A modified Ehrenfest formalism for efficient large-scale ab initio molecular dynamics

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package.Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perde

On the Combination of TDDFT with Molecular Dynamics: New Developments

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there is a corresponding functional of the ground-state density. Yet the unavailability of such magic functionals in many cases (the theorem is a non-constructive existence result) demands the development and use of the alternative exact reformulation of quantum mechanics provided by TDDFT. This theory defines a convenient route to electronic excitations and to the dynamics of a many-electron system subject to an arbitrary time-dependent perturbation. This is, in fact, the main purpose of inscribing TDDFT in a MD framework -the inclusion of the effect of electronic excited states in the dynamics. However, as we will show in this review, it may not be the only use of TDDFT in this context. In this manuscript, we review two recent proposals: In Section 1.2, we show how TDDFT can be used to design efficient gsBOMD algorithms -even if the electronic excited states are in this case not relevant. The work described in Section 1.3 addresses the problem of mixed quantum-classical systems at thermal equilibrium.Comment: 10 pages, 1 figure, to be published in the book "Time Dependent Density Functional Theory" by Springer Verla

Investigation of charge migration/transfer in radical cations using Ehrenfest method with fully quantum nuclear motion

The main focus of this thesis is to investigate the effect of charge migration on molecular dynamics. Upon the creation of a superposition of cationic states by a short ionizing pulse in an attosecond pump-probe experiment, the electronic wavefunction is in a non-stationary state and the initial dynamics are purely electronic, driven by Charge Migration (CM) before the onset of any nuclear motions. The CM can be simulated using a frozen nuclear framework but its importance on long-term dynamics and competition with vibrationally mediated charge motion (i.e. Charge Transfer (CT)) remains unknown. Unravelling the mechanism behind CM and its importance on electron and nuclear coherence can help in designing an initial superposition of electronic states to steer nuclear motions toward a specific product. Further control of the photo-reactivity could be achieved with the use of probe/control laser pulses and open the door for more direct comparison with experimental results. In order to investigate the dynamics upon photoionization with an attosecond pump-pulse, the coupled electron-nuclear dynamics of the system is simulated using nonadiabatic quantum dynamics techniques within the sudden approximation. A single-set approach is adopted for the expansion of the nuclear wavefunction using a linear combination of Gaussian Wavepackets (GWP). The calculation is done using the Quantum-Ehrenfest method (QuEh) and the time-dependent Potential Energy Surfaces (PES) are evaluated with the Complete Active Space Configuration Interatcion (CAS-CI) method. The resulting dynamics are analyzed with adiabatic/diabatic state populations, Normal Mode (NM) displacements and bond lengths averaged over the nuclear wavepacket using Gross Gaussian populations (GGP). To reduce the cost of computation, the algorithm implemented in QUANTICS is parallelized with a Message Passing Interface (MPI). Further, the section of code which interacts with the database that contains previously calculated points on the PES is rewritten using the Structured Query Language (SQL) and the SQLite engine. For the purpose of unravelling the mechanism behind CM, the nonadiabatic dynamics of a model retinal Protonated Schiff Base (rPSB) and benzene are investigated by defining the initial electronic wavefunction in a systematic way. As demonstrated by the results on rPSB, the relaxation mechanism such as single and double bond length alternation and isomerization can controlled by varying the initial composition of electronic states. With the rich symmetry of benzene, the initial nuclear dynamics which are controlled by an initial gradient and electron dynamics can be analyzed using symmetry rules. The initial gradient is a combination of totally symmetric motion and non-symmetric components which correspond to the intra- (eigenstate) and inter-state (couplings) gradients, respectively. The electron dynamics and its associated nuclear motions can be examined by grouping together the localized holes where the CM occurs. With the initial gradient and CM, one can predict the initial nuclear relaxation and possibly control the photo-products formed by designing a specific superposition of electronic eigenstates. To explore the effect of laser pulses on dynamics, an implementation within the dipole approximation using the dipole-electric field dot product is done in the GAUSSIAN program. The dynamics in the presence of an infrared probe pulse is simulated on model systems such as allene and the ethylene cation. The pulse is able to induce change in the electron and nuclear dynamics of the system and some of its effect can be explained using irreducible representations and the alignment of the electric fields. The work presented in this thesis offers an insight into the photocontrol of molecules and opens the door for further investigation of charge-directed dynamics

