Hopping Simulations Research Articles

Surface hopping simulation of vibrational predissociation of methanol dimer

The mixed quantum-classical surface hopping method is applied to the vibrational predissociation of methanol dimer, and the results are compared to more exact quantum calculations. Utilizing the vibrational SCF basis, the predissociation problem is cast into a curve crossing problem between dissociative and quasibound surfaces with different vibrational character. The varied features of the dissociative surfaces, arising from the large amplitude OH torsion, generate rich predissociation dynamics. The fewest switches surface hopping algorithm of Tully [J. Chem. Phys. 93, 1061 (1990)] is applied to both diabatic and adiabatic representations. The comparison affords new insight into the criterion for selecting the suitable representation. The adiabatic method's difficulty with low energy trajectories is highlighted. In the normal crossing case, the diabatic calculations yield good results, albeit showing its limitation in situations where tunneling is important. The quadratic scaling of the rates on coupling strength is confirmed. An interesting resonance behavior is identified and is dealt with using a simple decoherence scheme. For low lying dissociative surfaces that do not cross the quasibound surface, the diabatic method tends to overestimate the predissociation rate whereas the adiabatic method is qualitatively correct. Analysis reveals the major culprits involve Rabi-like oscillation, treatment of classically forbidden hops, and overcoherence. Improvements of the surface hopping results are achieved by adopting a few changes to the original surface hopping algorithms.

Nonadiabatic Decay Dynamics of a Benzylidene Malononitrile

The photoinduced nonadiabatic decay dynamics of 2-[4-(dimethylamino)benzylidene]malononitrile (DMN) in the gas phase is investigated at the semiempirical OM2/MRCI level using surface hopping simulations. A lifetime of 1.2 ps is predicted for the S(1) state, in accordance with experimental observation. The dominant reaction coordinate is found to be the twisting around the C7═C8 double bond accompanied by pronounced pyramidalization at the C8 atom. Motion along this coordinate leads to the lowest-energy conical intersection (CI(01α)). Several other S(0)/S(1) conical intersections have also been located by full optimization but play no role in the dynamics. The time-resolved fluorescence spectrum of DMN is simulated by computing emission energies and oscillator strengths along the trajectories. It compares well with the experimental spectrum. The use of different active spaces in the OM2/MRCI calculations yields similar results and thus demonstrates their internal consistency.

Nonadiabatic decay dynamics of 9H-guanine in aqueous solution

The nonadiabatic decay of the biologically relevant guanine tautomer (9H-guanine) in aqueous solution has been investigated by trajectory surface hopping simulations in a quantum mechanical-molecular mechanical (QM-MM) framework. The QM part (9H-guanine) was treated at the semiempirical OM2/MRCI level, while the MM part (water) was described by the TIP3P force field. The optimized geometries for the relevant minima and conical intersections are qualitatively similar for 9H-guanine in the gas phase and in aqueous solution, while there are notable solvent-induced shifts in the computed vertical excitation energies (up to about 0.4 eV). Overall, the results from the static OM2/MRCI-based calculations are in reasonable agreement with the available ab initio and experimental data. The dynamics simulations show ultrafast nonradiative decay for 9H-guanine in water that is even slightly faster than in the gas phase, with time constants of 20 fs and around 0.3 ps for the S(2)→ S(1) and S(1)→ S(0) internal conversions, respectively. They predict a change in the S(1)→ S(0) decay mechanism when going from the gas phase to aqueous solution: the major pathway for 9H-guanine in water involves a conical intersection with an out-of-plane distortion of the carbonyl oxygen atom, which does not play any significant role in the gas phase, where the decay mainly proceeds via two other conical intersections characterized by ring distortions and out-of-plane displacement of the amino group, respectively. Possible reasons for this change in the mechanism are analyzed.

Surface Hopping Excited-State Dynamics Study of the Photoisomerization of a Light-Driven Fluorene Molecular Rotary Motor.

