Ehrenfest Molecular Dynamics Research Articles

Photoinduced Dynamics at the Water/TiO_{2}(101) Interface.

We present a femtosecond time-resolved optical pump-soft x-ray probe photoemission study in which we follow the dynamics of charge transfer at the interface of water and anatase TiO_{2}(101). By combining our observation of transient oxygen O 1s core level peak shifts at submonolayer water coverages with Ehrenfest molecular dynamics simulations we find that ultrafast interfacial hole transfer from TiO_{2} to molecularly adsorbed water is completed within the 285fs time resolution of the experiment. This is facilitated by the formation of a new hydrogen bond between an O_{2c} site at the surface and a physisorbed water molecule. The calculations fully corroborate our experimental observations and further suggest that this process is preceded by the efficient trapping of the hole at the surface of TiO_{2} by hydroxyl species (-OH), that form following the dissociative adsorption of water. At a water coverage exceeding a monolayer, interfacial charge transfer is suppressed. Our findings are directly applicable to a wide range of photocatalytic systems in which water plays a critical role.

Electronic stopping power of magnesium including inner-electron excitation

The electronic stopping power of magnesium for protons and He ions is studied by a nonequilibrium approach based on real-time time-dependent density-functional theory combined with Ehrenfest molecular-dynamics simulation. The electronic stopping power of Mg for energetic protons and He ions is calculated, and the microscopic excitation mechanism for the inner $2p$ electron of Mg and its contribution to electronic stopping power is revealed. In the low-energy range, the velocity proportionality of the electronic stopping power of Mg for protons is displayed. The low-energy stopping power of Mg for He ions displays deviations from the velocity proportionality, which is ascribed to the electronic structure of He ions that enables an additional energy-loss channel due to charge exchange. Our calculated stopping power is in a quantitative agreement with the experimental data up to the stopping maximum, and the stopping power including also $2p$-electron excitation is considerably improved compared to that with only the valence electron taken into account. Our results showed that the contribution of $p$-electron excitation to the electronic stopping is remarkable in the high-velocity regime. The scaling relationship $\sqrt{{S}_{\ensuremath{\alpha}}/{S}_{H}}$ = ${\overline{q}}_{\ensuremath{\alpha}}/{\overline{q}}_{H}$ can be extended to low velocities provided that the mean steady-state charge is employed instead of assuming fully ionized charges and considering also $2p$-electron excitation of Mg.

Emergence of negative viscosities and colored noise under current-driven Ehrenfest molecular dynamics

Molecules in molecular junctions are subject to current-induced forces that can break chemical bonds, induce reactions, destabilize molecular geometry, and halt the operation of the junction. Theories behind current-driven molecular dynamics simulations rely on a perturbative time-scale separation within the system with subsequent use of nonequilibrium Green's functions (NEGF) to compute conservative, non-conservative, and stochastic forces exerted by electrons on nuclear degrees of freedom. We analyze the effectiveness of this approximation, paying particular attention to the phenomenon of negative viscosities. The perturbative approximation is directly compared to the nonequilibrium Ehrenfest approach. We introduce a novel time-stepping approach to calculate the forces present in the Ehrenfest method via exact integration of the equations of motion for the nonequilibrium Green's functions, which does not necessitate a time-scale separation within the system and provides an exact description for the corresponding classical dynamics. We observe that negative viscosities are not artifacts of a perturbative treatment but also emerge in Ehrenfest dynamics. However, the effects of negative viscosity have the possibility of being overwhelmed by the predominantly positive dissipation due to the higher-order forces unaccounted for by the perturbative approach. Additionally, we assess the validity of the white-noise approximation for the stochastic forces, finding that it is justifiable in the presence of a clear time-scale separation and is more applicable when the current-carrying molecular orbital is moved outside of the voltage window. Finally, we demonstrate the method for molecular junction models consisting of one and two classical degrees of freedom.

