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arXiv:2604.06927

Development of ab initio Hubbard parameter calculation schemes in the k-point sampling real-time TDDFT program in CP2K

Kota Hanasaki, Sandra Luber

Published Apr 8, 2026• 0 citations
arXivHTMLPDF

Abstract

We implemented ab initio Hubbard parameter calculation schemes in the k-point sampling real-time TDDFT (RT-TDDFT) program in CP2K. We propose a new linear-response-based calculation scheme for energy-dependent Hubbard parameters. Our scheme extends the minimum-tracking linear-response method proposed in [Moynihan et al., arXiv preprint arXiv:1704.08076(2017); E. B. Linscott et al., Phys. Rev. B 98, 235157 (2018)] to realize the calculation of energy-dependent Hubbard parameters that reflect the exchange-correlation (xc) effects included in the xc-functional. We discuss the properties of the minimum-tracking linear-response method in comparison to another promising scheme, ACBN0 [Agapito et al., Phys. Rev. X, 5, 011006 (2015)]. We show that, while neither clearly outperforms the other in the accuracy of static property calculations, each has a distinct dynamical application depending on its theoretical formulation.

DOI
10.48550/arxiv.2604.06927

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We implemented ab initio Hubbard parameter calculation schemes in the k-point sampling real-time TDDFT (RT-TDDFT) program in CP2K. We propose a new linear-response-based calculation scheme for energy-dependent Hubbard parameters. Our scheme extends the minimum-tracking linear-response method proposed in [Moynihan et al., arXiv preprint arXiv:1704.08076(2017); E. B. Linscott et al., Phys. Rev. B 98, 235157 (2018)] to realize the calculation of energy-dependent Hubbard parameters that reflect the exchange-correlation (xc) effects included in the xc-functional. We discuss the properties of the minimum-tracking linear-response method in comparison to another promising scheme, ACBN0 [Agapito et al., Phys. Rev. X, 5, 011006 (2015)]. We show that, while neither clearly outperforms the other in the accuracy of static property calculations, each has a distinct dynamical application depending on its theoretical formulation.
This chapter discusses the linear-response framework of time-dependent density-functional theory (TDDFT). It begins with a thorough and self-contained exposition of general linear-response theory for many-body systems. The time-dependent as well as the frequency-dependent response are discussed. Several exact representations and properties of the density-density response function are reviewed, such as the Lehmann representation and fluctuation-dissipation theorem, and the Kramers-Kronig relations. It is shown how several important spectroscopic observables are obtained from linear-response theory. Then, the TDDFT formulation of linear-response theory is derived. The key quantity in this formalism is the so-called exchange-correlation kernel. The remainder of the chapter demonstrates how this linear-response formalism can be used to calculate excitation energies in principle exactly with TDDFT. The Casida equation is derived, as well as several approximate schemes. A comparison is made with time-dependent Hartree-Fock theory.
We present some details of our recently-proposed Time-Dependent Density-Functional Theory (TDDFT) for strongly-correlated materials in which the exchange-correlation (XC) kernel is derived from the charge susceptibility obtained using Dynamical Mean-Field Theory (the TDDFT + DMFT approach). We proceed with deriving the expression for the XC kernel for the one-band Hubbard model by solving DMFT equations via two approaches, the Hirsch–Fye Quantum Monte Carlo (HF-QMC) and an approximate low-cost perturbation theory approach, and demonstrate that the latter gives results that are comparable to the exact HF-QMC solution. Furthermore, through a variety of applications, we propose a simple analytical formula for the XC kernel. Additionally, we use the exact and approximate kernels to examine the nonhomogeneous ultrafast response of two systems: a one-band Hubbard model and a Mott insulator YTiO3. We show that the frequency dependence of the kernel, i.e., memory effects, is important for dynamics at the femtosecond timescale. We also conclude that strong correlations lead to the presence of beats in the time-dependent electric conductivity in YTiO3, a feature that could be tested experimentally and that could help validate the few approximations used in our formulation. We conclude by proposing an algorithm for the generalization of the theory to non-linear response.
Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical \textit{ab initio} method for studying solids under photoexcitation, we develop momentum-resolved real-time time dependent density functional theory (rt-TDDFT) algorithm using numerical atomic basis, together with the implementation of both length and vector gauge of electromagnetic field. When applied to simulate elementary excitations in 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.
In this comparative study we benchmark a recently developed nonadiabatic exchange-correlation potential within time-dependent density-functional theory (TDDFT) [Phys. Rev. Lett. 120, 157701 (2018)] by (a) validating the transient dynamics using a numerically exact density-matrix renormalization-group approach as well as by (b) comparing the RCRCRC time, a typical linear-response quantity, to up to second-order perturbation theory results. As a test bed we use the dynamics of the single-impurity Anderson model. These benchmarks show that the nonadiabatic potential yields quantitatively accurate results for the transient dynamics for temperatures of the order of the hybridization strength, while the TDDFT RCRCRC times quantitatively agree with those from second-order perturbation theory for temperatures which are large compared to the hybridization strength. Both results are particularly intriguing given the relatively low numerical cost of a TDDFT calculation.
Abstract We formulate a rigorous method for calculating a nonadiabatic (frequency-dependent) exchange-correlation (XC) kernel appropriate for accurate description of both equilibrium and nonequilibrium properties of strongly correlated systems within the time-dependent density functional theory (TDDFT) via the charge susceptibility, which is in turn obtained from dynamical mean field theory (DMFT) based on the effective multi-orbital Hubbard model. Application to the simple case of the one-orbital Hubbard model already shows the importance of the nonadiabatic kernel as it leads to significant modification of the excitation spectrum—shifting the (adiabatic) peak and disclosing another that is reminiscent of the solution from DMFT. The impact of dynamical effects, naturally included through the nonadiabaticity of the XC kernel, becomes even more transparent in our consideration of the nonequilibrium charge-density response of a multi-orbital perovskite, YTiO 3 , to a perturbation by a femtosecond (fs) laser pulse. These initial results indicate that electron–electron correlations and nonadiabatic features may significantly affect the spectrum and nonequilibrium properties of strongly correlated systems. We also propose an algorithm for extension of the approach to non-linear response. The transparency and computational efficiency of this non-adiabatic TDDFT+DMFT approach opens the door to examination of the spectra and response of multi-orbital systems with many nonequivalent atoms—bulk material, films and nanostructures.
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schrödinger equations—the Kohn–Sham equations. The complication of the problem is hidden in the—unknown—time-dependent exchange and correlation potential that appears in the Kohn–Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe–Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.