The induced magnetic field of C_2N (N = 3-14) carbon rings was dissected to contributions from out-of-plane and in-plane π orbitals revealing two concurrent long-range shielding or deshielding cones as a manifestation of the dual aromatic and antiaromatic character of C_4n+2 and of C_4n rings respectively. Aromaticity based on the magnetic criterion was evaluated with regard to bonding pattern and geometrical characteristics elucidating the influence of bond length and bond angle alternation on out-of-plane and in-plane magnetic response. Ground state polyynic geometries of C_4n+2 rings exhibit comparable shielding cones to annulenes, decreasing magnetic response with regard to ring size and similar π_out and π_in diatropicity. Transition state cumulenic rings display increased aromaticity expressed by a constant very strong magnetic response and augmented π_out diatropicity with regard to π_in. The variations of the induced magnetic field are explained on the basis of frontier orbital interactions through rotational excitations, which enable further rationalization of the aromatic/antiaromatic behavior.

Orbital contributions to the magnetic response depend on the method used to compute them. Here, we show that dissecting nuclear magnetic shielding tensors using natural localized molecular orbitals (NLMOs) leads to anomalous core contributions. The arbitrariness of the assignment might significantly affect the interpretation of the magnetic response of nonplanar molecules such as C₆₀ or [14]helicene and the assessment of their aromatic character. We solve this problem by computing the core- and σ-components of the induced magnetic field (and NICS) and the magnetically induced current density by removing the valence electrons (RVE). We estimate the core contributions to the magnetic response by performing calculations on the corresponding highly charged molecules, such as C₆H₆ ³⁰⁺ for benzene, using gauge-including atomic orbitals and canonical molecular orbitals (CMOs). The orbital contributions to nuclear magnetic shielding tensors are usually estimated by employing a natural chemical shielding (NCS) analysis in NLMO or CMO bases. The RVE approach shows that the core contribution to the magnetic response is small and localized at the nuclei, contrary to what NCS calculations suggest. This may lead to a completely incorrect interpretation of the magnetic σ-orbital response of nonplanar structures, which may play a major role in the overall magnetic shielding of the system. The RVE approach is thus a simple and inexpensive way to determine the magnetic response of the core- and σ-electrons.