It is well-known that the kinetic energy density (KED) functional is the most difficult to approximate in density functional theory (DFT), yet to take full advantage of DFT with its density-based descriptive capability of molecular properties, an accurate account of KED is a must. To have a better idea of how an approximate KED formula behaves and where we should focus in the future development of better approximate KEDs, in this work we propose to employ the Pauli energy to assess their quality. We tested the performance of a total of 22 approximate semilocal noninteracting KED functionals from the literature for 18 neutral atoms and 20 small molecules. We found that generalized gradient approximation formulas of the KED functional can often reasonably accurately predict the total kinetic energy value for atoms and molecules but failed miserably to forecast the integrated values for Pauli energy related properties. The reason behind this is that presently available approximate KED functionals are unable to accurately account for the kinetic energy distribution in the medium range away from nuclei, where the Pauli energy plays a crucial role. Our results strongly suggest that the key information missing in approximate KED functionals comes from the medium regions, not nuclear cusps nor asymptotic areas, and the Pauli energy is a reliable measure of the quality of approximate KED functionals. Future efforts in developing better KED approximations should be invested in the regions of molecules where chemical bonds are formed in order to accurately account for the Pauli energy.

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.