A Practical
Computational Approach to Study Molecular
Instability Using the Pseudo-Jahn–Teller Effect
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Abstract
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 <i>a</i><sub>2</sub>″ 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