Kinetic-energy/fisher-information indicators of chemical bonds

Roman F. Nalewajski, Piotr de Silva, Janusz Mrozek

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review


The kinetic energy (contragradience) criterion, related to the non-additive Fisher information in the resolution determined by the basis-functions X ={Xi}, e.g., the Atomic-Orbitals (AO), is used to localize chemical bonds in molecules. The interference, non-additive (nadd.) contribution to the molecular Fisher-information density, fnadd.[X; r] = ftotal[X; r] - fadd.[X; r], where ftotal[�; r] = f [X; r] is the overall distribution for the molecular electron density � and fadd.[X; r] = σi f[ Xi; r] denotes its AO-additive part, is used to determine the bonding regions in molecules. These closed basins of the physical space, for which fnadd. 0 identify regions of a diminished Fisher information (increased delocalization) content, compared to the reference AO-additive value. Indeed, such volumes represent a locally-decreased gradient content of the system wave-function thus reflecting less "order" (more "uncertainty") in the molecular distribution of electrons, and hence their increased delocalization via the system chemical bonds. This suggests the use of the zero-contra-gradience surface fnadd.[X; r] = 0, as the sensitive detector of the local presence of chemical bonds. The representative results from the minimum-basis-set (STO-3G) SCF MO calculations are reported for representative diatomics (H2, N2, HF, HCl, NaCl, CO) and selected polyatomic systems (ethylene, acetylene, ethane, butadiene, benzene, diborane and small propellanes). These illustrative examples convincingly validate the applicability of this contragradience probe in exploring the bonding patterns in molecules from the novel perspective of the Fisher-information/kinetic-energy redistribution. © 2012 by Nova Science Publishers, Inc. All rights reserved.
Original languageEnglish
Title of host publicationTheoretical and Computational Developments in Modern Density Functional Theory
EditorsAmlan K. Roy
Number of pages27
PublisherNova publishers
Publication date2012
Publication statusPublished - 2012
Externally publishedYes


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