Oxidation State, A Long‐Standing Issue!

Abstract

What is an oxidation state? Oxidation state has defining algorithms but lacks a comprehensive definition. Results of an IUPAC project to find such a definition have recently been published in an extensive Technical Report. A summary in this Essay is illustrated with applications on Lewis, bond-graph, and summary formulas of molecules, ions, or solids, together with the most recent information regarding tricky cases. The oxidation state is the simplest attribute of an element in a compound. It is taught early in the chemistry curriculum as a convenient electron-counting scheme for redox reactions. Its applications range from descriptive chemistry of elements to nomenclature and electrochemistry, or as an independent variable in plots and databases of bonded-atom properties (such as radius, bond-valence parameter, standard reduction potentials, spectral parameters, or spin). The history of the oxidation state goes back about 200 years when it described the stepwise increase in the amount of oxygen bound by elements that form more than one oxide. In his 1835 textbook Unorganische Chemie,1 Wöhler speaks of such an “oxydationsstufe” (an older German spelling for oxidation grade). This expression remains in use for oxidation state in several languages. The equivalent term oxidation number is also common; in English this refers more to redox balancing than to the chemical systematics of an element.2 Under the entry for oxidation number, the IUPAC “Gold Book”3 gives a defining algorithm for the oxidation state of a central atom as the charge it obtains after removal of its ligands along with the shared electron pairs. The entry for oxidation state in Ref. 3 complements this with a set of charge-balance rules and of postulated oxidation states for oxygen and hydrogen with exceptions. Details vary from textbook to textbook. Some list the rules according to decreasing priority to avoid the explicit exceptions; here is an example:4 Atoms in an element have oxidation state 0. The sum of the oxidation states for atoms in a compound is 0. Fluorine in compounds has the oxidation state −1. Alkaline metals in compounds have the oxidation state +1, alkaline-earth metals +2. Hydrogen in compounds has the oxidation state +1. Oxygen in compounds has the oxidation state −2. In recent debates, Steinborn5 and Loock6 advocate Pauling’s7 approach of assigning shared electron pairs to the more electronegative atom. Jensen8 elaborates on some of the points considered by Loock. Smith9 and Parkin10 address the oxidation state in the context of related terms. Calzaferri11 as well as Linford and co-workers12 make suggestions on the oxidation state of organic compounds. Jansen and Wedig13 point out the heuristic nature of the oxidation state and require that “concepts need to be defined as precisely as possible, and these definitions must always be kept in mind during applications”. IUPAC also realized the need to approach a connotative definition of the oxidation state. In 2009, a project was initiated “Toward Comprehensive Definition of Oxidation State”, led by the author of this Essay, and its results have recently been published in an extensive Technical Report.14 We started with a generic definition of oxidation state in terms broad enough to ensure validity. Then we refined those terms to obtain typical values by algorithms tailored for Lewis, summary, and bond-graph formulas. The oxidation state is the atom’s charge after ionic approximation of its bonds. The terms to be clarified are the “atom’s charge”, “its bonds”, and the “ionic approximation”. The atom’s charge is the usual count of valence electrons relative to the free atom. The oxidation state is a quantitative concept that operates on integer values of counted electrons. This may require idealizing visual representations or rounding off numerical results. Approximating all bonds to be ionic may lead to unusual results. If the NN bond in N2O were extrapolated to be ionic, the central nitrogen atom would have an oxidation state of +5 and the terminal one −3. To obtain less extreme values, bonds between atoms of the same element should be divided equally upon ionic approximation. Several criteria were considered for the ionic approximation: 1) Extrapolation of the bond’s polarity; a) from the electronegativity difference, b) from the dipole moment, c) from quantum-chemical calculations of charges. 