Analyzing Excitation-Energy Transfer Based on the Time-Dependent Density Functional Theory in Real Time

Excitation-energy transfer is a key step in processes such as photosynthesis that convert light into other forms of energy. Time-dependent density functional theory (DFT) in real time is ideal for the first-principles simulation of such processes due to its computational efficiency. We here demonstrate how real-time DFT can be used for analyzing excitation-energy transfer from first-principles. We discuss several measures of energy transfer that are based solely on the time-dependent density, are well founded in the DFT framework, allow for intuitive understanding and visualization, and reproduce important limiting cases of an analytical model. We demonstrate their usefulness in calculations for model systems, both with static nuclei and in the context of DFT-based Ehrenfest dynamics.

Effects of electronic correlation on the high harmonic generation in helium: a time-dependent configuration interaction singles vs time-dependent full configuration interaction study

In this paper, we investigate the effects of full electronic correlation on the high harmonic generation in the helium atom subjected to laser pulses of extremely high intensity. To do this, we perform real-time propagations of the helium atom wavefunction using quantum chemistry methods coupled to Gaussian basis sets. The calculations are done within the real-time time-dependent configuration interaction framework, at two levels of theory: time-dependent configuration interation with single excitations (TD-CIS, uncorrelated method) and time-dependent full configuration interaction (TD-FCI, fully correlated method). The electronic wavefunction is expanded in Dunning basis sets supplemented with functions adapted to describing highly excited and continuum states. We also compare the TD-CI results with grid-based propagations of the helium atom within the single-active-electron approximation. Our results show that when including the dynamical electron correlation, a noticeable improvement to the description of HHG can be achieved, in terms of e.g. a more constant intensity in the lower energy part of the harmonic plateau. However, such effects can be captured only if the basis set used suffices to reproduce the most basic features, such as the HHG cutoff position, at the uncorrelated level of theory.

Time-dependentab initioapproaches for high-harmonic generation spectroscopy

High-harmonic generation (HHG) is a nonlinear physical process used for the production of ultrashort pulses in XUV region, which are then used for investigating ultrafast phenomena in time-resolved spectroscopies. Moreover, HHG signal itself encodes information on electronic structure and dynamics of the target, possibly coupled to the nuclear degrees of freedom. Investigating HHG signal leads to HHG spectroscopy, which is applied to atoms, molecules, solids and recently also to liquids. Analysing the number of generated harmonics, their intensity and shape gives a detailed insight of, e.g., ionisation and recombination channels occurring in the strong-field dynamics. A number of valuable theoretical models has been developed over the years to explain and interpret HHG features, with the three-step model being the most known one. Originally, these models neglect the complexity of the propagating electronic wavefunction, by only using an approximated formulation of ground and continuum states. Many effects unravelled by HHG spectroscopy are instead due to electron correlation effects, quantum interference, and Rydberg-state contributions, which are all properly captured by anab initioelectronic-structure approach. In this review we have collected recent advances in modelling HHG by means ofab initiotime-dependent approaches relying on the propagation of the time-dependent Schrödinger equation (or derived equations) in presence of a very intense electromagnetic field. We limit ourselves to gas-phase atomic and molecular targets, and to solids. We focus on the various levels of theory employed for describing the electronic structure of the target, coupled with strong-field dynamics and ionisation approaches, and on the basis used to represent electronic states. Selected applications and perspectives for future developments are also given.

Role of exchange and correlation in high-harmonic generation spectra of H2, N2, and CO2: Real-time time-dependent electronic-structure approaches

This study arises from the attempt to answer the following question: how different descriptions of electronic exchange and correlation affect the high-harmonic generation (HHG) spectroscopy of H₂, N₂, and CO₂ molecules? We compare HHG spectra for H₂, N₂, and CO₂ with different ab initio electronic structure methods: real-time time-dependent configuration interaction and real-time time-dependent density functional theory (RT-TDDFT) using truncated basis sets composed of correlated wave functions expanded on Gaussian basis sets. In the framework of RT-TDDFT, we employ Perdew-Burke-Ernzerhof (PBE) and long-range corrected Perdew-Burke-Ernzerhof (LC-ωPBE) functionals. We study HHG spectroscopy by disentangling the effect of electronic exchange and correlation. We first analyze the electronic exchange alone, and in the case of RT-TDDFT with LC-ωPBE, we use ω = 0.3 and ω = 0.4 to tune the percentage of long-range Hartree-Fock exchange and short-range exchange PBE. Then, we added the correlation as described by the PBE functional. All the methods give very similar HHG spectra, and they seem not to be particularly sensitive to the different description of exchange and correlation or to the correct asymptotic behavior of the Coulomb potential. Despite this general trend, some differences are found in the region connecting the cutoff and the background. Here, the harmonics can be resolved with different accuracy depending on the theoretical schemes used. We believe that the investigation of the molecular continuum and its coupling with strong fields merits further theoretical investigations in the near future.

Developing new and understanding old approximations in TDDFT

When a system has evolved far from a ground-state, the adiabatic approximations commonly used in time-dependent density functional theory calculations completely fail in some applications, while giving qualitatively good predictions in others, and sometimes even quantitative predictions. It is not clearly understood why this is so, and developing practical approximations going beyond the adiabatic approximation remains a challenge. This paper explores three different lines of investigation. First, an expression for the exact time-dependent exchange-correlation potential suggests that the accuracy of an adiabatic approximation is intimately related to the deviation between the natural orbital occupation numbers of the physical system and those of the Kohn-Sham system, and we explore this on some exactly-solvable model systems. The exact expression further suggests a path to go beyond the adiabatic approximations, and in the second part we discuss a newly proposed class of memory-dependent approximations developed in this way. Finally, we derive a new expression for the exact exchange-correlation potential from a coupling-constant path integration.

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.

Exponential integrators in time-dependent density-functional calculations

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.