Electronegativity

"Electronegative" redirects here. For the Nightfall EP, seeElectronegative (EP).

Electrostatic potential map of a water molecule, where the oxygen atom has a more negative charge (red) than the positive (blue) hydrogen atoms

Electronegativity,symbolized asχ,is the tendency for anatomof a givenchemical elementto attract sharedelectrons(orelectron density) when forming achemical bond.An atom's electronegativity is affected by both itsatomic numberand the distance at which itsvalence electronsreside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate thebond energy,and the sign and magnitude of a bond'schemical polarity,which characterizes a bond along the continuous scale fromcovalenttoionic bonding.The loosely defined termelectropositivityis the opposite of electronegativity: it characterizes an element's tendency to donate valence electrons.

On the most basic level, electronegativity is determined by factors like thenuclear charge(the moreprotonsan atom has, the more "pull" it will have on electrons) and the number and location of other electrons in theatomic shells(the more electrons an atom has, the farther from thenucleusthe valence electrons will be, and as a result, the less positive charge they will experience—both because of their increased distance from the nucleus and because the other electrons in the lower energy coreorbitalswill act toshieldthe valence electrons from the positively charged nucleus).

The term "electronegativity" was introduced byJöns Jacob Berzeliusin 1811, though the concept was known before that and was studied by many chemists includingAvogadro. In spite of its long history, an accurate scale of electronegativity was not developed until 1932, whenLinus Paulingproposed an electronegativity scale which depends on bond energies, as a development ofvalence bond theory.It has been shown to correlate with a number of other chemical properties. Electronegativity cannot be directly measured and must be calculated from other atomic or molecular properties. Several methods of calculation have been proposed, and although there may be small differences in the numerical values of the electronegativity, all methods show the sameperiodic trendsbetweenelements.

The most commonly used method of calculation is that originally proposed by Linus Pauling. This gives adimensionless quantity,commonly referred to as thePauling scale(χ_r), on a relative scale running from 0.79 to 3.98 (hydrogen= 2.20). When other methods of calculation are used, it is conventional (although not obligatory) to quote the results on a scale that covers the same range of numerical values: this is known as an electronegativity inPauling units.

As it is usually calculated, electronegativity is not a property of an atom alone, but rather a property of an atom in amolecule.Even so, the electronegativity of an atom is strongly correlated with thefirst ionization energy.The electronegativity is slightly negatively correlated (for smaller electronegativity values) and rather strongly positively correlated (for most and larger electronegativity values) with theelectron affinity.It is to be expected that the electronegativity of an element will vary with its chemical environment,but it is usually considered to be atransferable property,that is to say that similar values will be valid in a variety of situations.

Caesiumis the least electronegative element (0.79);fluorineis the most (3.98).

Methods of calculation

Pauling electronegativity

Paulingfirst proposedthe concept of electronegativity in 1932 to explain why thecovalent bondbetween two different atoms (A–B) is stronger than the average of the A–A and the B–B bonds. According tovalence bond theory,of which Pauling was a notable proponent, this "additional stabilization" of theheteronuclearbond is due to the contribution ofioniccanonical formsto the bonding.

The difference in electronegativity between atoms A and B is given by: $$|\chi _{\rm {A}}-\chi _{\rm {B}}|=({\rm {eV}})^{-1/2}{\sqrt {E_{\rm {d}}({\rm {AB}})-{\frac {E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})}{2}}}}$$ where thedissociation energies,E_d,of the A–B, A–A and B–B bonds are expressed inelectronvolts,the factor (eV)^−1⁄2being included to ensure a dimensionless result. Hence, the difference in Pauling electronegativity between hydrogen andbromineis 0.73 (dissociation energies: H–Br, 3.79 eV; H–H, 4.52 eV; Br–Br 2.00 eV)

As only differences in electronegativity are defined, it is necessary to choose an arbitrary reference point in order to construct a scale. Hydrogen was chosen as the reference, as it forms covalent bonds with a large variety of elements: its electronegativity was fixed firstat 2.1, later revisedto 2.20. It is also necessary to decide which of the two elements is the more electronegative (equivalent to choosing one of the two possible signs for the square root). This is usually done using "chemical intuition": in the above example,hydrogen bromidedissolves in water to form H⁺and Br⁻ions, so it may be assumed that bromine is more electronegative than hydrogen. However, in principle, since the same electronegativities should be obtained for any two bonding compounds, the data are in fact overdetermined, and the signs are unique once a reference point has been fixed (usually, for H or F).

