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Theoretical study of formation of ion pairs in (NH3·HCl)(H2O)6 and (NH3·HF)(H2O)6

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Abstract

We have performed theoretical studies on sixteen molecular cubes for both (NH3·HCl)(H2O)6 and (NH3·HF)(H2O)6. We use an empirical gauge, based upon the N–H and H–X bond lengths, to categorize the degree to which the cubes are neutral adduct or ion pair in character. On this basis, we describe all sixteen cubes of the former as highly ionized, but only five of the latter as greater than 85% ionic in character. Addition of one or two bridging water molecules to form (NH3·HF)(H2O)7 or (NH3·HF)(H2O)8 raises the percent ionic character to greater than 85% for these systems. The relative energy of the cubes can be categorized based on simple chemical principles. The computed vibrational frequency corresponding to the proton stretch in the N–H–F framework shows the highest degree of redshifting for systems near 50% ion-pair character. Molecular cubes close to neutral adduct or to ion-pair character show less redshifting of this vibrational motion.

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Acknowledgments

We gratefully acknowledge the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. We thank Laura A. Schipper and Stephanie C. Dykhouse for the preliminary work that they performed on this project. Computer hardware was provided by a Major Research Instrumentation Grant from the National Science Foundation, Award No. OCI-0722819.

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Authors and Affiliations

  1. Department of Chemistry and Biochemistry, Calvin College, 1726 Knollcrest Circle SE, Grand Rapids, MI, 49546-4403, USA

    Roger L. DeKock, Benjamin M. Brandsen & John R. Strikwerda

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  1. Roger L. DeKock
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  2. Benjamin M. Brandsen
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  3. John R. Strikwerda
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Correspondence to Roger L. DeKock.

Additional information

Dedicated to Professor Akira Imamura on the occasion of his 77th birthday and published as part of the Imamura Festschrift Issue.

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Appendix

Appendix

1.1 Empirical gauge of hydrogen bond versus ion-pair structure

We define a “reference” bond length and examine the relative difference between the reference bond length and that found in the molecule at hand. We use NH3·HF and NH3·HCl as our example molecules and employ our theoretical results to illustrate the method. Our empirical gauge relates the bond lengths \( {\text{X}}\overset {r_{1} } \longleftrightarrow {\text{H}}\overset {r_{2} } \longleftrightarrow {\text{N}} \) to reference bond lengths. It is the distortion between the actual bond length and a reference bond length for each bond that measures the extent to which the structure is classified as a hydrogen bond adduct versus an ion-pair structure. In the following paragraph, we employ the aug-cc-pVDZ set for our theoretical results. Where experimental work is known, we place that in parentheses directly after the theoretical value.

The free molecule HF has a bond length of 0.926 Å (0.917 Å), and the corresponding value for HCl is 1.295 Å (1.274 Å). These computed values are labeled r 1ref for HF and HCl, respectively. The second reference, r 2ref, is the N–H bond length in NH4 +; we chose its value to be 1.0217 Å, [60].

We then define the following quantities that refer to ion-pair character and hydrogen bond character.

$$ {\text{i-p character}} = \frac{{r_{1} - r_{{1{\text{ref}}}} }}{{r_{{1{\text{ref}}}} }} $$
$$ {\text{h-b character}} = \frac{{r_{2} - r_{{2{\text{ref}}}} }}{{r_{{2{\text{ref}}}} }} $$

The experimental structure of NH3·HF has not been reported, but the theoretical results are r 1 = 0.966 Å and r 2 = 1.662 Å. The corresponding theoretical values for NH3·HCl are r 1 = 1.370 Å and r 2 = 1.668 Å. From these results, we obtain i-p character = 0.043 and h-b character = 0.583 for NH3·HF and obtain i-p character = 0.058 and h-b character = 0.589 for NH3·HCl. In order to convert these into a percent contribution of each structure, we divide by a normalization factor, N, defined as the sum of these quantities.

$$ N = \frac{{r_{1} - r_{{1{\text{ref}}}} }}{{r_{{1{\text{ref}}}} }} + \frac{{r_{2} - r_{{2{\text{ref}}}} }}{{r_{{2{\text{ref}}}} }} $$

The percent ion-pair character and percent hydrogen bond character for a given molecular structure are defined as follows:

$$ \% {\text{i-p}} = \frac{{r_{1} - r_{{1{\text{ref}}}} }}{{Nr_{{1{\text{ref}}}} }} \times 100 $$
$$ \% {\text{h-b}} = \frac{{r_{2} - r_{{2{\text{ref}}}} }}{{Nr_{{2{\text{ref}}}} }} \times 100. $$

We obtain 93% h-b, 7% i-p for NH3·HF and 91% h-b, 9% i-p for NH3·HCl. These results provide a quantitative way to report the amount of distortion that the acid undergoes upon bonding to the base. They confirm that the hydrogen bond is overwhelmingly an adduct pair, and not an ion pair. They show that NH3·HCl is more “ionic” than NH3·HF, which makes qualitative sense, since chemists have many reasons to refer to HF as a weaker acid than HCl.

The empirical formula that we utilize here provides results that allow a quick empirical look at the nature of the molecular adduct. Scheiner [1] provided an alternative view based upon a parameter he called ρ defined as ρ = Δr(XH) − Δr(NH).

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DeKock, R.L., Brandsen, B.M. & Strikwerda, J.R. Theoretical study of formation of ion pairs in (NH3·HCl)(H2O)6 and (NH3·HF)(H2O)6 . Theor Chem Acc 130, 871–881 (2011). https://doi.org/10.1007/s00214-011-1032-7

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