A graphene flake under external electric fields reconstructed from field-perturbed kernels

The energy, dipole moment, and polarizability of a finite hydrogen terminated zigzag graphene flake (C46H20, in 2 × 7 rings) are calculated in the absence of and in the presence of external electric fields reaching 5 × 109 Vm−1 [=0.01 atomic units (a.u.)]. The field intensities studied are typically found in nanoelectronics and in the tip-sample gap of a scanning tunneling microscope (STM). The change in the total energy ΔE(eV) can be closely fitted to a quadratic function of the field {1.549 × 104 [E (a.u.)]2} while the dipole moment μ(debye) to a linear function [2.7 × E (a.u.)]. The results obtained with three different chemical models [MP2, density functional theory (B3LYP), and Hartree-Fock calculations, all with a 6-311G(2d,2p) basis set] are consistent in both trends and in absolute values. These results obtained from direct calculations are reproduced with a remarkable accuracy from a linear scaling fragmentation scheme called the kernel energy method (KEM). The KEM reproduces all studied field-free and response properties of this graphene flake model, in relative and absolute terms, independently of the underlying chemical model. An observation consistent with the known stiffness of graphene is that geometry optimization under a field as strong as 0.01 a.u. insignificantly alters the total energy and the geometry of a (smaller) zigzag C28H14 flake, the difference in the field-induced stabilization energy (ΔΔE) being only 0.006 eV (less than 1% of ΔE) and the average field-induced displacement of nuclear positions ∼0.0046 Å [B3LYP/6-31G(d,p)].