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Register a new userNonlocal and nonadiabatic Pauli potential for time-dependent orbital-free density functional theory
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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.
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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.
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.
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hookes atoms, jellium, and model atoms up to $sim 1000$ electrons show that reasonable total energies can be obtained with almost a negligible computational cost. The results are also consistent in the important large-$N$ limit.
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 present a rigorous framework that combines single-particle Greens function theory with density functional theory based on a separation of electron-electron interactions into short-range and long-range components. Short-range contributions to the total energy and exchange-correlation potential are provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Greens function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Greens function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Greens function theory. We illustrate that similarly to density functional approximations the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamical correlation. The many-body contribution to the functional allows us to mitigate the many-electron self-interaction error present in most of density functional approximations and provides a better description of molecular properties. Additionally, the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.
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