Wave Packet Simulations Research Articles

Heat transfer mechanism across few-layer graphene by molecular dynamics

We use nonequilibrium molecular dynamics to study heat transfer across structures consisting of a few layers of graphene sandwiched between silicon crystals. We find that when heat transfers from a silicon lead on one side across the graphene layers to a silicon lead on the other side, the interfacial conductance is essentially independent of the number of layers, in agreement with recent experimental findings. By contrast, wave-packet simulations show that the transmission coefficient of individual vibrational modes depends strongly on frequency and the number of graphene layers, indicating significant interference effects. This apparent contradiction is resolved by a theoretical calculation, which shows that the integrated contribution of the phonons to the interfacial thermal conductance is essentially independent of the number of layers. When one atomic layer of graphene is heated directly, the effective interfacial conductance associated with heat dissipation to the silicon substrate is much smaller. We attribute this to the resistance associated with heat transfer between high and low frequency modes within heated graphene.

Influence of Coulomb Blockade on Wave Packet Dynamics in Nanoscale Structures

Influence of Coulomb blockade on electron scattering by a quantum dot has been theoretically investigated using a multielectron wave packet simulation technique based on the time-dependent Hartree–Fock approximation. In our simulation, the bound states of electrons in the dot are self-consistently determined. We confirmed that Koopman's theorem keeps its validity only for weak Coulomb interactions. Moreover, we show that the maximum number of electrons trapped in the dot does depend on the strength of Coulomb interactions. Consequently, the transmission and reflection probabilities of an incident wave packet toward the dot are strongly influenced by the number of trapped electrons in the dot.

Application of the wavelet transform to nanoscale thermal transport

The continuous wavelet transform is employed to analyze the dynamics and time-dependent energy distribution of phonon wave-packet propagation and scattering in molecular dynamics simulations. The equations of the one-dimensional continuous wavelet transform are presented and then discretized for implementation. Practical aspects and limitations of the transform are discussed, with attention to its application in the analysis of molecular dynamics simulations. The transform is demonstrated using three examples that are relevant to nanoscale thermal transport. First, a system of wave packets that interfere in both the spatial and Fourier domains are separated by the wavelet transform, allowing the measurement of each packet's contribution to the system energy. Second, the wavelet transform is applied to a multiple wave-packet simulation of a silicon, heavy-silicon interface. The wavelet-based calculation of mode-dependent transmission is validated through comparison to literature results and theoretical predictions. Third, the dynamic scattering of a large amplitude wave packet is studied using the wavelet transform. The transform reveals a transition in the structure of the energy distribution. Unlike current techniques, the wavelet transform can be used to determine how the energy of a simulated system is distributed in time, in space, and among wave numbers, simultaneously. The ability to resolve phonon motion and energy from a vibrating ensemble of atoms in a molecular dynamics simulation makes the wavelet transform a promising technique for probing the physical mechanisms of nanoscale thermal transport.

Laser-Polarization Effects on Coherent Vibronic Excitation of Molecules with Quasi-Degenerate Electronic States

The laser-polarization effects on nonadiabatically coupled π-electron rotation (ring current) and molecular vibration have been theoretically analyzed for aromatic molecules with quasi-degenerate excited states irradiated by an ultrashort laser pulse of arbitrary polarization. We first derived general formulations of the coherent electronic wave packet and expectation value of electronic angular momentum within a frozen-nuclei model. The relative quantum phase of the superposed quasi-degenerate states, which determines the oscillating behavior of angular momentum, can be manipulated by the ellipticity and orientation of the incident laser. Nuclear wave packet simulations with a model molecule confirmed the controllability of π-electron rotation, although the angular momentum is gradually reduced by nonadiabatic couplings. The amplitude of molecular vibration depends prominently on the orientation of linear polarization vectors rather than the helicity of circular polarization. The characteristic feature in vibrational amplitudes is attributed to the interference in nonadiabatic transition governed by the relative quantum phase between nuclear wave packets. This offers a new strategy for laser control of molecular vibrations through the wave packet interference in nonadiabatic transition.

Wave packet simulations of phonon boundary scattering at graphene edges

Wave packet dynamics is used to investigate the scattering of longitudinal (LA), transverse (TA), and bending-mode (ZA) phonons at the zigzag and armchair edges of suspended graphene. The interatomic forces are calculated using a linearized Tersoff potential. The strength of a boundary scattering event at impeding energy flow is described by a forward scattering coefficient, similar in spirit to a specularity parameter. For armchair boundaries, this scattering coefficient is found to depend strongly on the magnitude, direction, and polarization of the incident wavevector, while for zigzag boundaries, the forward scattering coefficient is found to always be unity regardless of wavevector and polarization. Wave packet splitting is observed for ZA phonons incident on armchair boundaries, while both splitting and mode conversion are observed for LA and TA phonons incident on both zigzag and armchair boundaries. These simulation results show that armchair boundaries impede the forward propagation of acoustic phonon energy much more strongly than zigzag boundaries do, suggesting that graphene nanoribbons will have substantially lower thermal conductivity in armchair rather than zigzag orientation.

