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Hydrogen bonding and delocalization in the ELF analysis approach
Bernard Silvi1, Henryk Ratajczak2
1Sorbonne Universités, UPMC, Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France. silvi@lct.jussieu.fr.
Insights
Electron density delocalization in proton donor fragments was studied across various hydrogen bond strengths. The study found a correlation between electron density variance and hydrogen bond strength, offering insights into bonding in crystals like ice.
Area of Science:
- Quantum Chemistry
- Materials Science
- Solid-State Physics
Background:
- Understanding electron density delocalization is crucial for characterizing hydrogen bond strength.
- Existing methods for fragment partitioning in hydrogen bonds have limitations.
Purpose of the Study:
- To investigate electron density delocalization in proton donor fragments for a wide range of hydrogen bond strengths.
- To correlate electron density variance with hydrogen bond strength using the Electron Localization Function (ELF) partition.
- To apply the ELF partition method to study hydrogen-bonded crystals.
Main Methods:
- Studied 21 molecular complexes (A-HB) with varying hydrogen bond strengths.
- Defined proton donor and acceptor fragments using the minimum variance principle via ELF partition.
- Compared ELF partition with the Quantum Theory of Atoms in Molecules (QTAIM) framework.
- Applied ELF to analyze electron density in KHF2, KDP, and ice VIII (including pressure-induced phase transitions).
Main Results:
- Electron density variance and charge transfer are correlated with hydrogen bond strength for both ELF and QTAIM.
- The ELF partition method provides a more accurate measure of variance and charge transfer compared to QTAIM.
- Variance scales with the square root of the ELF value at the interaction point, validating its use as an indicator of hydrogen bond strength.
- Analysis of crystals revealed very strong hydrogen bonds in KHF2 and KDP, and medium-weak bonds in ice VIII, which strengthen with pressure leading to a phase transition to ice X.
Conclusions:
- The choice of partition scheme significantly impacts the analysis of proton donor fragments.
- Electron density delocalization, often mislabeled as covalence, plays a key role in hydrogen bonding.
- The ELF partition method offers a robust approach for quantifying hydrogen bond strength and electron density delocalization in molecular complexes and crystals.
Abstract:
Delocalization of the electron density in the proton donor fragment has been studied for 21 complexes, A-HB (A = F, Cl; B = Ne, Ar, CO2, N2, FH, ClH, H2O, PH3, NH3, Cl-, F-, covering the whole range of hydrogen bond strength. The proton donor and proton acceptor fragments are defined by a minimum variance principle achieved by the ELF partition. It is shown that the variance of the proton donor population as well as the charge transfer between the fragments calculated from the ELF partition is always smaller than that evaluated within the QTAIM framework. For both partition schemes, the variance and the charge transfer are correlated with the hydrogen bond strength. It is shown that the variance varies as the square root of the value of the ELF at the hydrogen bond interaction point (i.e. the saddle point at the boundary of the proton donor and proton acceptor moieties)ηvv' providing a numerical proof of the conjecture that the ELF partition satisfies a minimum variance condition and an explanation of the success of the core valence bifurcation index as an indicator of the hydrogen bond strength. The ELF technique has been then applied to the study of hydrogen bonded crystals for which the variance of the fragment population has been estimated from ηvv'. The systems investigated are KHF2, KDP and ice VIII. The results are consistent with very strong hydrogen bonds in the two former crystals and medium-weak bonding in ice. In ice VIII the variance, and therefore the hydrogen bond strength, increases with pressure yielding a phase transition toward ice X in which the hydrogen bond is characterized as very strong. Our study emphasizes the importance of the partition scheme which defines the proton donor fragment and the role of electron density delocalization between the fragments which is, according to us, often improperly termed as covalence.
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