A simple DFT-based diagnostic for nondynamical correlation

We propose a simple DFT-based diagnostic for nondynamical correlation effects, namely A λ = (1 − TAE[X λ C]/TAE[XC])/λ where TAE stands for the molecular total atomization energy, XC is a pure-DFT exchange-correlation functional, and X λ C represents the corresponding hybrid with 100λ % Hartree–Fock-type exchange. The diagnostic is a good predictor for sensitivity of energetics to the level of theory, unlike most wavefunction-based diagnostics. For GGA functionals, A λ values approaching unity indicate severe nondynamical correlation, while values between 0 and about 0.1 indicate systems where correlation is predominantly dynamical in character (or entirely absent). The diagnostic is only weakly sensitive to the basis set (beyond polarized valence double zeta) and can easily be applied to problems beyond the practical reach of wavefunction ab initio methods required for other diagnostics. We also propose a simple measure for the importance of dynamic correlation.