We report a theoretical study of the photoisomerization step in the operating cycle of a prototypical fluorene-based molecular rotary motor (1). The potential energy surfaces of the ground electronic state (S0) and the first singlet excited state (S1) are explored by semiempirical quantum-chemical calculations using the orthogonalization-corrected OM2 Hamiltonian in combination with a multireference configuration interaction (MRCI) treatment. The OM2/MRCI results for the S0 and S1 minima of the relevant 1-P and 1-M isomers and for the corresponding S0 transition state are in good agreement with higher-level calculations, both with regard to geometries and energetics. The S1 surface is characterized at the OM2/MRCI level by locating two S0-S1 minimum-energy conical intersections and nearby points on the intersection seam and by computing energy profiles for pathways toward these MECIs. Semiclassical Tully-type trajectory surface hopping (TSH) simulations with on-the-fly OM2/MRCI calculations are carried out to study the excited-state dynamics after photoexcitation to the S1 state. Fast relaxation to the ground state is observed through the conical intersection regions, predominantly through the lowest-energy one with a strongly twisted central C═C double bond and pyramidalized central carbon atom. The excited-state lifetimes for the direct and inverse photoisomerization reactions (1.40 and 1.79 ps) and the photostationary state ratio (2.7:1) from the TSH-OM2 simulations are in good agreement with the available experimental data (ca. 1.7 ps and 3:1). Excited-state lifetimes, photostationary state ratio, and dynamical details of the TSH-OM2 simulations also agree with classical molecular dynamics simulations using a reparametrized optimized potentials for liquid simulations (OPLS) all-atom force field with ad-hoc surface hops at predefined conical intersection points. The latter approach allows for a more extensive statistical sampling.

Atomistic Simulation of Water Percolation and Proton Hopping in Nafion Fuel Cell Membrane

We have performed a detailed analysis of water clustering and percolation in hydrated Nafion configurations generated by classical molecular dynamics simulations. Our results show that at low hydration levels H(2)O molecules are isolated and a continuous hydrogen-bonded network forms as the hydration level is increased. Our quantitative analysis has established a hydration level (λ) between 5 and 6 H(2)O/SO(3)(-) as the percolation threshold of Nafion. We have also examined the effect of such a network on proton transport by studying the structural diffusion of protons using the quantum hopping molecular dynamics method. The mean residence time of the proton on a water molecule decreases by 2 orders of magnitude when the λ value is increased from 5 to 15. The proton diffusion coefficient in Nafion at a λ value of 15 is about 1.1 × 10(-5) cm(2)/s in agreement with experiment. The results provide quantitative atomic-level evidence of water network percolation in Nafion and its effect on proton conductivity.

The photodynamics of 2,4-diaminopyrimidine in comparison with 4-aminopyrimidine: The effect of amino-substitution

Nonadiabatic photodynamical surface hopping simulations of 4-aminopyrimidine and 2,4-diaminopyrimidine were performed at multi-configurational level. Additional NH2 substitution blocks part of the ring puckering modes necessary to reach ultrafast deactivation channels but does not affect the excited-state lifetime of 2,4-diaminopyrimidine significantly since other pathways leading to ultrafast relaxation can be utilized.The effect of the excess energy on the relaxation mechanism of 2,4-diaminopyrimidine was studied. It is shown that the amount of initial energy influences the time to reach the crossing seam and thus the lifetime. This study is important when interpreting the experimental results performed at different pump energies.

Mechanism of Charge Transport along Zinc Porphyrin-Based Molecular Wires

In this study charge transport along zinc porphyrin-based molecular wires is simulated, considering both bandlike and hopping mechanisms. It is shown that bandlike transport simulations yield significantly overestimated hole mobility values. On the basis of kinetic and thermodynamic considerations, it is inferred that charge transport along zinc porphyrin-based molecular wires occurs by small polaron hopping. Hole mobility values on the order of 0.1 cm(2) V(-1) s(-1) are found from small polaron hopping simulations, which agree well with previously reported experimental results. It is suggested that the experimentally observed increase of the charge carrier mobility on formation of supramolecular ladderlike structures is determined by two factors. One of these is an increase of charge transfer integrals between monomer units due to molecular wire planarization. A more important factor is the reduction of the amount of energetic disorder along the molecular wire and in its environment. General guidelines for determining the mechanism of charge transport along molecular wires are discussed.

