Neural network algorithm to analyze IR Spectroscopic data: Application to CO ₂

The $\mathbf{C O}_{\mathbf{2}}$ molecule, a greenhouse gas, is characterized by three vibrational modes: $i) v_{1}$, a symmetric stretching vibration, ii) $v_{2}$, a double degenerate symmetric bending mode and iii) $v_{3}$, an anti-symmetric stretching vibration, with absorption frequencies in the mid infrared range. In a recent publication, it was shown that at the harmonic level, the CO<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> molecule preserves its vibrational symmetry when trapped in nanocages of Clathrate or rare gas matrices with a degeneracy lifting of the bending mode. The symmetry of the molecule is preserved even for the fermi levels that originate from the interaction between fundamental $v_{1}$ and $2 v_{2}$ states when their frequency values coincide. This work, is an attempt to analyze the vibrational degrees of freedom of $\mathbf{C O}_{\mathbf{2}}$ from a numerical algorithm based on a neural network algorithm used as a tool to sample the electronic environment from the vibrational motion of the nuclei clamped to form the molecule either when it moves freely as in gas phase or under an electro-magnetic constraint when trapped in a nanocage. To achieve this goal, the molecule is characterized by its force constant as determined in the previous work rather than by its harmonic vibrational frequencies. Different recognition strategies will be shown through the application of standard neural network with back-propagation algorithm.