First and second energy derivative analyses of the vinylidene and acetylene triplet state potential energy hypersurfaces

First and second derivatives of the orbital, electronic, nuclear, and total energies for the self-consistent-field (SCF) wave function have been used to study the triplet state of the CCH2 and HCCH molecules. The diagonal elements of the Lagrangian matrix for the general open-shell SCF wave function are used as the ‘‘orbital’’ energies. The first and second derivatives of the orbital energies in terms of the normal coordinates are determined by the finite difference method, while the corresponding derivatives of the electronic, nuclear, and total SCF energies are obtained via analytic derivative techniques. It is demonstrated that the derivatives of the energies with respect to the normal coordinates provide useful chemical information for the triplet state potential energy hypersurfaces of the CCH2 and HCCH molecules. Specifically, the isomerization reactions from ã 3B2 vinylidene to b̃ 3Bu acetylene and from ã 3B2 acetylene to b̃ 3Bu acetylene are found to be electronically stable processes and their negative force constants (or imaginary vibrational frequencies) are seen to be controlled by the negative nuclear contributions. Energy derivative analysis may give strong quantitative support for arguments based on the conventional qualitative molecular orbital (MO) theory.