(Invited) Density-Potential Functional Theoretic Models for Electrochemical Interfaces

ABACUS (Atomic-orbital Based Ab initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and molecular dynamics functions and is compatible with both plane wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as deep potential with attention models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several artificial intelligence-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, HamGNN, etc.

The formation and migration energies for various point defects, including vacancies and self-interstitials, in aluminium are systematically reinvestigated using the supercell approximation in the framework of orbital-free density functional theory. In particular, the finite-size effects and the accuracy of various kinetic energy density functionals are examined. It is demonstrated that as the supercell size increases, the finite-size errors asymptotically decrease as . Notably, the formation energies of self-interstitials converge much more slowly than that of vacancies. With carefully chosen kinetic energy density functionals, the calculated results agree quite well with the available experimental data and those obtained through Kohn–Sham density functional theory, which has an exact kinetic term.

One obstacle in orbital-free density functional theory (OF-DFT) is the lack of accurate and transferable local pseudopotentials (LPSs). In this work, we build high quality LPSs by inverting Kohn-Sham (KS) equations on bulk valence electron densities to obtain an atom-centered local pseudopotential. With this approach, we build LPSs for Mg, Al, and Si, and then test them in KS DFT calculations of static bulk properties for several Mg, Al, and Si bulk structures as well as beta''-Al3Mg. Our Mg, Al, and Si LPSs produce correct ground state properties and phase orderings. These LPSs are then tested in KS-DFT calculations of surface energies for several low-index Mg and Al surfaces, point defect properties in hexagonal-close-packed (hcp) Mg, face-centered cubic (fcc) Al, and diamond Si, and stacking fault energies in fcc Al. All of these LPS results agree quantitatively with the results from nonlocal pseudopotentials with errors less than or equal to 40 meV per atom. Finally, we perform OF-DFT calculations for various Mg and Al structures, employing the Wang-Govind-Carter (WGC) nonlocal kinetic energy density functional (KEDF). The OF-DFT results generally agree well with the corresponding KS-DFT results. With our new Mg and Al LPSs and the WGC KEDF, OF-DFT now provides a practical method for accurate, large-scale first principles simulations of main group metals and their alloys.

Density functional theory and quantum mechanics studies of 2D carbon nanostructures (graphene and graphene oxide) for Lenalidomide anticancer drug delivery

We describe the simplest single–photon encoding schemes and introduce the concept of a quantum optical gate. These gates can be used to build up arbitrary entangled states of many initially separate single photons. Experimental realization of such a gate involves the development of nonlinear phase shift elements sensitice at the single quantum level. We report our experimental efforts using linear optical elements and non–classical sources where we are able to demonstrate interference and entanglement of initially separate single–photon pulses.

IS A GRAVITON DETECTABLE?

We consider a steady-state (but transient) situation in which a warm dense aggregate is a two-temperature system with equilibrium electrons at temperature Te, ions at Ti, and Te ≠ Ti. Such states are achievable by pump–probe experiments. For warm dense hydrogen in such a two-temperature situation, we investigate nuclear quantum effects (NQEs) on structure and thermodynamic properties, thereby delineating the limitations of ordinary ab initio molecular dynamics. We use path integral molecular dynamics (PIMD) simulations driven by orbital-free density functional theory (OFDFT) calculations with state-of-the-art noninteracting free-energy and exchange-correlation functionals for the explicit temperature dependence. We calibrate the OFDFT calculations against conventional (explicit orbitals) Kohn–Sham DFT. We find that when the ratio of the ionic thermal de Broglie wavelength to the mean interionic distance is larger than about 0.30, the ionic radial distribution function is meaningfully affected by the inclusion of NQEs. Moreover, NQEs induce a substantial increase in both the ionic and electronic pressures. This confirms the importance of NQEs for highly accurate equation-of-state data on highly driven hydrogen. For Te > 20 kK, increasing Te in the warm dense hydrogen has slight effects on the ionic radial distribution function and equation of state in the range of densities considered. In addition, we confirm that compared with thermostatted ring-polymer molecular dynamics, the primitive PIMD algorithm overestimates electronic pressures, a consequence of the overly localized ionic description from the primitive scheme.

Incorporating nuclear shell effects within the framework of orbital-free density functional theory (DFT) has remained a long-standing challenge in nuclear physics. While the Hohenberg-Kohn theorem formally guarantees the existence of an orbital-free density functional that is capable of describing all many-body effects, including shell effects, practical attempts since the 1970s have consistently failed to capture such effects. This persistent difficulty has even led to the misconception that the orbital-free DFT is inherently unable to describe nuclear shell effects. Here we develop a nonlocal orbital-free DFT approach for atomic nuclei and demonstrate that nuclear shell effects can be successfully incorporated into the orbital-free DFT through the construction of a nonlocal kinetic energy density functional. In particular, we show that the nonlocal orbital-free functional yields a nucleon localization function that, as an established indicator of shell effects, exhibits consistent behavior with the exact Kohn-Sham solution.

We explore a new formalism to study the nonlinear electronic density response based on Kohn–Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wavenumbers q < 2qF, with qF being the Fermi wavenumber. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the nonlinear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods.

Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence of symmetry or equal occupation of degenerate orbitals. To demonstrate the resulting methodology, we apply it to the iron atom in the central field approximation, perturbed by an electric quadrupole. This system was chosen because it displays both symmetry required degeneracy, between the five 3\textit{d} orbitals, as well as accidental degeneracy, between the 3\textit{d} and 4\textit{s} orbitals. The quadrupole potential couples the degenerate 3\textit{d} and 4\textit{s} states, serving as an example of the most general perturbation.

