Comparison shopping for a gradient‐corrected density functional

Gradient corrections to the local spin density (LSD) approximation for the exchange-correlation energy are making density functional theory as useful in quantum chemistry as it is in solid-state physics. But which of the many gradient-corrected density functionals should be preferred a priori? We make a graphical comparison of the gradient dependencies of some popular approximations, discussing the exact formal conditions which each obeys and identifying which conditions seem most important. For the exchange energy, there is little formal or practical reason to choose among the Perdew-Wang 86, Becke 88, or Perdew-Wang 91 functionals. But, for the correlation energy, the best formal properties are displayed by the nonempirical PW91 correlation functional. Furthermore, the real-space foundation of PW91 yields an insight into the character of the gradient expansion which suggests that PW91 should work especially well for solids. Indeed, while improving dissociation energies over LSD, PW91 remains the most “local” of the gradient-corrected exchange-correlation functionals and, thus, the least likely to overcorrect the subtle errors of LSD for solids. To show that our analysis of spin-unpolarized functionals is sufficient, we also compute spin-polarization energies for atoms, finding PW91 values only slightly more negative than LSD values. © 1996 John Wiley & Sons, Inc.