Contribution of f -electron excitation to electronic stopping power of platinum for protons

The electronic stopping power of protons traveling along the channeling and off-channeling trajectories in platinum (Pt) is reported based on time-dependent density functional theory calculations for electrons combined with Ehrenfest molecular dynamics simulations for ions in real time and real space. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the excitation mechanism for the inner $4f$ electrons of Pt. The comparison of calculation results with experimental data showed that conduction electrons are sufficient to describe the electronic stopping power of Pt accurately in the low-energy range. The excitation of $4f$ electrons contributes substantially to the electronic stopping power of Pt as the proton velocity exceeds 1.0 a.u. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, the velocity dependence of the mean steady-state charge of protons was quantified, and the results showed that the instantaneous charge state of protons exhibits periodic oscillations in the low-energy region, while the periodic oscillations disappears in the high-energy region due to more ionization of protons.

The energetical, electronic and optical properties of the intermetallic fullerene Fe@C60

Understanding the charge transfer pathway and ionization behavior of fullerenes is one of the main conditions for its broad application in batteries. In this paper we observed the possibility to enhance and to control charge transfer by encaging Fe atom inside the carcass of single unit of fullerene C60 in gas phase. By quantum chemical methods it was shown that inside the C60 the Fe atom could be located in three potential wells that determined Fermi level, energy gap and electronic absorption spectrum of the Fe@C60 composite. The influence of external electric field in the range of 0.1÷0.5 V/Å on behavior of the Fe atom inside the fullerene C60 was studied by means of Ehrenfest molecular dynamics. The regularities of charge transfer depending on the initial potential well of the Fe atom were revealed.

First-principles study of the electronic stopping power of indium for protons and He ions

The electronic stopping power of protons and He ions traveling along the channeling and off-channeling trajectories in indium is reported based on time-dependent density functional theory combined with Ehrenfest molecular dynamics simulations. We provided an intuitive description of the electronic stopping power for a wide range of ion energies, and revealed the microcosmic excitation mechanism of the semicore $4d$ electrons of In. The velocity-proportional electronic stopping power and the kink velocity which is due to $4d$-electron excitation are reproduced in the low-energy regime. Because the $5s5p$ valence electrons are uniformly distributed in indium, the electronic excitation of valence electrons via Coulomb scattering is independent of the impact parameter in the investigated velocity range. On the contrary, due to the highly localized nature of semicore electrons, the excitation of $4d$ electrons increases significantly with decreasing of the impact parameter, which suggests that it is triggered by direct ion-electron collision. Our calculated stopping power is in quantitative agreement with the experimental data up to the stopping maximum, and showed that the stopping power obtained from the off-channeling geometry is greatly improved in comparison with the channeling results. Finally, we examined the extent to which the linear response theory is applicable to describe the electronic stopping power by quantifying the velocity dependence of the mean steady-state charge of protons and $\ensuremath{\alpha}$ particles and the effective charge state for $\ensuremath{\alpha}$ particles, and it is found that the linear response theory can be used to predict the stopping power in a wider energy range if the mean steady-state charge is used instead of assuming fully ionized charges.

Single and double charge transfer in the Ne2++He collision within time-dependent density-functional theory

We calculate the charge-transfer cross sections for the ${\mathrm{Ne}}^{2+}+\text{He}$ collision. To this end, we employ Ehrenfest molecular dynamics with time-dependent density-functional theory. The active electrons of the projectile are handled by applying an initial velocity to the Kohn-Sham orbitals via a Galilean boost. The dynamical calculations are performed in an inverse collision framework---the reference frame considers ${\mathrm{Ne}}^{2+}$ to be initially at rest, which ensures numerically converged final-time scattering states. The charge-transfer probabilities are extracted by extending the particle number projection technique to be able to handle the degenerate ${\mathrm{Ne}}^{2+}$ ion. Compared with experimental data available at 10--3000 keV, a fairly good agreement is found for the calculated single- and double-charge transfer cross sections, superior to other theoretical calculations for this ${\mathrm{Ne}}^{2+}+\text{He}$ collision. A time-resolved analysis of the charge-transfer probabilities finds that ionization to the continuum also takes place after the charge transfer has occurred. To account for it, the final scattering states should be followed for a long time, approximately 350 fs, until they stabilize.

