Variational Monte Carlo and Configurational Interaction Studies of $C_{60}$ and its Fragments

TL;DR

This study employs CI and VMC methods within the Hubbard model to analyze $C_{60}$ and its fragments, providing insights into their electronic structure, bond orders, and correlation functions, with comparisons to exact calculations.

Contribution

It applies and compares CI and VMC techniques to $C_{60}$ and fragments, revealing detailed electronic and bonding characteristics within the Hubbard model framework.

Findings

Bond orders vary among fragments and are influenced by the Hubbard parameter.

Corannulene shows larger hexagon-hexagon bonds than hexagon-pentagon bonds.

Bond strength depends on coordination and is affected by bond alternation.

Abstract

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact calculations. The fragments of $C_{60}$ studied are pyracylene, fluoranthene and corannulene. The energies, bond orders, spin-spin and charge-correlation functions of these systems are obtained for various values of the Hubbard parameter, $U$. The analysis of bond orders and correlation functions of these individual molecules allow us to visualise pyracylene as a naphthalene unit with two ethylenic moieties and fluoranthene as weakly bridged benzene and naphthalene units. Corannulene is the largest fragment of $C_{60}$ that we have studied. The hexagon-hexagon(h-h) bond orders are slightly larger than those of the hexagon-pentagon bonds(h-p), a feature also found in other fragments. We also find bonds between two co-ordinated carbon sites to be stronger than bonds involving three coordinated carbon sites. In $C_{60}$, the h-h bonds are stronger than in corannulene and the h-p bonds weaker than in corannulene for all correlation strengths. Introducing bond alternation in the buckyball enhances this difference.