of APESs were estimated from the best-fit results. The characteristics of thermally activated processes among APESs are revealed in weak and strong electron-lattice interaction systems.

ANT 2023: A program for adiabatic and nonadiabatic trajectories

ANT 2023 is a program for quasiclassical and semiclassical trajectories, both single-surface trajectories for which the Born-Oppenheimer approximation is valid and multi-surface calculations with electronic state changes, i.e., for electronically adiabatic and electronically nonadiabatic trajectories. There are several methods available for multisurface problems: surface hopping with or without time uncertainty and with or without decoherence, semiclassical Ehrenfest, self-consistent decay of mixing, and coherent switching with decay of mixing (CSDM). The potential surface for single-surface problems may be an analytic potential function supplied by the user, or one may use direct dynamics. To use the adiabatic representation (i.e., electronically adiabatic basis functions) for electronically nonadiabatic dynamics, the user may either provide the adiabatic surfaces and nonadiabatic couplings by direct dynamics, or the program may calculate them from diabatic surfaces and diabatic couplings, which are usually analytic. One can also use analytic fits to the surfaces and couplings to carry out calculations entirely in the diabatic representation. The curvature-driven approximation is available as an option for use with CSDM and trajectory surface hopping. The ANT 2023 program is especially recommended for calculations with analytic potential energy surfaces and couplings because of its high efficiency for such calculations. Program SummaryProgram Title: ANT 2023, revision BCPC Library link to program files:https://doi.org/10.17632/gr74wwckcp.1Developer's repository link: https://doi.org/10.5281/zenodo.10011563Licensing Provisions: Apache-2.0Programming language: Fortran 90Interfaces to other programs: For direct dynamics, the code has well tested interfaces to the Gaussian 09 [1], Gaussian 16 [2], MOPACmn [3], and Molpro [4] electronic structure codes. The interfaces are included, but these electronic structure programs must be obtained separately. Users may also provide their own interfaces to other electronic structure programs.[1] M. J. Frisch et al. Gaussian 09, Gaussian, Inc., Wallingford CT, 2016.[2] M. J. Frisch et al., Gaussian 16, Gaussian, Inc., Wallingford CT, 2016.[3] J. J. P. Stewart et al., MOPAC 5.022mn, University of Minnesota, Minneapolis, MN, 2015; Zenodo. https://doi.org/10.5281/zenodo.8153079[4] H.-J. Werner et al., J. Chem. Phys. 152 (2020) 144107.Nature of problem: classical, quasiclassical, or semiclassical molecular dynamics for electronically adiabatic or electronically nonadiabatic collisions and unimolecular processes of atoms, molecules, and clustersSolution method: The program integrates the classical or semiclassical equations of motion for the motion of the nuclei. ANT 2023 can use anharmonic initial-state selection for initial states of diatomics or harmonic initial-state selection for general polyatomics. The equations of motion for electronically adiabatic processes are Hamilton's equations with potential energy functions corresponding to the Born-Oppenheimer approximation. The equations of motion for electronically nonadiabatic processes (non-Born-Oppenheimer processes) include trajectory surface hopping (fewest switches with or without time uncertainty and with or without decoherence) or several possible mean-field methods, including the semiclassical Ehrenfest method (also called the time-dependent Hartree method), self-consistent decay of mixing, and coherent switching with decay of mixing. Electronically nonadiabatic processes may be treated using either the adiabatic representation or a diabatic representation, and the potential surfaces and couplings may be obtained from analytic fits in a user-supplied subroutine or by direct dynamics, which involves requesting energies, gradients, and couplings as needed from a quantum chemistry electronic structure program. In the adiabatic representation, the coupling may be nonadiabatic coupling vectors (based on gradients of electronic wave functions), time-derivative couplings (based on overlaps of electronic wave functions), or curvature-driven couplings (based on the curvatures of the adiabatic potential energy surfaces).Additional comments: The ANT 2023 program authors are Y. Shu, L. Zhang, J. Zheng, Z. H. Li, A. W. Jasper, D. A. Bonhommeau, R. Valero, R. Meana-Pañeda, S. L. Mielke, Z. Varga, and D. G. Truhlar [5]; the authors of the article [6] describing ANT 2023 are Y. Shu, L. Zhang, and D. G. Truhlar.

What is Missing in the Mean Field Description of Spatial Distribution of Population? Important Role of Auxiliary Wave Packets in Trajectory Branching.

