A computational study of the hydrogen-bonded complexes FArH⋯OCO and FKrH⋯OCO

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Abstract

Linear hydrogen-bonded complexes of carbon dioxide with the rare-gas compounds HArF and HKrF were found to be stable at the MP2/6-311++G(2d,2p) level of theory. The FArH⋯OCO and FKrH⋯OCO complexes have zero-point energy corrected binding energies of 13 and 8 kJ mol−1, respectively. Large blue shifts of the Rg–H harmonic stretching frequency and red shifts of the F–Rg stretch were obtained for both complexes. The electron density rearrangement on complexation was also examined. A perturbation theory model of frequency shifts was found to be in good agreement with the ab initio results.

Introduction

The experimental preparation of HArF [1] was a major development leading to a renewed interest in the chemistry of rare-gas compounds, especially compounds having the general formula HRgX (Rg represents a rare gas atom and X represents an atom or fragment with a high electron affinity). The bonding in HRgX molecules is characterised mainly by a covalent H–Rg bond and an ionic Rg–X bond and the molecules exhibit (HRg)+X ion-pair character [2], [3], [4].

These rare-gas compounds also form hydrogen-bonded complexes [5], [6], [7] with unusual vibrational characteristics. For example, theoretical and experimental studies on complexes of HRgX molecules with nitrogen revealed large increases in the H–Rg stretching frequency (a blue shift) [6], [7], [8], [9]. These studies indicate that there are two complex geometries (linear and bent), with electrostatic forces making the most important contributions to the binding energy in the linear (hydrogen-bonded) complexes. In the bent complexes (where bonding occurs between the Rg atom and a nitrogen atom), the electrostatic and dispersion forces are comparable [6], [7].

The blue shift in hydrogen-bonded systems is uncommon since most hydrogen bonds (in say A–H⋯B) are characterised by a decrease in the A–H stretching frequency (a red shift) [10] which is thought to arise from (i) the attractive force between the H atom of the proton donor A–H and a region of high electron density on the proton acceptor B (usually lone pairs or π-electrons) and (ii) charge transfer from B to the antibonding σ* orbital of the A–H bond. The net result is an increase in the A–H bond length and a red shift of the A–H stretch. However, the blue shift of the Rg–H vibration in FArH⋯N2[8] and FKrH⋯N2[9] can be rationalized by considering mainly the electrostatic intermolecular interaction.

Ab initio computational methods were employed to determine the stability and properties of FRgH interacting with OCO (which, like N2, also has a negative quadrupole moment, but which is larger in magnitude). Only linear FRgH⋯OCO structures were found. A bent geometry is probably unstable because of the larger repulsive interaction between O and Rg (in the bent form of FRgH⋯OCO) as compared with a similar interaction between N and Rg (in the bent form of FRgH⋯N2), i.e., the interatomic electron–electron repulsion should be larger for the Rg⋯O contact since it has two lone pair electrons compared with N which has only one lone pair.

A perturbation theory model of vibrational frequency shifts [11], [12], [13] was also used to predict the frequency shifts in the FRgH⋯OCO dimers. The theory involves the application of first- and second-order quantum mechanical perturbation theory. The interaction potential energy U of the monomer A–H and the partner B is expanded as a power series in the displacement of the A–H bond from equilibrium and treated, along with the cubic anharmonicity, as a perturbation to the harmonic oscillator. The frequency shift is related to the first and second derivatives of U (i.e., U′ and U″) averaged over the positions and orientations of B. The details of this model and its application to systems in which A–H  FRgH have been outlined in detail elsewhere (see, for example [11], [12], [13], [14], [15]).

In the present work, we consider the frequency shifts of the Rg–H (and F–Rg) stretching modes by treating the FRgH molecule as a pseudo-diatomic species, with the F–Rg bond being fixed at its equilibrium length when the Rg–H bond length is allowed to vary, and vice versa. The separation of the Rg atom and the OCO molecule is also fixed at its equilibrium value in FRgH⋯OCO. Only the equilibrium configuration is considered (i.e., no configurational averaging of the frequency shift). The perturbative model approximates the complexation-induced vibrational frequency shift, Δω, for the fundamental absorption band of a particular vibrational mode of an oscillator as [13]hcΔω=(Be/ωe)(U-3aU),where Be is the rotational constant h/(8π2mcre2), m the reduced mass, e the frequency of the harmonic oscillator and a is the cubic anharmonic constant. The constants ωe, Be, and a are all determined by ab initio computations, while U′ and U″ are determined numerically by ab initio single-point energy computations on FRgH, OCO and FRgH⋯OCO.

Section snippets

Computational methods

Equilibrium structures, dipole moments, harmonic vibrational frequencies and frequency shifts, and binding energies for FRgH⋯OCO were determined at the MP2/6-311++G(2d,2p) level of theory using the Gaussian 03W suite of programs [16]. The harmonic vibrational frequencies confirm that the linear structures obtained are true minima. Binding energies were computed, with and without correction for the basis set superposition error (BSSE), using the counterpoise correction method of Boys and

Results and discussion

Table 1 shows that in both complexes the H-bonded O–C bond of OCO is extended while the other C–O bond is compressed (relative to the isolated OCO monomer). In both complexes the Rg–H and F–Rg bond lengths are elongated due to the interaction with the carbon dioxide molecule. These structural changes are larger in magnitude for FArH⋯OCO.

The H⋯O internuclear distance is smaller for FArH⋯OCO, which is consistent with the larger binding energy of this dimer (15 kJ mol−1) compared with FKrH⋯OCO (11 kJ 

Acknowledgement

The author wishes to thank Prof. A.D. Buckingham of the University of Cambridge for suggesting CO2 as a possible bonding partner for the HRgF molecules.

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On leave from: Department of Biological and Chemical Sciences, University of the West Indies, Cave Hill Campus, Bridgetown, Barbados.

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