Analysis of carbon‐carbon bonding in small hydrocarbons and dicarbon using dynamic orbital forces: Bond energies and sigma/pi partition. Comparison with sila compounds

Abstract

The CC bonding is analyzed using dynamic orbital forces (DOF) in the series cyclopropane-ethane-benzene-ethylene-acetylene. The sum Σ(DOF) t of the DOF over occupied molecular orbitals (MOs) is found linearly correlated to bond energies and thus can be used as a tool for determination of CC bond strength. A partition of bonding into σ and π components indicates a weakening of the σ bonding along the series, mainly due to the decrease of the bonding character of the highest σ MO. For C 2 molecule, Σ(DOF) t was computed taking into account the four dominant configurations.On the basis of the preceding correlation, the C 2 bond was found about 15 kcal/mol weaker than that of acetylene, with a 25% σ participation; the bond order of C 2 can be evaluated at about 2.8 if we assume bond orders of 3 for acetylene and 2 for ethylene.Some sila homologs of the preceding carbon compounds have been studied. They exhibit characteristics generally close to the carbon compounds. A quite good correlation between Σ(DOF) t and bond energies is also observed. K E Y W O R D SCC bond energy, dicarbon, hydrocarbons, orbital forces, silanes | INTRODUCTIONAfter the pioneer work of Tal and Katriel, [1] the molecular orbital (MO) derivatives with respect to bond length have successfully been used as an index of their bonding character in diatomic molecules. [2] It can be easily justified, in the case of Hartree-Fock (H-F) canonical MOs, from generalized Koopman's theorem. As a matter of fact, the energy ε i of the ith MO is:where E 0 is the H-F energy of the neutral molecule, and E + i is the energy of the cation resulting from the removal of one electron from the ith MO. The derivative with respect to the internuclear distance R yields:The MO derivative thus appears as the variation of the forces exerted by electrons on nuclei when one electron is removed, in the approximation of frozen MOs. If the geometry has been optimized at R = R e , dE /dR = 0 and one gets:

The “Inverted Bonds” Revisited: Analysis of “In Silico” Models and of [1.1.1]Propellane by Using Orbital Forces

“…In particular, their DOFs are consistent with the bond lengthening in N 2 + and the bond shortening in CO + , with respect to the neutral species. The σ g + LUMO of C 2 , in its dominant configuration, also belongs to the same “inverted” type, with a DOF of −0.003 a.u …”

“…Recently, it has been found that the C−C bond energy in a series of hydrocarbons is linearly correlated to Σ. Moreover the σ/π partition of the total bonding was obtained by comparing the sums Σ σ and Σ π over occupied σ and π MOs, respectively . These results require that the system is essentially mono‐configurational.…”

Comment on “The ‘Inverted Bonds’ Revisited. Analysis of ‘in Silico’ Models and of [1.1.1]Propellane Using Orbital Forces“

“…As an extension of this model, the DOFs with respect to a given interatomic distance are summed over all the MOs (ϕ i ) of a molecule, and the result Σ(DOF i ) is considered as the central quantity that determines the nature and strength of a particular bond. A large positive Σ(DOF i ) corresponds to a strong bond, while a negative Σ(DOF i ) signifies a repulsive interaction . This method was recently applied to a series of hydrocarbons and a linear correlation was found between the CC bonding energies and the CC Σ(DOF i ) …”

The ‘Inverted Bond’ revisited. Analysis of ‘in silico’ models and of [1.1.1]Propellane using Orbital Forces

“…Moreover the / partition of the total bonding was obtained by comparing the sums   and   over occupied  and  MOs, respectively. 18 These results require that the system is essentially mono-configurational. It is indeed the case for propellane as evidenced by the fact that its CASPT2 and MP2 energies differ by less than 0.01 a.u.…”

“…The  g + LUMO of C 2 , in its dominant configuration, also belongs to the same "inverted" type, with a DOF of -0.003 a.u. 18 In order to further delve on the nature of these orbitals, we have also analyzed [1.1.1]bicyclopentane 2. The MOs of 2 mainly differ from the preceding ones by the HOMO a" 2 , which is strongly antibonding, resulting from the 4-electron interaction of the  orbitals of both C-H bonds at a very short CC distance (ca.…”