Wave Packet Molecular Dynamics Research Articles

Exploring the vibrational series of pure trilobite Rydberg molecules

In trilobite Rydberg molecules, an atom in the ground state is bound by electron-atom scattering to a Rydberg electron that is in a superposition of high angular momentum states. This results in a homonuclear molecule with a permanent electric dipole moment in the kilo-debye range. Trilobite molecules have previously been observed only with admixtures of low-l states. Here we report on the observation of two vibrational series of pure trilobite Rubidium-Rydberg molecules that are nearly equidistant. They are produced by three-photon photoassociation and lie energetically more than 15 GHz below the atomic 22F state of rubidium. We show that these states can be used to measure the electron-atom scattering length at low energies in order to benchmark current theoretical calculations. In addition to measuring their kilo-Debye dipole moments, we also show that the molecular lifetime is increased compared to the 22F state due to the high-l character. The observation of an equidistant series of vibrational states opens the way to observe coherent molecular wave packet dynamics.

Equilibrium properties of warm dense deuterium calculated by the wave packet molecular dynamics and density functional theory method.

A joint simulation method based on the wave packet molecular dynamics and density functional theory (WPMD-DFT) is applied to study warm dense deuterium (nonideal deuterium plasmas). This method was developed recently as an extension of the wave packet molecular dynamics (WPMD) in which the equations of motion are solved simultaneously for classical ions and semiclassical electrons represented as Gaussian wave packets. Compared to the classical molecular dynamics and WPMD simulations, the method of WPMD-DFT provides a more accurate representation of quantum effects such as electron-ion coupling and electron degeneracy. It allows studying nonadiabatic dynamics of electrons and ions in equilibrium and nonequilibrium states while being more accurate and efficient at high densities than WPMD and classical molecular dynamics. In the paper, we discuss particular features of the method such as special boundary conditions and the procedure of isentrope calculation as well as the results obtained by WPMD-DFT for the shock-compressed deuterium. The compression isentrope and principal Hugoniot curves obtained by WPMD-DFT are compared with available experimental data and other simulation approaches to validate the method. It opens up a possibility of further application of the method to study nonequilibrium states and relaxation processes.

An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter

Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

High performance wave packet molecular dynamics with density functional exchange-correlation term for non-ideal plasma simulations

We report on development of the wave packet molecular dynamics (WPMD) with density functional theory (DFT) simulation technique that we proposed earlier for nonideal plasma and warm dense matter simulations. The method is based on the WPMD where the electron exchange-correlation effects are taken into account using the DFT approach. It is aimed at studying simultaneous dynamics of electrons and ions in equilibrium and non-equilibrium conditions for a wide range of temperatures and densities. Compared to classical molecular dynamics and WPMD simulations the method of WPMD-DFT provides more accurate representation of quantum effects such as electron–ion coupling and electron degeneracy. At this stage of the method development we pay a special attention to the performance issues such as acceleration with graphical processing units, the choice of an optimal simulation box size with respect to the boundary conditions, the use of an adaptive mesh for calculation of the exchange-correlation energy, and implementation of our algorithm in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The results for internal energy of equilibrium dense hydrogen plasma are presented for evaluation of the method.

Ion modes in dense ionized plasmas through nonadiabatic molecular dynamics

We perform nonadiabatic simulations of warm dense aluminum based on the electron-force field (EFF) variant of wave-packet molecular dynamics. Comparison of the static ion-ion structure factor with density functional theory (DFT) is used to validate the technique across a range of temperatures and densities spanning the warm dense matter regime. Focusing on a specific temperature and density (3.5 eV, 5.2 g/cm3), we report on differences in the dynamic structure factor and dispersion relation across a variety of adiabatic and nonadiabatic techniques. We find the dispersion relation produced with EFF is in close agreement with the more robust and adiabatic Kohn-Sham DFT.

Two-path phonon interference resonance induces a stop band in a silicon crystal matrix with a multilayer array of embedded nanoparticles

In this work, we report a new stop-band formation mechanism by performing the atomistic Green's function calculation and the wave-packet molecular dynamics simulation for a system with germanium-nanoparticle array embedded in a crystalline silicon matrix. When only a single nanoparticle is embedded, the local resonance, induced through destructive interference between two different phonon wave paths, gives rise to several sharp and significant transmittance dips. On the other hand, when the number of embedded nanoparticles further increases to ten, a stop band with complete phonon reflection is formed due to the two-path resonance Bragg-like phonon interference. The wave packet simulations further uncover that the stop band originates from the collective phonon resonances at the embedded nanoparticles. Compared with the traditional stop-band formation mechanism that is the single-path Bragg reflection, the resonance mechanism has a significant advantage in not requiring the strict periodicity in the embedded nanoparticles array. We also demonstrate that the stop band can significantly suppress thermal conductance in the low-frequency regime. Our work provides a robust, scalable. and easily modulable stop-band formation mechanism. which opens a new degree of freedom for phononics-related heat control.

