Hopping Dynamics Research Articles

Derivation of Some Translation-Invariant Lindblad Equations for a Quantum Brownian Particle

We study the dynamics of a Brownian quantum particle hopping on an infinite lattice with a spin degree of freedom. This particle is coupled to free boson gases via a translation-invariant Hamiltonian which is linear in the creation and annihilation operators of the bosons. We derive the time evolution of the reduced density matrix of the particle in the van Hove limit in which we also rescale the hopping rate. This corresponds to a situation in which both the system-bath interactions and the hopping between neighboring sites are small and they are effective on the same time scale. The reduced evolution is given by a translation-invariant Lindblad master equation which is derived explicitly.

Low-lying electronic states and their nonradiative deactivation of thieno[3,4-b]pyrazine: Anab initiostudy

State-averaged complete active space self-consistent field (SA-CASSCF) calculations have been used to locate the four low-lying electronic states of thieno[3,4-b]pyrazine (TP), and their vertical excitation energies and emission energies have been determined by means of the multistate complete active space with second-order perturbation theory (MS-CASPT2) calculations. The present results indicate that the first weak (1)nπ∗ excited state has a C(s)-symmetry structure, unlike two bright (1)ππ∗ excited states in C(2v) symmetry. The predicted vertical excitation energies of the three low-lying excited states in the gas phase are 3.41, 3.92, and 4.13 eV at the restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] optimized geometry, respectively. On the basis of calculations, a new assignment to the observed spectra of TP was proposed, in which the (1)nπ∗ state should be responsible for the weak absorption centred at 3.54 eV and the two closely spaced (1)ππ∗ states account for the two adjacent absorption bands observed at 3.99 and 4.15 eV. The predicted vertical emission energies lend further support to our assignments. Surface hopping dynamics simulations performed at the SA-CASSCF level suggest that the plausible deactivation mechanism comprises an ultrafast relaxation of the (1)ππ∗ excited states to (1)nπ∗ excited state, followed by a slow conversion to the S(0) ground state via a conical intersection. This internal conversion is accessible, since the MS-CASPT2 predicted energy barrier is ∼0.55 eV, much lower than the Franck-Condon point populated initially under excitation. The dynamical simulations on the low-lying states for 500 fs reveal that the relatively high (1)ππ∗ excited states can be easily trapped in the (1)nπ∗ excited state, which will increase the lifetime of the excited thieno[3,4-b]pyrazine.

Nonadiabatic ab initio molecular dynamics of photoisomerization in bridged azobenzene

The photoisomerization mechanisms of bridged azobenzene are investigated by means of surface hopping dynamics simulations based on the Zhu-Nakamura theory. In the geometry optimizations and potential energy surface calculations, four minimum-energy conical intersections between the ground state and the lowest excited state are found to play important roles in the trans-cis and cis-trans isomerization processes. The trans-cis photoisomerization proceeds through two minimum-energy conical intersections. Ultrafast pedal motion of the N atoms and twisting of phenyl rings around their N-C bonds allows the molecule to move to a minimum-energy conical intersection, after which surface hopping from S(1) to S(0) occurs. In the S(0) state, further rotation occurs around the N=N bond and two N-C bonds until the azo moiety and phenyl rings complete their isomerization. Finally, the cis form is achieved by subsequent adjustment of the ethylene bridge. In the cis-trans photodynamics, there is one rotational pathway, in the middle of which two CIs are responsible for the surface hopping to the S(0) state. After the nonadiabatic transition, the molecule reaches the trans form through a barrierless pathway and the two phenyl rings and the additional bridge complete their reorientation almost at the same time.

