Exchange functionals with improved long-range behavior and adiabatic connection methods without adjustable parameters: The mPW and mPW1PW models

Starting from an analysis of the low-density and large gradient regions which dominate van der Waals interactions, we propose a modification of the exchange functional introduced by Perdew and Wang, which significantly enlarges its field of applications. This is obtained without increasing the number of adjustable parameters and retaining all the asymptotic and scaling properties of the original model. Coupling the new exchange functional to the correlation functional also proposed by Perdew and Wang leads to the $m\mathrm{PWPW}$ model, which represents the most accurate generalized gradient approximation available until now. We next introduce an adiabatic connection method in which the ratio between exact and density functional exchange is determined a priori from purely theoretical considerations and no further parameters are present. The resulting $m\mathrm{PW1PW}$ model allows to obtain remarkable results both for covalent and noncovalent interactions in a quite satisfactory theoretical framework encompassing the free electron gas limit and most of the known scaling conditions. The new functionals have been coded with their derivatives in the Gaussian series of programs, thus allowing fully self-consistent computations of energy and properties together with analytical evaluation of first and second geometry derivatives.