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.Comment: Submitted as a roadmap article to Modelling and Simulation in Materials Science and Engineering; Address any correspondence to Vikram Gavini ([email protected]) and Danny Perez ([email protected]

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing

Roadmap on Electronic Structure Codes in the Exascale Era

Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing

GPAW: open Python package for electronic-structure calculations

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE) providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation (BSE), variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support of GPU acceleration has been achieved with minor modifications of the GPAW code thanks to the CuPy library. We end the review with an outlook describing some future plans for GPAW

Effects of Electron and Ion Irradiation on Two-Dimensional Molybdenum-Disulfide

Since their discovery at the beginning of the 21st century, two-dimensional (2D) materials have emerged as one of the most exciting material groups offering unique properties which promise a plethora of potential applications in nanoelectronics, quantum computing, and surface science. The progress in the study of 2D materials has advanced rapidly stimulated by the ever-growing interest in their behavior and the fact that they are the ideal specimen for transmission electron microscopy (TEM), as their geometry allows to identify every single atom. Their morphology – 2D materials consist of “surface” only – at the same time makes them sensitive to beam damage, since high-energy electrons easily sputter atoms and introduce defects. While this is in general not desirable – as non-destructive imaging is aimed at – it allows to precisely quantify the damage in TEM and even pattern the 2D material with atomic resolution using the electron beam. Alternatively, patterning of 2D materials can be achieved using focused ion irradiation, which makes studying its effect on 2D materials relevant and essential. In this thesis, we theoretically study the effects of electron and ion irradiation on 2D materials, exemplarily on 2D MoS2 . Specifically, we address the combined effect of electronic excitations and direct momentum transfer by high-energy electrons (knock-on damage) in 2D MoS2 using advanced first-principles simulation techniques, such as Ehrenfest dynamics based on time-dependent density functional theory (DFT). Here, we stress the importance of the combined effect of ionization damage and knock-on damage as neither of these alone can account for experimentally-observed defect production below the displacement threshold – the minimum energy required for the displacement of an atom from the pristine system. A mechanism of defect production relying on the localization of the electronic excitation at the emerging vacancy site is presented. The localized excitation eventually leads to a significant drop in the displacement threshold. The combination of electronic excitation and knock-on damage may in addition to beam-induced chemical etching explain the observed sub-threshold damage in low voltage TEM experiments. Apart from non-destructive imaging, electrons may be used to modify the 2D material intentionally. In this light, we consider the electron-beam driven phase transformation in 2D MoS2 , where the semiconducting polymorph transforms into its metallic counterpart. The phase energetics and a possible transformation mechanism under electron irradiation are investigated using DFT based first-principles calculations. The detailed understanding of the interaction of the electron beam with the 2D material promises to improve the patterning resolution enabling circuit design on the nanoscale. Ion irradiation employed in focussed ion beams (FIB), e.g., the helium ion microscope (HIM) constitutes another tool widely used to pattern and even image 2D materials. Ion bombardment experiment usually carried out for the 2D material placed on a substrate are frequently rationalized using simulations for free-standing systems neglecting the effect of the substrate. Combining Monte Carlo with analytical potential molecular dynamics simulations, we demonstrate that the substrate plays a crucial role in damage production under ion irradiation and cannot be neglected. Especially for light ions such as He and Ne, which are usually used in the HIM, the effect of the substrate needs to be considered to account for the increased number of defects