An evaluation of exchange-correlation functionals for the calculations of the ionization energies for atoms and molecules

In this paper, ionization energies of gas-phase atoms and molecules are calculated by energy-difference method and by approximate transition-state models with density functional theory (DFT). To determine the best functionals for ionization energies, we first study the H to Ar atoms. An approximation is used in which the electron density is first obtained from Kohn-Sham computations with an exchange-correlation potential Vxc known as statistical average of orbital potentials (SAOP), after which the energy is computed from that density with 59 different exchange-correlation energy functionals Exc. For the 18 atoms, the best Exc functional providing an average absolute deviation (AAD) of only 0.110 eV is one known as the Krieger-Chen-Iafrate-Savin functional modified by Krieger, Chen, Iafrate, and Kurth, if one uses the spin-polarized spherical atom description. On the other hand, if one imposes the condition of integer-electrons, the best functional is the Becke 1997 functional modified by Wilson, Bradley, and Tozer, with an AAD of 0.107 eV, while several other functionals perform almost as well. For molecules, we can achieve an accuracy of AAD = 0.21 eV for valence VIPs of nonperhalo molecules with ΔE(Vxc = SAOP;PBE0) using integer-electron description. For perhalo molecules our best approach is ΔE(Vxc from either Exc or SAOP;mPW1PW) with full symmetry to obtain an AAD = 0.24 eV.