NMR Diffusometry with Beds of Nanoporous Host Particles: An Assessment of Mass Transfer in Compartmented Two-Phase Systems

Molecular diffusion in a bed of zeolite crystallites is mimicked by dynamic Monte Carlo simulation of a particle hopping on a two-dimensional square lattice. The resulting probability distribution of molecular propagation (the "mean propagator") is used for a rigorous determination of the resulting dependencies of diffusion measurement by pulsed field gradient NMR. In the limiting cases of intracrystalline, restricted, and long-range diffusion, these dependencies are found to coincide with the well-known relations resulting from the application of a simplifying exchange model (the "two-region" approximation). The intensity of transport resistances on the boundary between the intra- and intercrystalline spaces, i.e., on the compartment boundaries, is only accessible in the intermediate case, i.e., for observation times comparable with the mean lifetimes within the different compartments. In this case, significant differences between the results of the rigorous treatment and the "two-region" approximation may occur.

Photodynamics of azobenzene in a hindering environment

We have run trajectory surface hopping simulations of the trans → cis photoisomerization of azobenzene, subject to a pulling force. The model mimics two situations: a trans-azobenzene derivative with bulky substituents that may not be easily displaced, and a recent experiment by Gaub’s group [T. Hugel, N.B. Holland, A. Cattani, L. Moroder, M. Seitz, H.E. Gaub, Science 296 (2002) 1103; N.B. Holland, T. Hugel, G. Neuert, A. Cattani-Scholz, C. Renner, D. Oesterhelt, L. Moroder, M. Seitz, H.E. Gaub, Macromolecules 36 (2003) 2015; G. Neuert, T. Hugel, R.R. Netz, H.E. Gaub, Macromolecules 39 (2005) 789], in which a polymer with azobenzene units was stretched in an atomic force microscope. In both cases, the shortening of the azobenzene moiety in going from the trans to the cis form is opposed by a pulling force. Our simulations show that the trans → cis photoconversion is only partially suppressed by considerably large forces (≈500 pN or more). However, the cis isomer reverts to trans in the ground state, with the help of the pulling force and using the vibrational energy that is available in the first 1–2 ps. The lowering of the quantum yields is therefore the combined result of hindering of the excited state process and of the hot ground state back reaction.

Excited state dynamics with the direct trajectory surface hopping method: azobenzene and its derivatives as a case study

We review the recent studies of the photoisomerization dynamics of azobenzene and its derivatives by surface hopping simulations based on semiempirical potential energy surfaces. We examine the ability of semiclassical methods to predict the excited state dynamics and to reproduce transient spectroscopic signals that constitute the most direct experimental evidence in this field. We show that the available simulation methods yield a deep insight into the mechanism of photochemical reactions and excited state decay, and a fairly good quantitative agreement with experimental findings. Probably the most important technical improvements we can envisage concern the surface hopping algorithm and the usage of ab initio data in the simulation of transient spectra. Concerning azobenzene, our results show that the isomerization mechanism is torsion of the N=N double bond, both by n → π* and by π → π* excitation. The influence of the solvent and the findings of some recent femtochemistry experiments deserve further work to be fully interpreted.

Role of band potential roughness on the luminescence properties of InGaN quantum wells grown by MBE on bulk GaN substrates

Role of band potential roughness on luminescence decay time and stimulated emission in InGaN quantum wells (QWs) grown by rf plasma-assisted molecular beam epitaxy (MBE) on bulk GaN substrates was studied. A high-photoexcitation regime used ensured conditions similar to those in operating laser diodes. Standard deviation of the potential fluctuations in different thickness InGaN QWs was found to vary in the range of 13–22 meV as revealed by Monte Carlo simulation of localized exciton hopping. A negligible influence of this variation on the luminescence decay time (∼700 ps) and stimulated emission threshold (∼30 kW/cm2) was observed. We attribute this insensitivity to the low density of localized states (∼1 × 1018 cm–3) estimated in our high-quality QWs grown by MBE, and therefore, assign extended states to be mainly responsible for the properties of highly-excited luminescence. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Study of exciton hopping in AlGaN epilayers by photoluminescence spectroscopy and Monte Carlo simulation