Strikingly Different Effects of Hydrogen Bonding on the Photodynamics of Individual Nucleobases in DNA: Comparison of Guanine and Cytosine

Ab initio surface hopping dynamics calculations were performed to study the photophysical behavior of cytosine and guanine embedded in DNA using a quantum mechanical/molecular mechanics (QM/MM) approach. It was found that the decay rates of photo excited cytosine and guanine were affected in a completely different way by the hydrogen bonding to the DNA environment. In case of cytosine, the geometrical restrictions exerted by the hydrogen bonds did not influence the relaxation time of cytosine significantly due to the generally small cytosine ring puckering required to access the crossing region between excited and ground state. On the contrary, the presence of hydrogen bonds significantly altered the photodynamics of guanine. The analysis of the dynamics indicates that the major contribution to the lifetime changes comes from the interstrand hydrogen bonds. These bonds considerably restricted the out-of-plane motions of the NH(2) group of guanine which are necessary for the ultrafast decay to the ground state. As a result, only a negligible amount of trajectories decayed into the ground state for guanine embedded in DNA within the simulation time of 0.5 ps, while for comparison, the isolated guanine relaxed to the ground state with a lifetime of about 0.22 ps. These examples show that, in addition to phenomena related to electronic interactions between nucleobases, there also exist relatively simple mechanisms in DNA by which the lifetime of a nucleobase is significantly enhanced as compared to the gas phase.

Surface hopping dynamics using a locally diabatic formalism: Charge transfer in the ethylene dimer cation and excited state dynamics in the 2-pyridone dimer

In this work, the advantages of a locally diabatic propagation of the electronic wave function in surface hopping dynamics proceeding on adiabatic surfaces are presented providing very stable results even in challenging cases of highly peaked nonadiabatic interactions. The method was applied to the simulation of transport phenomena in the stacked ethylene dimer radical cation and the hydrogen bonded 2-pyridone dimer. Systematic tests showed the reliability of the method, in situations where standard methods relying on an adiabatic propagation of the wave function and explicit calculation of the nonadiabatic coupling terms exhibited significant numerical instabilities. Investigations of the ethylene dimer radical cation with an intermolecular distance of 7.0 Å provided a quantitative description of diabatic charge trapping. For the 2-pyidone dimer, a complex dynamics was obtained: a very fast (<10 fs) initial S(2)∕S(1) internal conversion; subsequent excitation energy transfers with a characteristic time of 207 fs; and the occurrence of proton coupled electron transfer (PCET) in 26% of the trajectories. The computed characteristic excitation energy transfer time of 207 fs is in satisfactory agreement with the experimental value of 318 fs derived from the vibronic exciton splittings in a monodeuterated 2-pyridone dimer complex. The importance of nonadiabatic coupling for the PCET related to the electron transfer was demonstrated by the dynamics simulations.

Temperature-Dependent Exciton Hopping in an Array of Inhomogeneously Broadened Quantum Dots

The dynamics of exciton hopping in an array of inhomogeneously broadened CdSe/ZnS quantum dot (QD) ensembles is examined by measuring time- and spectrally resolved fluorescence intensities. We have found a decrease in the fluorescence decay time as well as a dynamic redshift of the fluorescence spectrum originating from exciton transfer. Both show the characteristic temperature dependence reflecting the peculiar exciton dynamics in the QD ensemble. We propose a model of coupled QD arrays where inhomogeneous distribution and dark QDs that are related to a long-lasting off-state of blinking QDs are taken into account. Experimental results together with numerical calculations based on this model suggest that at low temperatures, an exciton transfers to a local low-energy site and tends to be trapped, whereas at high temperatures, thermally activated hopping of the exciton occurs repeatedly. Furthermore, we show that the decay time decrease of the QD array is attributable to exciton hopping to dark QDs.

Broadband dielectric response of Ba(Zr,Ti)O3ceramics: From incipient via relaxor and diffuse up to classical ferroelectric behavior

