arXiv subjects

E. K. U. Gross

Publications and source records attributed to E. K. U. Gross.

At least 55 records · Page 3Linked to original sources

arXiv2017

Exact single-electron approach to the dynamics of molecules in strong laser fields

We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wavefunction as a product of a marginal and a conditional amplitude. The marginal amplitude, which depends only on one electronic coordinate and yields the exact one-electron density and current density, obeys a time-dependent Schrödinger equation with an effective time-dependent potential. The exact equations are used to derive an approximation that is a step towards a general and feasible ab-initio single-electron approximation for molecules. The derivation also challenges the usual interpretation of the single-active electron approximation. From the study of model systems, we find that the exact and approximate single-electron potentials for processes with negligible two-electron ionization lead to a qualitatively similar dynamics, but that the ionization barrier may be explicitly time-dependent.

physics.chem-ph↗

arXiv2016

Exact factorization-based density functional theory of electrons and nuclei

The ground state energy of a system of electrons and nuclei is proven to be a variational functional of the conditional electronic density $n_R(\mathbf{r})$, the nuclear wavefunction $χ(R)$ and an induced vector potential $A_μ(R)$ and quantum geometric tensor $\mathcal{T}_{μν}(R)$ derived from the conditional electronic wavefunction $Φ_R(r)$ over nuclear configuration space, where $r=\mathbf{r}_1,\mathbf{r}_2,\ldots$ are electronic coordinates and $R=\mathbf{R}_1,\mathbf{R}_2,\ldots$ are nuclear coordinates. The ground state $(n_R,χ,A_μ,\mathcal{T}_{μν})$ can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing an effective potential $v_{\rm s}(\mathbf{r})$ that depends parametrically on $R$, (ii) the Schrödinger equation for $χ(R)$ and (iii) Euler-Lagrange equations that determine $\mathcal{T}_{μν}$. The theory is applied to the $E\otimes e$ Jahn-Teller model.

physics.chem-ph↗

arXiv2016

Surface hopping methodology in laser-driven molecular dynamics

A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL $\textbf{105}$, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable $\textrm H_2^{\;+}$-like model system, it is shown that the deterministic classical nuclear motion on a single time-dependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely.

physics.chem-ph↗

arXiv2016

On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation

Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.

physics.chem-ph↗

arXiv2016

An Exact Factorization Perspective on Quantum Interferences in Nonadiabatic Dynamics

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface - the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly-solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics the one of the exact nuclear probability density.

physics.chem-ph↗

arXiv2016

Ultrafast Local Magnetization and Demagnetization in Heusler Alloys

With the goal of pushing Spintronic devices towards faster and faster timescales, we demonstrate, using ab-intio time-dependent density functional theory simulations of bulk Heusler compounds subject to ultrashort intense laser pulses, that the local magnetic moment can increase or decrease in a few femtoseconds. This speed is due to the all optical nature of the process, which transfers spin moment from one sublattice to another. This transfer depends on easily tunable laser parameters. By comparing the spin dynamics of a variety of Heusler (or half-Heusler) compounds, we demonstrate that the density of states explains the observed moment transfer; most the physics of inter sublattice moment transfer is due to the flow of spin current which is governed by availability of states above the Fermi level.

cond-mat.mtrl-sci↗

arXiv2016

Quantum-Classical Non-Adiabatic Dynamics: Coupled- vs. Independent-Trajectory Methods

Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories, and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.

quant-ph↗

arXiv2016

A single-electron approach for many-electron dynamics in high-order harmonic generation

We present a novel ab-initio single-electron approach to correlated electron dynamics in strong laser fields. By writing the electronic wavefunction as a product of a marginal one-electron wavefunction and a conditional wavefunction, we show that the exact harmonic spectrum can be obtained from a single-electron Schrödinger equation. To obtain the one-electron potential in practice, we propose an adiabatic approximation, i.e. a potential is generated that depends only on the position of one electron. This potential, together with the laser interaction, is then used to obtain the dynamics of the system. For a model Helium atom in a laser field, we show that by using our approach, the high-order harmonic generation spectrum can be obtained to a good approximation.

physics.atom-ph↗

arXiv2016

Molecular geometric phase from the exact electron-nuclear factorization

The Born-Oppenheimer electronic wavefunction $Φ_R^{BO}(r)$ picks up a topological phase factor $\pm 1$, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in $R$-space. We show that this topological quantity reverts to a geometric quantity $e^{iγ}$ if the geometric phase $γ= \oint \mathrm{Im} \langle Φ_R |\nabla_μ Φ_R\rangle \cdot d\mathbf{R}_μ$ is evaluated with the conditional electronic wavefunction $Φ_R(r)$ from the exact electron-nuclear factorization $Φ_R(r)χ(R)$ instead of the adiabatic function $Φ_R^{BO}(r)$. A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.

physics.chem-ph↗

arXiv2015

Superconductivity in metastable phases of phosphorus-hydride compounds under high pressure

Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur-hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of the superconducting phase have been conclusively determined. In this work the phase diagram of PH$_n$ ($n=1,2,3,4,5,6$) was extensively explored by means of {\it ab initio} crystal structure predictions using the Minima Hopping Method (MHM). The results do not support the existence of thermodynamically stable PH$_n$ compounds, which exhibit a tendency for elemental decomposition at high pressure even when vibrational contributions to the free energies are taken into account. Although the lowest energy phases of PH$_{1,2,3}$ display T$_{c}$'s comparable to experiments, it remains uncertain if the measured values of T$_{c}$ can be fully attributed to a phase-pure compound of PH$_n$.

