The electrostatic potential near to the oxygen atom in each of the cyclic ethers 2,5-dihydrofuran, oxetane and oxirane has been calculated by using a distributed multipole analysis (DMA) of each molecule. The electrostatic potential energy _{2} axis of the cyclic ether and a vector of length _{min} at the minima are compared with the angles _{0} and _{e} made by the O⋯H bond with the _{2} axes in the cyclic ether⋯HF complexes, as determined by rotational spectroscopy and ab initio calculations at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory, respectively. An electrostatic model of cyclic ether⋯HF complexes in which the DMA of the cyclic ether interacts with a simple extended electric dipole representation of HF is also used to calculate the variation of the potential energy _{HF}(_{min} generated by this model are also compared with _{0} and _{e}. The extent to which the electrostatic potential and the extended electric dipole HF model can be used as probes for the directions of non-bonding electron pairs carried by O in these cyclic ethers is discussed.

The hydrogen bond and the halogen bond are the best-known of non-covalent interactions and have recently been defined by IUPAC Working Parties [

In this article, we shall focus attention on the nucleophilic region of the Lewis base B that accepts the hydrogen atom on hydrogen bond formation, particularly the non-bonding electron pairs (n-pairs) of B. The geometries of simple hydrogen-bonded complexes B⋯HX (where X is a halogen atom, a CN group or C≡CH) isolated in the gas phase at very low pressure have been extensively investigated by microwave and infrared spectroscopy over many years. The systematic variation of B led to a set of simple rules [

The gas-phase equilibrium angular geometry of a complex B⋯HX can be obtained by assuming that:

These rules are electrostatic in origin, a conclusion that was tested by examining the angular dependence of the electrostatic potential in the vicinity of the acceptor atom/centre of B [_{2}O⋯HF) from the O atom in H_{2}O [

A detailed analysis of the rotational spectrum of H_{2}O⋯HF [_{e} = ±46(8)°. An even better match with the experimentally determined function _{HF}(_{0} bond length 0.9256 Å of HF (calculated from its ground-state rotational constant [_{e} = ±55°.

The success of the extended electric dipole moment model of HF in reproducing the experimentally determined function _{2}O⋯HF and for predicting _{e} values for H_{2}S and H_{2}CO [

In the original investigations of the rotational spectra of complexes B⋯HF formed in equilibrium gas mixtures of B and HF [

_{e} made by the O⋯H hydrogen bond with the _{2} symmetry axis of the cyclic ether. The values were _{e} = 48.2°, 57.4° and 73.1°, respectively for 2,5-dihydrofuran⋯HF, oxetane⋯HF and oxirane⋯HF. The corresponding experimental (zero-point) values _{0}, determined from rotational spectroscopy by assuming unperturbed component geometries with the O⋯H–F nuclei collinear, were 48.48(1)° [_{0}. Clearly, there is good agreement between theory and experiment for this important quantity. Thus, if the corollary to the rules is valid, both the ab initio calculated angles 2_{e} and the experimental angles 2_{0} between the two n-pairs do appear to increase along the series. The angular deviation

As stated earlier, the rules for predicting angular geometries are electrostatic in origin in the sense that unperturbed electric charge distributions are assumed to define the angular geometry assumed by the interacting pair of molecules, i.e., the effects of polarisation of one molecule by the other and of charge transfer are assumed negligible. In fact, recently there has been considerable controversy and much discussion about the role of polarization [

The purpose of this article is to examine the electrostatic potential _{min} between the minima of these potential functions agree (1) with the values of 2_{0} from the microwave spectroscopic investigations of the cyclic ether⋯HF complexes and (2) with the values of 2_{e} obtained for the same set of complexes from ab initio calculations conducted at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory? The latter comparison is probably more suitable because both quantities refer to the equilibrium properties of the complex, while the values 2_{0} obtained from the rotational spectra are rather complicated averages over the large amplitude zero-point motions. The ab initio calculations also give more accurate values of the angular deviation

Geometries of isolated molecules and the interacting complexes were optimised using the explicitly correlated CCSD(T)-F12c method [_{0}^{−1} throughout. Full details of the optimized geometries are available as

Distributed multipole analyses [^{−3} but also with considerably larger isodensities.

