On the Strength of Ouroboros Hydrogen Bonds

Contrary to the traditional inter-molecular hydrogen bonds (HBs), the strength of intra-molecular (ouroboros) HBs (IMHBs) is not uniquely and in most instances not even well-defined. The problem arises from the difficulty in separating IMHBs into distinct fragments without breaking covalent bonds, making the zero energy reference level not uniquely defined. We propose a novel, spectroscopy-based approach to estimate the strength of an IMHB from the corresponding vibrational frequency. Our approach relates hydrogen bond energies to changes in vibrational frequencies via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Δ</mml:mi><mml:msubsup><mml:mi>E</mml:mi><mml:mi>e</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0.43</mml:mn><mml:mfrac><mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>m</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:mrow><mml:msqrt><mml:mrow><mml:mi>c</mml:mi><mml:msup><mml:mi>m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:msqrt></mml:mfrac><mml:msqrt><mml:mrow><mml:mi>Δ</mml:mi><mml:msub><mml:mi>ω</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>Δ</mml:mi><mml:msub><mml:mi>ω</mml:mi><mml:mi>M</mml:mi></mml:msub></mml:mrow></mml:msqrt></mml:math>, where <i>E</i>_<i>e</i>^HB is the hydrogen bond energy, Δω_HB is the hydrogen bond redshift, and Δω_M is the frequency shift of the isolated HB donor with respect to water and ammonia. We report a universal trend for estimating the hydrogen bond strength using the vibrational frequencies, 0.43 kcal/mol per square root of a wavenumber, and apply it to diverse intra-molecular hydrogen bonds and multihydrogen bonded complex systems. The new method produces results that are similar to more expensive computational methods and can utilize either experimental or theoretical vibrational frequencies to yield strengths of HBs. The proposed energetic-spectral relationship based on experimental infrared (IR) spectra produced values of ∼6.0 kcal/mol for peptide HBs in α helices and β sheets. It also suggests that the HBs in the A-T nucleotide base pair are stronger than in the C-G base pair. The proposed method shows promise in describing the major energetic driver that determines structure through hydrogen bonding, where previous methods have failed.