Nonadiabatic Electronic Transitions Research Articles

Mechanistic Insights into Nonadiabatic Interband Transitions on a Semiconductor Surface Induced by Hydrogen Atom Collisions.

To understand the recently observed enigmatic nonadiabatic energy transfer for hyperthermal H atom scattering from a semiconductor surface, Ge(111)c(2 × 8), we present a mixed quantum-classical nonadiabatic molecular dynamics model based on the time-dependent evolution of Kohn-Sham orbitals and a classical path approximation. Our results suggest that facile nonadiabatic electronic transitions from the valence band to the conduction band occur selectively at the rest atom site, where surface states are doubly occupied, but not at the adatom site, where empty surface states are localized. This drastic site specificity can be attributed to the changes of the local band structure upon energetic H collisions at different surface sites, leading to transient near degeneracies and significant couplings between occupied and unoccupied orbitals at the rest atom but not at the adatom. These insights shed valuable light on the collision-induced nonadiabatic dynamics at semiconductor surfaces.

Nonadiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation.

In this article, the nonadiabatic excited-state Molecular dynamics (NEXMD) package is linked with the SANDER package, provided by AMBERTOOLS. The combination of these software packages enables the simulation of photoinduced dynamics of large multichromophoric conjugated molecules involving several coupled electronic excited states embedded in an explicit solvent by using the quantum/mechanics/molecular mechanics (QM/MM) methodology. The fewest switches surface hopping algorithm, as implemented in NEXMD, is used to account for quantum transitions among the adiabatic excited-state simulations of the photoexcitation and subsequent nonadiabatic electronic transitions, and vibrational energy relaxation of a substituted polyphenylenevinylene oligomer (PPV3-NO2) in vacuum and methanol as an explicit solvent has been used as a test case. The impact of including specific solvent molecules in the QM region is also analyzed. Our NEXMD-SANDER QM/MM implementation provides a useful computational tool to simulate qualitatively solvent-dependent effects, like electron transfer, stabilization of charge-separated excited states, and the role of solvent reorganization in the molecular optical properties, observed in solution-based spectroscopic experiments.

Quantum and semiclassical studies of nonadiabatic electronic transitions between N(4S) and N(2D) by collisions with N2.

The dynamics and kinetics of spin-forbidden transitions between N(2D) and N(4S) via collisions with N2 molecules are investigated using a quantum wave packet (WP) method and the semi-classical coherent switches with decay of mixing (CSDM) method. These electronic transition processes are competing with exchange reaction channels on both the doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients are found in reasonable agreement with each other, and both reproduce the previous theoretical results. For the excitation process, the agreement between the two approaches is dependent on the treatment of the zero-point energy (ZPE) in the product, because the high endoergicity of this process leads to severe violation of the vibrational ZPE. The Gaussian-binning (GB) method is found to improve the agreement with the quantum result. The excitation rate coefficients are found to be two orders of magnitude smaller than that of the adiabatic exchange reaction, underscoring the inefficient intersystem crossing due to the weak spin-orbit coupling between the two spin manifolds of the N3 system.

Transition Path Flight Times and Nonadiabatic Electronic Transitions

Transition path flight times are studied for scattering on two electronic surfaces with a single crossing. These flight times reveal nontrivial quantum effects such as resonance lifetimes and nonclassical passage times and reveal that nonadiabatic effects often increase flight times. The flight times are computed using numerically exact time propagation and compared with results obtained from the Fewest Switches Surface Hopping (FSSH) method. Comparison of the two methods shows that the FSSH method is reliable for transition path times only when the scattering is classically allowed on the relevant adiabatic surfaces. However, where quantum effects such as tunneling and resonances dominate, the FSSH method is not adequate to accurately predict the correct times and transition probabilities. These results highlight limitations in methods which do not account for quantum interference effects, and suggest that measuring flight times is important for obtaining insights from the time-domain into quantum effects in nonadiabatic scattering.

Ab Initio Nonadiabatic Surface-Hopping Trajectory Simulations of Photocatalytic Water Oxidation and Hydrogen Evolution with the Heptazine Chromophore.

