Communication: The failure of correlation to describe carbon=carbon bonding in out-of-plane bends

Carbon-carbon multiply bonded systems are improperly described with standard, wave function-based correlation methods and Gaussian one-particle basis sets implying that thermochemical, spectroscopic, and potential energy surface computations are consistently erroneous. For computations of vibrational modes, the out-of-plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior as a combined one-particle and n-particle basis set effect for the first time. In essence, standard carbon basis sets do not describe equally well sp, sp², and sp³ hybridized orbitals, and this effect is exacerbated post-Hartree-Fock by correlation methods. The latter allow for occupation of the π and π^* orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space is non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem in wavefunction theory for describing carbon.