; Zhang Shuang-Nan] Tsing Hua Univ, Dept Phys, Beijing 100084, Peoples R China
; [Yang Rong-Jia
; Zhang Shuang-Nan] Tsing Hua Univ, Tsinghua Ctr Astrophys, Beijing 100084, Peoples R China
; [Zhang Shuang-Nan] Chinese Acad Sci, Inst High Energy Phys, Key Lab Particle Astrophys, Beijing 100049, Peoples R China
Purely kinetic k-essence models in which the Lagrangian contains only a kinetic factor and does not depend explicitly on the field itself are considered, and a theoretical constraint is obtained: F-x = F(0)a(-3). Under this theoretical constraint, we discuss a kind of purely k-essence with form F(X) = -(1 + 2X(n))(1/2n), which can be considered as the generalized tachyon field, and find that this kind of k-essence is not likely a candidate of dark energy to describe the present accelerated expansion of the Universe. This is contrary to a previous suggestion that k-essence with such a form may be used to describe phantom cosmologies.