The electrostatic potential energy _{min} = ~±50° and ~±60° for oxetane and oxirane, respectively, and both show substantial energy barriers to a planar configuration at O. These results are consistent with the various experimental investigations of the complexes via their rotational spectra. Thus, oxirane⋯HF and oxetane⋯HF both have a permanently pyramidal configuration at O in the zero-point energy state, with no evidence of inversion, and have angles _{0} = 72.0(4)° and 54.50°, respectively [

Although the experimental hydrogen bond length is also _{min} = ~±50°. Similar behaviour was reported in Ref. [_{2}O molecule, that is, when _{2}O⋯HF, both the height of the potential barrier at ^{−1}) and _{min} = ~±30° were underestimates when compared with the experimental potential energy function governing inversion of the configuration at O in H_{2}O⋯HF [^{−1} to the planar molecule and _{min} = ±46°. In a recent detailed study, Alonso and co-workers [^{−1} and _{min} = ±46°. An ab initio calculation of the inversion potential at the MP2/6-311+G(d,p) level confirmed their experimental result. Thus, the electrostatic potential

The electrostatic potential at any point near to a n-pair is determined only in part by the n-pair in question. It also has contributions from any partial positive charge on the protons, carbon atoms, etc. of the water or cyclic ether molecule and from the negative charge of the other n-pair. This partial positive charge acts to decrease the potential of the unit point positive charge for a given angle and becomes more effective as _{min} to zero. Hence, _{min} will always be less than that expected for an isolated nonbonding pair. This effect is more serious in H_{2}O and 2,5-dihydrofuran than in oxirane and oxetane because the angle between the nonbonding pairs is smaller in the first two.

Another popular approach to electrostatic potential is the molecular electrostatic surface potential (or MESP). This is the electrostatic potential at the isosurface for which the electron density has a constant value. It is conventional to use an electron density of 0.001 ^{−3} to define the isosurface, which then contains 99.3% of the electron density. ^{−3} for the three cyclic ethers under discussion, each viewed along the _{2} axis with O nearest the viewer. The calculations were carried out with the SPARTAN package [^{−1} and delineates the most nucleophilic region of the molecule. A blue colour corresponds to an electrostatic potential of +200 kJ mol^{−1} and is the most electrophilic region (not visible). There is clearly a significant nucleophilic region on the isosurface near O in each molecule. This corresponds to the two n-pairs carried by O, but we note that, at the resolution available in ^{−3} is chosen the electrophilic regions (blue) are exaggerated but it is then possible to resolve the two n-pairs, as can be seen in ^{−3} (95.6% of the electron density), while for 2,5-dihydrofuran, which has the smallest inter n- pair angle, the resolution is only just perceptible even at 0.055 ^{−3} (84.3%). Oxetane is an intermediate case, requiring 0.04 ^{−3} (87.6%). These observations about the MESPs agree with the conclusions suggested by the

Another way to test the explanation given earlier is to remove the multipoles from all atoms but O in 2,5-dihydrofuran. Then, there can be no swamping effect on the oxygen n-pairs arising from the charge distributions associated with H and C atoms in the rest of the molecule. The result of so doing is shown in _{min} = 54°, precisely half the tetrahedral angle, as expected from the COC ring angle of ~108° of 2,5-dihydrofuran. Thus, the potential energy curves in

As mentioned in the Introduction, the success of a simple extended electric dipole model of HF in predicting the angular geometries of H_{2}O⋯HF and H_{2}S⋯HF gave rise to a proposal that the HF molecules acts as a probe of n-pairs carried by Lewis bases, assuming the hydrogen bond is weak enough that the component molecules are not significantly perturbed by the interaction. We now test this proposal for the three Lewis bases 2,5-dihydrofuran, oxetane and oxirane.

The model used for the charge distribution of the HF molecule consists of a pair of charges 0.540 _{0} bond length (0.9256 Å) of HF. This model is the zeroth-order version of the DMA of hydrogen fluoride given in ref. [_{2} axis of the cyclic ether, so that the atoms lie in the order O⋯H–F and are collinear. The distance of H from O is _{H}(_{F}(_{HF}(_{H}(_{F}(

The plots of _{HF}(^{−1} at 1.5 and 1.6 Å, respectively. It was noted earlier that the potential energy function determined by Alonso and co-workers [^{−1} and minima at _{min}, for reasons discussed in _{min} increases and achieves the tetrahedral angle of ~110° when

The curves resulting when _{HF}(^{−1}. Also _{min} changes only slowly with ^{−1} and _{min} increases from 65° to 69° as

_{min} from the electrostatic potential energy functions _{HF}(_{0} (from rotational spectroscopy) and (b) the equilibrium counterparts _{e} (from ab initio calculations at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory). For convenience, the _{min} are presented in two versions: one is calculated for the experimental zero-point distance _{0}(O⋯H) and the other at the ab initio equilibrium distance _{e}(O⋯H). This is because the equilibrium distance is systematically shorter by ~0.04 Å. Also included in

As expected from the preceding discussion of 2,5-dihydrofuran, the potential energy _{HF}(_{min} at the minimum (and indeed the barrier at the planar configuration at O), for reasons discussed earlier. When the Lewis base is oxetane, _{min} is found to be in reasonable agreement with the experimental and ab initio values of this quantity. For oxirane, _{min} from the extended electric dipole model of HF appears to be a slight underestimate of both the zero-point and equilibrium values of _{min} as the OCO ring angle decreases from ~108°, through ~90° to ~60° on replacing 2,5-dihydrofuran, by oxetane and then oxirane, and is qualitatively the order expected.

