  Background: The nuclear kinetic density is one of many fundamental quantities
in density functional theory (DFT) dependent on the nonlocal nuclear density.
Often, approximations may be made when computing the density that may result in
spurious contributions in other DFT quantities. With the ability to compute the
nonlocal nuclear density from ab initio wave functions, it is now possible to
estimate effects of such spurious contributions. Purpose: We derive the kinetic
density using ab initio nonlocal scalar one-body nuclear densities computed
within the no-core shell model (NCSM) approach, utilizing two- and
three-nucleon chiral interactions as the sole input. With the ability to
compute translationally invariant nonlocal densities, it is possible to
directly gauge the impact of the spurious center-of-mass (COM) contributions in
DFT quantities such as the kinetic density. Methods: The nonlocal nuclear
densities are derived from the NCSM one-body densities calculated in second
quantization. We present a review of COM contaminated and translationally
invariant nuclear densities. We then derive an analytic expression for the
kinetic density using these nonlocal densities, producing an ab initio kinetic
density. Results: The ground state nonlocal densities of
\textsuperscript{4,6,8}He, \textsuperscript{12}C, and \textsuperscript{16}O are
used to compute the kinetic densities of the aforementioned nuclei. The impact
of the COM removal technique in the densities is discussed. The results of this
work can be extended to other fundamental quantities in DFT. Conclusions: The
use of a general nonlocal density allows for the calculation of fundamental
quantities taken as input in theories such as DFT. This allows benchmarking of
procedures for COM removal in different many-body techniques.