Thermodynamic properties of the nonideal hydrogen plasmas: Comparison of different simulation techniques

In this paper, we review the following simulation techniques for studying nonideal electron–ion plasmas: classical molecular dynamics, wave packet molecular dynamics and Monte Carlo and path integral Monte Carlo. As example the hydrogen nonideal plasma is considered for a wide range of densities and temperatures. The results for the thermodynamic properties such as the internal energy and pressure are compared. The area of applicability of the classical molecular dynamics and fundamental problems of the wave packet Monte Carlo are discussed.

Two New Methods To Generate Internal Coordinates for Molecular Wave Packet Dynamics in Reduced Dimensions.

The curse of dimensionality still remains as the central challenge of molecular quantum dynamical calculations. Either compromises on the accuracy of the potential landscape have to be made or methods must be used that reduce the dimensionality of the configuration space of molecular systems to a low dimensional one. For dynamic approaches such as grid-based wave packet dynamics that are confined to a small number of degrees of freedom this dimensionality reduction can become a major part of the overall problem. A common strategy to reduce the configuration space is by selection of a set of internal coordinates using chemical intuition. We devised two methods that increase the degree of automation of the dimensionality reduction as well as replace chemical intuition by more quantifiable criteria. Both methods reduce the dimensionality linearly and use the intrinsic reaction coordinate as guidance. The first one solely relies on the intrinsic reaction coordinate (IRC), whereas the second one uses semiclassical trajectories to identify the important degrees of freedom.

Excited state X-ray absorption spectroscopy: Probing both electronic and structural dynamics.

We investigate the sensitivity of X-ray absorption spectra, simulated using a general method, to properties of molecular excited states. Recently, Averbukh and co-workers [M. Ruberti et al., J. Chem. Phys. 140, 184107 (2014)] introduced an efficient and accurate L2 method for the calculation of excited state valence photoionization cross-sections based on the application of Stieltjes imaging to the Lanczos pseudo-spectrum of the algebraic diagrammatic construction (ADC) representation of the electronic Hamiltonian. In this paper, we report an extension of this method to the calculation of excited state core photoionization cross-sections. We demonstrate that, at the ADC(2)x level of theory, ground state X-ray absorption spectra may be accurately reproduced, validating the method. Significantly, the calculated X-ray absorption spectra of the excited states are found to be sensitive to both geometric distortions (structural dynamics) and the electronic character (electronic dynamics) of the initial state, suggesting that core excitation spectroscopies will be useful probes of excited state non-adiabatic dynamics. We anticipate that the method presented here can be combined with ab initio molecular dynamics calculations to simulate the time-resolved X-ray spectroscopy of excited state molecular wavepacket dynamics.

Tracing few-femtosecond photodissociation dynamics on molecular oxygen with a single-color pump-probe scheme in the VUV

Molecular wave-packet dynamics in oxygen are studied in the time domain, using a single-color VUV-pump--VUV-probe scheme. 17-fs VUV pulses, centered at 161 nm are generated via high-order harmonic generation driven by an intense 800-nm pulse leading to VUV pulse energies that reach 1.$1\ensuremath{\mu}\text{J}$ per pulse. An all-reflective interferometric pump-probe scheme is used for studying the delay dependence of the molecular oxygen ion signal with simultaneous nonresonant photoionization of krypton as a precise timing-reference. Access to the excited dissociative state lifetime is provided by the resulting delay-dependent ${{\mathrm{O}}_{2}}^{+}$ signal, ultimately limited by the molecular ionization window. The ability to use a two-photon VUV probe provides the delay-dependent detection of ${\mathrm{O}}^{+}$ as an additional observable, extending the dissociation observation window.

Reflecting Boundary Conditions for Classical and Quantum Molecular Dynamics Simulations of Nonideal Plasmas

AbstractThe influence of boundary conditions for the classical and wave packet molecular dynamics (MD) simulations of nonideal electron‐ion plasma is studied. We start with the classical MD and perform a comprehensive study of convergence of the per‐particle potential energy and pressure with the number of particles using both the nearest image method (periodic boundaries) and harmonic reflective boundaries. As a result an error caused by finiteness of the simulation box is estimated. Moreover electron oscillations given by the spectra of the current autocorrelation function are analyzed for both types of the boundary conditions. A special attention is paid to the reflecting boundaries since they prevent wave packet spreading in the Wave Packet MD. To speed up classical MD simulations we use the GPU‐accelerated code

Phonon Scattering Dynamics of Thermophoretic Motion in Carbon Nanotube Oscillators.

Using phonon wave packet molecular dynamics simulations, we find that anomalous longitudinal acoustic (LA) mode phonon scattering in low to moderate energy ranges is responsible for initiating thermophoretic motion in carbon nanotube oscillators. The repeated scattering of a single mode LA phonon wave packet near the ends of the inner nanotube provides a net unbalanced force that, if large enough, initiates thermophoresis. By applying a coherent phonon pulse on the outer tube, which generalizes the single mode phonon wave packet, we are able to achieve thermophoresis in a carbon nanotube oscillator. We also find the nature of the unbalanced force on end-atoms to be qualitatively similar to that under an imposed thermal gradient. The thermodiffusion coefficient obtained for a range of thermal gradients and core lengths suggest that LA phonon scattering is the dominant mechanism for thermophoresis in longer cores, whereas for shorter cores, it is the highly diffusive mechanism that provides the effective force.