AbstractMonte Carlo simulation of exciton hopping reveals the features of the potential profile in AlGaN (with Al content of ∼26%) responsible for S‐shaped and W‐shaped temperature dependences of photoluminescence band peak position and bandwidth, respectively. One of the samples was grown using the conventional metal‐organic chemical vapor deposition (MOCVD), while the second one was grown with the insertion of a buffer layer grown by migration enhanced MOCVD (MEMOCVDTM) technique. The potential profile is shown to be double‐scaled in both Al0.26Ga0.74N epilayers, and the exciton hopping occurs through random potential fluctuations within isolated low‐potential regions with the average energy of the localized states dispersed on the second scale. Both energy fluctuation scales were found to be in the range of 18‐20 meV and were independent of the growth technique used. Meanwhile, the carrier lifetime was 30 ps in the sample grown by conventional MOCVD and 190 ps in the sample grown using the MEMOCVDTM technique. We conclude that the difference in the lifetimes is caused by the density of nonradiative recombination centers rather than by the potential fluctuations affecting the carrier motion. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulation of the phononless hopping in a Coulomb glass

AbstractThe phononless hopping conductivity of a disordered system with localized states is studied in a broad range of frequencies by straightforward computer simulations taking into account Coulomb interactions. At sufficiently low temperatures, the conductivity is determined by the zero‐phonon absorption of the photon by pairs of states. The laser frequency dependence of the conductivity is examined and compared with the analytical model of Efros and Shklovskii and with recent experimental data obtained on Si:P. The range of parameters is determined, for which the conductivity dependence on photon energy best reproduces the experimental results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Basin hopping simulations for all-atom protein folding

We investigate different protocols of the basin hopping technique for de novo protein folding. Using the protein free-energy force field PFF01 we report the reproducible all-atom folding of the 20-amino-acid tryptophan-cage protein [Protein Data Bank (PDB) code: 112y] and of the recently discovered 26-amino-acid potassium channel blocker (PDB code: 1wqc), which exhibits an unusual fold. We find that simulations with increasing cycle length and random starting temperatures perform best in comparison with other parametrizations. The basin hopping technique emerges as a simple but very efficient and robust workhorse for all-atom protein folding.

Exciton hopping and nonradiative decay in AlGaN epilayers

Monte Carlo simulation of phonon-assisted localized exciton hopping has been employed to describe the photoluminescence linewidth variation with temperature and to reveal band potential profile of ternary AlGaN epilayers with different carrier lifetimes. The lifetimes of 30 and 190 ps were experimentally determined in the layers with AlN buffers grown by conventional metal-organic chemical vapor deposition (MOCVD) and by migration-enhanced MOCVD (MEMOCVD™), respectively. The potential profile in AlGaN is shown to consist of double-scaled fluctuations. Exciton hopping in Al0.26Ga0.74N occurs within the random potential fluctuations (on the scale σ≈19meV) in isolated low-potential regions with the average localization energy dispersed on the scale Γ≈19meV. Such a pattern of band potential profile was found to be independent on the growth technique used for the deposition of their AlN buffer layers. This implies that the large difference in carrier lifetimes estimated in the AlGaN epilayers with the same Al content is caused by different densities of nonradiative recombination centers rather than by carrier localization in the potential fluctuations.

