IR Spectral density of υ(S)(N-H⃗) band of 3-phenylpyrazole polymorphs: Elucidation of the synergistic influences of vibrational mode dynamics, anharmonic coupling, and direct relaxation within the framework of linear response theory.

Exploring of the behavior of hydrogen bonds and their dynamics in systems with varying strengths through the analysis of their respective polarized infrared spectral density (SD) continues to be a subject of significant interest. This paper introduces a quantum model aimed at elucidating how the synergistic effects of vibrational modes and their interactions with the surrounding environment of the hydrogen bond can elucidate and theoretically replicate the SD of theυN-H⃗ band in the crystals of the 3-phenylpyrazole (3PhPz) polymorphs, referred to as 'alpha' (α-3PhPz) and'beta' (β-3PhPz). In doing so, this study incorporates a quantum framework that encompasses various mechanisms commonly found in hydrogen-bonded systems: (i) a Morse potential is used to mimic the anharmonic behavior of the low-frequency mode, (ii) the fast mode is treated as exhibiting harmonic oscillation, (iii) an illustration depicting the effect of phase coherence delocalization on the absorption band,υN-H⃗, resulting from the interplay between the two primary vibrational modes, the fast and slow modes, along with the way the bending and rapid modes interact, which gives rise to Fermi resonances, and (iv) the integration of the direct damping mechanism on the absorption band using the quantum method suggested by Rösch and Ranter, where the autocorrelation function (ACF) shows exponential decay over time. The SD is derived from Kubo's theory, which asserts that the SD is the transition dipole moment's Fourier transform of the ACF, defining the band contours of the mid-infrared absorption band. By employing a combination of parameters that accurately represent the various mechanisms considered in our model, numerical experiments validate the efficiency of this simple approach in describing the primary spectral characteristics of the υN-H⃗ band in both 3PhPz polymorphs by anharmonically coupling the three main vibrational modes. Theoretical and/or experimentally significant results were utilized to substantiate the discussion regarding the validity of the used parameters. A strong correlation between the theoretical band contours and the experimental band shapes is demonstrated, along with an inherent analysis of the contribution of each mechanism to the overall spectral behavior.