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This Special Issue of the Journal of Chemical Physics is dedicated to the work and life of John P. Perdew. A short bio is available within the issue [J. P. Perdew, J. Chem. Phys. 160, 010402 (2024)]. Here, we briefly summarize key publications in density functional theory by Perdew and his collaborators, followed by a structured guide to the papers contributed to this Special Issue.
Kohn-Sham density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. The recent development of the strongly constrained and appropriately normed (SCAN) functional has renewed the interest in ab initio simulations of liquid water, yielding promising results that are, however, still unable to reproduce all the experimental data. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of coupled cluster theory, the “gold standard” for chemical accuracy. Building upon the accuracy and efficiency of DC-SCAN within a many-body formal- ism, we introduce a data-driven many-body potential energy function, the MB-SCAN(DC) PEF, that is able to quantitatively reproduce coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, the properties of liquid water calculated from molecular dynamics simulations carried out with the MB- SCAN(DC) PEF are found to be in excellent agreement with the experimental data, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the condensed phase. Since the many-body formalism adopted by the present MB-SCAN(DC) PEF for water is general, we believe it can open the door to the routine development of data-driven many-body PEFs for predictive simulations of generic (small) molecules in the gas, liquid, and solid phases.
We evaluate binding energies, ionization energies, and second-order energy differences as functions of valence electron number for small spherical clusters of stabilized jellium, using the Kohn–Sham equations with the local-spin-density (LSD) approximation. Cohesive energies are also reported. A comparison is made with semiclassical formulas (liquid drop model and Padé approximant, with surface and curvature coefficients derived from first principles). These formulas nicely average the shell-structure oscillations of the energy, which are found to be almost the same as for ordinary jellium. Spherical clusters with 1, 7, and 9 electrons have binding energies very close to those of the semiclassical predictions. © 1993 John Wiley & Sons, Inc.
There is a misprint in Eq. ͑51͒.The denominator should be 3 3 , not 3 2 .However, Fig.
Standard spin-density functionals for the exchange-correlation energy of a many-electron ground state make serious self-interaction errors which can be corrected by the Perdew-Zunger self-interaction correction (SIC). We propose a size-extensive construction of SIC orbitals which, unlike earlier constructions, makes SIC computationally efficient, and a true spin-density functional. The SIC orbitals are constructed from a unitary transformation that is explicitly dependent on the non-interacting one-particle density matrix. When this SIC is applied to the local spin-density approximation, improvements are found for the atomization energies of molecules.
First principles predictions of lattice dynamics are of vital importance for a broad range of topics in materials science and condensed matter physics. The large-scale nature of lattice dynamics calculations and the desire to design novel materials with distinct properties demands that first principles predictions are accurate, transferable, efficient, and reliable for a wide variety of materials. In this work, we demonstrate that the recently constructed r2SCAN density functional meets this need for general systems by demonstrating phonon dispersions for typical systems with distinct chemical characteristics. The functional's performance opens a door for phonon-mediated materials discovery from first principles calculations.
We propose a generalized gradient approximation (GGA) for the angle- and system-averaged exchange-correlation hole of a many-electron system. This hole, which satisfies known exact constraints, recovers the Perdew-Burke-Ernzerhof for solids (PBEsol) exchange-correlation energy functional, a GGA that accurately describes the equilibrium properties of densely packed solids and their surfaces. We find that our PBEsol exchange-correlation hole describes the wave-vector analysis of the jellium exchange-correlation surface energy in agreement with a sophisticated time-dependent density-functional calculation (whose three-dimensional wave-vector analysis we report here).
The authors show, on the basis of a semi-self-consistent density functional calculation of the equilibrium position of the first lattice plane at the three low index faces of aluminium, that the screening of the ionic relaxation dipole by the electrons is essentially perfect. As a result the surface energy and work function are nearly independent of small displacements of the first lattice plane. They also demonstrate that the 'frozen profile' approximation for the electron density grossly exaggerates the curvature of the potential in which the first lattice plane sits and so cannot be relied on for geometrical predictions. The results for the first interplanar spacing of the close-packed (111) surface agree with the 2% expansion (relative to bulk) found in the recent LEED analysis of Jona et al. (1980) and do not favour the 8% contraction suggested by the surface EXAFS study of Bianconi and Bachrach (1979).
Kohn-Sham density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. The recent development of the strongly constrained and appropriately normed (SCAN) functional has renewed the interest in ab initio simulations of liquid water, yielding promising results that are, however, still unable to reproduce all the experimental data. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of coupled cluster theory, the “gold standard” for chemical accuracy. Building upon the accuracy and efficiency of DC-SCAN within a many-body formal- ism, we introduce a data-driven many-body potential energy function, the MB-SCAN(DC) PEF, that is able to quantitatively reproduce coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, the properties of liquid water calculated from molecular dynamics simulations carried out with the MB- SCAN(DC) PEF are found to be in excellent agreement with the experimental data, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the condensed phase. Since the many-body formalism adopted by the present MB-SCAN(DC) PEF for water is general, we believe it can open the door to the routine development of data-driven many-body PEFs for predictive simulations of generic (small) molecules in the gas, liquid, and solid phases.
We propose a simple analytic representation of the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\mathit{r}}_{\mathit{s}}$ and relative spin polarization \ensuremath{\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ behavior as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Close agreement with numerical RPA values for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,0), ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,1), and the spin stiffness ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$)=${\mathrm{\ensuremath{\partial}}}^{2}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$, \ensuremath{\zeta}=0)/\ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{2}$, and recovery of the correct ${\mathit{r}}_{\mathit{s}}$ln${\mathit{r}}_{\mathit{s}}$ term for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \ensuremath{\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\mathit{r}}_{\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}^{\mathrm{\ensuremath{\sigma}}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) is evaluated for use in self-consistent density-functional calculations.
