Becke-Perdew functional

First principles solid-state density functional analyses have also been performed on the explosive pentaerythritol tetranitrate (PETN) [42] to further understand the relationships between the choice of computational parameters and the predictions of molecular and solid-state properties, such as intermolecular interactions within the crystal cell, in the THz region. This study concluded that the Becke-Perdew functional has the best overall performance and that the choice of basis set is most critical. 

Some effects that are left out of cluster calculations are illustrated in the work of Vittadini et al. [87]. They have suggested another prepairing mechanism, in which H atoms on the same side of adjacent singly occupied dimers ( interdimer airing) are more stable than independent singly occupied dimers. These are periodic slab calculations using a large unti eell and a local density functional (tests with the nonlocal Becke-Perdew functional do not... 

Table 3 Calculated J values (cm ) for the series of iron-sulfur complexes [Fe4S4(SCH3)4] (n=0, 1, 2, 3, and 4) by using the Becke-Perdew functional and performing a structural optimization, Also the available experimental data and the multiplicity of the obtained ground state are reported [59]...

The orbital occupation scheme of the doubly occupied orbitals was obtained by performing a DFT calculation with the Becke-Perdew functional [49, 50] and a 6-3IG basis set [47]. Geometry optimizations were performed with the TURBOMOLE [51, 52] package, and aU other calculations use COLUMBUS [53-55]. 

Calculations have been made in the framework of the Generalized Gradient Approximation (GGA) by means of the Becke-Perdew functional [22,23]. It is worth mentioning, however, that in the case of Cr in fluorides the Re values computed in the Local Density Approximation (LDA) for a 21 atoms cluster differ only by about 1% from those obtained through GGA [20]. The effects of the electrostatic potential due to the rest of the ions not included in the IFeAeMe " cluster have been considered in all the calculations. When such a potential is not taken into account the computed distances increase by about 1%. A similar situation is found in the case of Cr in elpasolites [12] where a further analysis on this point is given. 

Assuming that substituted Sb at the surface may work as catalytic active site as well as W, First-principles density functional theory (DFT) calculations were performed with Becke-Perdew [7, 9] functional to evaluate the binding energy between p-xylene and catalyst. Scalar relativistic effects were treated with the energy-consistent pseudo-potentials for W and Sb. However, the binding strength with p-xylene is much weaker for Sb (0.6 eV) than for W (2.4 eV), as shown in Fig. 4. 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

All electron calculations were carried out with the DFT program suite Turbomole (152,153). The clusters were treated as open-shell systems in the unrestricted Kohn-Sham framework. For the calculations we used the Becke-Perdew exchange-correlation functional dubbed BP86 (154,155) and the hybrid B3LYP functional (156,157). For BP86 we invoked the resolution-of-the-iden-tity (RI) approximation as implemented in Turbomole. For all atoms included in our models we employed Ahlrichs valence triple-C TZVP basis set with polarization functions on all atoms (158). If not noted otherwise, initial guess orbitals were obtained by extended Hiickel theory. Local spin analyses were performed with our local Turbomole version, where either Lowdin (131) or Mulliken (132) pseudo-projection operators were employed. Broken-symmetry determinants were obtained with our restrained optimization tool (136). Pictures of molecular structures were created with Pymol (159). 

A more sophisticated DFT study by Bridgeman and Rothery has also been published [18]. They used a functional consisting of a LSD part with nonlocal corrections from the Becke 1988 functional for exchange and the Perdew 1986 functional for correlation. The results were slightly better than those of Piechota and Suffczynski but the dissociation energies were still systematically overestimated. 

Nonlocal DFT with the Becke-88 functional for exchange (Ref. 107) and the Perdew-86 functional for correlation (Ref. 108). 

The results from the nonlocal and hybrid DFT calculations show trends similar to those observed for the MO calculations. The computed geometries are very similar to each other the calculated bond lengths for the breaking bond range from 2.14 A, calculated by the hybrid adiabatic connection method (ACM) [24], to 2.16 A, calculated by the nonlocal BLYP [25, 26] functional. A comparison of the results from the nonlocal Becke-Perdew [27] calculations using DZVP and a TZVP basis sets shows that the geometries are influenced to a very small extent by basis set effects [12]. The activation energies calculated by the different nonlocal methods are too low by 1-3 kcal/mol, whereas the hybrid DFT methods overestimate Ea by approximately the same amount. Both the nonlocal and the hybrid DFT methods tend to overestimate the heat of reaction by up to 7 kcal/mol, calculated by the ACM/6-31G method. 

DFT calculations with Becke-Perdew exchange-correlation functional were carried out for all the reaction intermediates present in the catalytic cycle of polar copolymerization, based on the simplified diimine catalyst in which the bulky diimine substituents were replaced by hydrogen atoms (model catalyst NAN-M+, NAN = -N(Ar)-CR-CR-N(Ar)- R=H, Ar=H, M=Ni, Pd). Some of the calculations, for the most important structures, were repeated using the real catalyst, containing bulky diimine substituents [real catalyst Ar=C6H3(o- -Pr)2, R=CH3],... 

Pugh and Streitwieser used semiempirical PM3, ab initio (HF/6-31-bG(d) and MP2/6-31-bG(d)) and density functional calculations (using the perturbative Becke-Perdew model pBp2i.22 together with DN split valence basis set, both included in the Spartan 5.1 suite of programs) to investigate the rotational barrier of the C—N bond in a simple enolate anion (lithioacetamide, 19), as shown in Figure 1. For comparison, the ami-date anion, vinylamine, and a simulated dimer were also calculated. All the rotational... 

The one-electron Kohn-Sham equations were solved using the Vosko-Wilk-Nusair (VWN) functional [27] to obtain the local potential. Gradient correlations for the exchange (Becke fimctional) [28] and correlation (Perdew functional) [29] energy terms were included self-consistently. ADF represents molecular orbitals as linear combinations of Slater-type atomic orbitals. The double- basis set was employed and all calculations were spin unrestricted. Integration accuracies of 10 -10 and 10 were used during the single-point and vibrational frequency calculations, respectively. The cluster size chosen for Ag or any bimetallic was... 

DF2 BP86 Becke excheinge functioned. Correlation functioned of Perdew, includes gradient corrections (23, 24). 

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