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Register a new userSelf-consistent energy approximation for orbital-free density-functional theory
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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.
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Orbital-Free Density Functional Theory (OF-DFT) promises to describe the electronic structure of very large quantum systems, being its computational cost linear with the system size. However, the OF-DFT accuracy strongly depends on the approximation made for the kinetic energy (KE) functional. To date, the most accurate KE functionals are non-local functionals based on the linear-response kernel of the homogeneous electron gas, i.e. the jellium model. Here, we use the linear-response kernel of the jellium-with-gap model, to construct a simple non-local KE functional (named KGAP) which depends on the band gap energy. In the limit of vanishing energy-gap (i.e. in the case of metals), the KGAP is equivalent to the Smargiassi-Madden (SM) functional, which is accurate for metals. For a series of semiconductors (with different energy-gaps), the KGAP performs much better than SM, and results are close to the state-of-the-art functionals with complicated density-dependent kernels.
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.
We propose a hybrid approach which employs the dynamical mean-field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent DFT+DMFT scheme in a basis of maximally localized Wannier orbitals using Wien2K, wien2wannier, and the DMFT impurity solver w2dynamics. As a testbed material we apply the method to SrVO$_3$ and report a significant improvement as compared to previous $d$+$p$ calculations. In particular the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle with unwelcome consequences for the $d$-$p$ hybridization and correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation renders the so-called double-counting problem obsolete.
Semi-local approximations to the density functional for the exchange-correlation energy of a many-electron system necessarily fail for lobed one-electron densities, including not only the familiar stretched densities but also the less familiar but closely-related noded ones. The Perdew-Zunger (PZ) self-interaction correction (SIC) to a semi-local approximation makes that approximation exact for all one-electron ground- or excited-state densities and accurate for stretched bonds. When the minimization of the PZ total energy is made over real localized orbitals, the orbital densities can be noded, leading to energy errors in many-electron systems. Minimization over complex localized orbitals yields nodeless orbital densities, which reduce but typically do not eliminate the SIC errors of atomization energies. Other errors of PZ SIC remain, attributable to the loss of the exact constraints and appropriate norms that the semi-local approximations satisfy, and suggesting the need for a generalized SIC. These conclusions are supported by calculations for one-electron densities, and for many-electron molecules. While PZ SIC raises and improves the energy barriers of standard generalized gradient approximations (GGAs) and meta-GGAs, it reduces and often worsens the atomization energies of molecules. Thus PZ SIC raises the energy more as the nodality of the valence localized orbitals increases from atoms to molecules to transition states. PZ SIC is applied here in particular to the SCAN meta-GGA, for which the correlation part is already self-interaction-free. That property makes SCAN a natural first candidate for a generalized SIC.
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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