Accurate prediction of the properties of materials using the CAM‐B3LYP density functional

Abstract

Density functionals with asymptotic corrections to the long-range potential provide entry-level methods for calculations on molecules that can sustain charge transfer, but similar applications in materials science are rare. We describe an implementation of the CAM-B3LYP range-separated functional within the Vienna Ab-initio Simulation Package (VASP) framework, together with its analytical functional derivatives.Results obtained for eight representative materials: aluminum, diamond, graphene, silicon, NaCl, MgO, 2D h-BN, and 3D h-BN, indicate that CAM-B3LYP predictions embody mean-absolute deviations (MAD) compared to HSE06 that are reduced by a factor of six for lattice parameters, four for quasiparticle band gaps, three for the lowest optical excitation energies, and six for exciton binding energies. Further, CAM-B3LYP appears competitive compared to ab initio G 0 W 0 and Bethe-Salpeter equation approaches. The CAM-B3LYP implementation in VASP was verified by comparison of optimized geometries and reaction energies for isolated molecules taken from the ACCDB database, evaluated in large periodic unit cells, to analogous results obtained using Gaussian basis sets. Using standard GW pseudopotentials and energy cutoffs for the plane-wave calculations and the aug-cc-pV5Z basis set for the atomic-basis ones, the MAD in energy for 1738 chemical reactions was 0.34 kcal mol À1 , while for 480 unique bond lengths this was 0.0036 Å; these values reduced to 0.28 kcal mol À1 (largest error 0.94 kcal mol À1 ) and 0.0009 Å by increasing the plane-wave cutoff energy to 850 eV.

Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials

“…Firstly, Table 3 shows the MAD error in calculated lattice constants for the methods for which data is available. As previously noted, 32 the error for CAM-B3LYP is much less than that for HSE06, and indeed much less than that for B3LYP, indicating the importance of asymptotic correction. When predicting spectroscopic properties of materials, it may be necessary to optimise structures and hence the apparent reliability of CAM-B3LYP in this regard is of note.…”

“…Nevertheless, in materials such as silicon, no charge transfer is involved. Hence effect (2) has only a minor effect that is accurately predicted by CAM-B3LYP, 32 with the consequence that CAM-B3LYP overestimates the orbital bandgap and spectroscopic transition energy by 1.1 eV (Table 3 and ESI Table S2†). Silicon is an unusual and (therefore) important material that has spawned modern generations of asymptotic corrected functionals (Table 3) that focus on the correct description of its dielectric properties.…”

“…The new CAM-B3LYP results reported for lattice parameters (ESI Table S1†), orbital bandgaps (ESI Table S2†) and exciton binding energies (text) were also determined using VASP 5.4.4, 32,138,139 with optimised coordinates and calculation details for each material listed in the ESI †. PBE-PAW pseudopotentials 140 were again used for B3LYP and HSE06 calculations, with GW-PAW ones used for CAM-B3LYP.…”

“…First, Results Section (a) reviews the effects of the asymptotic potential on the perceived spectroscopy of an iconic molecular system, chlorophyll- a , 9,10 identifying 5 key effects. Section (b) then reviews how these effects manifest concerning predictions of the lowest-energy transition (bandgap) of simple materials, 32 materials historically perceived 71 as being well-treated without the need for asymptotic-potential correction. Comparison of predicted properties from modern materials-only functionals with asymptotic-potential correction to those of generally applicable functionals such as CAM-B3LYP are also reviewed therein, with the results contrasted to those of hybrid functionals including HSE06, as well as some other GGA and meta -GGA approaches.…”

“…That such effects are also important for materials was recognised early on, 30 but functionals involving asymptotic correction were not implemented into appropriate software packages. This situation changed recently with the implementation of the CAM-B3LYP asymptotically-corrected functional into both the Car–Parrinello Molecular Dynamics (CPMD) package 31 (gamma-point only) and the Vienna Ab initio Simulation Package (VASP) 32 (full implementation). In parallel, new density functionals appropriate only to materials are being developed that link the asymptotic-potential correction to the evaluation of the dielectric constant.…”