The bond force constants of graphene and benzene calculated by density functional theory

Abstract

Stretching (kr) and bending (kθ) bond force constants appropriate to describe the bond stiffness of graphene and benzene are calculated using density functional theory. The effect of employing different exchange-correlation functionals for the calculation of kr and kθ is discussed using the generalised gradient approximation (GGA) and the local density approximation (LDA). For benzene, kr = 7.93 mdyn Å-1 and kθ = 0.859 mdyn Å rad-2 using LDA, while kr = 7.67 mdyn Å-1 and kθ = 0.875 mdyn Å rad-2 using GGA. For graphene, kr = 7.40 mdyn Å-1 and kθ = 0.769 mdyn Å rad-2 using LDA, while kr = 6.88 mdyn Å-1 and kθ = 0.776 mdyn Å rad-2 using GGA. This means the difference between the bond force constants for benzene and graphene can be as large as ∼12%. The comparison between these two systems allows for elucidation of the effect of periodicity and substitution of carbon atoms by hydrogen in the stiffness of C–C bonds. This effect can be explained by a different redistribution of the charge density when the systems are subjected to strain. The parameters kr and kθ computed here can serve as an input to molecular mechanics or finite element codes of larger carbon molecules, which in the past had frequently assumed the same bond force constants for graphene, benzene or carbon nanotubes.