To calculate Pauling electronegativity for an element, it is necessary to have data on the dissociation energies of at least two types of covalent bonds formed by that element. A. L. Allred updated Pauling's original values in 1961 to take account of the greater availability of thermodynamic data,and it is these "revised Pauling" values of the electronegativity that are most often used.

The essential point of Pauling electronegativity is that there is an underlying, quite accurate, semi-empirical formula for dissociation energies, namely: $$E_{\rm {d}}({\rm {AB}})={\frac {E_{\rm {d}}({\rm {AA}})+E_{\rm {d}}({\rm {BB}})}{2}}+(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}$$ or sometimes, a more accurate fit $$E_{\rm {d}}({\rm {AB}})={\sqrt {E_{\rm {d}}({\rm {AA}})E_{\rm {d}}({\rm {BB}})}}+1.3(\chi _{\rm {A}}-\chi _{\rm {B}})^{2}{\rm {eV}}$$

These are approximate equations but they hold with good accuracy. Pauling obtained the first equation by noting that a bond can be approximately represented as a quantum mechanical superposition of a covalent bond and two ionic bond-states. The covalent energy of a bond is approximate, by quantum mechanical calculations, thegeometric meanof the two energies of covalent bonds of the same molecules, and there is additional energy that comes from ionic factors, i.e. polar character of the bond.

The geometric mean is approximately equal to thearithmetic mean—which is applied in the first formula above—when the energies are of a similar value, e.g., except for the highly electropositive elements, where there is a larger difference of two dissociation energies; the geometric mean is more accurate and almost always gives positive excess energy, due to ionic bonding. The square root of this excess energy, Pauling notes, is approximately additive, and hence one can introduce the electronegativity. Thus, it is these semi-empirical formulas for bond energy that underlie the concept of Pauling electronegativity.

The formulas are approximate, but this rough approximation is in fact relatively good and gives the right intuition, with the notion of the polarity of the bond and some theoretical grounding in quantum mechanics. The electronegativities are then determined to best fit the data.

In more complex compounds, there is an additional error since electronegativity depends on the molecular environment of an atom. Also, the energy estimate can be only used for single, not for multiple bonds. The enthalpy of formation of a molecule containing only single bonds can subsequently be estimated based on an electronegativity table, and it depends on the constituents and the sum of squares of differences of electronegativities of all pairs of bonded atoms. Such a formula for estimating energy typically has a relative error on the order of 10% but can be used to get a rough qualitative idea and understanding of a molecule.

Periodic tableofelectronegativity by Pauling scale

→Atomic radiusdecreases →Ionization energyincreases → Electronegativity increases →

	1	2		3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Group→
↓Period
1	H 2.20																		He
2	Li 0.98	Be 1.57												B 2.04	C 2.55	N 3.04	O 3.44	F 3.98	Ne
3	Na 0.93	Mg 1.31												Al 1.61	Si 1.90	P 2.19	S 2.58	Cl 3.16	Ar
4	K 0.82	Ca 1.00		Sc 1.36	Ti 1.54	V 1.63	Cr 1.66	Mn 1.55	Fe 1.83	Co 1.88	Ni 1.91	Cu 1.90	Zn 1.65	Ga 1.81	Ge 2.01	As 2.18	Se 2.55	Br 2.96	Kr 3.00
5	Rb 0.82	Sr 0.95		Y 1.22	Zr 1.33	Nb 1.6	Mo 2.16	Tc 1.9	Ru 2.2	Rh 2.28	Pd 2.20	Ag 1.93	Cd 1.69	In 1.78	Sn 1.96	Sb 2.05	Te 2.1	I 2.66	Xe 2.60
6	Cs 0.79	Ba 0.89		Lu 1.27	Hf 1.3	Ta 1.5	W 2.36	Re 1.9	Os 2.2	Ir 2.20	Pt 2.28	Au 2.54	Hg 2.00	Tl 1.62	Pb 1.87	Bi 2.02	Po 2.0	At 2.2	Rn 2.2
7	Fr >0.79	Ra 0.9		Lr 1.3	Rf	Db	Sg	Bh	Hs	Mt	Ds	Rg	Cn	Nh	Fl	Mc	Lv	Ts	Og
				La 1.1	Ce 1.12	Pr 1.13	Nd 1.14	Pm –	Sm 1.17	Eu –	Gd 1.2	Tb 1.1	Dy 1.22	Ho 1.23	Er 1.24	Tm 1.25	Yb –
				Ac 1.1	Th 1.3	Pa 1.5	U 1.38	Np 1.36	Pu 1.28	Am 1.13	Cm 1.28	Bk 1.3	Cf 1.3	Es 1.3	Fm 1.3	Md 1.3	No 1.3

See also:Electronegativities of the elements (data page)
There are no reliable sources for Pm, Eu and Yb other than the range of 1.1–1.2; see Pauling, Linus (1960).The Nature of the Chemical Bond.3rd ed., Cornell University Press, p. 93.

