Empirical DFT functionals

Let us now turn to the density functional methods. All of them correctly predict the para-ortho ordering, but considering that this is the case even for a Hartree-Fock treatment this is a somewhat hollow victory. Without exception, all functionals wrongly predict p-protonation. Arguably, this small energy difference falls within the error margin of any type of calibration for (semi-) empirical DFT functionals. 

At this point some misleading nomenclature in publications of simulations has to be clarified. Frequently simulations based on DFT functionals are termed ab initio MD and first principle or -empirical. This is indeed not correct as all available density functionals are of a more or less semiempirical nature, as pointed out by their developers themselves, e.g., by Becke in his presentation of the B3LYP functional (15). The term ab initio should be reserved, therefore, for simulations where for the QM part a true ab initio procedure, i.e., HF or correlated methods like MP/2 or better, is employed. Only by this one is also enabled to perform a method-inherent control of accuracy and deficiencies by increasing the level of theory from a one-determinantal to a multi-determinantal method. 

These results give a flavor of the performances of the different functionals with respect to this set of covalently bonded molecules, and can be considered as a starting point for a deeper discussion about chemical applications. From these data, it is quite apparent that the PBE functional performs as well as more empirical DFT approaches, like the BLYP model (Becke 88 exhange [14] and Lee-Yang-Parr correlation [19]). 

Figure 4. Comparison of Mott-Littleton, periodic empirical potential functions and periodic DFT quantum mechanics. The horizontal scale is not significant. Transition state energies are shown as open symbols...

It should be noted here that there are more approximate ways to perform DFT calculations that correctly describe the vdW forces. For example, several groups have recently proposed semi-empirical schemes to correct the usual DFT functionals so that the dispersion forces are modelled properly. " Also, a non-local DFT has been developed that incorporates the dispersion forces in a truly ab initio way this theoretical breakthrough leads to a very... 

Table 1 Hydrogenation-reaction energies (in kcal/mol) for some small organic molecules from semi-empirical density-functional calculations (DFTB) in comparison with parameter-free density-functional calculations (DFT) and experiment (Exp.). From ref. 16...

While the choice of a DFT functional to be augmented with the empirical dispersion correction is somewhat arbitrary, the choice of E[ + E in nonlocal exchange-correlation functionals is crucial, because the E[ + E pair strongly affects van der Waals bonding. Nonlocal functionals were often developed on the basis of a GGA functional, and, as mentioned previously, GGA functionals produce spurious bonding when closed shells of some monomers are overlapped. Dispersion Interaction Is a correlation effect [26], therefore, such a spurious attraction should be avoided when a nonlocal functional is developed. 

Car-Parrinello molecular dynamics Grimme s third-generation dispersion correction with Becke-Johnson damping Density functional theory Empirically corrected DFT (functional or method)... 

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