Juxtaposing density matrix and classical path-based wave packet dynamics

In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed.

Strategies for tuning phonon transport in multilayered structures using a mismatch-based particle model

The performance of many micro- and nanoscale devices depends on the ability to control interfacial thermal transport, which is predominantly mediated by phonons in semiconductor systems. The phonon transmissivity at an interface is therefore a quantity of interest. In this work, an empirical model, termed the thermal mismatch model, is developed to predict transmissivity at ideal interfaces between semiconductor materials, producing an excellent agreement with molecular dynamics simulations of wave packets. To investigate propagation through multilayered structures, this thermal mismatch model is then incorporated into a simulation scheme that represents wave packets as particles, showing a good agreement with a similar scheme that used molecular dynamics simulations as input [P. K. Schelling and S. R. Phillpot, J. Appl. Phys. 93, 5377 (2003)]. With these techniques validated for both single interfaces and superlattices, they are further used to identify ways to tune the transmissivity of multilayered structures. It is shown that by introducing intermediate layers of certain atomic masses, the total transmissivity can either be systematically enhanced or reduced compared to that of a single interface. Thus, this model can serve as a computationally inexpensive means of developing strategies to control phonon transmissivity in applications that may benefit from either enhancement (e.g., microelectronics) or reduction (e.g., thermoelectrics) in thermal transport.

Theoretical study on ultrafast intersystem crossing of chromium(III) acetylacetonate

In the relaxation process from the 4T2g state of chromium(III) acetylacetonate, CrIII(acac)3, ultrafast intersystem crossing (ISC) competes with vibrational relaxation (VR). This contradicts the conventional cascade model, where ISC rates are slower than VR ones. We hence investigate the relaxation process with quantum chemical calculations and excited-state wavepacket simulations to obtain clues about the origins of the ultrafast ISC. It is found that a potential energy curve of the 4T2g state crosses those of the 2T1g states near the Franck–Condon region and their spin–orbit couplings are strong. Consequently, ultrafast ISC between these states is observed in the wavepacket simulation.

Electron dynamics of shocked polyethylene crystal

Electron force field (eFF) wave-packet molecular-dynamics simulations of the single shock Hugoniot are reported for a crystalline polyethylene (PE) model. The eFF results are in good agreement with previous density-functional theories and experimental data, which are available up to 80 GPa. We predict shock Hugoniots for PE up to 350 GPa. In addition, we analyze the structural transformations that occur due to heating. Our analysis includes ionization fraction, molecular decomposition, and electrical conductivity during isotropic compression. We find that above a compression of 2.4 $\mathrm{g}/{\mathrm{cm}}^{3}$, the PE structure transforms into an atomic fluid, leading to a sharp increase in electron ionization and a significant increase in system conductivity. eFF accurately reproduces shock pressures and temperatures for PE along the single shock Hugoniot.

Communication: Quantum Zeno-based control mechanism for molecular fragmentation

A quantum control mechanism is proposed for molecular fragmentation processes within a scenario grounded on the quantum Zeno effect. In particular, we focus on the van der Waals Ne-Br(2) complex, which displays two competing dissociation channels via vibrational and electronic predissociation. Accordingly, realistic three-dimensional wave packet simulations are carried out by using ab initio interaction potentials recently obtained to reproduce available experimental data. Two numerical models to simulate the repeated measurements are reported and analyzed. It is found that the otherwise fast vibrational predissociation is slowed down in favor of the slow electronic (double fragmentation) predissociation, which is enhanced by several orders of magnitude. Based on these theoretical predictions, some hints to experimentalists to confirm their validity are also proposed.

Localization behavior of Dirac particles in disordered graphene superlattices

Graphene superlattices (GSLs), formed by subjecting a monolayer graphene sheet to a periodic potential, can be used to engineer band structures and, from there, charge transport properties, but these are sensitive to the presence of disorder. The localization behavior of massless 2D Dirac particles induced by weak disorder is studied for both scalar-potential and vector-potential GSLs, computationally as well as analytically by a weak-disorder expansion. In particular, it is investigated how the Lyapunov exponent (inverse localization length) depends on the incidence angle to a 1D GSL. Delocalization resonances are found for both scalar and vector GSLs. The sharp angular dependence of the Lyapunov exponent may be exploited to realize disorder-induced filtering, as verified by full 2D numerical wave packet simulations.

