Covalent radius of fluorine
Encyclopedia
The covalent radius of fluorine is a measure of the size of a fluorine
Fluorine
Fluorine is the chemical element with atomic number 9, represented by the symbol F. It is the lightest element of the halogen column of the periodic table and has a single stable isotope, fluorine-19. At standard pressure and temperature, fluorine is a pale yellow gas composed of diatomic...

 atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

; it is approximated at about 60 picometre
Picometre
A picometre is a unit of length in the metric system, equal to one trillionth, i.e. of a metre, which is the current SI base unit of length...

s.

Since fluorine is a relatively small atom with a large electronegativity
Electronegativity
Electronegativity, symbol χ , is a chemical property that describes the tendency of an atom or a functional group to attract electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance that its valence electrons reside from the charged nucleus...

, its covalent radius
Covalent radius
The covalent radius, rcov, is a measure of the size of an atom that forms part of one covalent bond. It is usually measured either in picometres or angstroms , with 1 Å = 100 pm....

 is difficult to evaluate. The covalent radius is defined as half the bond lengths between two neutral atoms of the same kind connected with a single bond. By this definition, the covalent radius of F is 71 pm. However, the F-F bond in F2 is abnormally weak and long. Besides, 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 and the bond lengths calculated from these radii are almost always longer than the experimental values.

Bonds to fluorine have considerable ionic character, a result of its small atomic radius
Atomic radius
The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the nucleus to the boundary of the surrounding cloud of electrons...

 and large electronegativity. Therefore, the bond length of F is influenced by its ionic radius
Ionic radius
Ionic radius, rion, is the radius of an atom's ion. Although neither atoms nor ions have sharp boundaries, it is important to treat them as if they are hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice...

, the size of ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...

s 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, and the radius is larger.

Brockway

The first attempt at trying to find the covalent radius of fluorine was in 1938, by Brockway. Brockway prepared a vapour of F2 molecules by means of the electrolysis of potassium bifluoride
Potassium bifluoride
Potassium bifluoride is the inorganic compound with the formula KHF2. This colourless salt consists of the potassium cation and the bifluoride anion. The salt is used in etchant for glass...

 (KHF2) in a fluorine generator, which was constructed of Monel
Monel
Monel is a trademark of Special Metals Corporation for a series of nickel alloys, primarily composed of nickel and copper, with some iron and other trace elements. Monel was created by David H. Browne, chief metallurgist for International Nickel Co...

 metal. Then, the product was passed over potassium fluoride
Potassium fluoride
Potassium fluoride is the chemical compound with the formula KF. After hydrogen fluoride, KF is the primary source of the fluoride ion for applications in manufacturing and in chemistry. It is an alkali metal halide and occurs naturally as the rare mineral carobbiite...

 so as to remove any hydrogen fluoride
Hydrogen fluoride
Hydrogen fluoride is a chemical compound with the formula HF. This colorless gas is the principal industrial source of fluorine, often in the aqueous form as hydrofluoric acid, and thus is the precursor to many important compounds including pharmaceuticals and polymers . HF is widely used in the...

 (HF) and to condense the product into a liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

. A sample was collected by evaporating the condensed liquid into a Pyrex
Pyrex
Pyrex is a brand name for glassware, introduced by Corning Incorporated in 1915.Originally, Pyrex was made from borosilicate glass. In the 1940s the composition was changed for some products to tempered soda-lime glass, which is the most common form of glass used in glass bakeware in the US and has...

 flask. Finally, using electron diffraction
Electron diffraction
Electron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons at a sample and observing the resulting interference pattern...

, it was determined that the bond length between the two fluorine atoms was about 145 pm. He therefore assumed that the covalent radius of fluorine was half this value, or 73 pm. This value, however, is inaccurate due to the large electronegativity and small radius of fluorine atom.

