Two-electron Rabi oscillations in real-time time-dependent density-functional theory

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.

Size-dependent errors in real-time electron density propagation

Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although the RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.

Minimizing the Time-Dependent Density Functional Error in Ehrenfest Dynamics

Simulating electron-ion dynamics using time-dependent density functional theory within an Ehrenfest dynamics scheme can be done in two ways that are in principle exact and identical: propagating time-dependent electronic Kohn-Sham equations or propagating electronic coefficients on surfaces obtained from linear-response. We show here that using an approximate functional leads to qualitatively different dynamics in the two approaches. We argue that the latter is more accurate because the functionals are evaluated on domains close to the ground state where currently used approximations perform better. We demonstrate this on an exactly solvable model of charge transfer and discuss implications for time-resolved spectroscopy.

Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group

In this work, we simulate the electron dynamics in molecular systems with the time-dependent density matrix renormalization group (TD-DMRG) algorithm. We leverage the generality of the so-called tangent-space TD-DMRG formulation and design a computational framework in which the dynamics is driven by the exact nonrelativistic electronic Hamiltonian. We show that by parametrizing the wave function as a matrix product state, we can accurately simulate the dynamics of systems including up to 20 electrons and 32 orbitals. We apply the TD-DMRG algorithm to three problems that are hardly targeted by time-independent methods: the calculation of molecular (hyper)polarizabilities, the simulation of electronic absorption spectra, and the study of ultrafast ionization dynamics.

CAS without SCF-Why to use CASCI and where to get the orbitals

The complete active space self-consistent field (CASSCF) method has seen broad adoption due to its ability to describe the electronic structure of both the ground and excited states of molecules over a broader swath of the potential energy surface than is possible with the simpler Hartree-Fock approximation. However, it also has a reputation for being unwieldy, computationally costly, and un-black-box. Here, we discuss a class of alternatives, complete active space configuration interaction (CASCI) methods, paying particular attention to their application to electronic excited states. The goal of this Perspective is fourfold. First, we argue that CASCI is not merely an approximation to CASSCF, in that it can be designed to have important qualitative advantages over CASSCF. Second, we present several insights drawn from our experience experimenting with different schemes for computing orbitals to be employed in CASCI. Third, we argue that CASCI is well suited for application to nanomaterials. Finally, we reason that, with the rise in new low-scaling approaches for describing multireference systems, there is a greater need than ever to develop new methods for defining orbitals that provide an efficient and accurate description of both static correlation and electronic excitations in a limited active space.

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.

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.

Simulating Electron Dynamics of Complex Molecules with Time-Dependent Complete Active Space Configuration Interaction

Time-dependent electronic structure methods are growing in popularity as tools for modeling ultrafast and/or nonlinear processes, for computing spectra, and as the electronic structure component of mean-field molecular dynamics simulations. Time-dependent configuration interaction (TD-CI) offers several advantages over the widely used real-time time-dependent density functional theory: namely, that it correctly models Rabi oscillations; it offers a spin-pure description of open-shell systems; and a hierarchy of TD-CI methods can be defined that systematically approach the exact solution of the time-dependent Schrodinger equation (TDSE). In this work, we present a novel TD-CI approach that extends TD-CI to large complete active-space configuration expansions. Such extension is enabled by use of a direct configuration interaction approach that eliminates the need to explicitly build, store, or diagonalize the Hamiltonian matrix. Graphics processing unit (GPU) acceleration enables fast solution of the TDSE even for large active spaces-up to 12 electrons in 12 orbitals (853776 determinants) in this work. A symplectic split operator propagator yields long-time norm conservation. We demonstrate the applicability of our approach by computing the response of a large molecule with a strongly correlated ground state, decacene (C₄₂H₂₄), to various pulses (δ-function, transform limited, chirped). Our simulations predict that chirped pulses can be used to induce dipole-forbidden transitions. Simulations of decacene using the 6-31G(d) basis set and a 12 electrons/12 orbitals active space took 20.1 h to propagate for 100 fs with a 1 attosecond time step on a single NVIDIA K40 GPU. Convergence with respect to time step is found to depend on the property being computed and the chosen active space.

Exploring non-adiabatic approximations to the exchange–correlation functional of TDDFT

Decomposition of the exact time-dependent exchange–correlation potential offers a new starting point to build approximations with memory.

Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

Real-Time Description of the Electronic Dynamics for a Molecule Close to a Plasmonic Nanoparticle

The optical properties of molecules close to plasmonic nanostructures greatly differ from their isolated molecule counterparts. To theoretically investigate such systems from a quantum-chemistry perspective, one has to take into account that the plasmonic nanostructure (e.g., a metal nanoparticle-NP) is often too large to be treated atomistically. Therefore, a multiscale description, where the molecule is treated by an ab initio approach and the metal NP by a lower level description, is needed. Here we present an extension of one such multiscale model [Corni, S.; Tomasi, J. J. Chem. Phys.2001, 114, 3739], originally inspired by the polarizable continuum model, to a real-time description of the electronic dynamics of the molecule and of the NP. In particular, we adopt a time-dependent configuration interaction (TD CI) approach for the molecule, the metal NP is described as a continuous dielectric of complex shape characterized by a Drude-Lorentz dielectric function, and the molecule-NP electromagnetic coupling is treated by an equation-of-motion (EOM) extension of the quasi-static boundary element method (BEM). The model includes the effects of both the mutual molecule-NP time-dependent polarization and the modification of the probing electromagnetic field due to the plasmonic resonances of the NP. Finally, such an approach is applied to the investigation of the light absorption of a model chromophore, LiCN, in the presence of a metal-NP of complex shape.

Black-Box, Real-Time Simulations of Transient Absorption Spectroscopy

We introduce an atomistic, all-electron, black-box electronic structure code to simulate transient absorption (TA) spectra and apply it to simulate pyrazole and a GFP-chromophore derivative. The method is an application of OSCF2, our dissipative extension of time-dependent density functional theory. We compare our simulated spectra directly with recent ultrafast spectroscopic experiments. We identify features in the TA spectra to Pauli-blocking, which may be missed without a first-principles model. An important ingredient in this method is the stationary-TDDFT correction scheme recently put forward by Fischer, Govind, and Cramer that allows us to overcome a limitation of adiabatic TDDFT. We demonstrate that OSCF2 is able to reproduce the energies of bleaches and induced absorptions as well as the decay of the transient spectrum with only the molecular structure as input.

Time-dependent density functional theory beyond Kohn–Sham Slater determinants

Different choices of initial Kohn Sham wavefunction shape the time-dependent exchange–correlation potential.

Time-resolved spectroscopy in time-dependent density functional theory: an exact condition

A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to an exact condition for the exchange-correlation potential of time-dependent density functional theory. The Kohn-Sham potential typically continues to evolve after the field is turned off, which leads to time dependence in the response frequencies of the Kohn-Sham response function. The exchange-correlation kernel must cancel out this time dependence. The condition is typically violated by approximations currently in use, as we demonstrate by several examples, which has severe consequences for their predictions of time-resolved spectroscopy.