When the traditional Ehrenfest mean field approach is employed to simulate nonadiabatic dynamics, an effective wave packet (WP) on the average potential energy surface (PES) is utilized to describe the nuclear motion. In the fully quantum picture, however, the WP components on different adiabatic PESs gradually separate in space because they evolve under different velocities and forces. Due to trajectory branching of the WP components, proper decoherence needs to be taken into account, and the spatial distribution of population cannot be described by a single effective WP. Here, we propose an auxiliary branching corrected mean field (A-BCMF) method, where trajectories of auxiliary WPs on adiabatic PESs are introduced. As benchmarked in the three standard Tully models, A-BCMF not only gives correct channel populations but also captures an accurate time-dependent spatial distribution of population. Thereby, we reveal the important role of auxiliary WPs in solving intrinsic problems of the widely used mean field description of nonadiabatic dynamics.

Formation of N(2D) from Hyperthermal Collisions between O(3P) and NO(X2Π).

Hyperthermal collisions between O(3P) and NO(X2Π) could lead to the formation of the first electronically excited atomic nitrogen (N(2D)), which plays a key role in plasma formation in shock-heated air. This process is facilitated mainly by four doublet states, and to a much lesser extent by two quartet states. In this work, we report quasi-classical trajectory studies of this reactive process using the four analytical adiabatic potential energy surfaces for the doublet states developed previously from fitting high-level ab initio data. The reactions were found to be strongly enhanced by vibrational excitation of the NO reactant, consistent with the existence of potential energy barriers in the exit channel. Despite the large endothermicity of the reaction, the rate coefficient is significant at high temperatures, suggesting a possible role of this reaction in the hyperthermal kinetics in the shock layer of a hypersonic (re)entry vehicle.

Machine Learning Representations of the Three Lowest Adiabatic Electronic Potential Energy Surfaces for the ArH2+ Reactive System.

In this work, we present Gaussian process regression machine learning representations of the three lowest coupled 2A' adiabatic electronic potential energy surfaces of the ArH2+ reactive system in full dimensionality. Additionally, the nonadiabatic coupling matrix elements were calculated. These adiabatic potentials and their nonadiabatic couplings are necessary ingredients in the theoretical investigation of the nonadiabatic reaction dynamics of the Ar + H2+ → ArH+ + H and Ar+ + H2 → ArH+ + H reactions, as well as the competing charge transfer process, Ar + H2+↔ Ar+ + H2. Accurate ab initio electronic structure calculations (ic-MRCI+Q/aug-cc-pVQZ), whereby the effect of spin-orbit coupling in Ar+ has been accounted for through the state interaction method, serve as input for the machine learning training process. The potential energy surfaces are fitted with high accuracies, with root-mean-square errors on the order of 10-7 eV for the three surfaces, which meet the requirements for chemical dynamics at low temperature. It was found that quite a large number of training points (of the order of 5000 ab initio points) are needed in order to achieve these accuracies due to the complex topography of these electronic surfaces.

PotLib 2023: New version of a potential energy surface library for chemical systems

POTLIB is a library of global and semiglobal potential energy surface subprograms. The library currently features 410 entries, including both single-state entries and multi-state entries. When one calls the routine of a single-state entry, it returns the ground-electronic-state adiabatic potential energy surface at the input geometry. In addition, some entries also return the gradient of the surface. When one calls a multi-state entry, it returns a diabatic potential energy matrix (DPEM). If the entry also has the gradient of the DPEM, one can compute adiabatic surfaces, their gradients, and the nonadiabatic coupling vectors (NACs) from the DPEM and its gradient by diagonalization. Some but not all the routines conform to one of a set of standard interfaces. The goal is to facilitate chemical dynamics research by collecting and disseminating a comprehensive collection of state-of-the-art potential energy routines (developed by a wide, international group of researchers) with systematic and well-defined interfaces for use with chemical dynamics programs. Systems in the library include CHArO2, CHN2O+, CH2O, CH2O2, CH3N2, CH3O, CH4, CH4Br, CH4Cl, CH4F, CH4O, CH4OCl, CH4OF, CH4OH, CH5, CH5+, CH5N, CH5O2, CH8O2, C2H2N2O, C2H2O, C2H4N, C2H4O4, C2H6Cl, C2H6F, C2H6H, C2H6O, C2H6OH, C2H7, C2O2, C3H4O2, C3H7NO, C6H6O, C6H6S, C7H8S, HBrCl, HCl2, HF2, HI2, HLiF, HNaF, HO2, HO3, HOBr, HSiO, H2Br, H2ClO, H2F, H2F2, H2FO, H2Na, H2O, H2O2, H2OBr, H3, H3Cl, H3ClN, H3ClO, H3N, H3O, H3O2, H3+, H3S, H4ClSi, H4N, H4NO, H4O2, H5GeO, H5Si, H7+, AlmHn, Aln, ArNO, K2Rb2, NO2, N2O, N2O2, N3, N4, O3, and O4. New version program summaryProgram title: PotLib 2023CPC Library link to program files:https://doi.org/10.17632/chxxhnnt4p.1Licensing provisions: Apache 2.0Programming language: FortranDoes the new version supersede the previous version?: YesJournal references of previous versions: Comput. Phys. Comm. 144 (2002) 169–187 [1]; Erratum: Comput. Phys. Comm. 156 (2004) 319–32.Nature of problem: Within the Born–Oppenheimer approximation, the electronically adiabatic interactions of atoms and molecules can be represented by a potential energy surface (PES) that depends on the geometry of the reacting species [2-4]. An electronically nonadiabatic system can be approximately described by a diabatic potential energy matrix (DPEM) that also depends on molecular geometry [5,6]. The library contains Fortran subroutines of PESs and DPEMs for reactive and non-reactive systems.Solution method: The user can incorporate a PES, DPEM, or PES set from a DPEM into a chemical dynamics computer code to supply the needed potential or potentials and optionally the gradients (forces) and surface couplings.Summary of revisions: The new version includes many more potentials than the original version of the library.

