C_n, C_nH and their anions: Quest for linearity with n8 even versus odd, and beyond

Using the concept of quasi-molecule ("tile") and the database of quasi-molecules embedded on a parent molecule, it is discussed whether the latter can attain linear form or otherwise. Besides anew accurate optimization of all tiles (quasi-triatomics) at various levels of ab initio theory and basis-sets, the nature of the predicted stationary points for the title parent molecules is probed through a priori calculations here too reported. Also discussed is the common rule that even-n CnH- anions are linear while odd-numbered ones tend to have nonlinear isomers. The reported quasi-molecule approach is general, and allow the prediction of linearity or otherwise of the parent systems prior to calculations on them. When based on an extension of the bisection method (Varandas, Int. J. Quantum Chem. 2023, 123, e27036.), it is easy to use even for large parent molecules, as illustrated for neutral and anionic carbon clusters with n >= 9.