In the past decade, polymeric carbon nitrides consisting of heptazine (Hz) building blocks emerged as highly promising materials for photocatalytic hydrogen evolution from water or sacrificial electron donors with near-ultraviolet light. However, the complexity of these materials and their poor characterization at the atomic level are detrimental to the unraveling of the detailed mechanisms of the reactions leading to hydrogen evolution. Recently, it has been shown that a derivative of the Hz molecule, trianisole-heptazine (TAHz), is a potent photobase, which readily oxidizes various derivatives of phenol and even water by an excited-state proton-coupled electron-transfer (PCET) reaction. Energy profiles along minimum-energy reaction paths and relaxed PCET potential-energy surfaces, which previously were computed with ab initio electronic-structure methods for complexes of Hz and TAHz with protic substrates, led to qualitative insights. To obtain more quantitative insight, reaction dynamics simulations are required. In the present work, the time scales of the electron and proton transfer processes and the branching ratios of competing channels were explored with ab initio on-the-fly quasiclassical surface-hopping trajectory simulations for the hydrogen-bonded Hz-H2O complex. By the analysis of representative trajectories, detailed insight into the interplay of various nonadiabatic electronic transitions, electron transfer, proton transfer, and vibrational energy relaxation is obtained. The HzH radicals which are formed by the photoreduction of Hz can disproportionate to Hz and HzH2 in an exothermic reaction with a low reaction barrier. The time scales and branching ratios of competing channels in H-atom photodetachment from the HzH2 molecule also were explored with ab initio surface-hopping simulations. These results delineate for the first time a quantitatively supported scenario of water oxidation and hydrogen evolution with a molecular carbon nitride photocatalyst.

Exact analytical solution of time-independent Schrödinger equation for a system consisting of two flat potentials coupled by a rectangular potential

We have proposed an analytical method for finding the exact solution for the two-state scattering problems, where two flat potentials are coupled by a rectangular potential. We found a way to express the two-state problem by an effective single-state problem, where it is easy to estimate the transition probability from one potential to the other by estimating the amount of missing flux from the first potential. This has been an unsolved problem for a long time and is of considerable importance as a model for non-adiabatic electronic transition.

A SA-CASSCF and MS-CASPT2 study on the electronic structure of nitrosobenzene and its relation to its dissociation dynamics.

The photodissociation channels of nitrosobenzene (PhNO) induced by a 255 nm photolytic wavelength have been studied using the complete active space self-consistent method and the multistate second-order multiconfigurational perturbation theory. It is found that there exists a triplet route for photodissociation of the molecule. The reaction mechanism consists of a complex cascade of nonadiabatic electronic transitions involving triple and double conical intersections as well as intersystem crossing. Several of the relevant states (S2, S4, and S5 states) correspond to double excitations. It is worth noting that the last step of the photodissociation implies an internal conversion process. The experimentally observed velocity pattern of the NO fragment is a signature of such a conical intersection.

Dissociation mechanism from highly charged bromophenol: ab initio molecular dynamics simulations

Abstract Dissociation mechanisms are studied by ab initio molecular dynamics simulations based on density functional theory for the highly charged bromophenol (C6H4OHBr)n+ (n ≤ 10) in the ground electronic state and in an electronic state which has a high electronic temperature Te characterized by Fermi–Dirac distribution. In the case of the ground state, the dissociation occurs through a sequential multi-stage process. At times shorter than 20 fs after the molecule is charged, hydrogens are dissociated from the molecule and, subsequently, the carbon ring breaks at about 150 fs In the case of an electronic state with high Te, the mechanism changes from a sequential dissociation process to a simultaneous process occurring at Te > 5 eV. To estimate the charge transfer time in a molecular bromide parent ion with +6 charge, which is generated through Auger cascades, we also performed nonadiabatic quantum-mechanical molecular dynamics (NAQMD) simulations that include the effects of nonadiabatic electronic transition with a surface-hopping approach.

