Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systems

Over the last few years, extraordinary advances in experimental and theoretical tools have allowed us to monitor and control matter at short time and atomic scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, especially at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the physical and chemical properties of complex systems is of utmost importance. The first principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows us to describe non-equilibrium phenomena in molecular complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mechanical effects within a generalized time-dependent density functional theory. This article aims to present the new features that have been implemented over the last few years, including technical developments related to performance and massive parallelism. We also describe the major theoretical developments to address ultrafast light-driven processes, such as the new theoretical framework of quantum electrodynamics density-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in molecules and materials, and new emergent states of matter (quantum electrodynamical-materials).

Field-dependent electrical properties of carbon nanotubes from first-principles: negative differential conductance, current oscillations and molecular sensing

In certain materials, and for certain voltage ranges, electrical current flowing through the material decreases when the voltage across the sample is increased. This negative differential conductance (NDC) is important for oscillators, amplifiers, and fast switching devices. In this work, using real time quantum simulations, we show that this phenomenon occurs in isolated finite armchair single wall carbon nanotubes (SWCNT) without end contacts. For metallic SWCNT, like the armchair SWCNT, electron transfer to secondary valleys-the most common cause of NDC-is not expected to be observed, as there are two quantum channels at the Fermi energy available for conduction. The NDC is due to the finite nature of the SWCNT and the existence of excited states that are blocked, similarly to a Coulomb blockade system, thus preventing any further current flow. We also show that the SWCNT conductivity depends on its length and that the current flowing on the SWCNT behaves like a Bloch oscillation that is disrupted in the presence of a molecule, decreasing the conductivity, and thus providing a rationalisation for the behaviour of SWCNT organic gas sensors.

Large-Scale Parallel Implementation of Hartree-Fock Exchange Energy on Real-Space Grids Using 3D-Parallel Fast Fourier Transform

Two types of implementation of the Hartree-Fock (HF) exchange energy were developed with the real-space grid approach for the purpose of achieving high efficiency in the parallel execution of the hybrid exchange functional in the density functional theory. First, a parallel implementation of the three-dimensional fast Fourier transform (FFT), referred to as PFFT, was adapted to solve the Poisson equations for the electrostatic potentials of the densities of the orbital pairs. In the other approach, the Poisson equations were solved iteratively through the conjugate gradient (CG) procedures where the operation of Laplacian was parallelized by the domain decomposition scheme. Comparison of the parallel performances for the exchange energy calculation was made between these two approaches, and it was revealed that the calculation with the FFT method is faster than that with CG. The method with FFT is more advantageous than CG because a larger bandwidth can be made available in the collective message passing interface communication associated with the parallel execution of FFT. We also implemented the projection operator to circumvent the laborious calculation of the exchange energy at every self-consistent field step, which made a significant contribution to expedite the convergence. To assess the accuracy of our implementation, the association energies of a hydrated ion were computed, which showed excellent agreement with those given by the Gaussian 09 program employing sophisticated basis sets.

Time-Dependent Magnons from First Principles

We propose an efficient and non-perturbative scheme to compute magnetic excitations for extended systems employing the framework of time-dependent density functional theory. Within our approach, we drive the system out of equilibrium using an ultrashort magnetic kick perpendicular to the ground-state magnetization of the material. The dynamical properties of the system are obtained by propagating the time-dependent Kohn–Sham equations in real time, and the analysis of the time-dependent magnetization reveals the transverse magnetic excitation spectrum of the magnet. We illustrate the performance of the method by computing the magnetization dynamics, obtained from a real-time propagation, for iron, cobalt, and nickel and compare them to known results obtained using the linear-response formulation of time-dependent density functional theory. Moreover, we point out that our time-dependent approach is not limited to the linear-response regime, and we present the first results for nonlinear magnetic excitations from first principles in iron.

Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials

Topologically nontrivial two-dimensional materials hold great promise for next-generation optoelectronic applications. However, measuring the Hall or spin-Hall response is often a challenge and practically limited to the ground state. An experimental technique for tracing the topological character in a differential fashion would provide useful insights. In this work, we show that circular dichroism angle-resolved photoelectron spectroscopy provides a powerful tool that can resolve the topological and quantum-geometrical character in momentum space. In particular, we investigate how to map out the signatures of the momentum-resolved Berry curvature in two-dimensional materials by exploiting its intimate connection to the orbital polarization. A spin-resolved detection of the photoelectrons allows one to extend the approach to spin-Chern insulators. The present proposal can be extended to address topological properties in materials out of equilibrium in a time-resolved fashion.

Identification and Resolution of Unphysical Multielectron Excitations in the Real-Time Time-Dependent Kohn-Sham Formulation

We resolve a fundamental issue associated with the conventional Kohn-Sham formulation of real-time time-dependent density functional theory. We show that unphysical multielectron excitations, generated during time propagation of the Kohn-Sham equations due to fixation of the total number of Kohn-Sham orbitals and their occupations, result in incorrect electron density and, therefore, wrong predictions of physical properties. A new formulation is proposed in that the number of Kohn-Sham orbitals and their occupations are updated on the fly, the unphysical multielectron excitations are removed, and the correct electron density is determined. The correctness of the new formulation is demonstrated by simulations of Rabi oscillation, as analytical results are available for comparison in the case of noninteracting electrons.

On the Single Wall Carbon Nanotube Surface Plasmon Stability

The physics of surface plasmons has a long tradition in condensed matter theory but as the dimension of the systems reaches the nano scale, new effects appear. In this work, by calculating the absorption spectra of a single wall carbon nanotube, using time dependent density functional theory, the effect of adding/removing electrons on the surface plasmon energy is studied. It is shown that removing electrons from the single wall carbon nanotube does not affect the surface plasmon energy peak. In contrast, adding electrons to the single wall carbon nanotube will redshift the plasmonic peak energy, an effect that is explained by an increase of the electron effective mass.

Absorbing boundary conditions for the time-dependent Schrödinger-type equations in R^{3}

Absorbing boundary conditions are presented for three-dimensional time-dependent Schrödinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a semidiscrete approximation of the Schrödinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing boundary condition is expressed as a discrete Dirichlet-to-Neumann map, which can be further approximated in time by using rational approximations of the Laplace transform to enable a more efficient implementation. This approach can be applied to domains with arbitrary geometry. The stability of the zeroth-order and first-order absorbing boundary conditions is proved. We tested the boundary conditions on benchmark problems. The effectiveness is further verified by a time-dependent Hartree-Fock model with Skyrme interactions. The accuracy in terms of energy and nucleon density is examined as well.

The physical stage of radiolysis of solvated DNA by high-energy-transfer particles: insights from new first principles simulations

Electron dynamics simulations based on density functional theory are carried out on nanometric molecular systems to decipher the primary processes following irradiation of bio-macromolecules by high energy transfer charged particles.

Light-Matter Response in Nonrelativistic Quantum Electrodynamics

We derive the full linear-response theory for nonrelativistic quantum electrodynamics in the long wavelength limit and provide a practical framework to solve the resulting equations by using quantum-electrodynamical density-functional theory. We highlight how the coupling between quantized light and matter changes the usual response functions and introduces cross-correlated light-matter response functions. These cross-correlation responses lead to measurable changes in Maxwell's equations due to the quantum-matter-mediated photon-photon interactions. Key features of treating the combined matter-photon response are that natural lifetimes of excitations become directly accessible from first-principles, changes in the electronic structure due to strong light-matter coupling are treated fully nonperturbatively, and self-consistent solutions of the back-reaction of matter onto the photon vacuum and vice versa are accounted for. By introducing a straightforward extension of the random-phase approximation for the coupled matter-photon problem, we calculate the ab initio spectra for a real molecular system that is coupled to the quantized electromagnetic field. Our approach can be solved numerically very efficiently. The presented framework leads to a shift in paradigm by highlighting how electronically excited states arise as a modification of the photon field and that experimentally observed effects are always due to a complex interplay between light and matter. At the same time the findings provide a route to analyze as well as propose experiments at the interface between quantum chemistry, nanoplasmonics and quantum optics.