Mulliken electronegativity

The correlation between Mulliken electronegativities (x-axis, in kJ/mol) and Pauling electronegativities (y-axis).

Robert S. Mullikenproposed that thearithmetic meanof the firstionization energy(E_i) and theelectron affinity(E_ea) should be a measure of the tendency of an atom to attract electrons: $$\chi ={\frac {E_{\rm {i}}+E_{\rm {ea}}}{2}}$$

As this definition is not dependent on an arbitrary relative scale, it has also been termedabsolute electronegativity,with the units ofkilojoules per moleorelectronvolts.However, it is more usual to use a linear transformation to transform these absolute values into values that resemble the more familiar Pauling values. For ionization energies and electron affinities in electronvolts, $$\chi =0.187(E_{\rm {i}}+E_{\rm {ea}})+0.17\,$$ and for energies in kilojoules per mole, $$\chi =(1.97\times 10^{-3})(E_{\rm {i}}+E_{\rm {ea}})+0.19.$$

The Mulliken electronegativity can only be calculated for an element whose electron affinity is known.Measured values are availablefor 72 elements, while approximate values have beenestimated or calculatedfor the remaining elements.

The Mulliken electronegativity of an atom is sometimes said to be the negative of thechemical potential.By inserting the energetic definitions of the ionization potential and electron affinity into the Mulliken electronegativity, it is possible to show that the Mulliken chemical potential is a finite difference approximation of the electronic energy with respect to the number of electrons., i.e., $$\mu ({\rm {Mulliken)=-\chi ({\rm {Mulliken)={}-{\frac {E_{\rm {i}}+E_{\rm {ea}}}{2}}}}}}$$

Allred–Rochow electronegativity

The correlation between Allred–Rochow electronegativities (x-axis, in Å⁻²) and Pauling electronegativities (y-axis).

A. Louis AllredandEugene G. Rochowconsideredthat electronegativity should be related to the charge experienced by an electron on the "surface" of an atom: The higher the charge per unit area of atomic surface the greater the tendency of that atom to attract electrons. Theeffective nuclear charge,Z_eff,experienced byvalence electronscan be estimated usingSlater's rules,while the surface area of an atom in a molecule can be taken to be proportional to the square of thecovalent radius,r_cov.Whenr_covis expressed inpicometres, $$\chi =3590{{Z_{\rm {eff}}} \over {r_{\rm {cov}}^{2}}}+0.744$$

Sanderson electronegativity equalization

The correlation between Sanderson electronegativities (x-axis, arbitrary units) and Pauling electronegativities (y-axis).

R.T. Sandersonhas also noted the relationship between Mulliken electronegativity and atomic size, and has proposed a method of calculation based on the reciprocal of the atomic volume.With a knowledge of bond lengths, Sanderson's model allows the estimation of bond energies in a wide range of compounds.Sanderson's model has also been used to calculate molecular geometry,s-electron energy,NMRspin-spin coupling constants and other parameters for organic compounds.This work underlies the concept ofelectronegativity equalization,which suggests that electrons distribute themselves around a molecule to minimize or to equalize the Mulliken electronegativity.This behavior is analogous to the equalization of chemical potential in macroscopic thermodynamics.

Allen electronegativity

The correlation between Allen electronegativities (x-axis, in kJ/mol) and Pauling electronegativities (y-axis).

Perhaps the simplest definition of electronegativity is that of Leland C. Allen, who has proposed that it is related to the average energy of thevalence electronsin a free atom,

$$\chi ={n_{\rm {s}}\varepsilon _{\rm {s}}+n_{\rm {p}}\varepsilon _{\rm {p}} \over n_{\rm {s}}+n_{\rm {p}}}$$

whereε_s,pare the one-electron energies of s- and p-electrons in the free atom andn_s,pare the number of s- and p-electrons in the valence shell. It is usual to apply a scaling factor, 1.75×10⁻³for energies expressed in kilojoules per mole or 0.169 for energies measured in electronvolts, to give values that are numerically similar to Pauling electronegativities.

The one-electron energies can be determined directly fromspectroscopic data,and so electronegativities calculated by this method are sometimes referred to asspectroscopic electronegativities.The necessary data are available for almost all elements, and this method allows the estimation of electronegativities for elements that cannot be treated by the other methods, e.g.francium,which has an Allen electronegativity of 0.67.However, it is not clear what should be considered to be valence electrons for the d- and f-block elements, which leads to an ambiguity for their electronegativities calculated by the Allen method.

