Physical Mechanism of Spectra in Carbon Nanobelts under Quantum Size Effect

Since the successful synthesis of [6,6]carbon nanobelt (CNB), [8,8]CNB and [12,12]CNB have been synthesized successively. CNBs with different sizes ([2N,2N]CNB; N = 2, 3, 4, 5, 6, 7, and 8) have quantum size effects and exhibit completely different optical properties. In this work, the linear and nonlinear optical properties and spectral changes of [2N,2N]CNB are studied based on density functional theory (DFT). The molecular volume, pore volume, and stability of [2N,2N]CNB are investigated. The electron transition mechanism of the one-photon absorption (OPA) and two-photon absorption (TPA) spectra of [2N,2N]CNB is explained, and the extrapolation formula between the wavelength of the absorption peak and the absorption coefficient (ε) and size is given. The infrared (IR) and Raman spectra of [2N,2N]CNB are calculated, and the vibrational modes of characteristic peaks are provided. Finally, the nonlinear optical properties of [2N,2N]CNB are studied, which reflect the anisotropy of molecular polarization. The extrapolation formulas for the polarizability (α) and second hyperpolarizability (γ) of [2N,2N]CNB under different external fields are given. The extrapolation formulas given in this work will help to predict the linear and nonlinear optical properties of arbitrary [2N,2N]CNB beyond computational power, laying the foundation for the practical application of [2N,2N]CNB's theoretical basis.