Optimization of random phase approximation calculations for improved energies of molecules, solids, and surfaces

TL;DR

This study advances random phase approximation (RPA) energetics by introducing optRPA26, which generates wavefunctions from a long-range corrected hybrid functional (LC-srPBEx25) and applies a small, empirically determined energy scaling to the RPA correlation term. By calibrating the non-RPA portion via optHXX and including short-range PBE correlation, optRPA26 achieves a balanced, high-accuracy description across molecules, bulk solids, and surfaces, including metals and metal oxides, with mean deviations in the 0.05–0.12 eV range for key benchmarks. The method demonstrates low sensitivity to functional-specific biases, captures phase stability, and maintains compatibility with standard RPA implementations (e.g., in VASP), offering a practical, general-purpose reference for covalent, ionic, metallic, and van der Waals interactions. These results highlight the potential of optimized RPA and related double-hybrid strategies to surpass conventional RPA in accuracy, while remaining accessible to practitioners without bespoke code modification.

Abstract

We present an optimized random phase approximation method (optRPA26) that significantly improves upon conventional RPA. The method employs an empirically constructed hybrid functional to generate DFT orbitals to evaluate the RPA correlation energy, which is then scaled by a constant. Comprehensive benchmarks across molecules, bulk solids, and surface systems demonstrate that optRPA26 consistently achieves high accuracy, with mean absolute errors of 0.05 eV for W4-11 reaction energies, 0.07 eV for cohesive energies, 0.09 eV for metal oxide formation energies, 0.11-0.12 eV for adsorption of small molecules on metals, and 0.06 eV for adsorption on oxides. In addition, optRPA26 correctly captures phase stability in metal oxides and magnetic metals. The optRPA26 approach can be run using standard RPA implementations, highlighting its potential as a general-purpose reference method that can accurately capture covalent, ionic, and metallic, and van der Waals bonding in molecules, solids, and interfaces.

Figures (22)

• Figure 1: Absolute deviations from reference values for each molecular dataset. Datasets include W4-11 (n=124$^*$)karton2011w411, W4-11-RE (n=8,868$^*$)margraf2017w411re, BH76 (n=76)zhao2005BH76azhao2005BH76blars2010gmtkn24, BH76RC (n=30)lars2010gmtkn24, MOBH29 (n=87) iron2019mobh35dohm2020mobh29semidalas2022mobh35revgrotjahn2023mobh28, and S19 (n=19)rezac2011s66. Bars represent MAD (dark color) and RMSD (light color), and × symbols indicate maximum deviations. A horizontal red line denotes the chemical accuracy of 1kcal. $^*$W4-11 and W4-11-RE contain only the molecules listed in TAE_nonMR124.
• Figure 2: Absolute percentage deviations from ZPE-corrected experimental values for lattice constants harl2010Ecorr and bulk moduli harl2010Ecorrzhang2018bulk_prop for 24 (non-oxide) bulk solids. RPA (n=24) harl2010Ecorr, rALDA (n=10) patrick2015ralda_bulk, and rAPBE (n=4) olsen2014rA values are taken from the literature. Bars represent MAPD (dark color) and RMSPD (light color), and × symbols indicate maximum percentage deviations.
• Figure 3: Absolute deviations from (ZPE-corrected) experimental atomization energies (eV per formula unit) of 24 non-oxides harl2010Ecorr and (non-ZPE-corrected) formation energies (eV per oxygen) of 23 oxides yan2013rpa_oxdevoss2022oxide. For atomization energies, RPA values (n=24) are from Ref. harl2010Ecorr, and rALDA (n=19) and rAPBE (n=19) are from Ref. olsen2014rA. For oxide formation energies, RPA values (n=22) are from Ref. yan2013rpa_oxde, and rAPBE values (n=21) are from Ref. jauho2015rapbe_oxide. Bars represent MAD (dark color) and RMSD (light color), and × symbols indicate maximum deviations.
• Figure 4: Absolute deviations from ZPE-corrected experimental adsorption energies araujo2022ads38 on metals (Cu, Ru, Rh, Pd, Ir, Pt, and Ni) (n=$27$). $\textit{PBE+D3/M06}$araujo2022ads38 refers to a hybrid scheme that combines cluster (M06 level) and periodic model (PBE$+$D3 level). (a) Non-dissociative adsorption energies referenced to gas-phase adsorbates (e.g., O) as in Ref. araujo2022ads38. (b) Adsorption energies referenced to gas-phase molecules (e.g., O2) as in ADS41mall2019ads41. (c) Non-dissociative adsorption energies obtained by referencing $E(\text{slab+adsorbate})-E(\text{slab})$ to least-squares elemental chemical potentials, compared against experimental values adjusted by the formation energies of adsorbates. The adsorption energy values are defined on a per-adsorbate basis; for example, for O adsorption, the adsorption energy is $\Delta$E in (a, c) or $\Delta$E/2 in (b). Bars represent MAD (dark color) and RMSD (light color), and × symbols indicate maximum deviations. Red horizontal lines denotes the transition metal chemical accuracy of 3kcal.
• Figure 5: Surface energies and CO adsorption energies on four TM surfaces. The optRPA26 values for $E_\text{ads}$ correspond to those in \ref{['fig:ads_metal']}. The values of RPA$_\text{1}$schimka2010rpa_surf, RPA$_\text{2}$schmidt2018benchmarkRPA, rAPBEolsen2014rA, and experimentsvitos1998Esurf_expt are taken from the literature.