Reduced Density-Matrix Approach to Strong Matter-Photon Interaction

We present a first-principles approach to electronic many-body systems strongly coupled to cavity modes in terms of matter-photon one-body reduced density matrices. The theory is fundamentally nonperturbative and thus captures not only the effects of correlated electronic systems but accounts also for strong interactions between matter and photon degrees of freedom. We do so by introducing a higher-dimensional auxiliary system that maps the coupled fermion-boson system to a dressed fermionic problem. This reformulation allows us to overcome many fundamental challenges of density-matrix theory in the context of coupled fermion-boson systems and we can employ conventional reduced density-matrix functional theory developed for purely fermionic systems. We provide results for one-dimensional model systems in real space and show that simple density-matrix approximations are accurate from the weak to the deep-strong coupling regime. This justifies the application of our method to systems that are too complex for exact calculations and we present first results, which show that the influence of the photon field depends sensitively on the details of the electronic structure.

Machine Learning the Physical Nonlocal Exchange-Correlation Functional of Density-Functional Theory

We train a neural network as the universal exchange-correlation functional of density-functional theory that simultaneously reproduces both the exact exchange-correlation energy and the potential. This functional is extremely nonlocal but retains the computational scaling of traditional local or semilocal approximations. It therefore holds the promise of solving some of the delocalization problems that plague density-functional theory, while maintaining the computational efficiency that characterizes the Kohn-Sham equations. Furthermore, by using automatic differentiation, a capability present in modern machine-learning frameworks, we impose the exact mathematical relation between the exchange-correlation energy and the potential, leading to a fully consistent method. We demonstrate the feasibility of our approach by looking at one-dimensional systems with two strongly correlated electrons, where density-functional methods are known to fail, and investigate the behavior and performance of our functional by varying the degree of nonlocality.

Strong-field nonlinear optical properties of monolayer black phosphorus

Within the past few years, atomically thin black phosphorus (BP) has been demonstrated as a fascinating new 2D material that is promising for novel nanoelectronic and nanophotonic applications, due to its many unique properties such as a direct and widely tunable bandgap, high carrier mobility and remarkable intrinsic in-plane anisotropy. However, its important extreme nonlinear behavior and the ultrafast dynamics of carriers under strong-field excitation have yet to be revealed. Herein, we report nonperturbative high harmonic generation (HHG) in monolayer BP by first-principles simulations. We show that BP exhibits extraordinary HHG properties, with clear advantages over three major types of 2D materials under intensive study, i.e., semimetallic graphene, semiconducting MoS₂, and insulating hexagonal boron nitride, in terms of HHG cutoff energy and spectral intensity. This study advances the scope of current research activities on BP into a new regime, suggesting its promising future in the applications of extreme-ultraviolet and attosecond nanophotonics and also opening doors to investigate the strong-field and ultrafast carrier dynamics of this emerging material.

Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy

We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and molecules, based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-symmetric laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented atomic or molecular media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible physical mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calculations.

Many-body perturbation theory calculations using the yambo code

yambo is an open source project aimed at studying excited state properties of condensed matter systems from first principles using many-body methods. As input, yambo requires ground state electronic structure data as computed by density functional theory codes such as Quantum ESPRESSO and Abinit. yambo's capabilities include the calculation of linear response quantities (both independent-particle and including electron-hole interactions), quasi-particle corrections based on the GW formalism, optical absorption, and other spectroscopic quantities. Here we describe recent developments ranging from the inclusion of important but oft-neglected physical effects such as electron-phonon interactions to the implementation of a real-time propagation scheme for simulating linear and non-linear optical properties. Improvements to numerical algorithms and the user interface are outlined. Particular emphasis is given to the new and efficient parallel structure that makes it possible to exploit modern high performance computing architectures. Finally, we demonstrate the possibility to automate workflows by interfacing with the yambopy and AiiDA software tools.