Dielectric responses of ceramics from the lead-free isovalent BaZrO${}_{3}$-BaTiO${}_{3}$ (BZT) system were investigated from Hz frequencies up to the infrared in a broad temperature range, 10--700 K. Pure BaZrO${}_{3}$ is a displacive weak-incipient ferroelectric with a simple cubic perovskite structure down to low temperatures, whose dielectric response is fully determined by polar phonons, the lowest-frequency one being of the Last type, unlike BaTiO${}_{3}$, where it is of the Slater type. BaZr${}_{0.4}$Ti${}_{0.6}$O${}_{3}$ is a relaxor ferroelectric whose dielectric anomaly is caused by a strong, overdamped excitation, which softens from the THz down to MHz range according to the Arrhenius law and merges into a constant-loss background at low temperatures. Such a reponse is similar to lead-containing and heterovalent relaxors, but unlike them, the lowest-frequency TO1 polar phonon does not soften appreciably. In the case of BaZr${}_{0.2}$Ti${}_{0.8}$O${}_{3}$ we have investigated the dynamic response connected with a diffuse ferroelectric phase transition. The main dielectric anomaly is again due to similar overdamped THz-microwave excitation, which, however, softens only to the GHz range near the transition temperature and below it merges with a near-constant-loss background. The picture of polar nanoregions in BZT differs from that in heterovalent relaxors, because they are pinned to the regions of the off-centered Ti${}^{4+}$ ions, which are frozen in our temperature range. Therefore we assign the soft relaxations to hopping of the off-centered Ti${}^{4+}$ ions. This is compared with the behavior of pure BaTiO${}_{3}$ ceramics, in which the hopping of the off-centered Ti${}^{4+}$ ions also substantially contributes to the phase transition dynamics. Unlike BaTiO${}_{3}$, the dynamic instability, which is responsible for the diffuse ferroelectric and relaxor behavior in BZT, is fully due to the hopping dynamics of the off-centered Ti${}^{4+}$ ions rather than due to soft phonons, and therefore the diffuse transition is of the order-disorder type.

Site-selective spectroscopic study on the dynamics of exciton hopping in an array of inhomogeneously broadened quantum dots

Site-selective spectroscopic study on the dynamics of exciton hopping in an array of inhomogeneously broadened quantum dots

Reductive electron transfer dynamics in gold nanocluster films contacted with aqueous electrolytes

Reductive electron transfer dynamics in the multilayer film of alkanethiolate monolayer protected clusters (so-called MPCs) contacted with an aqueous electrolyte was studied. As determined by potential step chronoamperometry, electrons are transported within the film phenomenologically via the diffusion-like hopping (self-exchange) between the localized MPC sites with an average first order rate constant of 104s−1. This value is comparable with those for the similar kind of films immersed in organic electrolytes but much smaller than those for the all-solid or dry films. It thus reveals that the solvent swelling presents negligible effect on the electron hopping dynamics and that the electron transfer is most likely limited by the diffusive redistribution of the counterions in order to keep the local electroneutrality.

Realization of interacting quantum field theories in driven tight-binding lattices

It is theoretically shown that the coherent hopping dynamics of a non-relativistic particle in engineered tight-binding lattices subjected to combined ac and dc driving forces can mimic in Fock space relativistic quantum field theories (QFTs) of strongly interacting fields, enabling access to extreme dynamical regimes beyond weak coupling and perturbative predictions. In particular, the simulation of a QFT model describing a Dirac field strongly coupled to a scalar bosonic field via a Yukawa coupling is proposed, suggesting the possibility of implementing this model using engineered lattices of evanescently coupled optical waveguides with a bent optical axis.

An immersed boundary method for Brownian dynamics simulation of polymers in complex geometries: Application to DNA flowing through a nanoslit with embedded nanopits

This work presents an immersed boundary method that allows fast Brownian dynamics simulation of solutions of polymer chains and other Brownian objects in complex geometries with fluctuating hydrodynamics. The approach is based on the general geometry Ewald-like method, which solves the Stokes equation with distributed regularized point forces in O(N) or O(NlogN) operations, where N is the number of point forces in the system. Time-integration is performed using a midpoint algorithm and Chebyshev polynomial approximation proposed by Fixman. This approach is applied to the dynamics of a genomic DNA molecule driven by flow through a nanofluidic slit with an array of nanopits on one wall of the slit. The dynamics of the DNA molecule was studied as a function of the Péclet number and chain length (the base case being λ-DNA). The transport characteristics of the hopping dynamics in this device differ at low and high Péclet number, and for long DNA, relative to the pit size, the dynamics is governed by the segments residing in the pit. By comparing with results that neglect them, hydrodynamic interactions are shown to play an important quantitative role in the hopping dynamics.