We present a machine-learned (ML) model of kinetic energy for orbital-free density functional theory (OF-DFT) suitable for bulk light weight metals and compounds made of group III–V elements. The functional is machine-learned with Gaussian process regression (GPR) from data computed with Kohn-Sham DFT with plane wave bases and local pseudopotentials. The dataset includes multiple phases of unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In. A total of 433 materials were used for training, and 18 strained structures were used for each material. Averaged (over the unit cell) kinetic energy density is fitted as a function of averaged terms of the 4th order gradient expansion and the product of the density and effective potential. The kinetic energy predicted by the model allows reproducing energy-volume curves around equilibrium geometry with good accuracy. We show that the GPR model beats linear and polynomial regressions. We also find that unary compounds sample a wider region of the descriptor space than binary and ternary compounds, and it is therefore important to include them in the training set; a GPR model trained on a small number of unary compounds is able to extrapolate relatively well to binary and ternary compounds but not vice versa.

The effects of an explicit temperature dependence in the exchange correlation (XC) free-energy functional upon calculated properties of matter in the warm dense regime are investigated. The comparison is between the Karasiev-Sjostrom-Dufty-Trickey (KSDT) finite-temperature local-density approximation (TLDA) XC functional [Karasiev etal., Phys. Rev. Lett. 112, 076403 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.076403] parametrized from restricted path-integral Monte Carlo data on the homogeneous electron gas (HEG) and the conventional Monte Carlo parametrization ground-state LDA XC [Perdew-Zunger (PZ)] functional evaluated with T-dependent densities. Both Kohn-Sham (KS) and orbital-free density-functional theories are used, depending upon computational resource demands. Compared to the PZ functional, the KSDT functional generally lowers the dc electrical conductivity of low-density Al, yielding improved agreement with experiment. The greatest lowering is about 15% for T=15 kK. Correspondingly, the KS band structure of low-density fcc Al from the KSDT functional exhibits a clear increase in interband separation above the Fermi level compared to the PZ bands. In some density-temperature regimes, the deuterium equations of state obtained from the two XC functionals exhibit pressure differences as large as 4% and a 6% range of differences. However, the hydrogen principal Hugoniot is insensitive to the explicit XC T dependence because of cancellation between the energy and pressure-volume work difference terms in the Rankine-Hugoniot equation. Finally, the temperature at which the HEG becomes unstable is T≥7200 K for the T-dependent XC, a result that the ground-state XC underestimates by about 1000 K.

Multi-atom vacancies and pores in diamond-structured carbon phases play an important role in carbon sieves and carbon based storage. The size and shape of pores have a profound effect on the energetics of adsorptive storage. We are modeling large numbers of vacancy configurations with a combination of ab initio density functional theory (DFT), tight binding DFT and simpler methods based on Brenner-potentials and modified Brenner potentials. The more accurate calculations serve as the basis of the parametrization which is then used in lattice Monte Carlo simulations on more complex vacancies. The results will be put in the context of SiC-derived porous carbon materials with the purpose to explore basic questions of energetics in porous carbons.

Conspectus Ab initio modeling of matter has become a pillar of chemical research: with ever-increasing computational power, simulations can be used to accurately predict, for example, chemical reaction rates, electronic and mechanical properties of materials, and dynamical properties of liquids. Many competing quantum mechanical methods have been developed over the years that vary in computational cost, accuracy, and scalability: density functional theory (DFT), the workhorse of solid-state electronic structure calculations, features a good compromise between accuracy and speed. However, approximate exchange-correlation functionals limit DFT's ability to treat certain phenomena or states of matter, such as charge-transfer processes or strongly correlated materials. Furthermore, conventional DFT is purely a ground-state theory: electronic excitations are beyond its scope. Excitations in molecules are routinely calculated using time-dependent DFT linear response; however applications to condensed matter are still limited. By contrast, many-electron wavefunction methods aim for a very accurate treatment of electronic exchange and correlation. Unfortunately, the associated computational cost renders treatment of more than a handful of heavy atoms challenging. On the other side of the accuracy spectrum, parametrized approaches like tight-binding can treat millions of atoms. In view of the different (dis-)advantages of each method, the simulation of complex systems seems to force a compromise: one is limited to the most accurate method that can still handle the problem size. For many interesting problems, however, compromise proves insufficient. A possible solution is to break up the system into manageable subsystems that may be treated by different computational methods. The interaction between subsystems may be handled by an embedding formalism. In this Account, we review embedded correlated wavefunction (CW) approaches and some applications. We first discuss our density functional embedding theory, which is formally exact. We show how to determine the embedding potential, which replaces the interaction between subsystems, at the DFT level. CW calculations are performed using a fixed embedding potential, that is, a non-self-consistent embedding scheme. We demonstrate this embedding theory for two challenging electron transfer phenomena: (1) initial oxidation of an aluminum surface and (2) hot-electron-mediated dissociation of hydrogen molecules on a gold surface. In both cases, the interaction between gas molecules and metal surfaces were treated by sophisticated CW techniques, with the remainder of the extended metal surface being treated by DFT. Our embedding approach overcomes the limitations of conventional Kohn-Sham DFT in describing charge transfer, multiconfigurational character, and excited states. From these embedding simulations, we gained important insights into fundamental processes that are crucial aspects of fuel cell catalysis (i.e., O2 reduction at metal surfaces) and plasmon-mediated photocatalysis by metal nanoparticles. Moreover, our findings agree very well with experimental observations, while offering new views into the chemistry. We finally discuss our recently formulated potential-functional embedding theory that provides a seamless, first-principles way to include back-action onto the environment from the embedded region.

A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (${\text{Fe}}_{\text{Al}}$). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the ``double-counting'' correction. For ${\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}$ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the ${\mathrm{NV}}^{\ensuremath{-}}$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in ${\text{Fe}}_{\text{Al}}$.