cond-mat.supr-con↗

arXiv2015

Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.

physics.chem-ph↗

arXiv2015

Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations

We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-reduced density matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-reduced density matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-reduced density matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.

cond-mat.other↗

arXiv2015

Spectrum for non-magnetic Mott insulators from power functional within Reduced Density Matrix Functional Theory

A fully first principles theory capable of treating strongly correlated solids remains the outstanding challenge of modern day materials science. This is exemplified by the transition metal oxides, prototypical Mott insulators, that remain insulating even in the absence of long range magnetic order. Capturing the non-magnetic insulating state of these materials presents a difficult challenge for any modern electronic structure theory. In this paper we demonstrate that reduced density matrix functional theory, in conjunction with the power functional, can successfully treat the non-magnetic insulating state of the transition metal oxides NiO and MnO. We show that the electronic spectrum retains a gap even in the absence of spin order. We further discuss the detailed way in which RDMFT performs for Mott insulators and band insulators, finding that for the latter occupation number minimization alone is required, but for the former full minimization over both occupation numbers and natural orbitals is essential.

cond-mat.str-el↗

arXiv2015

Doping induced metal-insulator phase transition in NiO

The insulator to metal phase transition in NiO is studied within the framework of reduced density matrix functional theory and density functional theory. We find that the spectral density obtained using reduced density matrix functional theory is in good agreement with experiments both undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition \emph{qualitatively differs} depending on whether NiO is calculated within density functional theory or reduced density matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.

cond-mat.str-el↗

arXiv2015

A coupled-trajectory quantum-classical approach to decoherence in non-adiabatic processes

We present a novel quantum-classical approach to non-adiabatic dynamics, deduced from the coupled electronic and nuclear equations in the framework of the exact factorization of the electron-nuclear wave function. The method is based on the quasi-classical interpretation of the nuclear wave function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as effect of the coupling to the nuclei and correctly reproduces the expected quantum behaviour. Moreover, the splitting of the nuclear wave packet is captured as consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in the Letter is supported by numerical results that are compared to quantum mechanical calculations.

physics.chem-ph↗

arXiv2015

Laser-induced electron localization in H$_2^+$: Mixed quantum-classical dynamics based on the exact time-dependent potential energy surface

We study the exact nuclear time-dependent potential energy surface (TDPES) for laser-induced electron localization with a view to eventually developing a mixed quantum-classical dynamics method for strong-field processes. The TDPES is defined within the framework of the exact factorization [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] and contains the exact effect of the couplings to the electronic subsystem and to any external fields within a scalar potential. We compare its features with those of the quasistatic potential energy surfaces (QSPES) often used to analyse strong-field processes. We show that the gauge-independent component of the TDPES has a mean-field-like character very close to the density-weighted average of the QSPESs. Oscillations in this component are smoothened out by the gauge-dependent component, and both components are needed to yield the correct force on the nuclei. Once the localization begins to set in, the gradient of the exact TDPES tracks one QSPES and then switches to the other, similar to the description provided by surface-hopping between QSPESs. We show that evolving an ensemble of classical nuclear trajectories on the exact TDPES accurately reproduces the exact dynamics. This study suggests that the mixed quantum-classical dynamics scheme based on evolving multiple classical nuclear trajectories on the exact TDPES will be a novel and useful method to simulate strong field processes.

physics.chem-ph↗

arXiv2015

Demonstration of Optimal Control of Laser Induced Spin-Orbit Mediated Ultrafast Demagnetization

Laser induced ultrafast demagnetization is the process whereby the magnetic moment of a ferromagnetic material is seen to drop significantly on a timescale of $10-100$s of femtoseconds due to the application of a strong laser pulse. If this phenomenon can be harnessed for future technology, it offers the possibility for devices operating at speeds several orders of magnitude faster than at present. A key component to successful transfer of such a process to technology is the controllability of the process, i.e. that it can be tuned in order to overcome the practical and physical limitations imposed on the system. In this paper, we demonstrate that the spin-orbit mediated form of ultrafast demagnetization recently investigated [arXiv:1406.6607] by ab-initio time-dependent density functional theory (TDDFT) can be controlled. To do so we use quantum optimal control theory (OCT) to couple our TDDDT simulations to the optimization machinery of OCT. We show that a laser pulse can be found which maximizes the loss of moment within a given time interval while subject to several practical and physical constraints. Furthermore we also include a constraint on the fluence of the laser pulses and find the optimal pulse that combines significant demagnetization with a desire for less powerful pulses. These calculations demonstrate optimal control is possible for spin-orbit mediated ultrafast demagnetization and lay the foundation for future optimizations/simulations which can incorporate even more constraints.

cond-mat.mtrl-sci↗

arXiv2015

L1$_0$ stacked binaries as candidates for hard magnets: FePt, MnAl and MnGa

A novel strategy of stacking binary magnets to enhance the magneto crystalline anisotropy is explored. This strategy is used in the search for hard magnets by studying FePt/MnGa and FePt/MnAl stacks. The choice of these binaries is motivated by the fact that they already possess large magneto crystalline anisotropy. Several possible alternative structures for these materials are explored in order to reduce the amount of Pt owing to its high cost.

cond-mat.mtrl-sci↗