Ultrafast Nonradiative Decay of a Dipolar Plasmon-like State in Naphthalene.

Motivated by the uncertainty in our understanding of ultrafast plasmon decay mechanisms, we examine the effect of nuclear vibrations on the dynamical behavior of the strong plasmon-like dipole response of naphthalene, known as the β peak. The real-time time-dependent density functional (RT-TDDFT) method coupled with Ehrenfest molecular dynamics is used to describe the interconnected nuclear and electronic motion. Several vibrational modes promote drastic plasmon decay in naphthalene. The most astonishing finding of this study is that activation of one particular vibrational mode (corresponding to the B1u representation in D2h point group symmetry) leads to a continuous drop of the dipole response corresponding to the β peak into a totally symmetric, dark, quadrupolar electronic state. A second B1u mode provokes the sharp plasmon-like peak to split due to the breaking of structural symmetry. Nonadiabatic coupling between a B2g vibrational mode and the β peak (a B1u electronic state) gives rise to a B3u vibronic state, which can be identified as one of the p-band peaks that reside close in energy to the β peak energy. Overall, strong nonadiabatic coupling initiates plasmon decay into nearby electronic states in acenes, most importantly into dark states. These findings expand our knowledge about possible plasmon decay processes and pave the way for achieving high optical performance in acene-based materials such as graphene.

Decoherence-corrected Ehrenfest molecular dynamics on many electronic states.

Decoherence corrections increase the accuracy of mixed quantum-classical nonadiabatic molecular dynamics methods, but they typically require explicit knowledge of the potential energy surfaces of all occupied electronic states. This requirement renders them impractical for applications in which large numbers of electronic states are occupied. The authors recently introduced the collapse to a block (TAB) decoherence correction [M. P. Esch and B. G. Levine, J. Chem. Phys. 152, 234105 (2020)], which incorporates a state-pairwise definition of decoherence time to accurately describe dynamics on more than two electronic states. In this work, TAB is extended by introduction of a scheme for efficiently computing a small number of approximate eigenstates of the electronic Hamiltonian, eliminating the need for explicit knowledge of a large number of potential energy surfaces. This adaptation of TAB for dense manifolds of states (TAB-DMS) is systematically improvable by increasing the number of computed approximate eigenstates. Application to a series of one-dimensional model problems demonstrates that TAB-DMS can be accurate when even a very modest number of approximate eigenstates are computed (four in all models tested here). Comparison of TAB simulations to exact quantum dynamical simulations indicates that TAB is quite accurate so long as the decoherence correction is carefully parameterized.

Understanding real-time time-dependent density-functional theory simulations of ultrafast laser-induced dynamics in organic molecules.

Real-time time-dependent density functional theory, in conjunction with the Ehrenfest molecular dynamics scheme, is becoming a popular methodology to investigate ultrafast phenomena on the nanoscale. Thanks to recent developments, it is also possible to explicitly include in the simulations a time-dependent laser pulse, thereby accessing the transient excitation regime. However, the complexity entailed in these calculations calls for in-depth analysis of the accessible and yet approximate (either "dressed" or "bare") quantities in order to evaluate their ability to provide us with a realistic picture of the simulated processes. In this work, we analyze the ultrafast dynamics of three small molecules (ethylene, benzene, and thiophene) excited by a resonant laser pulse in the framework of the adiabatic local-density approximation. The electronic response to the laser perturbation in terms of induced dipole moment and excited-state population is compared to the results given by an exactly solvable two-level model. In this way, we can interpret the charge-carrier dynamics in terms of simple estimators, such as the number of excited electrons. From the computed transient absorption spectra, we unravel the appearance of nonlinear effects such as excited-state absorption and vibronic coupling. In this way, we observe that the laser excitation affects the vibrational spectrum by enhancing the anharmonicities therein, while the coherent vibrational motion contributes to stabilizing the electronic excitation already within a few tens of femtoseconds.

