Perdew-86 functional

Nonlocal DFT calculation with Becke-88-Perdew-86 functional Bickelhaupt and Bickelhaupt, Ref. 110. 

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

BP86/TZ2P (nonlocal DFT with the Becke-88-Perdew-86 functional). cMP4SDQ/6-31+G (fourth-order Moller-Plesset perturbation theory with single, double, and quadruple excitations). 

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. 

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... 

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. 

Perdew J P, Parr R G, Levy M and Balduz J L Jr 1982 Density-functional theory for fractional particle number derivative discontinuities of the energy Phys. Rev. Lett. 49 1691-4... 

Perdew J P and Zunger A 1981 Self-interaction correction to density-functional approximations for many-electron systems Phys. Rev. B 23 5048... 

Hammer B, Hansen L B and Norskov J K 1999 Improved adsorption energetics within density functional theory using revised Perdew-Burke-Enerhof functionals Phys. Rev. B 59 7413-21... 

Perdew J P and A Zunger 1981. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Physical Review B23 5048-5079. 

Similarly, there are local and gradient-corrected correlation functionals. For example, here is Perdew and Wang s formulation of the local part of their 1991 correlation functional ... 

Different functionals can be constructed in the same way by varying the component functionals—for example, by substituting the Perdew-Wang 1991 gradient-corrected correlation functional for LYP—and by adjusting the values of the three parameters. 

A modified form for Ecjaijs) has been given by Perdew and Wang, and is used in comiection with tlie PW91 functional described in Section 6.2. 

Perdew and Wang have proposed an exchange functional similar to B88 to be used in connection with the PW91 correlation functional given below (eq. (6.30)). 

This functional was later modified to the following form (also a correction to the LSDA energy) by Perdew and Wang in 1991 (PW91 or P91) ... 

The local density approximation is highly successful and has been used in density functional calculations for many years now. There were several difficulties in implementing better approximations, but in 1991 Perdew et al. successfully parametrised a potential known as the generalised gradient approximation (GGA) which expresses the exchange and correlation potential as a function of both the local density and its gradient ... 

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. 

Table4.4 Spectroscopic properties for Au2 q= -1,0, + 1) using ab-initio (Hartree Fock, HF, second-order Moller-Plesset, MP2, and coupled cluster, CCSD(T)) and DFT (local spin-density approximation, LSDA, Perdew-Wang CCA, PW91, and Becke three-parameter Lee-Yang-Parr functional, B3LYP) methods at the RPPA level of theory.

Functionals which are related to this approach include among others the recent FT97 functional of Filatov and Thiel, 1997, the PW91 exchange functional (Perdew, 1991, and Burke, Perdew, and Wang, 1998) and the CAM(A) and CAM(B) functionals developed by Handy and coworkers (Laming, Termath, and Handy, 1993). 

The second class of GGA exchange functionals use for F a rational function of the reduced density gradient. Prominent representatives are the early functionals by Becke, 1986 (B86) and Perdew, 1986 (P), the functional by Lacks and Gordon, 1993 (LG) or the recent implementation of Perdew, Burke, and Emzerhof, 1996 (PBE). As an example, we explicitly write down F of Perdew s 1986 exchange functional, which, just as for the more recent PBE functional, is free of semiempirical parameters ... 

The corresponding gradient-corrected correlation functionals have even more complicated analytical forms and cannot be understood by simple physically motivated reasonings. We therefore refrain from giving their explicit expressions and limit ourselves to a more qualitative discussion of the most popular functionals. Among the most widely used choices is the correlation counterpart of the 1986 Perdew exchange functional, usually termed P or P86. This functional employs an empirical parameter, which was fitted to the... 

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