Stability of the polyynic form of C, C, C, and C nanorings: a challenge tackled by range-separated double-hybrid density functionals.

We calculate the relative energy between the cumulene and polyyne structures of a set of C ( = 4-7) rings (C, C, C, and C prompted by the recent synthesis of the cyclo[18]carbon (or simply C) compounds. Reference results were obtained by a costly Quantum Monte-Carlo (QMC) approach, providing thus very accurate values allowing to systematically compare the performance of a variety of wavefunction methods [(, MP2, SCS-MP2, SOS-MP2, DLPNO-CCSD, and DLPNO-CCSD(T)] as well as DFT approaches, applying for the latter a diversity of density functionals covering global and range-separated hybrid and double-hybrid models. The influence of the use of a range-separation scheme for density functionals, for both hybrid and double-hybrid expressions, is discussed according to its key role. Overall, range-separated double-hybrid functionals (, RSX-QIDH) behave very accurately and provide competitive results compared with DLPNO-CCSD(T), at a more reasonable computational cost.