Coupling-constant dependence of atomization energies

The local spin-density (LSD) functional and Perdew–Wang 91 (PW91) generalized gradient approximations to atomization energies of molecules are investigated. We discuss the coupling-constant dependence of the atomization energy and why exchange errors of the functionals are greater than exchange–correlation errors. This fact helps to justify hybrid schemes which mix some exact exchange with density functional approximations for exchange and correlation. It is shown that the biggest errors in the atomization energies occur when there is a strong interaction between different electron pairs, which vanishes upon atomization. We argue that the amount of exchange character of a molecular property, such as the atomization energy, depends on the property itself. We define an exact mixing coefficient b, which measures this exchange character, and show that both LSD and PW91 typically overestimate this quantity. Thus, nonempirical hybrid schemes which approximate this quantity by its LSD or PW91 value typically do not improve the exchange–correlation energy. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 285–295, 1997