Single molecule diffusion on hard, soft and fluid surfaces

Molecular diffusion on a surface is often considered as a thermal energy-activated process of molecular hopping between adjacent adsorption sites on a surface and simply determined by molecule–surface interaction. In this work, we report distinct diffusive dynamics of probe molecules on methyl-terminated self-assembled monolayer (SAM), polymer brush layer and lipid bilayer by using fluorescence correlation spectroscopy (FCS) at a single-molecule level. We have observed that despite weaker molecule–surface interaction, the surface diffusion of probe molecules on soft polymer brush surface and fluid lipid bilayer can be much slower than that on hard SAM surface, suggesting a strong impact of interfacial dynamics of the underlying coating on molecular surface diffusion. To further examine the coupling of thermal activated molecular hopping and soft surface dynamics, we have investigated the diffusion of probe molecules on polymer brushes of varied grafting density and thickness, where the molecule–surface interaction remains nearly the same, yet the adopted conformations and dynamics of surface-grafted PNIPAM chains vary considerably; it is striking to observe that the diffusion of probe molecules could be further retarded on PNIPAM brush surfaces of lower grafting density or higher brush thickness, thereby exhibiting the presence of an optimal brush thickness range to facilitate fast surface diffusion of adsorbed probe molecules. All the observations combined lead to a general model by taking the dynamics of underlying surface layers into account to elucidate the molecular diffusion mechanism on varied surfaces.

ASYMMETRIC EXCLUSION PROCESS WITH CONSTRAINED HOPPING AND PARALLEL DYNAMICS AT A JUNCTION

In this article totally asymmetric simple exclusion process (TASEP) with constrained hopping and parallel dynamics at a junction is investigated using a mean-field approximation and Monte Carlo simulations. The constrained particle hopping probability r (r ≤ 1) at a junction may correspond to a delay caused by a driver choosing the right direction or a delay waiting for green traffic light in the real world. There are six stationary phases in the system, which can reflect free flow and congested traffic situations. Correlations at the junction point are investigated via simulations. It is observed that small r leads to stronger correlations. The theoretical results are agreement with computer simulations well.

Cellular automaton model for molecular traffic jams

We consider the time evolution of an exactly solvable cellular automaton with randominitial conditions both in the large-scale hydrodynamic limit and on the microscopic level.This model is a version of the totally asymmetric simple exclusion process with sublatticeparallel update and thus may serve as a model for studying traffic jams in systems ofself-driven particles. We study the emergence of shocks from the microscopic dynamics ofthe model. In particular, we introduce shock measures whose time evolution we cancompute explicitly, both in the thermodynamic limit and for open boundaries where aboundary-induced phase transition driven by the motion of a shock occurs. The motion ofthe shock, which results from the collective dynamics of the exclusion particles, is a randomwalk with an internal degree of freedom that determines the jump direction. This typeof hopping dynamics is reminiscent of some transport phenomena in biologicalsystems.

Ultrafast Hopping Dynamics of5fElectrons in the Mott InsulatorUO2Studied by Femtosecond Pump-Probe Spectroscopy

We describe a femtosecond pump-probe study of ultrafast hopping dynamics of 5f electrons in the Mott insulator UO₂ following Mott-gap excitation at temperatures of 5-300 K. Hopping-induced response of the lattice and electrons is probed by transient reflectivity at mid- and above-gap photon energies, respectively. These measurements show an instantaneous hop, subsequent picosecond lattice deformation, followed by acoustic phonon emission and microsecond relaxation. Temperature-dependent studies indicate that the slow relaxation results from Hubbard excitons formed by U³⁺-U⁵⁺ pairs.

Three-State Trajectory Surface Hopping Studies of the Photodissociation Dynamics of Formaldehyde on ab Initio Potential Energy Surfaces

Full-dimensional, three-state, surface hopping calculations of the photodissociation dynamics of formaldehyde are reported on ab initio potential energy surfaces (PESs) for electronic states S(1), T(1), and S(0). This is the first such study initiated on S(1) with ab initio-calculated spin-orbit couplings among the three states. We employ previous PESs for S(0) and T(1), and a new PES for S(1), which we describe here, as well as new spin-orbit couplings. The time-dependent electronic state populations and the branching ratio of radical products produced from S(0) and T(1) states and that of total radical products and molecular products at three total energies are calculated. Details of the surface hopping dynamics are described, and a novel pathway for isomerization on T(1) via S(0) is reported. Final translational energy distributions of H + HCO products from S(0) and T(1) are also reported as well as the translational energy distribution and final rovibrational distributions of H(2) products from the molecular channel. The present results are compared to previous trajectory calculations initiated from the global minimum of S(0). The roaming pathway leading to low rotational distribution of CO and high vibrational population of H(2) is observed in the present calculations.