and their broadened spatial distribution which limits the patterning resolution for typical HIM energies.Seit ihrer Entdeckung Anfang des 21. Jahrhunderts haben sich zwei-dimensionale (2D) Materialien zu einer der spannendsten Materialklassen im Forschungsfeld aus Materialwissenschaft, Physik und Chemie entwickelt. Ihre einzigartigen Eigenschaften versprechen eine Vielzahl potentieller Anwendungen in der Nanoelektronik, für Quantencomputer und in der Oberflächenwissenschaft. Beflügelt durch das wachsende Interesse an ihrem Verhalten und der Tatsache, dass sie die idealen Proben für die Transmissions-Elektronen-Mikroskopie (TEM) darstellen – ihre Geometrie erlaubt es, jedes einzelne Atom zu identifizieren – sind die Forschungen an 2D-Materialien rapide vorangeschritten. Ihre Morphologie – 2D-Materialien bestehen nur aus “Oberfläche” – bedingt zugleich ihre Sensitivität bezüglich Strahlschäden. Hochenergetische Elektronen lösen sehr leicht Atome aus dem 2D-Material und induzieren Defekte. Obwohl dies im Allgemeinen unerwünscht ist – Ziel ist eine nicht-destruktive Bildgebung – erlaubt es doch präzise Einblicke in die Schadensentstehung im TEM. Überdies können 2D-Materialien mit Hilfe des Elektronenstrahls mit atomarer Auflösung strukturiert werden. Alternativ kann die Strukturierung des 2D-Materials über fokussierte Ionenstrahlung erfolgen, weshalb es lohnenswert erscheint, auch deren Effekt auf 2D-Materialien zu untersuchen. In dieser Arbeit werden die Effekte von Elektronen- und Ionenstrahlung auf 2D-Materialien aus theoretischer Sicht exemplarisch an 2D-MoS2 untersucht. Besonderes Augenmerk liegt dabei auf dem kombinierten Effekt von elektronischer Anregung und dem direkten Impulsübertrag durch hochenergetische Elektronen (Kollisionsschaden) in 2D-MoS2 , der durch die Anwendung von Ab-Initio-Simulationstechniken wie der Ehrenfest-Molekulardynamik, basierend auf zeitabhängiger Dichtefunktionaltheorie (DFT), studiert wird. Dabei liegt die Betonung auf der Kombination beider Effekte, da weder Ionisierungs- noch Kollisionsschäden allein die experimentell beobachtete Defekterzeugung unterhalb der Displacement Threshold – der notwendigen Mindestenergie, um ein Atom aus dem reinen Material herauszulösen – erklären. Ein möglicher Mechanismus der Defekterzeugung, basierend auf der Lokalisierung der elektronischen Anregung an der entstehenden Vakanzstelle, wird vorgeschlagen. Die lokalisierte Anregung führt dabei schließlich zu einem signifikanten Absinken der Displacement Threshold. Die Kombination von elektronischer Anregung und Kollisionsschaden trägt neben strahlinduzierten chemischen Reaktionen zur Erklärung der beobachteten Schäden unterhalb der Displacement Threshold in Niederspannungs-TEM-Experimenten bei. Neben nicht-destruktiver Bildgebung können Elektronenstrahlen auch dafür benutzt werden, 2D-Materialien gezielt zu modifizieren. In diesem Sinne wird der elektronenstrahl-induzierte Phasenübergang in 2D-MoS2 , bei dem sich das Material von einem halbleitenden in einen metallischen Zustand transformiert, betrachtet. Die Phasenenergetik und ein möglicher Transformationsmechanismus werden unter Zuhilfenahme von DFT-basierten Ab-Initio-Simulationen untersucht. Das detaillierte Verständnis der Interaktion des Elektronenstrahls mit dem 2D-Material verspricht dabei die Strukturierungsauflösung zu verbessern und ermöglicht Schaltkreisdesign auf der Nanoskala. Fokussierte Ionenstrahlen, wie sie in Ionenstrahlinstrumenten – wie dem Helium-Ionen-Mikroskop (HIM) zum Einsatz kommen – stellen ein weiteres häufig verwendetes Werkzeug zur Modifikation sowie zur Bildgebung von 2D-Materialien dar. Ionenstrahlexperimente – üblicherweise mit dem auf einem Substrat platzierten 2D-Material durchgeführt – werden hingegen oft mit Simulationen für freistehende 2D-Materialien rationalisiert, wobei jegliche Einwirkung des Substrats vernachlässigt wird. Die Kombination von Monte-Carlo-Simulationen mit Molekulardynamik-Simulationen (auf der Basis analytischer Potentiale) in dieser Arbeit verdeutlicht, dass das Substrat eine wichtige Rolle in der Defekterzeugung spielt und nicht vernachlässigt werden kann. Besonders für leichte Ionen, wie He und Ne, wie sie typischerweise im HIM zum Einsatz kommen, sollte der Effekt des Substrats berücksichtigt werden. Dieses führt für typische Ionenenergien im HIM – im Vergleich zum freistehenden 2D-Material – zu einer ansteigenden Anzahl an Defekten und einer breiteren räumlichen Defektverteilung, welche die Strukturierungsauflösung begrenzt