Oscillations of the bandgap with size in armchair and zigzag graphene quantum dots

We determine here the evolution of the bandgap energy with size in graphene quantum dots (GQDs). We find oscillatory behaviour of the bandgap and explain its origin in terms of armchair and zigzag edges. The electronic energy spectra of GQDs are computed using both the tight binding model and ab initio density functional methods. The results of the tight binding model are analyzed by dividing zigzag graphene quantum dots into concentric rings. For each ring, the energy spectra, the wave functions and the bandgap are obtained analytically. The effect of inter-ring tunneling on the energy gap is determined. The growth of zigzag terminated GQD into armchair GQD is shown to be associated with the addition of a one-dimensional Lieb lattice of carbon atoms with a shell of energy levels in the middle of the energy gap of the inner zigzag terminated GQD. This introduces a different structure of the energy levels at the bottom of the conduction and top of the valence band in zigzag and armchair GQD which manifests itself in the oscillation of the energy gap with increasing size. The evolution of the bandgap with the number of carbon atoms is compared with the notion of confined Dirac Fermions and tested against ab initio calculations of Kohn-Sham and TD-DFT energy gaps.

High-harmonic spectroscopy of transient two-center interference calculated with time-dependent density-functional theory

We demonstrate high-harmonic spectroscopy in many-electron molecules using time-dependent density-functional theory. We show that a weak attosecond-pulse-train ionization seed that is properly synchronized with the strong driving mid-infrared laser field can produce experimentally relevant high-harmonic generation (HHG) signals, from which we extract both the spectral amplitude and the target-specific phase (group delay). We also show that further processing of the HHG signal can be used to achieve molecular-frame resolution, i.e., to resolve the contributions from rescattering on different sides of an oriented molecule. In this framework, we investigate transient two-center interference in CO2 and OCS, and how subcycle polarization effects shape the oriented/aligned angle-resolved spectra.

Real-Time Propagation TDDFT and Density Analysis for Exciton Coupling Calculations in Large Systems

Photoactive systems are characterized by their capacity to absorb the energy of light and transform it. Usually, more than one chromophore is involved in the light absorption and excitation transport processes in complex systems. Linear-Response Time-Dependent Density Functional (LR-TDDFT) is commonly used to identify excitation energies and transition properties by solving the well-known Casida’s equation for single molecules. However, in practice, LR-TDDFT presents some disadvantages when dealing with multichromophore systems due to the increasing size of the electron–hole pairwise basis required for accurate evaluation of the absorption spectrum. In this work, we extend our local density decomposition method that enables us to disentangle individual contributions into the absorption spectrum to computation of exciton dynamic properties, such as exciton coupling parameters. We derive an analytical expression for the transition density from Real-Time Propagation TDDFT (P-TDDFT) based on Linear Response theorems. We demonstrate the validity of our method to determine transition dipole moments, transition densities, and exciton coupling for systems of increasing complexity. We start from the isolated benzaldehyde molecule, perform a distance analysis for π-stacked dimers, and finally map the exciton coupling for a 14 benzaldehyde cluster.

Enhancing high harmonic generation by the global optimization of a two-color chirped laser field

Enhanced high harmonics are generated by local and global optimization approaches to achieve a supercontinuum spectrum. Based on time-dependent density functional theory calculations, the optimum convolution of a two-color chirped pulse from an N2O molecule implements a significant enhancement of cutoff frequency and high harmonic yield. The optimization is done by controlling the effective chirp parameters and the carrier-envelope phase of the designed laser field. Indeed, all of the effective parameters are adjusted simultaneously for the global optimization; whereas, just two variables are tuned to obtain the desired cutoff frequency based on the local optimization. The results show that the global optimization approach extends the cutoff frequency by 96% compared to the single-color field, which could produce an isolated 25 as output pulse. This method opens up a valuable route by a pulse shaping mechanism for the control of high harmonic generation and ultrafast measurements for reducing the computational time and repeatability of an experiment with high accuracy.

Quantum Effects In Imaging Nano-Structures Using Photon-Induced Near-Field Electron Microscopy

In this paper, we introduce the quantum mechanical approach as a more physically-realistic model to accurately quantify the electron-photon interaction in Photon-induced near-field electron microscopy (PINEM). Further, we compare the maximum coupling speed between the electrons and the photons in the quantum and classical regime. For a nanosphere of radius 2.13 nm, full quantum calculations show that the maximum coupling between photon and electron occurs at a slower speed than classical calculations report. In addition, a significant reduction in PINEM field intensity is observed for the full quantum model. Furthermore, we discuss the size limitation for particles imaged using the PIMEN technique and the role of the background material in improving the PINEM intensity. We further report a significant reduction in PINEM intensity in nearly touching plasmonic particles (0.3 nm gap) due to tunneling effect.