Molecular wave-packet dynamics on laser-controlled transition states

We present a kinematically complete and time-resolved study of the dissociation dynamics of ${\mathrm{H}}_{2}{}^{+}$ using ultrashort extreme-ultraviolet and near-infrared laser pulses. The reaction kinematics can be controlled by varying the time delay between the two pulses. We demonstrate that a time-dependent laser-dressed potential-energy curve enables the control of the nuclear motion. The dynamics is well reproduced by intuitive semiclassical trajectories on a time-dependent potential curve. From this most fundamental scenario we gain insight in the underlying mechanisms which may be applied as design principles for molecular quantum control, particularly for ultrafast molecular reactions involving the motion of protons.

Extension of the wave packet molecular dynamics method towards the accurate quantum simulations of electron dynamics

In this paper, we review a multiple-wavepacket version of the Antisymmetrized Wave Packet Molecular Dynamics (AWPMD), that may be utilized to increase the accuracy and the performance of this quantum simulation method. The original WPMD method is based on parameterization of the electron wave function by a single Gaussian wave packet. It gives qualitatively better results than the classical Molecular Dynamics but the quantitative description of essentially quantum systems is rather poor. In this work, we describe a new technique based on multiple Gaussian expansion of the single-electron wave function, which is called Split Wave Packet Molecular Dynamics (SWPMD). The related theoretical formalism is given, followed by the analysis of static and dynamical properties of a quantum system of several particles, where the simulation results may be compared to the theoretical predictions. The tests are based on ionization of hydrogen atom under a strong laser pulse. We demonstrate that the SWPMD method may significantly improve the accuracy of the model wave function and enables one to simulate the quantum branching processes, including the tunneling, which was impossible in the single-wavepacket version of the method.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach.

Liquid para-hydrogen (p-H2) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H2. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computational cost, by which basic experimental properties of p-H2 liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.

Wave packet spreading and localization in electron-nuclear scattering

The wave packet molecular dynamics (WPMD) method provides a variational approximation to the solution of the time-dependent Schrödinger equation. Its application in the field of high-temperature dense plasmas has yielded diverging electron width (spreading), which results in diminishing electron-nuclear interactions. Electron spreading has previously been ascribed to a shortcoming of the WPMD method and has been counteracted by various heuristic additions to the models used. We employ more accurate methods to determine if spreading continues to be predicted by them and how WPMD can be improved. A scattering process involving a single dynamic electron interacting with a periodic array of statically screened protons is used as a model problem for comparison. We compare the numerically exact split operator Fourier transform method, the Wigner trajectory method, and the time-dependent variational principle (TDVP). Within the framework of the TDVP, we use the standard variational form of WPMD, the single Gaussian wave packet (WP), as well as a sum of Gaussian WPs, as in the split WP method. Wave packet spreading is predicted by all methods, so it is not the source of the unphysical diminishing of electron-nuclear interactions in WPMD at high temperatures. Instead, the Gaussian WP's inability to correctly reproduce breakup of the electron's probability density into localized density near the protons is responsible for the deviation from more accurate predictions. Extensions of WPMD must include a mechanism for breakup to occur in order to yield dynamics that lead to accurate electron densities.

Molecular wave packet dynamics decelerated by solvent environment: A theoretical approach

We present a new dynamic continuum ansatz to describe the frictional force exerted on moving wave packets in a solvent cage. The solvent interferes on the femtosecond time scale, but decides the reaction outcome.

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.

Improvement of Wave Packet Molecular Dynamics Using Packet Splitting

AbstractThe method of Wave Packet Molecular Dynamics Method (WPMD) is a promising replacement of the classical molecular dynamics for the simulations of many‐electron systems including nonideal plasmas. In this contribution we report on a packet splitting technique where an electron is represented by multiple Gaussians, with mixing coefficients playing the role of additional dynamic variables. It provides larger flexibility and better accuracy than the original WPMD with a single Gaussian per electron. As a test case we consider ionization of hydrogen atom in a short laser pulse, where the split packets provide a basis for quantum branching (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Light-Induced Conical Intersections: Topological Phase, Wave Packet Dynamics, and Molecular Alignment

In previous publications (J. Phys. B: At., Mol. Opt. Phys.2008, 41, 221001; J. Phys. B: At., Mol. Opt. Phys. 2011, 44, 045603) a novel and physically interesting phenomenon was found in the field of light-matter interactions. It was shown theoretically that exposing a molecule to a laser field can give rise to the appearance of so-called light-induced conical intersections (LICIs). The existence of such LICIs may change significantly the field free physical properties of a molecular system. In this article we review the LICIs in diatomics and provide a new insight to the LICI phenomenon. The sodium dimer is chosen as an explicit sample system. We calculated the Berry phase for a contour that surrounds the point of LICI and found it to be π, which is the same value as for the case of a "natural" CI in triatomic or larger molecules. We also present results to stress the impact of LICIs on molecular wave packet dynamics and molecular alignment in different electronic states.