2) Assignment of electrons according to the atom’s contribution to the molecular orbital (MO). As discussed in Appendix B of Ref. 14, most electronegativity scales depend on the atom’s bonding state, which makes the assignment of the oxidation state a somewhat circular argument. Some scales lead to unusual oxidation states, such as −6 for platinum in PtH42− with Pauling or Mulliken scales. Appendix E of Ref. 14 shows that a Lewis-basic atom with an electronegativity lower than its Lewis-acidic bond partner would lose the often weak and long bond upon ionic approximation of their adduct, thereby yielding an unusual oxidation state. Appendix A of Ref. 14 points out that dipole moments of molecules such as CO and NO, which are oriented with their positive end towards oxygen,15–17 would lead to abnormal oxidation states. Appendix C of Ref. 14 illustrates the variety of calculated quantum-chemical atomic charges. This leaves the atom’s contribution to the bonding MO, the atomic-orbital energy, as the criterion for ionic approximation (Figure 1). The essence of the adopted ionic approximation based on the contribution to the bonding MO. The mixing coefficients cA and cB refer to the atomic-orbital wavefunctions ψA and ψB in an MO-LCAO approach (LCAO=linear combination of atomic orbitals). Figure 1 implies that while AA bonds are divided equally, in an AB compound the atom contributing more to the bonding molecular orbital receives negative charge under ionic approximation of the bond. Ref. 14a emphasizes that the said contribution does not concern the actual origin of the bond’s electrons upon its formation, only their final allegiance. Figure 1 is not an instruction to use the mixing coefficients; it merely illustrates a concept. The same ionic approximation is obtained when the more heuristic orbital energies are considered. Should complicated MO schemes make the above criterion impractical, the ionic approximation can be estimated from electronegativities. Of several scales discussed in Appendix B of Ref. 14, only the Allen electronegativity is truly independent of the oxidation state, as it relates to the average valence-electron energy of the free atom.18–20 Such an ionic approximation is obtained when the bonds implied in Figure 1 are abstracted away (Figure 2). The ionic approximation according to the relative energies of the free-atom valence orbitals, conveniently derived from Allen’s electronegativities. The electronegativity criterion for the ionic approximation carries an exception if the more electronegative atom is reversibly bonded as a Lewis acid (a so called Z-ligand, Appendix E of Ref. 14): Its acceptor orbital is high, and the less-electronegative Lewis-base donor atom retains the electrons because of its larger contribution to the bonding MO. An allegiance criterion by Haaland21 identifies such an adduct: Applied to ionic approximation, one asks where the bonding electrons go when the bond is split thermally. If the split is heterolytic, the ionic approximation follows the electrons; if homolytic, electronegativity applies. Table 1 lists the Allen scale. H 2.300 He 4.16 Li 0.912 Be 1.576 B 2.051 C 2.544 N 3.066 O 3.610 F 4.193 Ne 4.787 Na 0.912 Mg 1.293 Al 1.613 Si 1.916 P 2.253 S 2.589 Cl 2.869 Ar 3.242 K 0.734 Ca 1.034 Ga 1.756 Ge 1.994 As 2.211 Se 2.424 Br 2.685 Kr 2.966 Rb 0.706 Sr 0.963 In 1.656 Sn 1.834 Sb 1.984 Te 2.158 I 2.359 Xe 2.582 Cs 0.659 Ba 0.881 Tl 1.789 Pb 1.854 Bi 2.01 Po 2.19 At 2.39 Rn 2.60 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 1.59 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 1.52 Lu[a] 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 1.76 The octet rule22 concerns the most electronegative atoms in the periodic system. On a sufficiently simple summary formula involving such atoms, it the oxidation states. The algorithm is ionic in Ref. Atoms are according to their decreasing electronegativity all the valence electrons are The atom the oxidation states. are of one element (Figure or with a periodic bonding of compounds of or more elements may with the discussed in Appendix of Ref. Oxidation states in CO and from ionic on a summary formula by valence electrons in according to decreasing algorithms on Lewis formulas that all the valence are to the more negative bond partner by ionic approximation. The atom the oxidation state (Figure As only bonds are divided the bond is only between those pairs of atoms of the same element that the of the the of their ionic approximation: the bond in Figure would not so long as the were kept the bond in an N2O Lewis formula always Oxidation states in obtained by assigning bonds to more electronegative on Lewis formula with all valence-electron pairs An of the exception to the of ionic approximation according to electronegativity is on the of Figure the electronegativity of the Lewis-basic Fe atom the electrons it to bond B is by (Figure the same in with the Fe and Al electronegativities. The weak bonds in these are the of the criterion of in Ref. 14 to of electron allegiance electronegativity such as the one on the of Figure Oxidation states by assigning a bond according to the to the bonding MO. An assignment