Acta Phys. -Chim. Sin. ›› 2018, Vol. 34 ›› Issue (6): 631-638.doi: 10.3866/PKU.WHXB201710201

Special Issue: Special issue for Chemical Concepts from Density Functional Theory

• ARTICLE • Previous Articles     Next Articles

Understanding Chemical Reactivity in Extended Systems: Exploring Models of Chemical Softness in Carbon Nanotubes

Carlos CÁRDENAS1,2,*(),Macarena MUÑOZ1,3,Julia CONTRERAS4,Paul W. AYERS5,Tatiana GÓMEZ6,Patricio FUENTEALBA1,2,*   

  1. 1 Departamento de Fısica, Facultad de Ciencias, Universidad de Chile, Casilla, 653 Santiago, Chile
    2 Centro para el Desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Avenida Ecuador 3493, Santiago, Chile
    3 Núcleo de Matemáticas, Física y Estadística, Facultad de Ciencias, Universidad Mayor, Manuel Montt 367, Providencia, Santiago, Chile
    4 Sorbonne Universités, UPMC and CNRS, Laboratoire de Chimie Théorique (LCT), 75005 Paris, France
    5 Department of Chemistry & Chemical Biology; McMaster University; Hamilton, L8S 4M1 Ontario, Canada
    6 Institute of Applied Chemical Sciences, Theoretical and Computational Chemistry Center, Universidad Autónoma de Chile, El Llano Subercaceaux 2801, San Miguel, Santiago, Chile
  • Received:2017-08-30 Published:2018-03-20
  • Contact: Carlos CÁRDENAS,Patricio FUENTEALBA
  • Supported by:
    This work has been supported by FONDECYT grants 1140313 and 11150164. CC and PF acknowledge support by Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia-FB0807, and project RC-130006 CILIS, granted by the Fondo de Innovación para la Competitividad del Ministerio de Economía, Fomento y Turismo de Chile. MM acknowledge supports by CONICYT through grant 21130691. PWA acknowledges support from NSERC, Compute Canada, and the Canada Research Chairs


Chemical reactivity towards electron transfer is captured by the Fukui function. However, this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states. In such a case, the first-order chemical response is not independent of the perturbation and the correct response has to be computed using the mathematical formalism of perturbation theory for degenerate states. Spatial pseudo-degeneracy is ubiquitous in nanostructures with high symmetry and totally extended systems. Given the size of these systems, using degenerate-state perturbation theory is impractical because it requires the calculation of many excited states. Here we present an alternative to compute the chemical response of extended systems using models of local softness in terms of the local density of states. The local softness is approximately equal to the density of states at the Fermi level. However, such approximation leaves out the contribution of inner states. In order to include and weight the contribution of the states around the Fermi level, a model inspired by the long-range behavior of the local softness is presented. Single wall capped carbon nanotubes (SWCCNT) illustrate the limitation of the frontier orbital theory in extended systems. Thus, we have used a C360 SWCCNT to test the proposed model and how it compares with available models based on the local density of states. Interestingly, a simple Hückel approximation captures the main features of chemical response of these systems. Our results suggest that density-of-states models of the softness along simple tight binding Hamiltonians could be used to explore the chemical reactivity of more complex system, such a surfaces and nanoparticles.

Key words: Local softness, Fukui function, Reactivity, Carbon nanotubes, Density of states