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

Abstract

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
Pages561-588
Publication statusPublished - 2012
Externally publishedYes

Cite this

Nalewajski, R. F., de Silva, P., & Mrozek, J. (2012). Kinetic-energy/fisher-information indicators of chemical bonds. In A. K. Roy (Ed.), Theoretical and Computational Developments in Modern Density Functional Theory (pp. 561-588). Nova publishers.
Nalewajski, Roman F. ; de Silva, Piotr ; Mrozek, Janusz. / Kinetic-energy/fisher-information indicators of chemical bonds. Theoretical and Computational Developments in Modern Density Functional Theory. editor / Amlan K. Roy. Nova publishers, 2012. pp. 561-588
@inbook{7f3039d41f1949468a7614181bddfc1c,
title = "Kinetic-energy/fisher-information indicators of chemical bonds",
abstract = "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[{\"I}�; r] = f [X; r] is the overall distribution for the molecular electron density {\"I}� and fadd.[X; r] = {\"I}ƒi 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. {\^A}{\circledC} 2012 by Nova Science Publishers, Inc. All rights reserved.",
author = "Nalewajski, {Roman F.} and {de Silva}, Piotr and Janusz Mrozek",
year = "2012",
language = "English",
pages = "561--588",
editor = "Roy, {Amlan K.}",
booktitle = "Theoretical and Computational Developments in Modern Density Functional Theory",
publisher = "Nova publishers",

}

Nalewajski, RF, de Silva, P & Mrozek, J 2012, Kinetic-energy/fisher-information indicators of chemical bonds. in AK Roy (ed.), Theoretical and Computational Developments in Modern Density Functional Theory. Nova publishers, pp. 561-588.

Kinetic-energy/fisher-information indicators of chemical bonds. / Nalewajski, Roman F.; de Silva, Piotr; Mrozek, Janusz.

Theoretical and Computational Developments in Modern Density Functional Theory. ed. / Amlan K. Roy. Nova publishers, 2012. p. 561-588.

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

TY - CHAP

T1 - Kinetic-energy/fisher-information indicators of chemical bonds

AU - Nalewajski, Roman F.

AU - de Silva, Piotr

AU - Mrozek, Janusz

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

M3 - Book chapter

SP - 561

EP - 588

BT - Theoretical and Computational Developments in Modern Density Functional Theory

A2 - Roy, Amlan K.

PB - Nova publishers

ER -

Nalewajski RF, de Silva P, Mrozek J. Kinetic-energy/fisher-information indicators of chemical bonds. In Roy AK, editor, Theoretical and Computational Developments in Modern Density Functional Theory. Nova publishers. 2012. p. 561-588