Nonlocal Orbital-Free Density Functional Theory Incorporating Nuclear Shell Effects.

Bulk and neutron–proton asymmetry coefficients of the semi-empirical mass formula tuned to ground state mass excess of AME2020 and/or FRDM(2012)

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.

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme–Hartree–Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoretical results are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached. Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupy significantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of valence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ, ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.

The formalism of (nonlocal) density functional theory provides an attractive way to describe the physical adsorption process at the fluid-solid interface. It provides numerical results of analytic precision in a small fraction of the time required by a simulation technique. In particular, the ability to model adsorption in a pore space of slit-like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. However, critical comparisons of experimental isotherms with the isotherms predicted by density functional theory have shown important differences when using the usual prescription for the nonlocal free energy density functional. It is clear that these differences would affect the accuracy of such pore size information. We show in this paper how a small modification to the mean field computation of the intermolecular attractive potential results in excellent agreement with experiment for the systems studied.

We investigate the dependences of the potential energy surfaces (PES) and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy's contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding 208Pb are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.

In the present work, the cluster radioactivity of even A uranium isotopes (218–236U) with the emission of both alpha‐like and non‐alpha‐like neon clusters (20,22,24,26,28Ne) was studied. The decimal logarithm of half‐lives (expressed in seconds) were calculated by three different approaches based on (i) the single line of Universal curve (UNIV) for alpha and cluster radioactive decay, (ii) the Universal Decay law (UDL) and (iii) by considering a fission‐like model in which the interacting nuclear potential barrier was taken to be the sum of Coulomb and proximity potentials (CPPM) respectively. Based on the half‐lives calculated by using the three different approaches mentioned above, significance of the role of 208Pb nucleus (doubly magic nucleus) and nuclear shell effects in trans‐lead cluster radioactivity were investigated. The calculated half‐lives have also been compared with available experimental results. It was observed that cluster decay modes leading to the formation of 208Pb daughter nucleus have the lowest half‐lives. This implies that there is a shell closure at proton number (Z) = 82 and neutron number (N) = 126. Hence, it confirms the existence of nuclear shell effect and stresses the significance of role of 208Pb daughter nucleus in the trans‐lead cluster radioactivity. It can be noticed that the calculated half‐lives for several cluster decay modes are well within the present experimental upper limit for measurements (T1/2 < 1030S). These results may be useful for future experiments.

We analyze argon adsorption isotherms and isosteric heat of adsorption on graphitized and nongraphitized carbon black and silica surfaces by means of nonlocal density functional theory (NLDFT). It is shown that in the case of graphitized carbon black the behavior of the adsorbed phase is nearly identical to that in the bulk phase at a distance larger than about 3-4 molecular diameters from the surface. At a smaller distance argon forms solid-like molecular layers at a temperature at least 3.5 K above the triple point, with the interlayer distance being markedly smaller than the argon collision diameter. In the case of defected or amorphous surfaces adsorbed argon is liquid-like below its triple point. Our extension of the Tarazona NLDFT to amorphous solids (NLDFT-AS) and the Kierlik and Rosinberg version of NLDFT excellently fit argon adsorption isotherms and properly predict the isosteric heat of adsorption. We showed that the surface roughness affects the calculated heat of adsorption, which allowed us to adjust the width of the diffuse zone of the nongraphitized carbon black and the silica surface.

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.

