Van-der-Waals exchange-correlation functionals and their high pressure and warm dense matter applications

TL;DR

This study systematically tests van-der-Waals, r$^{2}$SCAN, and hybrid xc functionals against PBE for hydrogen under warm dense conditions to gauge their impact on bond lengths, dissociation energies, intermolecular interactions, and the molecular-to-metal transition. Using DFT/MD with multiple benchmarks, including i-FCIQMC/NCBS-corrected CCSD(T) data, the authors find that vdW functionals do not reliably improve predictions for the LLPT or equation of state; in fact, vdW corrections often overbind, shifting the LLPT to higher pressures. Bond lengths are best reproduced by r$^{2}$SCAN and HSE06, while dissociation energies favor r$^{2}$SCAN; however, the overall EOS, static/dynamic structure, and DOS show limited sensitivity to vdW corrections, with many observables better captured by PBE/HSE06. The results suggest using PBE (or HSE06) as a practical baseline for warm dense hydrogen EOS studies, and highlight that vdW corrections mainly affect high-energy binding scales rather than the relevant nanometer-scale structure and dynamics in these regimes. The work provides guidance for functional choice in simulations of planetary interiors and fusion-relevant hydrogen, and points to the need for improved electron-electron correlation treatments to accurately capture the transition physics.

Abstract

We investigate basic hydrogen quantities like the molecular bond length, the molecular dissociation energy and the van-der-Waals interaction in idealized situations in an effort to discern a suitable exchange-correlation functional for the molecular to metal transition in warm dense hydrogen. The best reproduction of bond length and dissociation energy is given by the r2SCAN functional, several vdW functionals and also HSE06 fair qualitatively and quantitatively no better than PBE or worse. In addition we investigate quantities like the static and dynamic ion structure factor, and the electronic DOS to determine differences between exchange-correlation functionals with and without van-der-Waals corrections in the transition region from the molecular to the metallic regime of hydrogen.

Figures (15)

• Figure 1: (Top) H$_2$ dissociation curves for different xc functionals. QMC result (CISD) taken from Ref. Bonfim2017. (Bottom) Close up of the potential curve minimum for the H$_2$ molecule. The bond lengths as predicted by DFT are shown as dashed vertical lines in the inset.
• Figure 2: Model interaction geometry 1. The left panel shows the relative position of the four atoms ($L\ldots$ edge length of supercell, $d\ldots$ distance between molecules, $a\ldots$ molecule bond length): $(L/2,L/2,L/2-d/2)\,,(L/2+a,L/2,L/2-d/2)\,,(L/2+a/2,L/2,L/2+d/2)\,,(L/2+a/2,L/2,L/2+d/2+a)$ The right panel contains DFT results (black, blue, green) and QMC results (red) for the energy of the system of two molecules as function of the distance of their centre of mass. The energy at maximum intermolecular distance was taken as the zero point of the energy. The inset shows an enhanced view of the area of the minimum of the energy.
• Figure 3: Model interaction geometry 2. The left panel shows the relative position of the four atoms ($L\ldots$ edge length of supercell, $d\ldots$ distance between molecules, $a\ldots$ molecule bond length): $(L/2,L/2,L/2-d/2)\,,(L/2+a,L/2,L/2-d/2)\,,(L/2,L/2,L/2+d/2)\,,(L/2+a,L/2,L/2+d/2)$ The right panel contains DFT results (black, blue, green) and QMC results (red) for the energy of the system of two molecules as function of the distance of their centre of mass. The energy at maximum intermolecular distance was taken as the zero point of the energy. The inset shows an enhanced view of the area of the minimum of the energy.
• Figure 4: Model interaction geometry 3. The left panel shows the relative position of the four atoms ($L\ldots$ edge length of supercell, $d\ldots$ distance between molecules, $a\ldots$ molecule bond length): $(L/2-a/2,L/2,L/2-d/2)\,,(L/2+a/2,L/2,L/2-d/2)\,,(L/2,L/2-a/2,L/2+d/2)\,,(L/2,L/2+a/2,L/2+d/2)$ The right panel contains DFT results (black, blue, green) and QMC results (red) for the energy of the system of two molecules as function of the distance of their centre of mass. The energy at maximum intermolecular distance was taken as the zero point of the energy. The inset shows an enhanced view of the area of the minimum of the energy.
• Figure 5: Model interaction geometry 4. The left panel shows the relative position of the four atoms ($L\ldots$ edge length of supercell, $d\ldots$ distance between molecules, $a\ldots$ molecule bond length): $(L/2,L/2,L/2-d/2)\,,(L/2,L/2,L/2-d/2+a/2)\,,(L/2,L/2,L/2+d/2)\,,(L/2,L/2,L/2+d/2+a/2)$ The right panel contains DFT results (black, blue, green) and QMC results (red) for the energy of the system of two molecules as function of the distance of their centre of mass. The energy at maximum intermolecular distance was taken as the zero point of the energy. The inset shows an enhanced view of the area of the minimum of the energy.