Accurate quadruple-ζ basis-set approximation for double-hybrid density functional theory with an order of magnitude reduction in computational cost

Abstract

In the present study, we investigate a scheme for the approximation of quadruple-ζ (QZ) energies for doublehybrid density functional theory (DHDFT) procedures, using smaller double-ζ and triple-ζ basis sets. Such an approach would allow DHDFT/QZ energies to be estimated in cases where the explicit calculations might be too demanding computationally. We find this approach, denoted Q[D,T], to be very accurate for the MP2 same-spin (MP2SS) component and generally reasonable for the MP2 opposite-spin (MP2OS) component. The performance of the Q[D,T] approximation is quite insensitive to the type of basis sets used, as well as to the specific DHDFT procedure. Overall, we find that the approximation, when used in combination with the maug-cc-pVQ[D,T]Z basis sets, performs well for the calculation of relative energies. The use of explicit MP2OS/maug-cc-pVQZ energies together with the Q[D,T] MP2SS energies yields even better agreement with complete QZ energies, but at a somewhat greater computational cost. For a representative large system for DHDFT, namely C₆₀, we find that the Q[D,T] approximation leads to a reduction in CPU time by more than an order of magnitude when compared with the corresponding explicit QZ calculation, with little reduction in accuracy.