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.
dAB = rA + rB – C|xA – xB|

of the two atoms, and |xA – xB| is the absolute difference
Absolute difference
The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. It describes the distance on the real line between the points corresponding to x and y...

 in the electronegativities of elements A and B. C is a constant which Shomaker and Stevenson took as 9 pm.)

This equation predicts a bond length which closer to the experimental value. Its major weakness is the use of the covalent radius of fluorine that is known as being too large.

Pauling

In 1960, Pauling proposed an additional effect called "back bonding" to account for the smaller experimental values compared to the theory. His model predicts that F donates electrons into a vacant atomic orbital
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

 in the atom it is bonded to, giving the bonds a certain amount of sigma bond
Sigma bond
In chemistry, sigma bonds are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry groups. In this formal approach, a σ-bond is...

 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
Double bond
A double bond in chemistry is a chemical bond between two chemical elements involving four bonding electrons instead of the usual two. The most common double bond, that between two carbon atoms, can be found in alkenes. Many types of double bonds between two different elements exist, for example in...

 character through (p-p)π or (p-d)π "back bonding". 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
Ligand
In coordination chemistry, a ligand is an ion or molecule that binds to a central metal atom to form a coordination complex. The bonding between metal and ligand generally involves formal donation of one or more of the ligand's electron pairs. The nature of metal-ligand bonding can range from...

 lone pair
Lone pair
In chemistry, a lone pair is a valence electron pair without bonding or sharing with other atoms. They are found in the outermost electron shell of an atom, so lone pairs are a subset of a molecule's valence electrons...

s into X-F orbitals. 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.

Ronald Gillespie

In 1992, Ronald Gillespie
Ronald Gillespie
Ronald James Gillespie, CM , a chemistry professor at McMaster University, specializes in the field of Molecular Geometry in Chemistry. In 2007 he was awarded the Order of Canada....

 and Edward A. Robinson suggested that the value of 71 pm was too large because of the unusual weakness of the F-F bond in F2. Therefore, they proposed using the value of 54 pm for the covalent radius of fluorine. However, there are two variations on this predicted value: if they have either long bonds or short bonds.
  1. An XFn molecule will have a bond length longer than the predicted value whenever there are one or more lone pairs in a filled valence shell. For example, BrF5
    Bromine pentafluoride
    Bromine pentafluoride, BrF5, is an interhalogen compound and a fluoride of bromine. It is a strong fluorination reagent.It melts at −61.30 °C and boils at 40.25 °C. BrF5 finds use in oxygen isotope analysis. Laser ablation of solid silicates in the presence of bromine pentafluoride releases O2 for...

     is a molecule
    Molecule
    A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

     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
    Octet rule
    The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low (The octet rule is a chemical rule of thumb that states that atoms of low (...

     (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. For example, the short bond length of BF3 can be attributed to the delocalization of the fluorine lone pairs.


In 1997, Gillespie et al. found that his original prediction was too low, and that the covalent radius of fluorine is about 60 pm. Using the Gaussian 94 package, they calculated the wave function and electron density
Electron density
Electron density is the measure of the probability of an electron being present at a specific location.In molecules, regions of electron density are usually found around the atom, and its bonds...

 distribution for several fluorine molecules. Contour plots of the electron density distribution were then drawn, which were used to evaluate the bond length of fluorine to other molecules. The authors found that the length of X-F bonds decrease as the product of the charges on A and F increases. Furthermore, the X-F bond length decreases with a decreasing coordination number
Coordination number
In chemistry and crystallography, the coordination number of a central atom in a molecule or crystal is the number of its nearest neighbours. This number is determined somewhat differently for molecules and for crystals....

 n. The number of fluorine atoms that are packed around the central atom is an important factor for calculating the bond length
Bond length
- Explanation :Bond length is related to bond order, when more electrons participate in bond formation the bond will get shorter. Bond length is also inversely related to bond strength and the bond dissociation energy, as a stronger bond will be shorter...

. Also, the smaller the bond angle (The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
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