  It is known that the adiabatic approximation in time-dependent density
functional theory usually provides a good description of low-lying excitations
of molecules. In the present work, the capability of the adiabatic nonempirical
meta-generalized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov,
and Scuseria (TPSS) to describe atomic and molecular excitations is tested. The
adiabatic (one-parameter) hybrid version of the TPSS meta-GGA and the adiabatic
GGA of Perdew, Burke, and Ernzerhof (PBE) are also included in the test. The
results are compared to experiments and to two well-established hybrid
functionals PBE0 and B3LYP. Calculations show that both adiabatic TPSS and
TPSSh functionals produce excitation energies in fairly good agreement with
experiments, and improve upon the adiabatic local spin density approximation
and, in particular, the adiabatic PBE GGA. This further confirms that TPSS is
indeed a reliable nonhybrid universal functional which can serve as the
starting point from which higher-level approximations can be constructed. The
systematic underestimate of the low-lying vertical excitation energies of
molecules with time-dependent density functionals within the adiabatic
approximation suggests that further improvement can be made with nonadiabatic
corrections.