Chemical activation of oxygen molecule by quantum electronic state selected vanadium cation: observation of spin–orbit state effects

By employing two-colour laser pulsed field ionisation-photoion (PFI-PI) double-quadrupole-double-octopole ion-molecule apparatus, we have examined the absolute integral cross-section (σ) for the reaction between vanadium cation (V+) and oxygen molecule (O2), covering the centre-of-mass kinetic energy (E cm) range of 0.2–10.0 eV. Here, V+ ion was prepared exclusively in its lowest 13 spin–orbit or J-states, a5DJ=0-4, a5FJ=1-5 , and a3FJ=2-4. The formation of VO+ + O is identified as the only product channel for these exothermic reactions. At E cm = 0.2–5.0 eV, the σ values for the three electronic states are found to be in the order: σ(a3FJ) > σ(a5DJ) > σ(a5FJ), whereas these cross-sections become nearly identical at E cm = 5.0–10.0 eV. This observation has been rationalised by collision-mediated non-adiabatic electronic transitions. The J-state effect for the V+(a3F2, 3) + O2 reactions are unambiguously identified for the first time for a reaction involving a transition metal cation. This J-state dependent chemical reactivity observed calls for rigorous theoretical interpretation. The fact that chemical reactivity for the a5FJ excited state is lower than that for the a5DJ ground state indicates that the difference in chemical reactivity is originated from quantum-electronic-state instead of energy effects.

Assessing the performance of trajectory surface hopping methods: Ultrafast internal conversion in pyrazine.

Trajectory surface hopping (TSH) methods have been widely used to study photoinduced nonadiabatic processes. In the present study, nonadiabatic dynamics simulations with the widely used Tully's fewest switches surface hopping (FSSH) algorithm and a Landau-Zener-type TSH (LZSH) algorithm have been performed for the internal conversion dynamics of pyrazine. The accuracy of the two TSH algorithms has been critically evaluated by a direct comparison with exact quantum dynamics calculations for a model of pyrazine. The model comprises the three lowest excited electronic states (B3u(nπ*), A1u(nπ*), and B2u(ππ*)) and the nine most relevant vibrational degrees of freedom. Considering photoexcitation to the diabatic B2u(ππ*) state, we examined the time-dependent diabatic and adiabatic electronic population dynamics. It is found that the diabatic populations obtained with both TSH methods are in good agreement with the exact quantum results. Fast population oscillations between the B3u(nπ*) and A1u(nπ*) states, which reflect nonadiabatic electronic transitions driven by coherent dynamics in the normal mode Q8a, are qualitatively reproduced by both TSH methods. In addition to the model study, the TSH methods have been interfaced with the second-order algebraic diagrammatic construction ab initio electronic-structure method to perform full-dimensional on-the-fly nonadiabatic dynamics simulations for pyrazine. It is found that the electronic population dynamics obtained with the LZSH method is in excellent agreement with that obtained by the FSSH method using a local diabatization algorithm. Moreover, the electronic populations of the full-dimensional on-the-fly calculations are in excellent agreement with the populations of the three-state nine-mode model, which confirms that the internal conversion dynamics of pyrazine is accurately represented by this reduced-dimensional model on the time scale under consideration (200 fs). The original FSSH method, in which the electronic wave function is propagated in the adiabatic representation, yields less accurate results. The oscillations in the populations of the diabatic B3u(nπ*) and A1u(nπ*) states driven by the mode Q8a are also observed in the full-dimensional dynamics simulations.

Accuracy of trajectory surface-hopping methods: Test for a two-dimensional model of the photodissociation of phenol.

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.

