The Decomposition of Normal Vibrational Modes in Different Chemistry Problems

The least action principle yields the Euler-Lagrange equations, which explain molecular vibrations in minimizing action. Subsequently, the Lagrangian gives rise to the equations of motion using the Euler-Lagrange equations. We can then solve the characteristic value problem to obtain normal vibrational modes. Ultimately, the vibrational spectrum of a molecule can be extracted from the characteristic values. Normal coordinates are linear combinations of internal or Cartesian coordinates. However, the delocalization of normal vibrational modes across the molecule restricts the direct use of normal mode frequencies and force constants for measuring bond strength. From the force constant matrix and the normal mode vectors, the Konkoli-Cremer approach provides local vibrational modes, along with the associated local mode frequencies and force constants. The so-called CNM procedure, which is part of the local vibrational mode theory, furnishes a novel method for analyzing vibrational spectra by decomposing a given normal vibrational mode into local mode contributions. The physical foundation of CNM is an important one-to-one correspondence between a complete set of non-redundant local modes and their normal mode counterparts via an adiabatic connection scheme. My research contributions focused on the conceptual and theoretical approach to the rationale behind the proper selection of local mode sets for CNM, as well as its application in a variety of chemistry problems, including those that overlap with the fundamentals of chemistry and statistical thermodynamics