Covalent radius of fluorine
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The covalent radius of fluorine is a measure of the size of a fluorine
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, ...
; it is approximated at about 60 picometres. Since fluorine is a relatively small atom with a large
electronegativity Electronegativity, symbolized as , is the tendency for an atom of a given chemical element to attract shared electrons (or electron density) when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the ...
, its
covalent radius The covalent radius, ''r''cov, is a measure of the size of an atom that forms part of one covalent bond. It is usually measured either in picometres (pm) or angstroms (Å), with 1 Å = 100 pm. In principle, the sum of the two coval ...
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 The atomic radius of a chemical element is a measure of the size of its atom, usually the mean or typical distance from the center of the nucleus to the outermost isolated electron. Since the boundary is not a well-defined physical entity, there ...
and large electronegativity. Therefore, the bond length of F is influenced by its
ionic radius Ionic radius, ''r''ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the catio ...
, the size of
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
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 A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mas ...
to the
electrons The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no ...
is weaker, and the radius is larger.


Brockway

The first attempt at trying to find the covalent radius of fluorine was in 1937, by Brockway. Brockway prepared a vapour of F2 molecules by means of the electrolysis of
potassium bifluoride Potassium bifluoride is the inorganic compound with the formula . This colourless salt consists of the potassium cation () and the bifluoride anion (). The salt is used as an etchant for glass. Sodium bifluoride is related and is also of commercial ...
(KHF2) in a fluorine generator, which was constructed of
Monel Monel is a group of alloys of nickel (from 52 to 67%) and copper, with small amounts of iron, manganese, carbon, and silicon. Monel is not a cupronickel alloy because it has less than 60% copper. Stronger than pure nickel, Monel alloys are res ...
metal. Then, the product was passed over
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 halide and occurs naturally as the rare ...
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 Pyrex (trademarked as ''PYREX'' and ''pyrex'') is a brand introduced by Corning Inc. in 1915 for a line of clear, low-thermal-expansion borosilicate glass used for laboratory glassware and kitchenware. It was later expanded to include kitchenwa ...
flask. Finally, using electron diffraction, 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, :(where ''dAB'' is the predicted bond length or distance between two atoms, ''rA'' and ''rB'' are the covalent radii (in picometers) of the two atoms, and '', xA – xB, '' is the
absolute difference The absolute difference of two real numbers x and 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. It is a special case of the Lp distance for ...
in the electronegativities of elements A and B. ''C'' is a constant which Schomaker 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, Linus Pauling proposed an additional effect called "
back bonding In chemistry, π backbonding, also called π backdonation, is when electrons move from an atomic orbital on one atom to an appropriate symmetry antibonding orbital on a ''π-acceptor ligand''. It is especially common in the organometallic chemi ...
" to account for the smaller experimental values compared to the theory. His model predicts that F donates electrons into a vacant
atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in an ...
in the atom it is bonded to, giving the bonds a certain amount of
sigma bond In chemistry, sigma bonds (σ bonds) are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most simply defined for diatomic molecules using the language and tools of s ...
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 In chemistry, a double bond is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist betwee ...
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 In coordination chemistry, a ligand is an ion or molecule ( functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's elec ...
lone pairs 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 James Gillespie, (August 21, 1924 – February 26, 2021) was a British chemist specializing in the field of molecular geometry, who arrived in Canada after accepting an offer that included his own laboratory with new equipment, which post ...
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. # 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 is a
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
where the experimental bond length is longer than the predicted value of 54 pm. # In molecules in which a central atom does not complete the
octet rule The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rul ...
(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 A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
and
electron density In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...
distribution for several fluorine molecules.
Contour plot A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional grap ...
s 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 In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central io ...
n. The number of fluorine atoms that are packed around the central atom is an important factor for calculating the
bond length In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of ...
. Also, the smaller the
bond angle Bond or bonds may refer to: Common meanings * Bond (finance), a type of debt security * Bail bond, a commercial third-party guarantor of surety bonds in the United States * Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
(

Pekka Pyykkö

Theoretical chemist Pekka Pyykkö estimated that the covalent radius for a fluorine atom to be 64 pm in a single bond, 59 pm and 53 pm in molecules where the bond to the fluorine atom has a double bond and triple bond character, respectively.


References

{{reflist Fluorine Atomic radius