Kinetic and exchange energy semilocal functionals derived from model potentials by Q-path integration

Model exchange, exchange-correlation, and kinetic potentials are still useful in solid-state and quantum chemistry electronic structure calculations, even if they violate important exact conditions, such as the translational and rotational invariance. Moreover, the energy of model potentials is ill-defined, as it is dependent on the path-integral. We show that the Q-path integral given by the homogeneous density scaling, nλ(r) = λn(r), is related to the gauge of the semilocal functionals in the slowly-varying density regime. This fact makes the Q-path integral a useful method for developing density functionals for solid-state systems. To prove this statement, we construct generalized gradient approximation kinetic and exchange energy functionals, starting from simple model potentials and using the Q-path approach. We test these functionals for several equilibrium properties of bulk solids.