Broken Symmetry Approach and Chemical Susceptibility of Carbon Nanotubes

TL;DR

This paper presents a broken symmetry approach using UBS HF calculations to quantify the chemical susceptibility of carbon nanotubes by analyzing effectively unpaired electrons, aiding in predicting reactivity and addition sites.

Contribution

It introduces a method to quantify atomic chemical susceptibility in nanotubes using UBS HF effectively unpaired electrons, applicable to various nanotube structures and lengths.

Findings

NDA correlates with nanotube reactivity.

Method applicable to different nanotube types and end structures.

Algorithms enable quantitative description of nanotubes of any length.

Abstract

Constituting a part of odd electrons that are excluded from the covalent bonding, effectively unpaired electrons are posed by the singlet instability of the single-determinant broken spin-symmetry unrestricted Hartree-Fock (UBS HF) SCF solution. A correct determination of the total number of effectively unpaired electrons ND and its fraction on each atom NDA is well provided by the UBS HF solution. The NDA value is offered to be a quantifier of atomic chemical susceptibility (or equivalently, reactivity) thus highlighting targets that are the most favorable for addition reactions of any type. The approach is illustrated for two families involving fragments of arm-chair (n,n) and zigzag (m,0) single-walled nanotubes differing by length and end structure. Short and long tubes as well as tubes with capped end and open end, in the latter case, both hydrogen terminated and empty, are considered. Algorithms of the quantitative description of any length tubes are suggested.