We extended our studies of the effect of dynamical electron correlation on the covalent bonds in the AH and AF series (A = B–F) to the recoupled pair bonds in the excited a4Σ− states of the CH and CF molecules. Dynamical correlation is energetically less important in the a4Σ− states than in the corresponding X2Π states for both molecules, which is reflected in smaller changes in bond energies (De). Changes in the equilibrium bond distance (Re) and vibrational frequency (ωe), on the other hand, are influenced by the changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance R, EDEC(R). In the CH(a4Σ−) state, these changes are much smaller than in the CH(X2Π) state, but in the CF(a4Σ−) state, they are larger, reflecting a significant difference in the shapes of EDEC(R) curves. At large R, the shape of EDEC(R) curves for covalent and recoupled pair bonds is similar although different in magnitude. For the CH(a4Σ−) state, EDEC(R) has a minimum at R = Re + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. EDEC(R) for the CF(a4Σ−) state decreases continuously throughout the bound region of the potential energy curve because the dynamical correlation energy associated with the electrons in the lone pair orbitals is increasing. These results support our earlier conclusion that we still have much to learn about the nature of dynamical electron correlation in molecules.
Note that, to the extent that the CCSD(T) energy does not include all the non-dynamical correlation energy, EDEC(R) will be underestimated. This error is not expected to be significant for the molecules considered here, which only have single σ bonds, but could be significantly larger for other molecules, e.g., those with multiple bonds.