Accelerated Broadband Spectra Using Transition Dipole Decomposition and Padé Approximants

Resolution-of-identity accelerated relativistic two- and four-component electron dynamics approach to chiroptical spectroscopies

We present an implementation and application of electron dynamics based on real-time time-dependent density functional theory (RT-TDDFT) and relativistic 2-component X2C and 4-component Dirac-Coulomb (4c) Hamiltonians to the calculation of electron circular dichroism and optical rotatory dispersion spectra. In addition, the resolution-of-identity approximation for the Coulomb term (RI-J) is introduced into RT-TDDFT and formulated entirely in terms of complex quaternion algebra. The proposed methodology was assessed on the dimethylchalcogenirane series, C₄H₈X (X = O, S, Se, Te, Po, Lv), and the spectra obtained by non-relativistic and relativistic methods start to disagree for Se and Te, while dramatic differences are observed for Po and Lv. The X2C approach, even in its simplest one-particle form, reproduces the reference 4c results surprisingly well across the entire series while offering an 8-fold speed-up of the simulations. An overall acceleration of RT-TDDFT by means of X2C and RI-J increases with system size and approaches a factor of almost 25 when compared to the full 4c treatment, without compromising the accuracy of the final spectra. These results suggest that one-particle X2C electron dynamics with RI-J acceleration is an attractive method for the calculation of chiroptical spectra in the valence region.

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.

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.

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Excited-state absorption in tetrapyridyl porphyrins: comparing real-time and quadratic-response time-dependent density functional theory

Three meso-substituted tetrapyridyl porphyrins (free base, Ni(ii), and Cu(ii)) were investigated for their optical limiting (OL) capabilities using real-time (RT-), linear-response (LR-), and quadratic-response (QR-) time-dependent density functional theory (TDDFT) methods. These species are experimentally known to display a prominent reverse saturable absorption feature between the Q and B bands of the ground-state absorption (GSA), which has been attributed to increased excited-state absorption (ESA) relative to GSA. A recently developed RT-TDDFT based method for calculating ESA from a LR-TDDFT density was utilized with eight exchange-correlation functionals (BLYP, PBE, B3LYP, CAM-B3LYP, PBE0, M06, BHLYP, and BHandH) and contrasted with calculations of ESA using QR-TDDFT with five exchange-correlation functionals (BLYP, B3LYP, CAM-B3LYP, BHLYP, and BHandH). This allowed for comparison between functionals with varying amounts of exact exchange as well as between the ability of RT-TDDFT and QR-TDDFT to reproduce OL behavior in porphyrin systems. The absorption peak positions and intensities for GSA and ESA are significantly impacted by the choice of DFT functional, with the most critical factor identified as the amount of exact exchange in the functional form. Calculating ESA with QR-TDDFT is found to be significantly more sensitive to the amount of exact exchange than GSA and ESA with RT-TDDFT, as well as GSA with LR-TDDFT. An analogous behavior is also demonstrated for the polycyclic aromatic hydrocarbon coronene. This is problematic when using the same approximate functional for calculation of both GSA and ESA, as the LR- and QR-TDDFT excitation energies will not have similar errors. Overall, the RT-TDDFT method with hybrid functionals reproduces the OL features for the porphyrin systems studied here and is a viable computational approach for efficient screening of molecular complexes for OL properties.

Coupling Real-Time Time-Dependent Density Functional Theory with Polarizable Force Field

Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for obtaining spectroscopic observables and understanding complex, time-dependent properties. Currently, performing RT-TDDFT calculations on large, fully quantum mechanical systems is not computationally feasible. Previously, polarizable mixed quantum mechanical and molecular mechanical (QM/MMPol) models have been successful in providing accurate, yet efficient, approximations to a fully quantum mechanical system. Here we develop a coupling scheme between induced dipole based QM/MMPol and RT-TDDFT. Our approach is validated by comparing calculated spectra with both real-time and linear-response TDDFT calculations. The model developed within provides an accurate method for performing RT-TDDFT calculations on extended systems while accounting for mutual polarization between the quantum mechanical and molecular mechanical regions.

Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.

Attosecond Charge Migration with TDDFT: Accurate Dynamics from a Well-Defined Initial State

We investigate the ability of time-dependent density functional theory (TDDFT) to capture attosecond valence electron dynamics resulting from sudden X-ray ionization of a core electron. In this special case the initial state can be constructed unambiguously, allowing for a simple test of the accuracy of the dynamics. The response following nitrogen K-edge ionization in nitrosobenzene shows excellent agreement with fourth-order algebraic diagrammatic construction (ADC(4)) results, suggesting that a properly chosen initial state allows TDDFT to adequately capture attosecond charge migration. Visualizing hole motion using an electron localization picture (ELF), we provide an intuitive chemical interpretation of the charge migration as a superposition of Lewis dot resonance structures.

Can Quantized Vibrational Effects Be Obtained from Ehrenfest Mixed Quantum-Classical Dynamics?

We explore the question of whether mean-field or "Ehrenfest" mixed quantum-classical dynamics is capable of capturing the quantized vibrational features in photoabsorption spectra that result from infrared and Raman-active vibrational transitions. We show that vibrational and electronic absorption spectra can indeed be obtained together within a single Ehrenfest simulation. Furthermore, the electronic transitions show new sidebands that are absent in electronic dynamics simulations with fixed nuclei. Inspection of the electronic sidebands reveals that the spacing corresponds to vibrational frequencies of totally symmetric vibrational modes of the ground electronic state. A simple derivation of the time-evolving dipole in the presence of external fields and vibrational motion shows the origin of these features, demonstrating that mixed quantum-classical Ehrenfest dynamics is capable of producing infrared, Raman, and electronic absorption spectra from a single simulation.