Simulating electron transfer at reactive solid-liquid interfaces under constant electrochemical potentials of the constituents (electrons, ions, solvent etc.) is crucial to understanding the formation, functional and failure of electrochemical devices. Albeit being sufficiently accurate in decreasing breaking and formation of chemical bond at solid surfaces, existing methods based on Kohn-Sham density functional theory (DFT) are unsatisfactory in system consistency, namely, simulating the open solid-liquid interface under grand-canonical conditions, as well as in scaling up the simulation due to its high computational cost. Herein, to improve the system consistency and computational efficiency, we develop density-potential functional theoretic (DPFT) schemes out of Kohn-Sham DFT, drawing upon ideas of orbital-free DFT, frozen density embedding theory, and tight-binding DFT. The DPFT transforms an all-atom, Kohn-Sham DFT description of the nonreactive electrolyte solution into a coarse-grained, field-based description, while retaining a Kohn-Sham DFT description for the reactive subsystem. In the absence of surface reactions, the solid electrode can be described using orbital-free DFT, reducing the computational cost further. On the conceptual level, the physical meaning of potential in DPFT is examined. Recent applications of DPFT to simulate EDLs with mesoscopic roughness and EDLs at supported nanoparticles will be introduced. Related papers Zhang, Y., Binninger, T., Huang, J., & Eikerling, M. H. (2025). Theory of Electro-Ionic Perturbations at Supported Electrocatalyst Nanoparticles. Physical Review Letters, 134(6), 066201.Zhang, M., Chen, Y., Eikerling, M., & Huang, J. (2025). Structured solvent on a split electron tail: A semiclassical theory of electrified metal-solution interfaces. Physical Review Applied, 23(2), 024009.Huang, J., Domínguez-Flores, F., & Melander, M. (2024). Variants of surface charges and capacitances in electrocatalysis: Insights from density-potential functional theory embedded with an implicit chemisorption model. PRX Energy, 3(4), 043008. Acknowledgements Our research is supported financially by the Initiative and Networking Fund of the Helmholtz Association (no. VH-NG-1709), and European Research Council (ERC) Starting Grant (MESO-CAT, Grant agreement No. 101163405).

Orbital-free density functional theory (OFDFT) replaces the wavefunction in the kinetic energy by an explicit energy functional and thereby speeds up significantly the calculation of ground state properties of the solid state systems. So far, the application of OFDFT has been centered on closed systems and less attention is paid on the transport properties in open systems. In this paper, we use OFDFT and combine it with non-equilibrium Green's function to simulate equilibrium electronic transport properties in silicon nanostructures from first principles. In particular, we study ac transport properties of a silicon atomic junction consisting of a silicon atomic chain and two monoatomic leads. We have calculated the dynamic conductance of this atomic junction as a function of ac frequency with one to four silicon atoms in the central scattering region. Although the system is transmissive with dc conductance around 4 to 5 e2/h, capacitive-like behavior was found in the finite frequency regime. Our analysis shows that, up to 0.1 THz, this behavior can be characterized by a classic RC circuit consisting of two resistors and a capacitor. One resistor gives rise to dc resistance and the other one accounts for the charge relaxation resistance with magnitude around 0.2 h/e2 when the silicon chain contains two atoms. It was found that the capacitance is around 5 aF for the same system.

A new algorithm for efficient and fully time-reversible integration of first-principles molecular dynamics based on orbital-free density functional theory (OFDFT) is presented. The algorithm adapts to this nontrivial case, the recently introduced Mass-Zero (MaZe) constrained dynamics. The formalism ensures that full adiabatic separation is enforced between nuclear and electronic degrees of freedom and, consequently, that the exact Born-Oppenheimer probability for the nuclei is sampled. Numerical integration of the MaZe dynamics combines standard molecular dynamics algorithms, e.g., Verlet or velocity Verlet, with the SHAKE method to impose the minimum conditions on the electronic degrees of freedom as a set of constraints. The developments presented in this work, which include a bespoke adaptation of the standard SHAKE algorithm, ensure that the quasilinear scaling of OFDFT is preserved by the new method for a broad range of kinetic and exchange-correlation functionals, including nonlocal ones. The efficiency and accuracy of the approach are demonstrated via calculations of static and dynamic properties of liquid sodium in the constant energy and constant temperature ensembles.

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.

