A Generalized Badger's Rule Quantifying The Structure-spectra Relationship For Hydrogen-bonded Systems

Heindel, Joseph P

Permalink

https://hdl.handle.net/2142/111335 Copy

Description

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.

Issue Date

2021-06-22

Keyword(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.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

Text

Language

eng

Permalink

http://hdl.handle.net/2142/111335

DOI

10.15278/isms.2021.TD08

Owning Collections