Non-local DFT methods

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... 

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. 

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]). 

Let us first consider those cases where the direct contribution vanishes due to symmetry reasons. As already discussed the net spin density at the center under consideration solely arises from the interaction between the singly and doubly occupied shells so that the indirect contributions represent an observable. The non-local nature of this interaction is obvious, since the density of the unpaired electron vanishes at the point where the effect of the interaction is measured, i.e. at the position of the center under consideration. The difficulties to describe non-local effects within the DFT are known [167] and explain the errors in the isotropic hfcc s computed with the DFT method. 

Essential progress has been made recently in the area of molecular level modeling of capillary condensation. The methods of grand canonical Monte Carlo (GCMC) simulations [4], molecular dynamics (MD) [5], and density functional theory (DFT) [6] are capable of generating hysteresis loops for sorption of simple fluids in model pores. In our previous publications (see [7] and references therein), we have shown that the non-local density functional theory (NLDFT) with properly chosen parameters of fluid-fluid and fluid-solid intermolecular interactions quantitatively predicts desorption branches of hysteretic isotherms of nitrogen and argon on reference MCM-41 samples with pore channels narrower than 5 nm. 

Modeling physical adsorption in confined spaces by Monte Carlo simulation or non-local density functional theory (DFT) has enjoyed increasing popularity as the basis for methods of characterizing porous solids. These methods proceed by first modeling the adsorption behavior of a gas/solid system for a distributed parameter, which may be pore size or adsorptive potential. These models are then used to determine the parameter distribution of a sample by inversion of the integral equation of adsorption, Eq. (1). 

Nguyen and Bhatia476,477 have developed new (molecular) non-local density functional theories that account for the finite thickness of pore walls in porous systems. It has been demonstrated using experimental data that nanoporous carbons such as activated carbons and coal chars have pore walls that typically only consist of one or two layers. The extension of the DFT methods to treat such systems was therefore essential if accurate modelling is to be carried out. These models have been used to determine the capacity of C02 in carbon slit pores, and the results are compared with simulation.478... 

Recently, Becke has derived theoretically the need to include part of the Hartree-Fock exact exchange (i.e. non-local effects) in the exchange functional to improve the predictions of the gradient-corrected DFT methods (16,17). Becke (17) proposed the functional... 

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