Nonequilibrium Solvent Polarization Effects in Real-Time Electronic Dynamics of Solute Molecules Subject to Time-Dependent Electric Fields: A New Feature of the Polarizable Continuum Model

We develop an extension of the time-dependent equation-of-motion formulation of the polarizable continuum model (EOM-TDPCM) to introduce nonequilibrium cavity field effects in quantum mechanical calculations of solvated molecules subject to time-dependent electric fields. This method has been implemented in Octopus, a state-of-the-art code for real-space, real-time time-dependent density functional theory (RT-TDDFT) calculations. To show the potential of our methodology, we perform EOM-TDPCM/RT-TDDFT calculations of trans-azobenzene in water and in other model solvents with shorter relaxation times. Our results for the optical absorption spectrum of trans-azobenzene show (i) that cavity field effects have a clear impact in the overall spectral shape and (ii) that an accurate description of the solute shape (as the one provided within PCM) is key to correctly account for cavity field effects.

Polarization-state-resolved high-harmonic spectroscopy of solids

Attosecond metrology sensitive to sub-optical-cycle electronic and structural dynamics is opening up new avenues for ultrafast spectroscopy of condensed matter. Using intense lightwaves to precisely control the fast carrier dynamics in crystals holds great promise for next-generation petahertz electronics and devices. The carrier dynamics can produce high-order harmonics of the driving field extending up into the extreme-ultraviolet region. Here, we introduce polarization-state-resolved high-harmonic spectroscopy of solids, which provides deeper insights into both electronic and structural sub-cycle dynamics. Performing high-harmonic generation measurements from silicon and quartz, we demonstrate that the polarization states of the harmonics are not only determined by crystal symmetries, but can be dynamically controlled, as a consequence of the intertwined interband and intraband electronic dynamics. We exploit this symmetry-dynamics duality to efficiently generate coherent circularly polarized harmonics from elliptically polarized pulses. Our experimental results are supported by ab-initio simulations, providing evidence for the microscopic origin of the phenomenon.

High-harmonic generation in solids is related to the carrier dynamics and can be used to probe dynamic processes. Here, Klemke et al. show that the polarization states of high harmonics generated from silicon and quartz are determined by the crystal symmetries but can also be dynamically controlled.

Circularly polarized extreme ultraviolet high harmonic generation in graphene

Circularly polarized extreme ultraviolet (XUV) radiation is highly interesting for investigation of chirality-sensitive light-matter interactions. Recent breakthroughs have enabled the generation of such light sources via high harmonic generation (HHG) from rare gases. There is a growing interest in extending HHG medium from gases to solids, especially to 2D materials, as they hold great promise to develop ultra-compact solid-state photonic devices and provide insights into electronic properties of the materials themselves. However, so far reported, HHG in graphene driven by terahertz to mid-infrared fields generates only low harmonic orders, and no harmonics driven by circularly polarized lasers have been reported. Here, using first-principles simulations within a time-dependent density-functional theory framework, we show that it is possible to generate HHG extending to the XUV spectral region in monolayer extended graphene excited by near-infrared lasers. Moreover, we demonstrate that a single circularly polarized driver is enough to ensure HHG in graphene with circular polarization. The corresponding spectra reflect the six-fold rotational symmetry of the graphene crystal. Extending HHG in graphene to the XUV spectral regime and realizing circular polarization represent an important step toward the development of novel nanoscale attosecond photonic devices and numerous applications, such as spectroscopic investigation and nanoscale imaging of ultrafast chiral and spin dynamics in graphene and other 2D materials.