Coherent Real-Space Charge Transport Across a Donor-Acceptor Interface Mediated by Vibronic Couplings.

There is growing experimental and theoretical evidence that vibronic couplings, couplings between electronic and nuclear degrees of freedom, play a fundamental role in ultrafast excited-state dynamics in organic donor-acceptor hybrids. Whereas vibronic coupling has been shown to support charge separation at donor-acceptor interfaces, so far, little is known about its role in the real-space transport of charges in such systems. Here we theoretically study charge transport in thiophene:fullerene stacks using time-dependent density functional tight-binding theory combined with Ehrenfest molecular dynamics for open systems. Our results reveal coherent oscillations of the charge density between neighboring donor sites, persisting for ∼200 fs and promoting charge transport within the polymer stacks. At the donor-acceptor interface, vibronic wave packets are launched, propagating coherently over distances of more than 3 nm into the acceptor region. This supports previous experimental observations of long-range ballistic charge-carrier motion in organic photovoltaic systems and highlights the importance of vibronic coupling engineering as a concept for tailoring the functionality of hybrid organic devices.

Nonadiabatic Quantum Molecular Dynamics in Dense Manifolds of Electronic States.

Most nonadiabatic molecular dynamics methods require the determination of a basis of adiabatic or diabatic electronic states at every time step, but in dense manifolds of electronic states, such approaches become intractable. A notable exception is Ehrenfest molecular dynamics, which can be implemented without explicit determination of such a basis but suffers from unphysical behavior when propagation on a mean-field potential energy surface (PES) does not accurately reflect the true dynamics on multiple electronic states. Here we introduce the multiple cloning for dense manifolds of states (MCDMS) method, a systematically improvable approximation to the multiple cloning method. MCDMS avoids both the mean-field PES problem and the need to compute the full electronic spectrum. This is achieved by reformulating multiple cloning to use a subspace of approximate eigenstates constructed from the time-dependent Ehrenfest electronic wave function. By application to model systems, we show that this approach allows a substantial reduction in the size of the required electronic basis without significant loss in accuracy.

QM–MM Ehrenfest dynamics from first principles: photodissociation of diazirine in aqueous solution

This article describes an implementation of Ehrenfest molecular dynamics based on TDDFT and Gaussian basis sets, optimized for hybrid QM–MM simulations in GPU. The present method makes use of the equations of motion proposed by Chen et al. (J Chem Phys 135:044126, 2011), which, at variance with previous formulations of the Ehrenfest dynamics, takes into account the movement of the localized basis functions, thus improving accuracy and energy conservation. This methodology is used to explore the evolution and the stability of excited state dynamics for two different constructions of the initial excited state, consisting in the linear response TDDFT $$S_1$$ solution, and in the ground state density matrix where the HOMO–LUMO occupancies have been switched, which is a widespread approach to model photoexcitation in electron dynamics simulations. It is found that the second kind of starting state leads to a larger numerical noise and to a poorer stability of the dynamics, aside from “awakening” inner electronic modes that become manifest in the frequency spectrum, and which are absent if the dynamics departs from the linear response TDDFT density matrix. Then, the method is applied to investigate the photodissociation of the diazirine molecule, CH $$_2$$ N $$_2$$ , both in vacuum and in aqueous solution. Diazirine decomposes into carbene and molecular nitrogen upon irradiation with UV light, and for this reason it has been widely adopted to photolabel biomolecules through the insertion of carbenes in the macromolecular surface. Our simulations suggest that the quantum yield of the dissociative reaction experiences a decrease in solution with respect to the gas phase, that can be understood in terms of the vibrational relaxation facilitated by the solvent molecules. Besides, the present results indicate that the isomerization and dissociation mechanism occur fully on the $$S_1$$ excited state.

