Explicitly Correlated Electrons in Molecules

A comprehensive review of explicitly correlated approaches, beginning with the early ideas and methods and progressing to the state of the art of the field, is presented. Antisymmetric wave functions correlate electrons over and above the correlation present in a Hartree product description. The energetic consequences of Fermi correlation and the strength of mixing of states due to Coulombic interactions both depend on the internuclear separation. Pack and Byers Brown's analysis may be applied to the HartreeFock equations for the orbitals in a Slater determinant wave function, showing that the electronnucleus coalescence conditions apply to each orbital individually. The Hylleraas, Hy-CI, and ECG methods aim at reaching ultimate accuracy for few-electron atoms and small molecules. Persson and Taylor suggested to fit the electronelectron distance with only a few Gaussian functions with good accuracy.