Canonical orbital energy derivative studies of the C₂H₂ and H₂CO ground state potential energy hypersurfaces

A study of first and second derivatives of the canonical orbital energies for the closed-shell self-consistent-field (SCF) wavefunction has been extended to tetratomic molecular systems. The first derivatives of the orbital energies in terms of the Cartesian coordinate were determined analytically and the second derivatives via the finite difference method, while the first and second derivatives of the electronic, nuclear and total energies were obtained analytically. At the stationary points these energy derivatives were uniquely transformed from the Cartesian to the normal coordinate system. Using the four equilibrium and three transition state structures of the closed-shell C₂H₂, : CCH₂, H₂CO and trans-HCOH molecules as examples, it is demonstrated that the derivatives of the energies with respect to the normal coordinates provide useful chemical information concerning the molecular structures and reactivities. The orbital energy derivative method may be used as a powerful semi-quantitative model in understanding and interpreting various chemical phenomena.