Assessment of Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) in Radiation Chemistry: Ionized Water Dimer.

Ionization in the condensed phase and molecular clusters leads to a complicated chain of processes with coupled electron-nuclear dynamics. It is difficult to describe such dynamics with conventional nonadiabatic molecular dynamics schemes since the number of states swiftly increases as the molecular system grows. It is therefore attractive to use a direct electron and nuclear propagation such as the real-time time-dependent density functional theory (RT-TDDFT). Here we report a RT-TDDFT benchmark study on simulations of singly and doubly ionized states of a water monomer and dimer as a prototype for more complex processes in a condensed phase. We employed the RT-TDDFT based Ehrenfest molecular dynamics with a generalized gradient approximate (GGA) functional and compared it with wave-function-based surface hopping (SH) simulations. We found that the initial dynamics of a singly HOMO ionized water dimer is similar for both the RT-TDDFT/GGA and the SH simulations but leads to completely different reaction channels on a longer time scale. This failure is attributed to the self-interaction error in the GGA functionals and it can be avoided by using hybrid functionals with large fraction of exact exchange (represented here by the BHandHLYP functional). The simulations of doubly ionized states are reasonably described already at the GGA level. This suggests that the RT-TDDFT/GGA method could describe processes following the autoionization processes such as Auger emission, while its applicability to more complex processes such as intermolecular Coulombic decay remains limited.

Optimal control with nonadiabatic molecular dynamics: Application to the Coulomb explosion of sodium clusters

We present an implementation of optimal control theory for the first-principles non-adiabatic Ehrenfest Molecular Dynamics model, which describes a condensed matter system by considering classical point-particle nuclei, and quantum electrons, handled in our case with time-dependent density-functional theory. The scheme is demonstrated by optimizing the Coulomb explosion of small Sodium clusters: the algorithm is set to find the optimal femtosecond laser pulses that disintegrate the clusters, for a given total pulse duration, fluence, and cut-off frequency. We describe the numerical details and difficulties of the methodology.

The electron–ion dynamics in ionization of lithium carbide molecule under femtosecond laser pulses

The electron–ion dynamics of the linear lithium carbide molecule under femtosecond laser pulses have been investigated in the framework of Ehrenfest molecular dynamics, in which valence electrons are treated quantum mechanically by time-dependent density functional theory (TDDFT) and ions are described classically. The on- and off-resonant multiphoton ionization processes have been induced by regulating laser frequency and laser intensity. The laser pulse with on-resonant frequency induces pronounced enhancement in electron ionization, bond length vibration, and energy absorption. Moreover, the coulomb explosion is preferred to occur in the on-resonant case, which is in qualitative agreement with previous theoretical investigations. The subtle relations between escaped electron number and absorbed photon number are well discussed with the increasing of laser intensity. Finally, the effect of self-interaction error is analyzed by comparing escaped electron number calculated with LDA and LDA-ADSIC. And the revTPSS-meta-GGA, a currently more accurate nonempirical exchange–correlation energy functional from a point of static density functional theory, is introduced to display its capability for the description of ionization process within nonlinear and the nonperturbative regime of isolated systems.

Combining Linear-Scaling DFT with Subsystem DFT in Born-Oppenheimer and Ehrenfest Molecular Dynamics Simulations: From Molecules to a Virus in Solution.