The application of the SCAN density functional to color centers in diamond.

Detailed characterization of deep-level color centers requires understanding their electronic and atomic structure, which is most commonly investigated utilizing the Kohn-Sham density functional theory. Standard semilocal functionals based on the generalized gradient approximation (GGA) are inclined toward an imprecise quantitative description of defects' electronic structure. Hybrid functionals provide an improved prediction of electronic properties, albeit at a much higher computational cost. In this work, we test the newly developed Strongly Constrained and Appropriately Normed (SCAN) family of meta-GGA density functionals for selected color centers in diamond. In particular, we study nitrogen-, silicon-, germanium-, and tin-vacancy centers that have been recently investigated for their use in quantum technological applications. We show that SCAN and its derivatives, the rSCAN and r2SCAN functionals, significantly improve the calculated energies of optical transitions within the delta-self-consistent-field approach, almost reaching the accuracy of the hybrid Heyd-Scuseria-Ernzerhof (HSE) functional. In the case of the NV- center, we also show that the SCAN family of functionals improves the description of the adiabatic potential energy surfaces compared to both GGA and hybrid functionals, improving calculated luminescence lineshapes. As a result of these findings, we recommend using the SCAN family of functionals as a promising alternative for studying color centers in solids.

IR Spectra of Entrance and Exit Channels of Methane Molecule and Oxygen Atom Reaction at MP2 Theory

IR spectra of entrance and exit channels of methane and radical oxygen reaction are predicted in the ground state energy. Ab initio calculations at perturbation theory (MP2) with Dunning correction- consistent basis set (aug-cc-pVDZ) have been used. The calculations predicted structures, vibrational frequencies and potential energy surface. Three van der Waals minima from three adiabatic potential energy surfaces have been predicted in entrance and exit channels. Vibration frequency of 3209 cm-1 and 3212 cm-1 of C-H stretching in entrance structures are predicted while O-H vibrational frequency is predicted to be at 3673 cm-1 in the other channel. The lowest energy structure in entrance channel has - 0.18 kJ/ mol minimum energy.

Coupled three-dimensional quantum mechanical wave packet study of proton transfer in H2+ + He collisions on accurate abinitio two-state diabatic potential energy surfaces.

We have carried out fully close-coupled three dimensional quantum mechanical wave packet dynamical calculations for the reaction He+H2+→HeH++H on the ground electronic adiabatic potential energy surface and on the lowest two electronic states of newly constructed abinitio calculated diabatic potential energy surfaces for the system [Naskar et al., J. Phys. Chem. A 127, 3832 (2023)]. With the reactant diatom (H2+) in its roto-vibrational ground state (v = 0, j = 0), the calculations have been carried out in hyperspherical coordinates to obtain the reaction attributes. Convergence profiles of the reaction probability with respect to the total angular momentum quantum number at different collision energies are presented for the title reaction. State-to-state as well as initial state selected integral reaction cross sections are calculated from the fully converged reaction probabilities over a range of collision energies. The integral cross section values computed using the two-state diabatic potential energy surfaces are significantly lower than those obtained using the ground electronic state adiabatic potential energy surface and are in much better agreement with the available experimental results than the latter for total energy greater than 1.1eV. Therefore, it becomes clear that it is important to include the nonadiabatic coupling terms for a quantitative prediction of the dynamical observables.

