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.
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