A simpler ingredient for a complex calculation

Walter Kohn, Pierre Hohenberg, and Lu Sham first formulated density functional theory in the 1960s. Since then, DFT has become the most popular approach in quantum chemistry and condensed-matter physics for calculating the electronic structure and ground-state properties of atoms and molecules. (See the article by Andrew Zangwill, Physics Today, July 2015, page 34 .) The approach eases the computational burden of finding the many-body wavefunction by reducing the problem to finding the electron density. Even so, the solution entails calculating the electrons’ interactions not only with any external potential but also with each other. Besides the repulsive effects of the Coulomb interaction and the Pauli exclusion principle, the interactions include collective effects—the so-called correlation-energy functional—which, even for the simple case of a uniform electron gas, must be approximated (except in the high- and low-density limits). Teepanis Chachiyo of the Institute for Fundamental Study at Naresuan University in Phitsanulok, Thailand, has now derived a simple formula for finding the correlation energy in a uniform electron gas. With only two parameters, whose values can be obtained from fits to the high-density behavior, Chachiyo’s formula yields accurate results for the mid- and low-density regimes. Indeed, for a paramagnetic system, the results are closer to the detailed simulation results than are those from standard, much more complicated formulas. Though Chachiyo’s expression applies only to a uniform electron gas, it should be a useful starting point for considering the nonuniform densities in molecules and bulk solids. (T. Chachiyo, J. Chem. Phys. 145, 021101, 2016, doi: 10.1063/1.4958669 .)