In this work, methods for the efficient simulation of large systems embedded in a molecular environment are presented. These methods combine linear-scaling (LS) Kohn-Sham (KS) density functional theory (DFT) with subsystem (SS) DFT. LS DFT is efficient for large subsystems, while SS DFT is linear scaling with a smaller prefactor for large sets of small molecules. The combination of SS and LS, which is an embedding approach, can result in a 10-fold speedup over a pure LS simulation for large systems in aqueous solution. In addition to a ground-state Born-Oppenheimer SS+LS implementation, a time-dependent density functional theory-based Ehrenfest molecular dynamics (EMD) using density matrix propagation is presented that allows for performing nonadiabatic dynamics. Density matrix-based EMD in the SS framework is naturally linear scaling and appears suitable to study the electronic dynamics of molecules in solution. In the LS framework, linear scaling results as long as the density matrix remains sparse during time propagation. However, we generally find a less than exponential decay of the density matrix after a sufficiently long EMD run, preventing LS EMD simulations with arbitrary accuracy. The methods are tested on various systems, including spectroscopy on dyes, the electronic structure of TiO2 nanoparticles, electronic transport in carbon nanotubes, and the satellite tobacco mosaic virus in explicit solution.

A new implementation of ab initio ehrenfest dynamics using electronic configuration basis: Exact formulation with molecular orbital connection and effective propagation scheme with locally quasi‐diabatic representation

We propose a new implementation of Ehrenfest molecular dynamics based on the configuration interaction theory using configuration state functions (CSF) as basis set originally proposed by Amano and Takatsuka (J. Chem. Phys. 2005, 122, 084113). Our development consists of two independet new features. The first one deals with the problem on how to “identify” the molecular orbitals at a simulation time step in terms of those at the previous time step. By giving an exact expression of CSF Ehrenfest method, this problem naturaly vanishes. To actually perform this method, the concept of molecular orbital connection which allows the MOs to be noncanonical is necessary. The second feature of our method is aimed to reduce the computational cost. We propose an approximaion to effectively perform the time propagation of the electron wavefunction. Due to the analogy to the locally diabatic representation method, we name our method locally quasi‐diabatic representation method. In the present work, these two new features were combined and employed to perform test computations. © 2016 Wiley Periodicals, Inc.

Multiscale modeling and computation of optically manipulated nano devices

We present a multiscale modeling and computational scheme for optical-mechanical responses of nanostructures. The multi-physical nature of the problem is a result of the interaction between the electromagnetic (EM) field, the molecular motion, and the electronic excitation. To balance accuracy and complexity, we adopt the semi-classical approach that the EM field is described classically by the Maxwell equations, and the charged particles follow the Schrödinger equations quantum mechanically. To overcome the numerical challenge of solving the high dimensional multi-component many-body Schrödinger equations, we further simplify the model with the Ehrenfest molecular dynamics to determine the motion of the nuclei, and use the Time-Dependent Current Density Functional Theory (TD-CDFT) to calculate the excitation of the electrons. This leads to a system of coupled equations that computes the electromagnetic field, the nuclear positions, and the electronic current and charge densities simultaneously. In the regime of linear responses, the resonant frequencies initiating the out-of-equilibrium optical-mechanical responses can be formulated as an eigenvalue problem. A self-consistent multiscale method is designed to deal with the well separated space scales. The isomerization of azobenzene is presented as a numerical example.

Polaron Properties in Armchair Graphene Nanoribbons

By means of a 2-D tight-binding model with lattice relaxation in a first-order expansion, we report different polaron properties depending on the armchair graphene nanoribbons width family as well as on its size. We find that representatives of the 3p+2 family do not present a polaronic-mediated charge transport. As for 3p and 3p+1 families, the polaron behavior was completely dependent on the system's width. In particular, we observed a greater degree of delocalization for broader nanoribbons; narrower nanoribbons of both families, on the contrary, typically presented a more localized polaronic-type transport. Energy levels and occupation numbers analysis are performed to rigorously assess the nature of the charge carrier. Time evolution in the scope of the Ehrenfest molecular dynamics was also carried out to confirm the collective behavior and stability of the carrier as a function of time. We were able to determine that polarons in nanoribbons of 3p family present higher mobility than those in 3p+1 nanoribbons. These results identify the transport process that takes place for each system, and they allow the prediction of the mobility of the charge carriers as a function of the structural properties of the system, thus providing guidance on how to improve the efficiency of graphene nanoribbon-based devices.