DFT model

In one of the earliest DFT models, the Thomas-Fermi theory, the kinetic energy of an atom or a molecule is approximated using the above type of treatment on a local level. That is, for each volume element in r space, one... 

DFT MODELING AND SPECTROSCOPIC INVESTIGATIONS INTO MOLECULAR ASPECTS OF DeNO CATALYSIS... 

This has been well documented both experimentally (mainly by IR and EPR spectroscopies) and theoretically by means of molecular DFT modeling [3,22,24,41,49,52],... 

Calculations were performed within the periodic DFT model, using the VASP code[8] (the same computational strategy as in Ref. [9] was adopted, including the B3LYP correction). Thus, calculated interaction energies are of the B3LYP quality and they include ZPVE correction. The unit cell of FER fitted previously was used [10] UC... 

The X-ray diffraction pattern of the spheres before the immersion in SBF shows the typical diffraction peak ascribable to the (100) reflection of the ordered mesophase with a dioo of 3.45 nm. Nitrogen adsorption-desorption isotherms are of type IV and pore size from DFT model results 2.4 nm (data not reported). 

Introduction of the static density response function for a system with a constant number of electrons yields the RF - DFT model. This second approach is expected to be more useful in the analysis of chemical reactivity in condensed phases. 

With the work still in the infant stages, there is no accepted method of modeling electrode reactions with DFT. A few recent studies have attempted to include both electrostatic and solvent effects in DFT models of electrochemical reactions using different approaches.84-89 However, the lack of surface techniques available for in situ study of electrochemical cells hinders validation of models by experimental data. Results can only offer qualitative information at best. Despite the challenges, DFT modeling of electrochemical reactions offers promise as a method for providing insights into the electrochemical interface in cases where experiments are difficult. 

Lastly, the SF approach implemented within the time-dependent. (TD) density functional theory (DFT) extends DFT to multi-reference situations with no cost increase relative to the non-SF TD-DFT. Similarly to DFT and TD-DFT, the SF-DFT model (27) is formally exact and therefore will yield exact answers with the exact density functional. With the available inexact ftmctionals, the SF-DFT represents an improvement over its non-SF counterparts. It has been shown to yield accurate equilibrium properties and singlet-triplet energy gaps in diradicals (27). 

Co2(CO)g has been used to obtain encapsulated cobalt clusters in Y-faujasite, which have been used as model catalysts for methane homologation [152]. The gas phase adsorption of Co2(CO)8 under N2 rendered predominately encaged Co4(CO)i2 species whereas Co,s(CO)iis was obtained when the impregnation of Co2(CO)8 was carried out under a CO/H2 atmosphere [152, 155], Samples were oxidized at 80°C, subsequently reduced at 400 °C and then structurally characterized by EXAFS. Clusters of two and three cobalt atoms were formed from encaged Co4(CO)i2 and COis(CO)iis, respectively. Higher methane conversion and selectivity to C2+ products in the CH4 homologation reaction have been obtained for the two atoms-size cluster sample the results were discussed using a DFT model [152]. 

The NH3 treatment for 120 min completed the clusterization of the Re species as shown in Figure 10.9. The CN of the Re-Re bonds was 5.210.3 (0.276 0.002 nm) (Table 10.7). A desorphon peak of N2 in TPD of the NHs-treated Re/HZSM-5 catalyst appeared at around 673 K, which indicates that the Re cluster possesses N atoms supplied by the NH3 treatment [73]. The amount of N2 evolved was 1.2 N2 per Reio. DFT modeling of the structure of the Re cluster based on the structural parameters obtained by FXAFS analysis revealed the formation of an N-interstitial Reio cluster in the HZSM-5 pore (structure is illustrated in Scheme 10.4) [73]. N atoms at the edge and hollow sites of the Re cluster never stabilized the Re cluster framework with the Re-Re bonds at 0.276 nm. Adsorption of nitrogen atoms on the exterior surface of the Re cluster also did not reproduce the Re-Re bond distances. 

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