2. Long-range and other corrections for density functionals

In this century, the main concerns of theoretical chemistry obviously make the transition from accurate investigations of small molecules to the designs of complicated large molecular systems; e.g. proteins, nano-materials, environmental catalyses, and so forth. What is necessary for approaching these systems is an accurate theory of low computational order. Density Functional Theory (DFT),, is expected to be a major candidate for such a theory at present, because this theory gives accurate chemical properties despite of its low computational order that may be reduced to order-N. In DFT, electronic states are usually determined by solving the nonlinear Kohn-Sham equation with an exchange-correlation density functional. The most remarkable characteristic of DFT is the exchange-correlation energy part that is approximated by a one-electron potential functional. Hence, calculated DFT results depend on the form of this exchange-correlation functional. In last two decades, various kinds of exchange functionals have been suggested especially for generalized gradient approximations (GGA),,, beyond the local density approximation (LDA) functional. Due to the requirement of order, these GGA exchange functionals are usually