The Bond Order of C2 from a Strictly N-Representable Natural Orbital Energy Functional Perspective

• Published in: Chemistry : a European journal Vol. 22; no. 12; pp. 4109 - 4115
• Main Authors: Piris, Mario, Lopez, Xabier, Ugalde, Jesus M.
• Format: Journal Article
• Language: English
• Published: Germany Blackwell Publishing Ltd 14.03.2016; Wiley Subscription Services, Inc
• Subjects: Acetylene; bond order; Bonding; Carbon; Chemistry; Correlation; density matrix functional calculations; Discontinuity; Electron states; Energy; Energy conservation; Ethylene; Euler-Lagrange equation; Functional anatomy; Ionization; Mathematical analysis; Mathematical models; natural orbitals; Occupations; Optimization; Orbitals; natural orbitals; density matrix functional calculations; bond order
• ISSN: 0947-6539; 1521-3765
• DOI: 10.1002/chem.201504491

The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N‐representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ–σ* linked pair of natural orbitals and three degenerate pseudo‐bonding like orbitals, paired each with one triply degenerate pseudo‐antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree–Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C2 intermediate between acetylene and ethylene. Order in the C2 court please! Calculations with the N‐representable natural orbital functional PNOF5, complemented with size‐consistent multiconfigurational perturbation theory corrections, PNOF5‐PT2, reveal the complexity of the electronic structure of the ground state of C2 as illustrated by the existence of at least three different solutions that expand upon increasing internuclear distances. The inclusion of interpair correlation effects, PNOF6, leads to a continuous dissociation curve and a bond order for C2 intermediate between acetylene and ethylene.