Strain-controlled high harmonic generation with Dirac fermions in silicene

Two-dimensional (2D) materials with zero band gap exhibit remarkable electronic properties with wide tunability. High harmonic generation (HHG) in such materials offers unique platforms to develop novel optoelectronic devices at the nanoscale, as well as to investigate strong-field and ultrafast nonlinear behaviour of massless Dirac fermions. However, control of HHG by modulating the electronic structures of materials has remained largely unexplored to date. Here we report controllable HHG by tuning the electronic structures via mechanical engineering. Using an ab initio approach based on time-dependent density-functional theory (TDDFT), we show that the HHG process is sensitive to the modulation of band structures of monolayer silicene while preserving the Dirac cones under biaxial and uniaxial strains, which can lead to significant enhancement of harmonic intensity up to an order of magnitude. With the additional advantage of silicene in compatibility and integration into the current silicon-based electronic industry, this study may open a new avenue to develop efficient solid-state optoelectronic nano-devices, and provide a valuable tool to understand the strong-field and mechanically induced ultrafast nonlinear response of Dirac carriers in 2D materials.

Identifying Electronic Modes by Fourier Transform from δ-Kick Time-Evolution TDDFT Calculations

Time-dependent density-functional theory (TDDFT) is widely used for calculating electron excitations in clusters and large molecules. For optical excitations, TDDFT is customarily applied in two distinct approaches: transition-based linear-response TDDFT (LR-TDDFT) and the real-time formalism (RT-TDDFT). The former directly provides the energies and transition densities of the excitations, but it requires the calculation of a large number of empty electron states, which makes it cumbersome for large systems. By contrast, RT-TDDFT circumvents the evaluation of empty orbitals, which is especially advantageous when dealing with large systems. A drawback of the procedure is that information about the nature of individual spectral features is not automatically obtained, although it is of course contained in the time-dependent induced density. Fourier transform of the induced density has been used in some simple cases, but the method is, surprisingly, not widely used to complement the RT-TDDFT calculations; although the reliability of RT-TDDFT spectra is now widely accepted, a critical assessment for the corresponding transition densities and a demonstration of the technical feasibility of the Fourier-transform evaluation for general cases is still lacking. In the present work, we show that the transition densities of the optically allowed excitations can be efficiently extracted from a single δ-kick time-evolution calculation even in complex systems like noble metals. We assess the results by comparison with the corresponding LR-TDDFT ones and also with the induced densities arising from RT-TDDFT simulations of the excitation process.

Automatic Construction of the Initial Orbitals for Efficient Generalized Valence Bond Calculations of Large Systems

We propose an efficient general strategy for generating initial orbitals for generalized valence bond (GVB) calculations which makes routine black-box GVB calculations on large systems feasible. Two schemes are proposed, depending on whether the restricted Hartree-Fock (RHF) wave function is stable (scheme I) or not (scheme II). In both schemes, the first step is the construction of active occupied orbitals and active virtual orbitals. In scheme I, active occupied orbitals are composed of the valence orbitals (the inner core orbitals are excluded), and the active virtual orbitals are obtained from the original virtual space by requiring its maximum overlap with the virtual orbital space of the same system at a minimal basis set. In scheme II, active occupied orbitals and active virtual orbitals are obtained from the set of unrestricted natural orbitals (UNOs), which are transformed from two sets of unrestricted HF spatial orbitals. In the next step, the active occupied orbitals and active virtual ones are separately transformed to localized orbitals. Localized occupied and virtual orbital pairs are formed using the Kuhn-Munkres (KM) algorithm and are used as the initial guess for the GVB orbitals. The optimized GVB wave function is obtained using the second-order self-consistent-field algorithm in the GAMESS program. With this procedure, GVB energies have been obtained for the lowest singlet and triplet states of polyacenes (up to decacene with 96 pairs) and the singlet ground state of two di-copper-oxygen-ammonia complexes. We have also calculated the singlet-triplet gaps for some polyacenes and the relative energy between two di-copper-oxygen-ammonia complexes with the block-correlated second-order perturbation theory based on the GVB reference.

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.

