Density gradient approximation-type

GGA correlation functionals are mainly classified into the density gradient approximation-types and the Colle-Salvetti (CS)-type functionals. 

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... 

Three types of exchange/correlation functionals are presently in use (i) functionals based on the local spin density approximation, (ii) functionals based on the generalized gradient approximation, and (iii) functionals which employ the exact Hartree-Fock exchange as a component. The first of these are referred to as local density models, while the second two are collectively referred to as non-local models or alternatively as gradient-corrected models. 

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. 

The calculations are performed within the framework of the Carr-Parrinello molecular dynamics [25, 26]. Our approach is based on the density functional theory with generalized gradient approximations after Becke for the exchange energy [27] and Lee, Yang, and Parr for the correlation energy [28]. Troullier-Martins type... 

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