Non-local DFT,

The density functional theory calculations of primary 14C KIE and secondary deuterium kinetic isotope effects (SKIE)220 did not reproduce satisfactorily all the experimentally determined 14C KIE and deuterium (4,4-2H2)- and 6,6-2H2-SKIE, though the non-local DFT methods provide transition state energies on a par with correlated molecular orbital theory221. 

Newton s second law, 2, 383 NMR shielding, 239 Non-adiabatic coupling elements, 55 Non-bonded energy, in force held methods, 18 Non-bonded list, in force held methods, 43 Non-local DFT methods, 184 Norm-extended Hessian ophmizahon method, 320... 

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... 

First, a series of calculations was performed to determine the interaction of halide ions with a Cu atom. The simultaneous tests of the basis sets and the functional were performed by use of the Gaussian92 program. Several different DFT variants were tested, for example SVWN, BP86 and B3LYP that are representative of the pure local DFT, pure non-local DFT and the hybrid HF/DFT non-local functional. Other DFT alternatives were also tested, but the trend in results seems to be close to that obtained with the methods mentioned above. 

For the MFP approach, most calculations have used SCF wave functions. However, Bak et aL have implemented the MFP theoretical approach at the correlated multiconfigura-tional self-consistent-field-level by using the complete active space wave functions (CASSCF) expressed over conventional and gauge invariant basis sets. In addition, the MFP approach has been implemented using correlated wave functions at the non-local DFT level and B3LYP (a hybrid HF/DFT) level. ... 

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. 

One current limitation of orbital-free DFT is that since only the total density is calculated, there is no way to identify contributions from electronic states of a certain angular momentum character /. This identification is exploited in non-local pseudopotentials so that electrons of different / character see different potentials, considerably improving the quality of these pseudopotentials. The orbital-free metliods thus are limited to local pseudopotentials, connecting the quality of their results to the quality of tlie available local potentials. Good local pseudopotentials are available for the alkali metals, the alkaline earth metals and aluminium [100. 101] and methods exist for obtaining them for other atoms (see section VI.2 of [97]). 

I he function/(r) is usually dependent upon other well-defined functions. A simple example 1)1 j functional would be the area under a curve, which takes a function/(r) defining the curve between two points and returns a number (the area, in this case). In the case of ni l the function depends upon the electron density, which would make Q a functional of p(r) in the simplest case/(r) would be equivalent to the density (i.e./(r) = p(r)). If the function /(r) were to depend in some way upon the gradients (or higher derivatives) of p(r) then the functional is referred to as being non-local, or gradient-corrected. By lonlrast, a local functional would only have a simple dependence upon p(r). In DFT the eiK igy functional is written as a sum of two terms ... 

DFT theory even seems to improve the performance of MP2 in cases where there is some small contribution of non dynamic correlation. This is seemingly the case in the BP86 computed first dissociation energies of a variety of metal carbonyls [51]. For instance, in the case of Cr(CO)6, the BP86 value is 192 kJ/mol, in exact (probably fortuitous) agreement with the (computationally most accurate) CCSD(T) value of 192 kJ/mol, but also reasonably close to the experimental value of 154 8 kJ/mol. In this case, the GGA DFT result improves clearly the local DFT SVWN value of 260 kJ/mol, and the MP2 result, wich is 243 kJ/mol. Comparable results can be found for the optimization of the Os-O distance in OsC>4 [52], which is relevant concerning olefin dihydroxylation. 

The quantum mechanical polarizability is calculated using the DFT, with B3P86 (Becke s three-parameter functional [53] with the non-local correlation provided by Perdew [54]). The basis set used for the water molecules is 6-311 + +G. Because of the very diffuse nature of the anion F, the basis set used is the specially designed, and very extensive, fully uncontracted 14s 9p 6d 2f Gaussian-type orbitals [55]. All the QM calculations were made with the Gaussian98 program [56]. 

The simplest exchange-correlation functionals, derived from the density alone, give reasonable results for many molecular properties. However, it has been found that adding terms proportional to the local gradient of the density in both the exchange and correlation integrands leads to much more accurate results. Most modern DFT computations use these so-called non-local or gradient-corrected functionals. 

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