Generalised gradient approximations

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 ... 

The first way has been followed in what has become known as Car-Parrinello molecular dynamics (CPMD) (9). A solute and 60-90 solvent molecules are considered to represent the system, and the QM calculations are performed with density functionals, usually of generalised gradient approximation type (GGA), such as the Becke-Lee-Young-Parr (BLYP) (10) or the Perdew-Burke-Enzerhofer (PBE) (11,12) functionals. It is clear that the semiempirical character of concurrent density functional theory (DFT) methods and the use of these simple functionals imply a number of error sources and do not really provide a method-inherent control procedure to test the reliability of results. Recently it has been shown that these functionals even do not enable a correct description of the solvent water itself, as at ambient temperature they will describe water not as liquid but as supercooled system... 

The knowledge of the structure of titanium in its different oxidation states (II to IV) should bring some information on its coordination to H, Cl and CH3. Here, we present optimised structures of titanium hydrides and chlorides using density functional theory with the generalised gradient approximation (DFT-GGA). Next, for the different oxidation states we study the addition of acids, radicals and bases on the chlorides. 

Car-Parrinello (CP) type simulations [32] achieve the necessary compromise between effort and accuracy by reducing the number of particles as well as the simulation time on the one hand and by the employment of simple generalised gradient approximation density functionals such as PBE [33,34] or BLYP [35] on the other hand. In the case of hydrated ions the reduction of the number of solvent molecules is in many cases chosen too low to properly hydrate the ion and to reflect the surrounding bulk liquid. The reduction of the simulation time is sometimes at the expense of a proper equilibration period. 

Perdew, J., Kurth, S., Zupan, A., Blaha, P. (1999). Accurate density functional with correct formal properties a step beyond the generalised gradient approximation. Phys. Rev. Lett. 82,2544-2547. Erratum 5179. 

Perdew, J. P, Burke, K., and Wang, Y. 1996. Generalised gradient approximation for the exchange-correlation hole of a many-electron system. Phys. Rev. B Condens. Matter. 54 16533. 

Electronic structure calculations for Sr2EeMo06 and Sr2EeRe06 with the full-potential augmented plane-wave (ELAPW) method based on the generalised gradient approximation (GGA) produce a half-metallic... 

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