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 Title: A Generalized Badger's Rule Quantifying The Structure-spectra Relationship For Hydrogen-bonded Systems Author(s): Heindel, Joseph P Contributor(s): Xantheas, Sotiris; McCoy, Anne B.; Markland, Thomas E; Marsalek, Ondrej; Boyer, Mark A. Subject(s): Fundamental interest Abstract: Badger’s rule originally described a non-linear relationship between the equilibrium bond length and force constant for diatomic molecules. This rule has since become synonymous with many different relationships between molecular structure and the frequency of a corresponding molecular vibration. In this work we provide an intuitive and general rule describing the relationship between the OH equilibrium bond lengths, $R_e$, and the harmonic OH stretch frequencies, $\omega_e$, as well as the vibrationally averaged OH bond lengths, $R_0$, and the anharmonic OH stretch frequencies, $\nu_0$. We show that the same rule applies for hydrogen bonds of varying strengths and corresponding red shifts in the OH vibrations such as the ones in neutral water clusters, protonated water clusters, and aqueous halide clusters. Remarkably, we find a simple linear correlation between the changes in the covalent OH bond length and corresponding stretching frequency of -19 $cm^{-1}$/ 0.001 \AA \ that holds for both the ($\omega_e$ vs $R_e$) and ($\nu_0$ vs $R_0$) pairs. We provide physical insights regarding the origin of this linear correlation by modeling the covalent, hydrogen bonded OH bond via a Morse oscillator. In particular, we show that the electric-field-dependent frequency shift for the harmonic and anharmonic frequencies lies on the same line. More importantly, using this simple linear relationship and scaling factor obtained from the aqueous clusters, we are able to reproduce both the structure and the position of the OH vibrational band in liquid water using the OH bond length distribution obtained from an ab initio molecular dynamics simulation. Issue Date: 2021-06-22 Publisher: International Symposium on Molecular Spectroscopy Genre: Conference Paper / Presentation Type: Text Language: English URI: http://hdl.handle.net/2142/111335 Date Available in IDEALS: 2021-09-24
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