according to the electronegativity to the of a Lewis-basic atom with electronegativity lower than the Lewis-acidic one the formula on the This algorithm is tailored to bond A bond the periodic of an It is on a formula of the with atom such that a is for of an atom’s bonding carries its bond To obtain the oxidation state, a sum is calculated of the of its bonds by their ionic that atom. Such an bond the atom’s oxidation state. Figure this on the with bond according to the and the The and of the with its bond of bond in obtained from the for the for and the for The bond are with which sum atom to that atom’s oxidation state The An atom with N valence electrons N bonds with atoms of The concerns metals and alkaline-earth The in its the The An electronegative atom with N valence electrons to form but not more than bonds with atoms of or lower As an with valence electrons 3 bonds in the and nitrogen does the same in In molecules, the is by In the concerns in and have all the of a In the and the bond by the octet only in O and F the bond towards and The is not the same as the octet as can be The Lewis formula of N2O can be as which has the on Hydrogen an The An element to electrons in its to lose those that or to in bonds those less than the form is by in the of the periodic the form is to Pt and which in such compounds are called and Oxidation state in and calculated from Lewis formulas of bond In this and are the bond valence and of the atoms and is the between and B is a variable often to for the is a of the number and oxidation state of the for a to a set of such a lists for related to the and from which is calculated for atom and As the oxidation state operates on integer a off is on the obtained bond or on their an atom. We in Figure The bond of its has a and Cl atoms, with W Cl atoms by and as estimated from bond in Ref. of more than one orbital the Cl above and makes its sum the A a and such a Cl atom in a Lewis formula would a charge of by of the W atoms it This can be in the bond in Figure A of the with bonds. of the with bond off to bond-valence which sum atom with the to the oxidation state of that atom The bond-valence approach to bond can also be for An is in Figure of the Cu atoms bonds to atoms, while the Cu atoms bond of the atoms bond to Cu atoms and the only to The oxidation state is as a off of the positive and negative of bond calculated with from bond in Ref. and obtained from in Ref. As the bonds are not to be ionic, only the bonds are the bonds from atom to the in Figure which bond valence of and Cu atom. A off a oxidation state for element in a of the in and the of the bond valence the atoms that the oxidation states upon rounding An of an shows of bonding This extreme Lewis formula emphasizes the of the bond because of the for the more electronegative atom. A bond of is calculated as above from the of As the is not but only the is somewhat to the only in the electronegativity of P and and it is that this bond has a ionic contribution from the and that would on the if As these with the the bond and of this is with as the formula its and the oxidation states to the of the bond the and +5 the atom. makes the as well as in its the bond the criterion is to in this An of an is It as molecules, where elements the (an This information is to obtain their oxidation states by of the bond (Figure Oxidation states obtained by the bond in that the A where the is to is It is the same as on the of Figure that N S while S atom with the which would require of bonds from the N to the S atom. As the bond and in are for are considered The has a with a point and bond of and than a bond of approach to oxidation states is to these weak and a with an summary to which to and for the oxidation states. algorithms the same (Figure on a Lewis formula with electron by the bond of is and by pairs of electrons with S atom one bond to S atom a charge N and charge The is in between these The bond valence calculated with from Ref. with a bond of is than the bond of the Lewis formula but not the by the The calculated sum of the bond valence S atom of the is about of the by the bond in the Lewis Oxidation states on formulas a periodic of a the weak bonds the atoms in the and a Lewis formula of and the with we obtain The electrons in of the S atom as one bond and one S atom in Lewis in this is somewhat electronegativity makes the as as is in bonding with the are with The electron in of would on thereby is the and the oxidation states in are by bond in Figure of with one Ga of the Se atoms are the and the oxidation states from its bond The bond by the is above the the bond valence is calculated from the bond by of formula are that are not bonds are not all the B atoms are the oxidation state can be by on a such as with electrons for The hydrogen atom obtains