Ab initio and nonlocal density functional theory (DFT) calculations were performed to determine reaction mechanisms for formation of the six-membered ring C3N3Cl3 (cyanuric chloride) from the monomer cyanogen chloride (ClCN). MP2 geometry optimizations followed by QCISD(T) energy refinements and corrections for zero-point energies for critical points on the potential energy surface were calculated using the 6-31G* and 6-311+G* basis sets. DFT (B3LYP) geometry optimizations and zero-point corrections for critical points on the potential energy surface were calculated with the 6-31G*, 6-311+G*, and cc-pVTZ basis sets. Good agreement is found for MP2 and DFT geometries and frequencies of cyanuric chloride and ClCN when compared with experimental values. Two formation mechanisms of cyanuric chloride were investigated, the concerted triple association (3 ClCN → cyanuric chloride) and the stepwise association (3ClCN → Cl2C2N2 + ClCN → cyanuric chloride). All calculations show that the lower energy path to formation of cyanuric chloride is the concerted triple-association. MP2 and DFT intrinsic reaction coordinate calculations starting from the transition state for concerted triple association reaction proceeding toward the isolated monomer resulted in the location of a local minimum, stable by as much as 8.0 kcal/mol, that corresponds to a weakly-bound cyclic (ClCN)3 cluster. The existence of this cluster on the reaction path for the concerted triple association could lower the entropic hindrance to this unusual association reaction mechanism. The DFT/cc-pVTZ barrier to concerted triple association relative to isolated ClCN is 42.9 kcal/mol. The QCISD(T)//MP2/6-311+G* barrier to concerted triple association is 41.0 kcal/mol. The DFT/cc-pVTZ barrier to formation of the dimer (stepwise association reaction) is 63.4 kcal/mol while the QCISD(T)//MP2/6-311+G* barrier is 76.7 kcal/mol. The barrier to formation of cyanuric chloride relative to the (ClCN)3 minimum requires ∼46−49 kcal/mol, indicating that the concerted triple-association reaction via formation of the (ClCN)3 prereaction intermediate is the lower energy path to formation of cyanuric chloride. The temperature-corrected (T = 298 K) heats of reaction for formation of cyanuric chloride from ClCN are −63.4 and −61.2 kcal/mol for the B3LYP/cc-pVTZ and the QCISD(T)//MP2/6-311+G* predictions, respectively.

Adsorption of carbon dioxide in slit-shaped carbon micropores at 273 K has been studied by means of the grand canonical Monte Carlo (GCMC) simulations and the nonlocal density functional theory (NLDFT). Three molecular models of CO2 have been used. Long-run GCMC simulations were performed with the three-center model of Harris and Yung (J. Phys. Chem. 1995, 99, 12021). For NLDFT calculations, we developed an effective Lennard-Jones (LJ) model. GCMC simulations of the effective LJ model of CO2 have been performed for comparison. For each model used, parameters of intermolecular potentials have been determined and validated against two-phase bulk equilibrium data and experimental adsorption isotherms on graphite at 273 and 195 K. In the range of pore widths from 3 to 15 Å, the NLDFT isotherms of CO2 adsorption are overall in a satisfactory agreement with the GCMC isotherms generated using the three-center model. Some deviations have been observed between 6.5 and 8.5 Å, where the adsorbate undergoes a transition from a single-layer to a two-layer structure. The models developed are recommended for studying carbon dioxide adsorption in microporous adsorbents and also for calculating pore size distributions in carbonaceous materials and soil particles. The NLDFT model has the advantage of being much less computationally demanding, whereas the three-center GCMC model serves as a benchmark for quantitative estimates and can be used for studying CO2 sorption at ambient conditions close to the critical temperature.

Orbital-free density functional theory (OFDFT) is a quantum-mechanics-based method that utilizes electron density as its sole variable. The main computational cost in OFDFT is the ubiquitous use of the fast Fourier transform (FFT), which is mainly adopted to evaluate the kinetic energy density functional (KEDF) and electron-electron Coulomb interaction terms. We design and implement a small-box FFT (SBFFT) algorithm to overcome the parallelization limitations of conventional FFT algorithms. We also propose real-space truncation of the nonlocal Wang-Teter KEDF kernel. The scalability of the SBFFT is demonstrated by efficiently simulating one full optimization step (electron density, energies, forces, and stresses) of 1,024,000 lithium (Li) atoms on up to 65,536 cores. We perform other tests using Li as a test material, including calculations of physical properties of different phases of bulk Li, geometry optimizations of nanocrystalline Li, and molecular dynamics simulations of liquid Li. All of the tests yield excellent agreement with the original OFDFT results, suggesting that the OFDFT-SBFFT algorithm opens the door to efficient first-principles simulations of materials containing millions of atoms.