High harmonic spectra computed using time-dependent Kohn–Sham theory with Gaussian orbitals and a complex absorbing potential

High harmonic generation (HHG) takes place in all phases of matter. In gaseous atomic and molecular media, it has been extensively studied and is very well understood. In solids, research is ongoing, but a consensus is forming for the dominant microscopic HHG mechanisms. In liquids, on the other hand, no established theory yet exists, and approaches developed for gases and solids are generally inapplicable, hindering our current understanding. We develop here a powerful and reliable ab initio cluster-based approach for describing the nonlinear interactions between isotropic bulk liquids and intense laser pulses. The scheme is based on time-dependent density functional theory and utilizes several approximations that make it feasible yet accurate in realistic systems. We demonstrate our approach with HHG calculations in water, ammonia, and methane liquids and compare the characteristic response of polar and nonpolar liquids. We identify unique features in the HHG spectra of liquid methane that could be utilized for ultrafast spectroscopy of its chemical and physical properties, including a structural minimum at 15–17 eV that is associated solely with the liquid phase. Our results pave the way to accessible calculations of HHG in liquids and illustrate the unique nonlinear nature of liquid systems.

Section: Methods Formulationmentioning

confidence: 99%

Ab Initio Cluster Approach for High Harmonic Generation in Liquids

Neufeld

Nourbakhsh

Tancogne-Dejean

et al. 2022

“…is the dipole acceleration function. 67 The quantity μ λ (ω) is the Fourier transform of μ λ (t) and can be used to compute the spectrum directly, in principle. 68−70 However, use of the dipole acceleration is thought to be less sensitive to the long-range description of the electron density.…”

Section: A Tdks Approachmentioning

confidence: 99%

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response

Herbert,

Zhu,

Alam

et al. 2023

Self Cite

We simulate X-ray absorption spectra at elemental K-edges using time-dependent density functional theory (TDDFT) in both its conventional linear-response implementation and its explicitly time-dependent or “real-time” formulation. Real-time TDDFT simulations enable broadband spectra calculations without the need to invoke frozen occupied orbitals (“core/valence separation”), but we find that these spectra are often contaminated by transitions to the continuum that originate from lower-energy core and semicore orbitals. This problem becomes acute in triple-ζ basis sets, although it is sometimes sidestepped in double-ζ basis sets. Transitions to the continuum acquire surprisingly large dipole oscillator strengths, leading to spectra that are difficult to interpret. Meaningful spectra can be recovered by means of a filtering technique that decomposes the spectrum into contributions from individual occupied orbitals, and the same procedure can be used to separate L- and K-edge spectra arising from different elements within a given molecule. In contrast, conventional linear-response TDDFT requires core/valence separation but is free of these artifacts. It is also significantly more efficient than the real-time approach, even when hundreds of individual states are needed to reproduce near-edge absorption features and even when Padé approximants are used to reduce the real-time simulations to just 2–4 fs of time propagation. Despite the cost, the real-time approach may be useful to examine the validity of the core/valence separation approximation.

“…This includes, beyond TDDFT with hybrids, correlated wave function methods such as multiconfigurational self-consistent-field (MCSCF), time-dependent configuration interaction (TD-CI), and coupled cluster (CC) . These real time techniques are essential for simulating the nonperturbative electronic response to electric fields in the strong-field regime, including phenomena such as charge redistribution, multiphoton absorption, high-harmonic generation, and strong-field ionization, in addition to photoelectron spectroscopy, which is the focus of this paper. − …”

Section: Introductionmentioning

confidence: 99%

“…This leads to damping of the wave function within the support of the CAP, which we refer to as an absorbing layer. CAPs are not restricted to grid-based numerical methods and have been applied to atomic-centered basis calculations − even in combination with TD-CI. − For good performancethat is, to successfully approximate the true free space wave function without an excessively large absorbing layer, which itself must be discretized by a gridCAPs require significant tuning of their functional form, the width of the absorbing layer, and the momentum components targeted for damping. We note that the popular MF method, which imposes an explicit damping of the wave function at each time step, is equivalent to a particular choice of CAP to first order accuracy in the time step size …”

Section: Introductionmentioning

confidence: 99%

Eliminating Artificial Boundary Conditions in Time-Dependent Density Functional Theory Using Fourier Contour Deformation

Kaye

Barnett

Greengard

et al. 2023

We present an efficient method for propagating the time-dependent Kohn–Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrödinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of nonlocal history integral operators. We adapt FCD to time-dependent density functional theory (TDDFT), and describe a simple algorithm to smoothly and automatically truncate long-range Coulomb-like potentials to a time-dependent constant outside of a bounded domain of interest, so that FCD can be used. This approach eliminates errors originating from the use of artificial boundary conditions, leaving only the error of the potential truncation, which is controlled and can be systematically reduced. The method enables accurate simulations of ultrastrong nonlinear electronic processes in molecular complexes in which the interference between bound and continuum states is of paramount importance. We demonstrate results for many-electron TDDFT calculations of absorption and strong field photoelectron spectra for one and two-dimensional models, and observe a significant reduction in the size of the computational domain required to achieve high quality results, as compared with the popular method of complex absorbing potentials.