Doping effect on photoabsorption and charge-separation dynamics in light-harvesting organic molecule

Using ab-initio theoretical methods, we demonstrate possible enhancement of photo-conversion efficiency of an organic solar cell via intentional doping in molecular graphene-fullerene heterojunction [the hexabenzocoronene (HBC)-triethylene glycol (TEG)–C60 molecule]. Photoabsorption analysis indicates oxygen substitution into HBC leads to an extension of the spectra up to an infrared regime. A quantum-mechanical molecular dynamics simulation incorporating nonadiabatic electronic transitions reveals that a dissociated charge state (D+ and A-) in the O-doped system is more stable than the pristine case due to the presence of an effective barrier by the TEG HOMO/LUMO level. We also find that oxygen doping in HBC enhances the intermolecular carrier mobility after charge separation. On the other hand, the pristine molecule undergoes rapid recombination between donor and acceptor charges at the interface. These analyses suggest that the graphene oxidation opens a new window in the application of organic super-molecules to solar cells.

Nuclear Dynamics at Molecule-Metal Interfaces: A Pseudoparticle Perspective.

We discuss nuclear dynamics at molecule-metal interfaces including nonequilibrium molecular junctions. Starting from the many-body states (pseudoparticle) formulation of the molecule-metal system in the molecular vibronic basis, we introduce gradient expansion to reduce the adiabatic nuclear dynamics (that is, nuclear dynamics on a single molecular potential surface) into its semiclassical form while maintaining the effect of the nonadiabatic electronic transitions between different molecular charge states. This yields a set of equations for the nuclear dynamics in the presence of these nonadiabatic transitions, which reproduce the surface-hopping formulation in the limit of small metal-molecule coupling (where broadening of the molecular energy levels can be disregarded) and Ehrenfest dynamics (motion on the potential of mean force) when information on the different charging states is traced out.

Dynamics of Energy Transfer in a Conjugated Dendrimer Driven by Ultrafast Localization of Excitations.

Solar energy conversion starts with the harvest of light, and its efficacy depends on the spatial transfer of the light energy to where it can be transduced into other forms of energy. Harnessing solar power as a clean energy source requires the continuous development of new synthetic materials that can harvest photon energy and transport it without significant losses. With chemically-controlled branched architectures, dendrimers are ideally suited for these initial steps, since they consist of arrays of chromophores with relative positioning and orientations to create energy gradients and to spatially focus excitation energies. The spatial localization of the energy delimits its efficacy and has been a point of intense research for synthetic light harvesters. We present the results of a combined theoretical experimental study elucidating ultrafast, unidirectional, electronic energy transfer on a complex molecule designed to spatially focus the initial excitation onto an energy sink. The study explores the complex interplay between atomic motions, excited-state populations, and localization/delocalization of excitations. Our findings show that the electronic energy-transfer mechanism involves the ultrafast collapse of the photoexcited wave function due to nonadiabatic electronic transitions. The localization of the wave function is driven by the efficient coupling to high-frequency vibrational modes leading to ultrafast excited-state dynamics and unidirectional efficient energy funneling. This work provides a long-awaited consistent experiment-theoretical description of excited-state dynamics in organic conjugated dendrimers with atomistic resolution, a phenomenon expected to universally appear in a variety of synthetic conjugated materials.

The envelope Hamiltonian for electron interaction with ultrashort pulses

For ultrashort VUV pulses with a pulse length comparable to the orbital time of the bound electrons they couple to, we propose a simplified envelope Hamiltonian. It is based on the Kramers–Henneberger representation in connection with a Floquet expansion of the strong-field dynamics but keeps the time dependence of the pulse envelope explicit. Thereby, the envelope Hamiltonian captures the essence of the physics—light-induced shifts of bound states, single-photon absorption, and non-adiabatic electronic transitions. It delivers quantitatively accurate ionization dynamics and allows for a physical insight into the processes occurring. Its minimal requirements for construction in terms of laser parameters make it ideally suited for a large class of atomic and molecular problems.

Large nonadiabatic quantum molecular dynamics simulations on parallel computers

We have implemented a quantum molecular dynamics simulation incorporating nonadiabatic electronic transitions on massively parallel computers to study photoexcitation dynamics of electrons and ions. The nonadiabatic quantum molecular dynamics (NAQMD) simulation is based on Casida’s linear response time-dependent density functional theory to describe electronic excited states and Tully’s fewest-switches surface hopping approach to describe nonadiabatic electron–ion dynamics. To enable large NAQMD simulations, a series of techniques are employed for efficiently calculating long-range exact exchange correction and excited-state forces. The simulation program is parallelized using hybrid spatial and band decomposition, and is tested for various materials.