On the calculation of the stress tensor in real-space Kohn-Sham density functional theory

We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham density functional theory calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling expression for the stress tensor that is applicable to simulations with unit cells of arbitrary symmetry, semilocal exchange-correlation functionals, and Brillouin zone integration. In particular, we rewrite the contributions arising from the self-energy and the nonlocal pseudopotential energy to make them amenable to the real-space finite-difference discretization, achieving up to three orders of magnitude improvement in the accuracy of the computed stresses. Using examples representative of static and dynamic calculations, we verify the accuracy and efficiency of the proposed formulation. In particular, we demonstrate high rates of convergence with spatial discretization, consistency between the computed energy and the stress tensor, and very good agreement with reference planewave results.

Optimal Basis Set for Electron Dynamics in Strong Laser Fields: The case of Molecular Ion H2. J Chem Theory Comput 2018;14:5846-5858. [PMID: 30247900 PMCID: PMC6255052 DOI: 10.1021/acs.jctc.8b00656]

A clear understanding of the mechanisms that control the electron dynamics in a strong laser field is still a challenge that requires interpretation by advanced theory. Development of accurate theoretical and computational methods, able to provide a precise treatment of the fundamental processes generated in the strong field regime, is therefore crucial. A central aspect is the choice of the basis for the wave function expansion. Accuracy in describing multiphoton processes is strictly related to the intrinsic properties of the basis, such as numerical convergence, computational cost, and representation of the continuum. By explicitly solving the 1D and 3D time-dependent Schrödinger equation for H2+ in the presence of an intense electric field, we explore the numerical performance of using a real-space grid, a B-spline basis, and a Gaussian basis (improved by optimal Gaussian functions for the continuum). We analyze the performance of the three bases for high-harmonic generation and above-threshold ionization for H2+. In particular, for high-harmonic generation, the capability of the basis to reproduce the two-center interference and the hyper-Raman phenomena is investigated.

All-optical nonequilibrium pathway to stabilising magnetic Weyl semimetals in pyrochlore iridates

Nonequilibrium many-body dynamics is becoming a central topic in condensed matter physics. Floquet topological states were suggested to emerge in photodressed bands under periodic laser driving. Here we propose a viable nonequilibrium route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining ab initio calculations for a time-dependent self-consistent light-reduced Hubbard U and nonequilibrium magnetism simulations for quantum quenches, we find dynamically modified magnetic order giving rise to transiently emerging Weyl cones that can be probed by time- and angle-resolved photoemission spectroscopy. Our work offers a unique and realistic pathway for nonequilibrium materials engineering beyond Floquet physics to create and sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds switching protocols for light-engineered Berry curvature in combination with ultrafast magnetism.

Momentum-resolved TDDFT algorithm in atomic basis for real time tracking of electronic excitation

Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical ab initio method for studying solids under photoexcitation, we develop a momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both the length and vector gauge of the electromagnetic field. When applied to simulate elementary excitations in two-dimensional materials such as graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.

Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials

We extend the first-principles analysis of attosecond transient absorption spectroscopy to two-dimensional materials. As an example of two-dimensional materials, we apply the analysis to monolayer hexagonal boron nitride (h-BN) and compute its transient optical properties under intense few-cycle infrared laser pulses. Nonadiabatic features are observed in the computed transient absorption spectra. To elucidate the microscopic origin of these features, we analyze the electronic structure of h-BN with density functional theory and investigate the dynamics of specific energy bands with a simple two-band model. Finally, we find that laser-induced intraband transitions play a significant role in the transient absorption even for the two-dimensional material and that the nonadiabatic features are induced by the dynamical Franz–Keldysh effect with an anomalous band dispersion.

High Magnetic Field Detunes Vibronic Resonances in Photosynthetic Light Harvesting

The origin and role of oscillatory features detected in recent femtosecond spectroscopy experiments of photosynthetic complexes remain elusive. A key hypothesis underneath of these observations relies on electronic-vibrational resonance, where vibrational levels of an acceptor chromophore match the donor-acceptor electronic gap, accelerating the downhill energy transfer. Here we identify and detune such vibronic resonances using a high magnetic field that exclusively shifts molecular exciton states. We implemented ultrafast pump-probe spectroscopy into a specialized 25 T magnetic field facility and studied the light-harvesting complex PC645 from a cryptophyte algae where strongly coupled chromophores form molecular exciton states. We detected a change in high-frequency coherent oscillations when the field was engaged. Quantum chemical calculations coupled with a vibronic model explain the experiment as a magnetic field-induced shift of the exciton states, which in turn affects the electronic-vibrational resonance between pigments within the protein. Our results demonstrate the delicate sensitivity of interpigment coherent oscillations of vibronic origin to electronic-vibrational resonance interactions in light-harvesting complexes.

