Revisiting the Half-and-Half Functional

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Hybrid density functionals offer improved accuracy over semilocal functionals.
• Conventional wisdom suggests limiting exact exchange to 20-25% to maintain thermochemical accuracy.
• The Becke-Lee-Yang-Parr
• half-and-half
• functional (BH&H-LYP) is often used for systems with self-interaction error, particularly in time-dependent density functional theory (TDDFT) for excitation energies.

Purpose of the Study:

• To investigate the assumption that 50% Hartree-Fock exchange in hybrid functionals compromises thermochemical accuracy.
• To evaluate the performance of functionals with varying percentages of exact exchange (B(α)LYP) across different chemical properties.
• To determine the optimal percentage of exact exchange for general chemical applications.

Main Methods:

• Systematic variation of the percentage of exact exchange (α) in B(α)LYP functionals.
• Assessment of thermochemical properties, including atomization energies and reaction barrier heights.
• Evaluation of excitation energies using time-dependent density functional theory (TDDFT).

Main Results:

• BH&H-LYP (α = 50%) demonstrates accuracy comparable to B3LYP for thermochemistry and barrier heights.
• BH&H-LYP shows similar accuracy to B3LYP for excitation energies, though B3LYP is superior for valence excitations.
• A significant decrease in accuracy for atomization energies is the primary drawback of BH&H-LYP compared to B3LYP.

Conclusions:

• The conventional taboo against using >25% exact exchange is not universally justified, as BH&H-LYP (50% exact exchange) offers competitive accuracy for many properties.
• BH&H-LYP is a suitable choice for systems dominated by self-interaction error, such as charge-transfer complexes and core-level excitations.
• BH&H-LYP presents an acceptable compromise for valence excitation energies, and its use for ground-state properties does not warrant undue concern regarding diminished accuracy.