Nonadiabatic dynamics at metal surfaces: Independent electron surface hopping with phonon and electron thermostats

Independent Electron Surface Hopping (IESH) is a computational method for accounting for nonadiabatic electronic transitions in simulations of molecular motion at metal surfaces. IESH is applicable in cases of strong coupling where the electronic friction model is suspect, and has been demonstrated to accurately reproduce the results of detailed molecular beam experiments on vibrationally inelastic scattering of nitric oxide from the (111) surface of gold. However, in its original form, IESH represents a closed system without energy flow outside the local region of explicitly included substrate atoms. In this paper we propose two "thermostats" for introducing energy flow to the bulk, one for phonons and the other for electronic excitations.

Atomistic mechanisms of rapid energy transport in light-harvesting molecules

Synthetic supermolecules such as π-conjugated light-harvesting dendrimers efficiently harvest energy from sunlight, which is of significant importance for the global energy problem. Key to their success is rapid transport of electronic excitation energy from peripheral antennas to photochemical reaction cores, the atomistic mechanisms of which remains elusive. Here, quantum-mechanical molecular dynamics simulation incorporating nonadiabatic electronic transitions reveals the key molecular motion that significantly accelerates the energy transport based on the Dexter mechanism.

Electronic excitations in magnesium epitaxy: Experiment and theory

The nonadiabatic response of the electronic system during growth of Mg films is investigated both experimentally by measuring chemicurrents in $\text{Mg}/p\text{-Si}(001)$ Schottky diodes, and theoretically by time-dependent perturbation theory applied to first-principles electronic-structure calculations. Reverse currents are detected in the diodes when they are exposed to thermally evaporated Mg atoms. Dissipation of condensation energy to the electronic system as well as absorption of infrared photons due to heat radiation are the current-generating mechanisms. They can be distinguished by studying the dependence of the currents on the evaporator temperature and on the Mg film thickness. In contrast to the photocurrents, the chemicurrent is proportional to the Mg atom flux as it reproduces the enthalpy of Mg sublimation in an Arrhenius diagram. Independent measurements of photocurrents by use of an empty evaporator as a source of heat radiation provide further evidence for a chemicurrent contribution to the overall signal. The presence of chemicurrents in Mg epitaxy is further supported by simulations of monolayer growth and calculations of the pertinent rates for nonadiabatic electronic transitions in Mg adsorption. The simulations show that the grown surface is atomically rough with many step and kink sites. Adsorption at these sites is sufficiently exothermic to induce energetic electron-hole pairs that give rise to a detectable current across the Schottky barrier of the diode. The calculated spectra of the excited electrons and holes are found to display high-energy tails above 0.4 eV. While the contribution of the electronic channel to the dissipation of condensation energy is very small (less than 1%), the calculated probability for high-energy electronic excitations in Mg epitaxy is compatible with the chemicurrent contribution extracted from the experimental data.

Time-resolved photoelectron imaging of ultrafast S2→S1 internal conversion through conical intersection in pyrazine

A nonadiabatic electronic transition through a conical intersection was studied by pump-probe photoelectron imaging spectroscopy with a 22 fs time resolution in the benchmark polyatomic molecule of pyrazine and deuterated pyrazine. The lifetimes of the S(2) state of pyrazine and deuterated pyrazine were determined to be 22+/-3 fs by the global fitting of the time-energy maps of photoelectron kinetic energy (PKE) distributions. The lifetime of S(3) was determined to be 40-43 fs. Two-dimensional maps of photoelectron distributions were obtained for time (t) and PKE, and individual PKE distributions upon ionization from S(2) and S(1) were extracted. Quantum beat with an approximately 50 fs period was observed after the S(2)-->S(1) internal conversion, which was attributed to the totally symmetric vibration nu(6a) in S(1).