Accurate all-electron correlation energies for the closed-shell atoms from Ar to Rn and their relationship to the corresponding MP2 correlation energies

Adiabatic connection interaction strength interpolation method made accurate for the uniform electron gas

The adiabatic connection interaction strength interpolation (ISI)-like method provides a high-level expression for the correlation energy, being, in principle, exact not only in the weak-interaction limit, where it recovers the second-order Görling-Levy perturbation term, but also in the strong-interaction limit that is described by the strictly correlated electron approach. In this work, we construct a genISI functional made accurate for the uniform electron gas, a solid-state physics paradigm that is a very difficult test for ISI-like correlation functionals. We assess the genISI functional for various jellium spheres with the number of electrons Z ≤ 912 and for the non-relativistic noble atoms with Z ≤ 290. For the jellium clusters, the genISI is remarkably accurate, while for the noble atoms, it shows a good performance, similar to other ISI-like methods. Then, the genISI functional can open the path using the ISI-like method in solid-state calculations.

On the Periodicity of the Information Theory and Conceptual DFT-Based Reactivity Descriptors

The periodic trends in conceptual density functional and information theory-based reactivity descriptors are reported for the atoms H to Ba (Z = 1 to 56). Ionization potential, electron affinity, electronegativity, and hardness show periodic behavior following the Aufbau principle and popular electronic structure principles. They are in agreement with those reported in standard chemistry textbooks. The trend in the electrophilicity index, however, shows an interesting behavior, where it contradicts earlier reports. Our calculation reveals that the noble gas elements correspond to minimum ω values in each period which obey the minimum electrophilicity principle as well as reflect their low reactivity. Periodic trends in electroaccepting and electrodonating powers, along with that of net electrophilicity, are as expected. The behavior of information theory-based Shannon and GBP entropies, along with the Shannon entropy of shape function are also explored across the periodic table.

Regularized SCAN functional

We propose modifications to the functional form of the Strongly Constrained and Appropriately Normed (SCAN) density functional to eliminate numerical instabilities. This is necessary to allow reliable, automatic generation of pseudopotentials (including projector augmented-wave potentials). The regularized SCAN is designed to match the original form very closely, and we show that its performance remains comparable.

Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance

We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches. NCAP is constructed by reconsidering the imposition of the asymptotic correctness of the X potential (-1/ r) as a constraint. Inclusion of derivative discontinuity and approximate integer self-interaction correction treatments along with first-principles determination of the effective second-order gradient expansion coefficient yields a major advance over our earlier correct asymptotic potential functional [CAP; J. Chem. Phys. 2015 , 142 , 054105 ]. The new functional reduces a spurious bump in the CAP atomic exchange potential and moves it to distances irrelevantly far from the nucleus (outside the tail of essentially all practical basis functions). It therefore has nearly correct atomic exchange-potential behavior out to rather large finite distances r from the nucleus but eventually goes as - c/ r with an estimated value for the constant c of around 0.3, so as to achieve other important properties of exact DFT exchange within the restrictions of the GGA form. We illustrate the results with the Ne atom optimized effective potentials and with standard molecular benchmark test data sets for thermochemical, structural, and response properties.

On the (N, Z) dependence of the second-order Møller-Plesset correlation energies for closed-shell atomic systems

Accurate Møller-Plesset (MP2) correlation energies calculated by means of the variational-perturbation and the finite-element methods are presented for several members of the Cu(+) isoelectronic series (N = 28), which represent closed-shell systems containing for the first time the 3d(10)-electron configuration and, consequently, closed M-shell. Total MP2 energies as well as their inner- and inter-shell components are reported for Cu(+), Zn(2+), Ge(4+), Kr(8+), Sr(10+), and Cd(20+). We found that for these ions the Z-dependence of the total MP2 energies is significantly weaker than for the members of the Ar-like series. The origin of this fact is rationalized by a detailed analysis performed at the levels of the shell- and inter-shell contributions to the MP2 energies. To get, for the first time, more general information about the (N, Z) characteristics of the MP2 energies for closed-shell atomic systems, we compare the Z-dependence of the Cu(+)-like systems with the MP2 energies calculated for other isoelectronic series. The weak Z-dependence is found for the He-, Ne-, and Cu(+)-like series, which consist of atoms having perfectly closed-shell K-, KL-, and KLM-electronic structures, respectively. In turn, for the Be-, Mg-, and Ar-series, the Z-dependence is considerably stronger.

Strongly Constrained and Appropriately Normed Semilocal Density Functional

The ground-state energy, electron density, and related properties of ordinary matter can be computed efficiently when the exchange-correlation energy as a functional of the density is approximated semilocally. We propose the first meta-generalized-gradient approximation (meta-GGA) that is fully constrained, obeying all 17 known exact constraints that a meta-GGA can. It is also exact or nearly exact for a set of "appropriate norms," including rare-gas atoms and nonbonded interactions. This strongly constrained and appropriately normed meta-GGA achieves remarkable accuracy for systems where the exact exchange-correlation hole is localized near its electron, and especially for lattice constants and weak interactions.

Perspective: Fifty years of density-functional theory in chemical physics

Since its formal inception in 1964-1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.

Ab initio calculation of the MgO(100) interaction with He and Ne: a HF + MP2 and HF + MP2(B3LYP) comparison

Second order Rayleigh Schrödinger perturbation theory is applied to calculate the correlation energy contribution to the London dispersion interaction to approximate the interaction of the He and Ne with the MgO(100) surface; single particle orbitals using either Hartree-Fock theory or hybrid-exchange density functional theory are used as the reference state.