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Register a new userNAC-TDDFT: Time-dependent density functional theory for nonadiabatic couplings
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First-order nonadiabatic coupling matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice. However, the lack of wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. The present account aims to analyze the available variants of NAC-TDDFT in a critical but concise manner and meanwhile point out the proper ways for implementation. It can be concluded, from both theoretical and numerical points of view, that the equation of motion-based variant of NAC-TDDFT is the right choice. Possible future developments of this variant are also highlighted.
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Time-dependent orbital-free density functional theory (TD-OFDFT) is an efficient ab-initio method for calculating the electronic dynamics of large systems. In comparison to standard TD-DFT, it computes only a single electronic state regardless of system size, but it requires an additional time-dependent Pauli potential term. We propose a nonadiabatic and nonlocal Pauli potential whose main ingredients are the time-dependent particle and current densities. Our calculations of the optical spectra of metallic and semiconductor clusters indicate that nonlocal and nonadiabatic TD-OFDFT performs accurately for metallic systems and semiquantitatively for semiconductors. This work opens the door to wide applicability of TD-OFDFT for nonequilibrium electron and electron-nuclear dynamics of materials.
Linear-response time-dependent (TD) density-functional theory (DFT) has been implemented in the pseudopotential wavelet-based electronic structure program BigDFT and results are compared against those obtained with the all-electron Gaussian-type orbital program deMon2k for the calculation of electronic absorption spectra of N2 using the TD local density approximation (LDA). The two programs give comparable excitation energies and absorption spectra once suitably extensive basis sets are used. Convergence of LDA density orbitals and orbital energies to the basis-set limit is significantly faster for BigDFT than for deMon2k. However the number of virtual orbitals used in TD-DFT calculations is a parameter in BigDFT, while all virtual orbitals are included in TD-DFT calculations in deMon2k. As a reality check, we report the x-ray crystal structure and the measured and calculated absorption spectrum (excitation energies and oscillator strengths) of the small organic molecule N-cyclohexyl-2-(4-methoxyphenyl)imidazo[1,2-a]pyridin-3-amine.
We propose a computationally efficient approach to the nonadiabatic time-dependent density functional theory (TDDFT) which is based on a representation of the frequency-dependent exchange correlation kernel as a response of a set of damped oscillators. The requirements to computational resources needed to implement our approach do not differ from those of the standard real-time TDDFT in the adiabatic local density approximation (ALDA). Thus, our result offers an exciting opportunity to take into account temporal nonlocality and memory effects in calculations with TDDFT in quantum chemistry and solid state physics for unprecedentedly low costs.
We present a time-dependent density functional theory (TDDFT) based approach to compute the light-matter couplings between two different manifolds of excited states relative to a common ground state. These quantities are the necessary ingredients to solve the Kramers--Heisenberg equation for resonant inelastic X-ray scattering (RIXS) and several other types of two-photon spectroscopies. The procedure is based on the pseudo-wavefunction approach, where TDDFT eigenstates are treated as a configuration interaction wavefunction with single excitations, and on the restricted energy window approach, where a manifold of excited states can be rigorously defined based on the energies of the occupied molecular orbitals involved in the excitation process. We illustrate the applicability of the method by calculating the 2p4d RIXS maps of three representative Ruthenium complexes and comparing them to experimental results. The method is able to accurately capture all the experimental features in all three complexes, with relative energies correct to within 0.6 eV at the cost of two independent TDDFT calculations.
Time-dependent orbital-free DFT is an efficient method for calculating the dynamic properties of large scale quantum systems due to the low computational cost compared to standard time-dependent DFT. We formalize this method by mapping the real system of interacting fermions onto a fictitious system of non-interacting bosons. The dynamic Pauli potential and associated kernel emerge as key ingredients of time-tependent orbital-free DFT. Using the uniform electron gas as a model system, we derive an approximate frequency-dependent Pauli kernel. Pilot calculations suggest that space nonlocality is a key feature for this kernel. Nonlocal terms arise already in the second order expansion with respect to unitless frequency and reciprocal space variable ($frac{omega}{q, k_F}$ and $frac{q}{2, k_F}$, respectively). Given the encouraging performance of the proposed kernel, we expect it will lead to more accurate orbital-free DFT simulations of nanoscale systems out of equilibrium. Additionally, the proposed path to formulate nonadiabatic Pauli kernels presents several avenues for further improvements which can be exploited in future works to improve the results.
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