Covalent radius of fluorine

The covalent radius of fluorine is a measure of the size of a fluorine atom, which is approximated at about 60 pm. However, the covalent radius of fluorine is a difficult value to measure for several reasons.

Since fluorine is a relatively small atom with a large electronegativity, it is difficult to find its covalent radius. The covalent radius of an atom is defined as half the distance between the bond lengths of two atoms of the same kind through a single bond in the neutral molecule (F-F). By the definition above, the covalent radius of F is calculated as 71 picometres (1 picometre = 10⁻¹² metres). However, the F-F bond in F₂ is abnormally weak, which makes the bond length abnormally long, invalidating the value of 71 picometers (pm). In addition, almost all bonds to fluorine are highly polar because of its large electronegativity, so the use of a covalent radius to predict the length of such a bond is inadequate. So the bond lengths calculated from these radii are almost always longer than their experimental values.

The covalent radius of fluorine is difficult to calculate because all bonds to fluorine have considerable ionic character, a result of its small atomic radius and large electronegativity. Therefore, the bond length of F is influenced by its ionic radius, the size of ions in an ionic crystal, which is about 133 pm for fluoride ions. The ionic radius of fluoride is much larger than its covalent radius. When F becomes F⁻, it gains one electron but has the same number of protons, meaning the attraction of the protons to the electrons is weaker, creating a larger radius.

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History of bond length

There have been numerous previous attempts to calculate the covalent bond length of fluorine atoms.

Brockway

The first attempt at trying to find the covalent radius of fluorine was in 1938, by Brockway⁽¹⁾. Brockway prepared a vapor of F₂ molecules by means of the electrolysis of potassium bifluoride (KHF₂) in a fluorine generator, which was constructed of Monel metal. Then, the product was passed over potassium fluoride so as to remove any hydrogen fluoride (HF) and to condense the product into a liquid. A sample was collected by evaporating the condensed liquid into a Pyrex flask. Finally, using electron diffraction, it was determined that the bond length between the two fluorines was about 1.45 angstroms⁽¹⁾. He therefore assumed that the covalent radius of fluorine was half this value, or 73 picometers. This value, however, is inaccurate due to the nature of the fluorine atom (its large electronegativity and small atomic radius).

Schomaker and Stevenson

In 1941, Schomaker and Stevenson proposed an empirical equation to determine the bond length of an atom based on the differences in electronegativities of the two bonded atoms⁽²⁾.

Although the predictions for bond lengths used by this equation have been closer than before, they rarely eliminate the discrepancy. The major weakness of the equation is that it is based on the covalent radius of fluorine that was already determined as being too large.

Pauling

In 1960, Pauling proposed an additional effect called “back bonding” to account for the experimental values being shorter than the equation predicted⁽²⁾. his model predicts that F donates electrons into a vacant atomic orbital in the atom it’s bonded to, giving the bonds a certain amount of sigma bond character. In addition, the fluorine atom also receives a certain amount of pi electron density back from the central atom giving rise to double bond character through (p-p)π or (p-d)π “back bonding.”⁽²⁾ Thus, this model suggests that the observed shortening of the lengths of bonds is due to these double bond characteristics.

Reed and Schleyer

Reed and Schleyer, who were skeptical of Pauling’s proposition, suggested another model in 1990. They determined that there was no significant back-bonding, but instead proposed that there is extra pi bonding, which arose from the donation of ligand lone pairs into X-F orbitals⁽²⁾. Therefore, Reed and Schleyer believed that the observed shortening of bond lengths in fluorine molecules was a direct result of the extra pi bonding originating from the ligand, which brought the atoms closer together.

Discovery of bond length

Ronald Gillespie

First attempt

  In 1992, Ronald Gillespie published a paper which attempted to determine the covalent radius of fluorine⁽³⁾. Gillespie realized that the value of 71 pm was too large because of the unusual weakness of the F-F bond in F₂. Therefore, he proposed a value of 54 pm for the covalent radius of fluorine⁽³⁾. However, there are two variations on this predicted value: if they have either long bonds or short bonds.

1. 1. An XF_n molecule will have a bond length longer than the predicted value whenever there are one or more lone pairs in a filled valence shell⁽³⁾. For example, BrF₅ is a molecule where the experimental bond length is longer than the predicted value of 54 pm.
   2. In molecules in which a central atom does not complete the octet rule (has less than the maximum number of electron pairs), then it gives rise to partial double bonding characteristics and thus, making the bonds shorter than 54 pm⁽³⁾. For example, the short bond length of BF₃ can be attributed to the delocalization of the fluorine lone pairs.

Second attempt

In a second paper, published in 1997, Ronald Gillespie goes back to the question of the covalent radius of fluorine and discovers that his previous analysis resulted in a wrong conclusion. Through more sophisticated analysis, Gillespie discovered that his original prediction was too low, and that the covalent radius of fluorine is about 60 pm⁽²⁾. Using the Gaussian 94 package, Gillespie and his associates were able to calculate the wave function and electron density distribution for several fluorine molecules. Contour plots of the electron density distribution were then drawn, which were used to discover the bond length of fluorine to other molecules⁽²⁾.

Gillespie discovered that the length of X-F bonds decrease as the product of the charges on A and F increases. Furthermore, the length of X-F bonds decreases with a decreasing coordination number n⁽²⁾. The number of fluorine atoms that are packed around the central atom is an important factor for calculating the bond length. Also, the smaller the bond angle ((2). Finally, the most accurate value for the covalent radius of fluorine has been found by plotting the covalent radii against the electronegativity⁽²⁾ (see Figure 1). From this, they discovered that the Schomaker-Stevenson and Pauling assumptions were too high, and their previous guess was too low, thus, resulting in a final value of 60 pm for the covalent bond length of fluorine.

References

1. Brockway, L.O. 1938. The Internuclear Distance in the Fluorine Molecule. Journal of the American Chemical Society, 60, pp.1348-1349.
2. Gillespie, Ronald, and Edward Robinson. 1992 Bond Lengths in Covalent Fluorides. A New Value for the Covalent Radius of Fluorine. Inorganic Chemistry, 31, 1960-1963.
3. Robinson, Edward, Samuel Johnson, Ting-Hua Tang, and Ronald Gillespie. 1997. Reinterpretation of the Lengths of Bonds to Fluorine in Terms of an Almost Ionic Model. Inorganic Chemistry, 36, 3022-3030.