The role of orbiting resonances in the vibrational relaxation of I2(B,v′ = 21) by collisions with He at very low energies: a theoretical and experimental study

The low-energy collisions of I(2)(B,v' = 21) with He involving collision-induced vibrational relaxation of I(2) are investigated both experimentally and by means of wave packet simulations. The theoretical cross sections exhibit a structure of peaks originated by orbiting resonances of the I(2)(B,v' = 21) - He van der Waals complex formed in the I(2) + He collisions. Such a structure has similar characteristics as the structure of peaks found in the experimental cross sections. In fact, four of the five peaks of the measured cross sections appear at positions nearly coincident with those of four of the peaks found in the theoretical cross sections. Thus this result confirms the experimental finding that enhancement of I(2) vibrational relaxation is caused by the population of I(2)(B,v' = 21) - He orbiting resonances populated upon the low-energy collisions. The possibility of using this mechanism in the vibrational cooling of diatomic molecules is discussed.

Rotational coherence imaging and control for CN molecules through time-frequency resolved coherent anti-Stokes Raman scattering

Numerical wave packet simulations are performed for studying coherent anti-Stokes Raman scattering (CARS) for CN radicals. Electronic coherence is created by femtosecond laser pulses between the X(2)Σ and B(2)Σ states. Due to the large energy separation of vibrational states, the wave packets are superpositions of rotational states only. This allows for a specially detailed inspection of the second- and third-order coherences by a two-dimensional imaging approach. We present the time-frequency domain images to illustrate the intra- and intermolecular interferences, and discuss the procedure to rationally control and experimentally detect the interferograms in solid Xe environment.

Ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate excited states in molecules: Population and vibrational coherence transfers

Results of a theoretical study of ultrafast coherent dynamics of nonadiabatically coupled quasi-degenerate π-electronic excited states of molecules were presented. Analytical expressions for temporal behaviors of population and vibrational coherence were derived using a simplified model to clarify the quantum mechanical interferences between the two coherently excited electronic states, which appeared in the nuclear wavepacket simulations [M. Kanno, H. Kono, Y. Fujimura, S.H. Lin, Phys. Rev. Lett 104 (2010) 108302]. The photon-polarization direction of the linearly polarized laser, which controls the populations of the two quasi-degenerate electronic states, determines constructive or destructive interference. Features of the vibrational coherence transfer between the two coupled quasi-electronic states through nonadiabatic couplings are also presented. Information on both the transition frequency and nonadiabatic coupling matrix element between the two states can be obtained by analyzing signals of two kinds of quantum beats before and after transfer through nonadiabatic coupling.

Molecular orbital concept on spin-flip transport in molecular junctions

The spin-dependent electron transport correlated with spin-flip dynamics in a molecular junction was investigated in the wave-packet and Green’s function approaches. The molecular junction adopted in this work is described by a simple one-dimensional tight-binding chain including a localized spin. The spin exchange coupling J between the localized and conduction electron spins was taken into account through the s-d Hamiltonian. The wave-packet simulations showed that the transmission probabilities in both the spin-flip and no-flip processes show large peaks at the eigenvalues of the spin singlet (−3J/4) and triplet (J/4) states, and that, different transmission properties appear at the mid-gap of the two eigenvalues: the spin-flip process shows a moderate decrease, whereas the no-flip process an abrupt drop. Dividing the s-d Hamiltonian into two submatrices and referring to the molecular orbital concept for the coherent electron transport, we found that the moderate decrease in the spin-flip process at the mid-gap is the result of a coherent-and-cooperative contribution from the singlet and triplet states of the conduction and localized electron spins, and that, the abrupt drop in the no-flip process at the mid-gap is mainly caused by the coherent cancellation from the singlet and triplet states. The molecular orbital concept available for the electron transport including spin-flip scattering processes is described in Green’s function method, in analogy to the one derived for the spinless electron transport.

Adiabatic and Nonadiabatic Bond Cleavages in Norrish Type I Reaction

One of the fundamental photoreactions for ketones is Norrish type I reaction, which has been extensively studied both experimentally and theoretically. Its α bond-cleavage mechanisms are usually explained in an adiabatic picture based on the involved excited-state potential energy surfaces, but scarcely investigated in terms of a nonadiabatic picture. In this work, the S(1) α bond-cleavage reactions of CH(3)OC(O)Cl have been investigated by using the CASSCF and MRCI-SD calculations, and the ab initio based time-dependent quantum wavepacket simulation. The numerical results indicate that the photoinduced dissociation dynamics of CH(3)OC(O)Cl could exhibit strong nonadiabatic bond-fission characteristics for the S(1) α C-Cl bond cleavage, while the dynamics of the S(1) α C-O bond cleavage is mainly of adiabatic characteristics. This nonadiabatic mechanism for Norrish type I reaction of CH(3)OC(O)Cl is uncovered for the first time. The quantum wavepacket dynamics, based on the reduced-dimensional coupled potential energy surfaces, to some extent illustrates the significance of the nonadiabatic effect in the transition-state region on the dynamics of Norrish type I reaction.

