This work describes a new approach for approximate obtaining the positively defined electronic kinetic energy density (KED) from electron density. KED is presented as a sum of the Weizs€ acker KED, which is calculated in terms of electron density exactly, and unknown Pauli KED. The latter is presented via local Pauli potential and Gritsenko-van Leeuwen-Baerends kinetic response potential, to which the second-order gradient expansion is applied. The resulting expression for KED contains only one empirical parameter. The approach allowed to correctly reproduce all the features of KED, and electron localization descriptors as electron localization function and phasespace defined Fisher information density for main types of bonds in molecules and molecular crystals. It is also demonstrated that the method is immediately applicable to derivation of mentioned bonding descriptors from experimental electron density. Herewith the method is significantly free from the drawback of Kirzhnits approximation, which is now commonly accepted for evaluation of the electronic kinetic energy characteristics from precise X-ray diffraction experiment.

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In this work, the electron organization of many‐electron systems is considered in a context of the linear response theory extending the Kohn‐Resta view on electron localization phenomenon. The variances of the local electronic position and momentum operators are linked via the fluctuation‐dissipation theorem to the optical conductivity tensor, that is, to observable spectroscopic properties. It is demonstrated that the electron position variance density quantifies a degree of electron delocalization in each point of position space and distinguishes between metallic and insulating character of electronic states. The momentum variance density estimates a degree of electron localization and is immediately related to electronic kinetic energy density in the Ghosh‐Berkowitz‐Parr form giving a physical interpretation to the later. We show that electron localization and delocalization phenomena in atoms and molecules can be probed by external electric field. This approach provides new electronic descriptors distinguishing and quantifying chemical bonds of different types.

A combined molecular docking, QM, and QM/MM dynamics modeling complemented with electron-density based descriptors computed at the B3LYP/6-311G++(d,p) level of theory have been carried out in order to understand the ability of the drugs rhodanine (RD) and 2,4-thiazolidinedione (TZD) in the effective treatment of type 2 diabetes mellitus. The global HOMO/LUMO descriptors provided just a very rough estimate of the chemical reactivity of both molecules, while the features of electron density studied in terms of its Laplacian and electrostatic potential allowed identifying the local electron rich/poor sites which were associated with the regions of electrophilic/nucleophilic attacks in RD and TZD. These results were thoroughly checked using the novel physically-grounded functional descriptors such as the phase-space Fisher information density and the internal kinetic electronic pressure density, which confirmed the information on bonding and lone electron pair details. The molecular docking, QM, and QM/MM dynamics analyses revealed the detailed picture of interactions of the drugs with the amino acid residues of the active site of the human pancreatic alpha-amylase protein (hPAA). The main difference in behavior of RD and TZD molecules is related to the hydrogen bond between the NH group of the ligand and Asp197. In hPAA complex with RD the proton from the NH group, which carries large positive charge (~ +0.45 e), spontaneously transfers to the carboxyl group of Asp197 and stays there, while in complex with TZD this proton frequently changes its position with the more preferable formation of covalent bond with the N atom. Upon deprotonation of the ligand, its hydrogen bonds with Arg195 and His299 become stronger. This process influences the binding with the difference of the binding constants of RD and TZD about 200 times with the higher value corresponding to the RD molecule. Thus, the cumulative results lead to the conclusion that rhodanine would have a higher binding affinity than the 2,4-thiazolidinedione molecule in the active site of human pancreatic alpha-amylase.