On this scale,neonhas the highest electronegativity of all elements, followed byfluorine,helium,andoxygen.

Electronegativity using the Allen scale
Group→	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
↓Period
1	H 2.300																	He 4.160
2	Li 0.912	Be 1.576											B 2.051	C 2.544	N 3.066	O 3.610	F 4.193	Ne 4.787
3	Na 0.869	Mg 1.293											Al 1.613	Si 1.916	P 2.253	S 2.589	Cl 2.869	Ar 3.242
4	K 0.734	Ca 1.034	Sc 1.19	Ti 1.38	V 1.53	Cr 1.65	Mn 1.75	Fe 1.80	Co 1.84	Ni 1.88	Cu 1.85	Zn 1.588	Ga 1.756	Ge 1.994	As 2.211	Se 2.424	Br 2.685	Kr 2.966
5	Rb 0.706	Sr 0.963	Y 1.12	Zr 1.32	Nb 1.41	Mo 1.47	Tc 1.51	Ru 1.54	Rh 1.56	Pd 1.58	Ag 1.87	Cd 1.521	In 1.656	Sn 1.824	Sb 1.984	Te 2.158	I 2.359	Xe 2.582
6	Cs 0.659	Ba 0.881	Lu 1.09	Hf 1.16	Ta 1.34	W 1.47	Re 1.60	Os 1.65	Ir 1.68	Pt 1.72	Au 1.92	Hg 1.765	Tl 1.789	Pb 1.854	Bi 2.01	Po 2.19	At 2.39	Rn 2.60
7	Fr 0.67	Ra 0.89
See also:Electronegativities of the elements (data page)

Correlation of electronegativity with other properties

The variation of the isomer shift (y-axis, in mm/s) of [SnX₆]²⁻anions, as measured by¹¹⁹SnMössbauer spectroscopy,against the sum of the Pauling electronegativities of the halide substituents (x-axis).

The wide variety of methods of calculation of electronegativities, which all give results that correlate well with one another, is one indication of the number of chemical properties that might be affected by electronegativity. The most obvious application of electronegativities is in the discussion ofbond polarity,for which the concept was introduced by Pauling. In general, the greater the difference in electronegativity between two atoms the more polar the bond that will be formed between them, with the atom having the higher electronegativity being at the negative end of the dipole. Pauling proposed an equation to relate the "ionic character" of a bond to the difference in electronegativity of the two atoms,although this has fallen somewhat into disuse.

Several correlations have been shown betweeninfrared stretching frequenciesof certain bonds and the electronegativities of the atoms involved:however, this is not surprising as such stretching frequencies depend in part on bond strength, which enters into the calculation of Pauling electronegativities. More convincing are the correlations between electronegativity and chemical shifts inNMR spectroscopyor isomer shifts inMössbauer spectroscopy(see figure). Both these measurements depend on the s-electron density at the nucleus, and so are a good indication that the different measures of electronegativity really are describing "the ability of an atom in a molecule to attract electrons to itself".

Trends in electronegativity

Periodic trends

The variation of Pauling electronegativity (y-axis) as one descends the main groups of the periodic table from the second period to the sixth period

In general, electronegativity increases on passing from left to right along a period and decreases on descending a group. Hence,fluorineis the most electronegative of the elements (not countingnoble gases), whereascaesiumis the least electronegative, at least of those elements for which substantial data is available.This would lead one to believe thatcaesium fluorideis thecompoundwhose bonding features the most ionic character.

There are some exceptions to this general rule.Galliumandgermaniumhave higher electronegativities thanaluminiumandsilicon,respectively, because of thed-block contraction.Elements of thefourth periodimmediately after the first row of the transition metals have unusually small atomic radii because the 3d-electrons are not effective at shielding the increased nuclear charge, and smaller atomic size correlates with higher electronegativity (seeAllred-Rochow electronegativityandSanderson electronegativityabove). The anomalously high electronegativity oflead,in particular when compared tothalliumandbismuth,is an artifact of electronegativity varying with oxidation state: its electronegativity conforms better to trends if it is quoted for the +2 state with a Pauling value of 1.87 instead of the +4 state.

Variation of electronegativity with oxidation number

In inorganic chemistry, it is common to consider a single value of electronegativity to be valid for most "normal" situations. While this approach has the advantage of simplicity, it is clear that the electronegativity of an element isnotan invariable atomic property and, in particular, increases with theoxidation stateof the element.