Cavity-Correlated Electron-Nuclear Dynamics from First Principles

The rapidly developing and converging fields of polaritonic chemistry and quantum optics necessitate a unified approach to predict strongly correlated light-matter interactions with atomic-scale resolution. Toward this overarching goal, we introduce a general time-dependent density-functional theory to study correlated electron, nuclear, and photon interactions on the same quantized footing. We complement our theoretical formulation with the first ab initio calculation of a correlated electron-nuclear-photon system. For a CO_{2} molecule in an optical cavity, we construct the infrared spectra exhibiting Rabi splitting between the upper and lower polaritonic branches, time-dependent quantum-electrodynamical observables such as the electric displacement field, and observe cavity-modulated molecular motion. Our work opens an important new avenue in introducing ab initio methods to the nascent field of collective strong vibrational light-matter interactions.

Ultrafast Modification of Hubbard U in a Strongly Correlated Material: Ab initio High-Harmonic Generation in NiO

Engineering effective electronic parameters is a major focus in condensed matter physics. Their dynamical modulation opens the possibility of creating and controlling physical properties in systems driven out of equilibrium. In this Letter, we demonstrate that the Hubbard U, the widely used on-site Coulomb repulsion in strongly correlated materials, can be modified on femtosecond timescales by a strong nonresonant laser pulse excitation in the prototypical charge-transfer insulator NiO. Using our recently developed time-dependent density-functional theory plus self-consistent U method, we demonstrate the importance of a dynamically modulated U in the description of the high-harmonic generation of NiO. Our study opens the door to novel ways of modifying effective interactions in strongly correlated materials via laser driving, which may lead to new control paradigms for field-induced phase transitions and perhaps laser-induced Mott insulation in charge-transfer materials.

Plasmonic Hot-Carrier-Mediated Tunable Photochemical Reactions

Hot-carrier generation from surface plasmon decay has found applications in many branches of physics, chemistry, materials science, and energy science. Recent reports demonstrated that the hot carriers generated from plasmon decay in nanoparticles can transfer to attached molecules and drive photochemistry which was thought impossible previously. In this work, we have computationally explored the atomic-scale mechanism of a plasmonic hot-carrier-mediated chemical process, H₂ dissociation. Numerical simulations demonstrate that, after photoexcitation, hot carriers transfer to the antibonding state of the H₂ molecule from the nanoparticle, resulting in a repulsive-potential-energy surface and H₂ dissociation. This process occurs when the molecule is close to a single nanoparticle. However, if the molecule is located at the center of the gap in a plasmonic dimer, dissociation is suppressed due to sequential charge transfer, which efficiently reduces occupation in the antibonding state and, in turn, reduces dissociation. An asymmetric displacement of the molecule in the gap breaks the symmetry and restores dissociation when the additional charge transfer is significantly suppressed. Thus, these models demonstrate the possibility of structurally tunable photochemistry via plasmonic hot carriers.

Density Functional Theory under the Bubbles and Cube Numerical Framework

Density functional theory within the Kohn-Sham density functional theory (KS-DFT) ansatz has been implemented into our bubbles and cube real-space molecular electronic structure framework, where functions containing steep cusps in the vicinity of the nuclei are expanded in atom-centered one-dimensional (1D) numerical grids multiplied with spherical harmonics (bubbles). The remainder, i.e., the cube, which is the cusp-free and smooth difference between the atomic one-center contributions and the exact molecular function, is represented on a three-dimensional (3D) equidistant grid by using a tractable number of grid points. The implementation of the methods is demonstrated by performing 3D numerical KS-DFT calculations on light atoms and small molecules. The accuracy is assessed by comparing the obtained energies with the best available reference energies.