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A Practical Computational Approach to Study Molecular Instability Using the Pseudo-Jahn-Teller Effect.

Vibronic coupling theory shows that the cause for spontaneous instability in systems presenting a nondegenerate ground state is the so-called pseudo-Jahn-Teller effect, and thus its study can be extremely helpful to understand the structure of many molecules. While this theory, based on the mixing of the ground and excited states with a distortion, has been long studied, there are two obscure points that we try to clarify in the present work. First, the operators involved in both the vibronic and nonvibronic parts of the force constant take only into account electron-nuclear and nuclear-nuclear interactions, apparently leaving electron-electron repulsions and the electron's kinetic energy out of the chemical picture. Second, a fully quantitative computational appraisal of this effect has been up to now problematic. Here, we present a reformulation of the pseudo-Jahn-Teller theory that explicitly shows the contributions of all operators in the molecular Hamiltonian and allows connecting the results obtained with this model to other chemical theories relating electron distribution and geometry. Moreover, we develop a practical approach based on Hartree-Fock and density functional theory that allows quantification of the pseudo-Jahn-Teller effect. We demonstrate the usefulness of our method studying the pyramidal distortion in ammonia and its absence in borane, revealing the strong importance of the kinetic energy of the electrons in the lowest a2″ orbital to trigger this instability. The present tool opens a window for exploring in detail the actual microscopic origin of structural instabilities in molecules and solids.