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.

Smooth Things Come in Threes: A Diabatic Surrogate Model for Conical Intersection Optimization.

The optimization of conical intersection structures is complicated by the nondifferentiability of the adiabatic potential energy surfaces. In this work, we build a pseudodiabatic surrogate model, based on Gaussian process regression, formed by three smooth and differentiable surfaces that can adequately reproduce the adiabatic surfaces. Using this model with the restricted variance optimization method results in a notable decrease of the overall computational effort required to obtain minimum energy crossing points.

Beyond Born-Oppenheimer Constructed Diabatic Potential Energy Surfaces for HeH2.

First-principles based beyond Born-Oppenheimer theory has been employed to construct multistate global Potential-Energy Surfaces (PESs) for the HeH2+ system by explicitly incorporating the Nonadiabatic Coupling Terms (NACTs). Adiabatic PESs and NACTs for the lowest four electronic states (12A', 22A', 32A' and 42A') are evaluated as functions of hyperangles for a grid of fixed values of the hyperradius in hyperspherical coordinates. Conical intersection between different states are validated by integrating the NACTs along appropriately chosen contours. Subsequently, adiabatic-to-diabatic (ADT) transformation angles are determined by solving the ADT equations to construct the diabatic potential matrix for the HeH2+ system which are smooth, single-valued, continuous, and symmetric and are suitable for performing accurate scattering calculations for the titled system.

Dynamics of an excitation-transfer trimer: Interference, coherence, Berry's phase development, and vibrational control of non-adiabaticity.

We detail several interesting features in the dynamics of an equilaterally shaped electronic excitation-transfer (EET) trimer with distance-dependent intermonomer excitation-transfer couplings. In the absence of electronic-vibrational coupling, symmetric and antisymmetric superpositions of two single-monomer excitations are shown to exhibit purely constructive, oscillatory, and purely destructive interference in the EET to the third monomer, respectively. In the former case, the transfer is modulated by motion in the symmetrical framework-expansion vibration induced by the Franck-Condon excitation. Distortions in the shape of the triangular framework degrade that coherent EET while activating excitation transfer in the latter case of an antisymmetric initial state. In its symmetrical configuration, two of the three single-exciton states of the trimer are degenerate. This degeneracy is broken by the Jahn-Teller-active framework distortions. The calculations illustrate closed, approximately circular pseudo-rotational wave-packet dynamics on both the lower and the upper adiabatic potential energy surfaces of the degenerate manifold, which lead to the acquisition after one cycle of physically meaningful geometric (Berry) phases of π. Another manifestation of Berry-phase development is seen in the evolution of the vibrational probability density of a wave packet on the lower Jahn-Teller adiabatic potential comprising a superposition of clockwise and counterclockwise circular motions. The circular pseudo-rotation on the upper cone is shown to stabilize the adiabatic electronic state against non-adiabatic internal conversion via the conical intersection, a dynamical process analogous to Slonczewski resonance. Strategies for initiating and monitoring these various dynamical processes experimentally using pre-resonant impulsive Raman excitation, short-pulse absorption, and multi-dimensional wave-packet interferometry are outlined in brief.

A mapping approach to surface hopping.

We present a nonadiabatic classical-trajectory approach that offers the best of both worlds between fewest-switches surface hopping (FSSH) and quasiclassical mapping dynamics. This mapping approach to surface hopping (MASH) propagates the nuclei on the active adiabatic potential-energy surface, such as in FSSH. However, unlike in FSSH, transitions between active surfaces are deterministic and occur when the electronic mapping variables evolve between specified regions of the electronic phase space. This guarantees internal consistency between the active surface and the electronic degrees of freedom throughout the dynamics. MASH is rigorously derivable from exact quantum mechanics as a limit of the quantum-classical Liouville equation (QCLE), leading to a unique prescription for momentum rescaling and frustrated hops. Hence, a quantum-jump procedure can, in principle, be used to systematically converge the accuracy of the results to that of the QCLE. This jump procedure also provides a rigorous framework for deriving approximate decoherence corrections similar to those proposed for FSSH. We apply MASH to simulate the nonadiabatic dynamics in various model systems and show that it consistently produces more accurate results than FSSH at a comparable computational cost.