Hawking radiation and the boomerang behavior of massive modes near a horizon

We discuss the behaviour of massive modes near a horizon based on a study of the dispersion relation and wave packet simulations of the Klein-Gordon equation. We point out an apparent paradox between two (in principle equivalent) pictures of black hole evaporation through Hawking radiation. In the picture in which the evaporation is due to the emission of positive-energy modes, one immediately obtains a threshold for the emission of massive particles. In the picture in which the evaporation is due to the absorption of negative-energy modes, such a threshold apparently does not exist. We resolve this paradox by tracing the evolution of the positive-energy massive modes with an energy below the threshold. These are seen to be emitted and move away from the black hole horizon, but they bounce back at a "red horizon" and are re-absorbed by the black hole, thus compensating exactly for the difference between the two pictures. For astrophysical black holes, the consequences are curious but do not affect the terrestrial constraints on observing Hawking radiation. For analogue gravity systems with massive modes, however, the consequences are crucial and rather surprising.

Modeling of interface thermal conductance in longitudinally connected carbon nanotube junctions

This article explores the behavior of interface thermal conductance of longitudinally connected (6,6) nanotubes—connected through CH2 linkages—using nonequilibrium molecular dynamics (NEMD) and wave packet simulations. Here, we study the effect of connected linkers on the interface thermal conductance and thermal energy transmission coefficients for several phonon modes. Our simulation results suggest that interface thermal conductance between nanotubes strongly depends on the number of CH2 linkers. The more the number of CH2 linkers, the higher the conductance. Further insights into phonon energy transmission are provided from wave packet simulations. Here, we find that the behavior of transmission for various studied acoustic and optical phonon modes is complex in nature, where the thermal transmission coefficients do not always correlate with number of CH2 linkages. However, when the contributions from all the modes are added together, the overall interface thermal conductance agrees well with NEMD simulations.

Large Shift and Small Broadening of Br2 Valence Band upon Dimer Formation with H2O: An Ab Initio Study

Valence electronic excitation spectra are calculated for the H(2)O···Br(2) complex using highly correlated ab initio potentials for both the ground and the valence electronic excited states and a 2-D approximation for vibrational motion. Due to the strong interaction between the O-Br and the Br-Br stretching motions, inclusion of these vibrations is the minimum necessary for the spectrum calculation. A basis set calculation is performed to determine the vibrational wave functions for the ground electronic state and a wave packet simulation is conducted for the nuclear dynamics on the excited state surfaces. The effects of both the spin-orbit interaction and temperature on the spectra are explored. The interaction of Br(2) with a single water molecule induces nearly as large a shift in the spectrum as is observed for an aqueous solution. In contrast, complex formation has a remarkably small effect on the T = 0 K width of the valence bands due to the fast dissociation of the dihalogen bond upon excitation. We therefore conclude that the widths of the spectra in aqueous solution are mostly due to inhomogeneous broadening.

Theoretical studies of absorption cross sections for the C̃ B12-X̃ A11 system of sulfur dioxide and isotope effects

The C (1)B(2)-X (1)A(1) photoexcitation of SO(2) was studied to investigate excited-state dynamics and the effects of the initial vibrational state. Ultraviolet photoabsorption cross sections (sigma's) of seven isotopologues ((32)S (16)O(2), (33)S (16)O(2), (34)S (16)O(2), (36)S (16)O(2), (32)S(16)O(17)O, (32)S(16)O(18)O, (34)S(16)O(18)O) were computed using the wave packet propagation technique based on the three-dimensional potential energy surfaces of the X and C states, which were calculated using the ab initio molecular orbital configuration interaction method. Numerous wave packet simulations were carried out under the adiabatic approximation and used to calculate the sigma's of the seven isotopologues at 298 K; we concluded that the absorption spectrum of SO(2) can be reliably modeled within the adiabatic framework based on the analysis of the time evolution of the wave packet. The calculated sigma's are in reasonable agreement with the recent experiment in the 190-228 nm region, and the isotope shifts of the peaks for (33)S (16)O(2) and (34)S (16)O(2) relative to the corresponding peaks for (32)S (16)O(2) are in good agreement with the observed data. Relative to the sigma of (32)S (16)O(2), isotopic substitution shows a significant increment for those of (34)S (16)O(2) and (36)S (16)O(2) in the 190-228 nm region. This trend is consistent with the observed data.