The electrostatic potential energy _{2} in each molecule). _{min} at the minima are smaller than those _{0} and _{e} found by experiment and by ab initio calculations, respectively, for these complexes. Reasons why _{min} are underestimates and why the underestimates are more serious the smaller is the angle between the n-pairs carried by the O atom are presented.

A better locator of the directions of the n-pairs carried by O atoms of the cyclic ethers is the electrostatic potential energy _{HF}(_{min} when using this model are in reasonable agreement with values from experiment and ab initio calculations and allow the conclusion that the corollary to the rules, namely that the HF molecule can be taken as a probe of n-pair directions, holds at least to a reasonable approximation. Thus, the angles between the n-pairs are in the order 2,5-dihydrofuran < oxetane < oxirane, a result consistent with the known increase in the ring angle OCO from ~60° in oxirane, through ~90° in oxetane to ~108° in 2,5-dihydrofuran.

The following are available online at

J. Grant Hill and Anthony C. Legon conceived and carried out the calculations. J. Grant Hill and Anthony C. Legon analyzed the data and shared in the writing of the paper.

The authors declare no conflict of interest.

_{2}O⋯HF determined from its microwave rotational spectrum

^{35}Cl and H

^{37}Cl absorption bands

_{2})

_{2}O⋯HF, by infrared and microwave spectroscopy

_{2})

_{3}O⋯HF formed between oxetane and hydrogen fluoride: Hydrogen bonding as a probe for lone pairs

_{0},

_{s}, and

_{m}structures of ethylene oxide

_{2})

_{2}O⋯HF

Variation of the electrostatic potential _{2}O. The angle _{2} axis of the molecule.

Variation of the electrostatic potential energy _{HF}(_{2} axis of the H_{2}O molecule. HF is treated as an extended electric dipole (see text for details). _{2}O. The O⋯H–F nuclei are assumed collinear in the model.

The cyclic ethers 2,5-dihydrofuran, oxetane and oxirane. The n-pairs on O in oxirane are drawn in the exaggerated form often used by chemists.

Equilibrium geometries of complexes of 2,5-dihydrofuran, oxetane and oxirane with HF from calculations at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory. The equilibrium angle

Variation of the electrostatic potential

Variation of the electrostatic potential

Molecular electrostatic potential at the 0.001 ^{−3} isodensity surfaces of (

Molecular electrostatic potential surfaces at the isodensities 0.010 ^{−3}, 0.040 ^{−3} and 0.055 ^{−3} in (

Variation of the electrostatic potential

The electrostatic potential energy _{HF}(

The electrostatic potential energy _{HF}(

The electrostatic potential energy _{HF}(

Comparison of properties of cyclic ether⋯HF complexes from ab initio calculations, from rotational spectroscopy, and from an electrostatic model in which HF is treated as an extended electric dipole (see text for discussion of how _{HF}(

Property | 2,5-Dihydrofuran⋯HF | Oxetane⋯HF | Oxirane⋯HF |
---|---|---|---|

_{e}(O⋯H)/Å |
1.631 ^{a} |
1.622 ^{a} |
1.663 ^{a} |

_{0}(O⋯H)/Å |
1.674 ^{b} |
1.660 ^{c} |
1.701 ^{d} |

_{e}/° |
48.24 ^{a} |
57.36 ^{a} |
73.08 ^{a} |

_{e}/° ^{e} |
6.05 | 9.26 | 13.20 |

_{0}/° |
46.3 ^{b} |
57.9 ^{c} |
72.0 ^{d} |

_{min}(at _{e}) ^{f}/° |
~14 | 62.0 | 66.0 |

_{min}(at _{0}) ^{g}/° |
~0 | 61.0 | 65.5 |

^{a} Equilibrium values, calculated ab initio at the CCSD(T)-F12c/cc-pVTZ-F12 level of theory. ^{b} Ref. [^{c} Ref. [^{d} Ref. [^{e} _{e} is the equilibrium value of the angular deviation of the O⋯H–F nuclei from collinearity from the ab initio calculations. ^{f} Value of angle _{HF}(^{g} Value of angle _{HF}(