Discontinuities of Kinetic Energy Densities within Finite and Complete Basis Sets.

Although electron densities are always continuous, other ingredients of density-functional approximations can be sharply discontinuous at isolated points. In particular, the positive-definite, Weizsäcker, and Pauli kinetic energy densities expressed in terms of Slater-type orbitals all have discontinuities at the positions of the atomic nuclei in molecules. The first two of those quantities are similarly discontinuous even in the basis-set limit. These striking features are not as widely recognized as they deserve to be. We show in detail how discontinuities of kinetic energy densities arise from asymmetric electron-nucleus cusps of molecular wave functions and point out instances of their significance in electronic structure theory.

Using Density Functional Theory for Testing the Robustness of Mobile-Proton Molecular Dynamics Simulations on Electrosprayed Ions: Structural Implications for Gaseous Proteins.

Current experiments only provide low-resolution information on gaseous protein ions generated by electrospray ionization (ESI). Molecular dynamics (MD) simulations can yield complementary insights. Unfortunately, conventional MD does not capture the mobile nature of protons in gaseous proteins. Mobile-proton MD (MPMD) overcomes this limitation. Earlier MPMD data at 300 K indicated that protein ions generated by "native" ESI retain solution-like structures with a hydrophobic core and zwitterionic exterior [Bakhtiari, M.; Konermann, L. J. Phys. Chem. B 2019, 123, 1784-1796]. MPMD redistributes protons using electrostatic and proton affinity calculations. The robustness of this approach has never been scrutinized. Here, we close this gap by benchmarking MPMD against density functional theory (DFT) at the B3LYP/6-31G* level, which is well suited for predicting proton affinities. The computational cost of DFT necessitated the use of small peptides. The MPMD energetic ranking of proton configurations was found to be consistent with DFT single-point energies, implying that MPMD can reliably identify favorable protonation sites. Peptide MPMD runs converged to DFT-optimized structures only when applying 300-500 K temperature cycling, which was necessary to prevent trapping in local minima. Temperature cycling MPMD was then applied to gaseous protein ions. Native ubiquitin converted to slightly expanded structures with a zwitterionic core and a nonpolar exterior. Our data suggest that such inside-out protein structures are intrinsically preferred in the gas phase, and that they form in ESI experiments after moderate collisional excitation. This is in contrast to native ESI (with minimal collisional excitation, simulated by MPMD at 300 K), where kinetic trapping promotes the survival of solution-like structures. In summary, this work validates the MPMD approach for simulations on gaseous peptides and proteins.