I am not so sure whether I understand the question correctly but I will say a few words about the kinetic energy in this context.
Density functional theory codes that use a plane-wave basis set rely on the pseudopotential approximation or use the projector-augmented-wave (PAW) approach which is in practice also used as a pseudopotential method because the computational demands required to go beyond the frozen-core approximation are rather large (but it is in principle possible).
In the pseudopotential approximation you perform for each chemical element a prototype calculation that includes all electrons. But you are mainly interested in the valence electrons as the chemical bonding of the atoms to other atoms is strongly dominated by these electrons and not by the core electrons or the higher-lying unoccupied states. Therefore you decide that in more demanding calculations beyond your prototype system you only want to consider the valence electrons. This is done by defining a sphere around the atom in which the valence wave functions are replaced by smooth pseudo wave functions that do not feature any nodes. With these pseudo wave functions you then go in the opposite direction and construct a potential for which these wave functions solve the respective <PERSON> equation and the resulting energy eigenvalues agree with those of the all-electron system.
In such a representation there are no core electrons any more. 795
The pseudo valence wave functions are the energetically lowest lying energy eigenstates. They feature a rather low kinetic energy and thus can be represented by the plane waves below the kinetic energy cutoff parameter. The real valence and core electron wave functions feature a kinetic energy that can be larger by several orders of magnitude. This is the reason why you rely on the pseudopotential approximation if you use a plane-wave basis: To represent the real all-electron wave functions you would need a gigantic kinetic energy cutoff parameter resulting in a basis set size that makes real computations infeasible.
Please note that the pseudopotential approximation is a very successful approach in density functional theory. But, of course, the question whether a pseudopotential is reasonably transferable to a certain chemical environment deviating from the prototype system is not always easy to answer. 976