The effect of bias-temperature stress on Na+ incorporation into thin insulating films

The action of Na(+) incorporation into thin insulating films and transport therein under influence of a bias voltage and temperature (BT stress) is the subject of this work. Deposited onto highly n-doped Si wafers, the insulators get BT stressed and subsequently investigated by means of time-of-flight-secondary ion mass spectrometry (ToF-SIMS). A thin PMMA film, spin-coated onto the insulator, serves as host matrix for a defined amount of Na(+), provided via sodium triflate. Combining BT stress and ToF-SIMS depth profiling enables the unambiguous detection of Na(+), incorporated into the insulating material. The insulators of interest vary in their nitride content: SiO(2), SiO(x)N(y), and Si(3)N(4). For SiO(2), it is shown that once a threshold BT stress is exceeded, Na(+) gets quantitatively incorporated from PMMA into the underlying insulator, finally accumulating at the SiO(2)/Si interface. A quantitative assessment by combination of Butler-Volmer kinetics with hopping dynamics reveals activation energies of E(a) = 1.55 - 2.04 eV for Na(+) transport in SiO(2) with varying thickness. On the other hand, SiO(x)N(y) and Si(3)N(4) films show a different Na(+) incorporation characteristic in this type of experiment, which can be explained by the higher coordination of nitrogen and hence the reduced Na(+) permeability within these insulators.

Ab Initio Based Surface-Hopping Dynamics Study on Ultrafast Internal Conversion in Cyclopropanone

Cyclopropanone exhibits an intriguing phenomenon that the fluorescence from the S(1) state disappears below 365 nm. This is ascribed to the ultrafast S(1) → S(0) internal conversion process via conical intersection, which deprives opportunity of the fluorescence emission. In this work, we have used ab initio based surface hopping dynamics method to study vibrational-mode-dependent S(1) → S(0) internal conversion of cyclopropanone. A new conical intersection between the S(1) and S(0) states is determined by the state-averaged CASSCF/cc-pVDZ calculations, which is confirmed to play a critical role in the ultrafast S(1) → S(0) internal conversion by the nonadiabatic dynamics simulations. It is found that the internal conversion occurs more efficiently when the initial kinetic energies are distributed in the four vibrational modes related to the C═O group, especially in the C-O stretching and the O-C-C-C out-of-plane torsional modes. Meanwhile, the S(1) lifetime and the time scale of the S(1) → S(0) internal conversion are estimated by the ab initio based dynamics simulations, which is consistent with the ultrafast S(1) → S(0) internal conversion and provides further evidence that the ultrafast internal conversion is responsible for the fluorescence disappearance of cyclopropanone.

Semiclassical dynamics simulations of charge transport in stacked π-systems

Charge transfer processes within stacked π-systems were examined for the stacked ethylene dimer radical cation with inclusion of a bridge containing up to three formaldehyde molecules. The electronic structure was treated at the complete active space self-consistent field and multireference configuration interaction levels. Nonadiabatic interactions between electronic and nuclear degrees of freedom were included through semiclassical surface hopping dynamics. The processes were analyzed according to fragment charge differences. Static calculations explored the dependence of the electronic coupling and on-site energies on varying geometric parameters and on the inclusion of a bridge. The dynamics simulations gave the possibility for directly observing complex charge transfer and diabatic trapping events.

The decay mechanism of photoexcited guanine − A nonadiabatic dynamics study

Ab initio surface hopping dynamics calculations were performed for the biologically relevant tautomer of guanine in gas phase excited into the first ππ∗ state. The results show that the complete population of UV-excited molecules returns to the ground state following an exponential decay within ∼220 fs. This value is in good agreement with the experimentally obtained decay times of 148 and 360 fs. No fraction of the population remains trapped in the excited states. The internal conversion occurs in the ππ∗ state at two related types of conical intersections strongly puckered at the C2 atom. Only a small population of about 5% following an alternative pathway via a nπ∗ state was found in the dynamics.