Allred used the Pauling method to calculate separate electronegativities for different oxidation states of the handful of elements (including tin and lead) for which sufficient data were available.However, for most elements, there are not enough different covalent compounds for which bond dissociation energies are known to make this approach feasible. This is particularly true of the transition elements, where quoted electronegativity values are usually, of necessity, averages over several different oxidation states and where trends in electronegativity are harder to see as a result.

Acid	Formula	Chlorine oxidation state	pKa
Hypochlorous acid	HClO	+1	+7.5
Chlorous acid	HClO2	+3	+2.0
Chloric acid	HClO3	+5	−1.0
Perchloric acid	HClO4	+7	−10

The chemical effects of this increase in electronegativity can be seen both in the structures of oxides and halides and in the acidity of oxides and oxoacids. HenceCrO₃andMn₂O₇areacidic oxideswith lowmelting points,whileCr₂O₃isamphotericandMn₂O₃is a completelybasic oxide.

The effect can also be clearly seen in thedissociation constantspK_aof theoxoacidsofchlorine.The effect is much larger than could be explained by the negative charge being shared among a larger number of oxygen atoms, which would lead to a difference in pK_aof log₁₀(1⁄4) = –0.6 betweenhypochlorous acidandperchloric acid.As the oxidation state of the central chlorine atom increases, more electron density is drawn from the oxygen atoms onto the chlorine, diminishing the partial negative charge of individual oxygen atoms. At the same time, the positive partial charge on the hydrogen increases with a higher oxidation state. This explains the observed increased acidity with an increasing oxidation state in the oxoacids of chlorine.

Electronegativity and hybridization scheme

The electronegativity of an atom changes depending on the hybridization of the orbital employed in bonding. Electrons in s orbitals are held more tightly than electrons in p orbitals. Hence, a bond to an atom that employs an sp^xhybrid orbital for bonding will be more heavily polarized to that atom when the hybrid orbital has more s character. That is, when electronegativities are compared for different hybridization schemes of a given element, the orderχ(sp³) < χ(sp²) < χ(sp)holds (the trend should apply tonon-integer hybridization indicesas well). While this holds true in principle for any main-group element, values for the hybridization-specific electronegativity are most frequently cited for carbon. In organic chemistry, these electronegativities are frequently invoked to predict or rationalize bond polarities in organic compounds containing double and triple bonds to carbon.

Hybridization	χ(Pauling)
C(sp3)	2.3
C(sp2)	2.6
C(sp)	3.1
'generic' C	2.5

Group electronegativity

In organic chemistry, electronegativity is associated more with different functional groups than with individual atoms. The termsgroup electronegativityandsubstituent electronegativityare used synonymously. However, it is common to distinguish between theinductive effectand theresonance effect,which might be described as σ- and π-electronegativities, respectively. There are a number oflinear free-energy relationshipsthat have been used to quantify these effects, of which theHammett equationis the best known.Kabachnik parametersare group electronegativities for use inorganophosphorus chemistry.

Electropositivity

Electropositivityis a measure of an element's ability to donateelectrons,and therefore formpositiveions;thus, it is antipode to electronegativity.

Mainly, this is an attribute ofmetals,meaning that, in general, the greater the metallic character of anelementthe greater the electropositivity. Therefore, thealkali metalsare the most electropositive of all. This is because they have a single electron in their outer shell and, as this is relatively far from the nucleus of the atom, it is easily lost; in other words, these metals have lowionization energies.

While electronegativity increases alongperiodsin theperiodic table,and decreases downgroups,electropositivitydecreasesalong periods (from left to right) andincreasesdown groups. This means that elements in the upper right of the periodic table of elements (oxygen, sulfur, chlorine, etc.) will have the greatest electronegativity, and those in the lower-left (rubidium, caesium, and francium) the greatest electropositivity.

See also

• Chemical polarity
• Electron affinity
• Electronegativities of the elements (data page)
• Ionization energy
• Metallic bonding
• Miedema's model
• Orbital hybridization
• Oxidation state
• Periodic table

Bibliography

• Jolly, William L. (1991).Modern Inorganic Chemistry(2nd ed.). New York:McGraw-Hill.pp. 71–76.ISBN978-0-07-112651-9.
• Mullay, J. (1987). "Estimation of atomic and group electronegativities".Electronegativity.Structure and Bonding. Vol. 66. pp. 1–25.doi:10.1007/BFb0029834.ISBN978-3-540-17740-1.

External links

• Media related toElectronegativityat Wikimedia Commons
• WebElements,lists values of electronegativities by a number of different methods of calculation
• Video explaining electronegativity
• Electronegativity Chart,a summary listing of the electronegativity of each element along with an interactive periodic table