Global Hybrid Functionals: A Look at the Engine under the Hood

Global hybrids, which add a typically modest fraction of the exact exchange energy to a complement of semilocal exchange correlation energy, are among the most widely used density functionals in chemistry and condensed matter physics. Here we briefly review the formal and practical advantages and disadvantages of global hybrids. We point out that empiricism seems unavoidable in the construction of global hybrids, as it is not for most other kinds of density functional. Then we use one to three parameters to hybridize many semilocal functionals (including recently developed nonempirical generalized gradient approximations or GGA's and meta-GGA's). We study the performance of these global hybrids for many properties of sp-bonded molecules composed from the lighter atoms of the periodic table: atomization energies, barrier heights, reaction energies, enthalpies of formation, total energies, ionization potentials, electron affinities, proton affinities, and equilibrium bond lengths. We find several new global hybrids that perform better in these tests than standard ones, and we correct some errors in literature assessments. We also discuss the representativity of small fitting sets and the adequacy of various Gaussian basis sets.