The specific π–π interactions between curved and planar structures, which are different from the general π–π interactions between planar arenes, have generated great attention due to their brand-new, unique, and fascinating photoelectric properties. Herein, the curved–planar (C–P) π–π interactions between corannulene, pyrene and coronene have been investigated using the DFT-D method. A series of structural and physical properties have been calculated including geometry, C–C distance, binding energy, population charge distribution, dipole moment, electrostatic potential (ESP), visualization of the interactions in real space, transfer integral, electronic transition behaviour and Raman shift. All the analyses indicate that the bowl–planar (CB–P) complexes are distinguishable from the mouth-tip–planar (CM–P) and planar–planar (P–P) packing motifs due to their coherent negative ESP, electronic attraction strength and Raman spectra. The C–P complexes are found to exhibit dominant electron transport characteristics. In addition, an unusual “negative Stokes shift” is found in the C–P π–π complexes, which is caused by state resonance. This provides a clue to help predict and explore the photoelectric properties of C–P π–π complexes. In particular, at the frequency of the out-of-plane CH bending vibration around 1400 cm−1, the planar molecules in the CB–P complexes possess a smaller Raman peak shift than in the CM–P complexes, and vice versa for the curved molecules. This specific Raman shift can be utilized as characteristic signals to identify the C–P structures.