Structure and Stability of Small TiO2 Nanoparticles

The effect of the nanostructure on the photochemistry of TiO2 is an active field of research owing to its applications in photocatalysis and photovoltaics. Despite this interest, little is known of the structure of small particles of this oxide with sizes at the nanometer length scale. Here we present a computational study that locates the global minima in the potential energy surface of Ti(n)O2n clusters with n = 1-15. The search procedure does not refer to any of the known TiO2 polymorphs, and is based on a novel combination of simulated annealing and Monte Carlo basin hopping simulations, together with genetic algorithm techniques, with the energy calculated by means of an interatomic potential. The application of several different methods increases our confidence of having located the global minimum. The stable structures are then refined by means of density functional theory calculations. The results from the two techniques are similar, although the methods based on interatomic potentials are unable to describe some subtle effects. The agreement is especially good for the larger particles, with n = 9-15. For these sizes the structures are compact, with a preference for a central octahedron and a surrounding layer of 4- and 5-fold coordinated Ti atoms, although there seems to be some energy penalty for particles containing the 5-fold coordinated metal atoms with square base pyramid geometry and dangling Ti=O bonds. The novel structures reported provide the basis for further computational studies of the effect of nanostructure on adsorption, photochemistry, and nucleation of this material.

Carrier localization effect in polarized InGaN multiple quantum wells

Carrier localization effects in polarized InGaN/GaN multiple quantum wells (MQWs) were investigated as a function of well width, d, and In content, x. Using photoreflectance (PR), photoluminescence (PL), PL excitation (PLE), selective excitation of PL, PL excitation power, and time-resolved PL spectroscopy, the dominance of the localization effect against the built-in field effect on carrier recombination dynamics in InxGa1–xN MQWs of different well width (d = 2.0–4.0 nm, x ≈ 0.15) and In content (x ≈ 0.22–0.27, d = 2.5 nm) was revealed. Based on the modeling of the PL spectra by Monte Carlo simulation of exciton hopping and the spectroscopic reference provided by PR, increased In content and well width were found to increase the band potential fluctuations and carrier localization depth. The density of localized states deduced from the simulation was found to be in a fair agreement with the PLE data. The built-in field strength in InGaN QWs containing 15% of In was estimated to be of 0.5 MV/cm. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Photoluminescence temperature behavior and Monte Carlo simulation of exciton hopping in InGaN multiple quantum wells

Application of Monte Carlo simulation of exciton (carrier) hopping for the analysis of the photolumines- cence (PL) temperature behavior in In0.2Ga0.8N/GaN multiple is reported. The PL linewidth and peak position measured in the 10-300 K range exhibited a W-shaped and S-shaped temperature be- havior, respectively. The W-shaped linewidth dependence was fitted with the results of Monte Carlo simulation, which involved phonon-assisted exciton hopping through energy states confined in the band potential fluctuation minima. The simulation yielded the values of the standard deviation for potential fluctuations within In-rich regions (31 meV), dispersion of the average exciton energy in different regions (29 meV), and the temperature dependence of the band gap, which was found to be in a fair agreement with the photoreflectance data. Our results, which infer in-plane motion of localized excitons within the wells, are consistent with the model of large In-rich regions (segmented wells or quantum discs) with band potential fluctuations inside these regions.

Surface hopping simulation of the vibrational relaxation of I2 in liquid xenon using the collective probabilities algorithm

A surface hopping simulation of the vibrational relaxation of highly excited I(2) in liquid xenon is presented. The simulation is performed by using the collective probabilities algorithm which assures the coincidence of the classical and quantum populations. The agreement between the surface hopping simulation results and the experimental measurements for the vibrational energy decay curves at different solvent densities and temperatures is shown to be good. The overlap of the decay curves when the time axis is linearly scaled is explained in terms of the perturbative theory for the rate constants. The contribution of each solvent atom to the change of the quantum populations of the solute molecule is used to analyze the mechanism of the relaxation process

Monte Carlo simulation of the exciton hopping in quaternary AlInGaN

Phonon-assisted exciton hopping in quaternary AlInGaN was simulated by using a Monte Carlo procedure. Simulation results based on the conventional model are unable to simultaneously describe the S- and W-shaped temperature dependences of the photoluminescence band peak and line width, respectively. In particular, such simulation yielded a much narrower line than that experimentally observed. To quantitatively describe the “anomalous” temperature behavior of the emission line in the temperature range of 8–150 K, we propose a model based on exciton hopping in isolated In-rich clusters with a random distribution in average localization energy. Our results confirm the formation of In-rich clusters in an AlInGaN alloy with a roughness of the potential profile in the individual clusters of ≈16 meV and their distribution in average localization energy of ≈42 meV. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)