Medium-range correlation

Are there functionals that address this problem and properly account for medium range correlation Zhao and Truhlar responded very quickly after the initial flurry of papers were published that pointed out these problems by noting that the highly parameterized M05-2x functional appears to fit the bill. As indicated in Table 3.16, M05-2x predicts that the branched alkane... 

Zhao, Y Truhlar, D. G. A density functional that accounts for medium-range correlation energies in organic chemistry, Org. Lett. 2006, 8, 5753-5755. 

The hybrid meta functional M06 was found to perform well for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights. 

Grimme suggested in his article that the failure of B3LYP is due to inadequate treatment of medium range electron correlation. This was disputed by Brittain and coworkers and by Song and coworkers. ... 

Second-order Moller-Plesset perturbation theory (MP2) is the computationally least expensive and most popular ab initio electron correlation method [4,15]. Except for transition metal compounds, MP2 equilibrium geometries are of comparable accuracy to DFT. However, MP2 captures long-range correlation effects (like dispersion) which are lacking in present-day density functionals. The computational cost of MP2 calculations is dominated by the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis which scales as 0(N5) with the system size. This four-index transformation can be avoided by introduction of the RI integral approximation which requires just the transformation of three-index quantities and reduces the prefactor without significant loss in accuracy [36,37]. This makes RI-MP2 the most efficient alternative for small- to medium-sized molecular systems for which DFT fails. 

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