electrons thereby electrons which that electrons; 3 that charge for the average oxidation state in To oxidation states, are As an has 14 valence-electron pairs of which are in 1 always is in a MO, and the in the form a of which one is in (a Figure Its B atoms are not all The atoms are bonded to hydrogen atoms that the of the bond with a positive an oxidation state of for of these B atoms in and for the The B atom has an oxidation state of from one bond to The bonding and in a we are to make the ionic as in Figure are simple compounds with oxidation states, such as the or Some elements also form the in that it in which Si atoms have bonds and Si atoms bonds to according to the but the compound is the assignment of electrons to one of the bonded atoms has its An of the is an electron or an bonding The is by the (Figure where its for which is in The may be illustrated on In with the does not have such it has of Pt as if were a of electrons the Pt atom. This that some electrons to make and it is this that is by bonds. If these bonds were their would be a and would be of and Pt in As the oxidation state for Ba leaves Pt with which does not with the actual for the in which bond of N and obtained from and an oxidation state for oxidation states are also obtained when is to with and by the such as or where the or rules for the most electronegative element are not If an oxidation state is to redox it is considered for all The applications of oxidation state in chemistry are and one does not always In descriptive the oxidation state out compounds of an in electrochemistry, it the compound or in and of standard Such oxidation states that from those by definition may be here and An of is Its that all its terminal atoms some of the if the and bond are not The bond of is than the bond of in or in but than the bond of in or in the bond is the approximation, Lewis formulas are considered in Figure Oxidation states in by assignment of bonds and by bond on Lewis formulas which the author to bonds to to avoid with a bond bond The formula on the oxidation state the terminal of the in The formula on oxidation states that are for a Lewis of the S it a This is not an as this in an is with standard that the average oxidation state which in and oxidation state. The only to oxidation states for S atoms in would be to the bond as in some the terminal has the central independent of their bond and the of the O and S oxidation state. the for ligands that the oxidation state of the central atom less information from or is Of the the simplest is molecular with molecular of or that only has a bond. to in the free of and atoms, as in a recent by and An with some ions, the atoms of the bonded to while with form a this to the central atom and The in the bonding MO that the while the this by back the MO of The extreme are in Figure of an with a generic atom In the with an the by it from a of in with An of the is obtained from and the also as of bonded hydrogen in the oxidation states of which are in Figure Oxidation states of hydrogen and in obtained by assigning bonds the electronegative partner and by bond The in Figure is by the and the on the are the in the is than in Its bond is a more than for a bond of and this can be to the for the more electronegative hydrogen atom. A by of shows that the bond to about 1.60 for the and also depend on the to that is an such as oxygen or a of to the central the is that is such as or when it is the is The with the of back from the central atom the MO of as by the and by the the atom its electrons back because it is the to this bonding which is with to the bond. Allen also for the oxidation state of all such hydrogen the is in is for the nitrogen oxidation NO, and in bond with or with or the nitrogen of in We the bond-valence of an bond of 1.12 than the in that the for oxygen to the actual bond towards the bond The of The electron Fe is and The of the upon reduction to it is the that is to not A truly are not as The should be for but for The is that the bond and and oxidation states in by a where is the number of valence electrons on the when the is A recent which with in which has an oxidation state of of CO with was not the is but the bond of a bond and quantum-chemical in Ref. an The Lewis-basic N atom of the electron pairs as bonds to the Fe central atom thereby the and the bond The oxidation state of for is in Ref. by the of the by of electrons the with electrons the with Ref. also lists these electrons in an was Figure illustrates the The Lewis formula of the and the oxidation state of by assigning bonds. to of the also as valence concerns involving ligands and central is an At has one and ligands a central Mn atom of oxidation state At the reduction to upon oxidation of the to Lewis formulas for the are in Figure where the is illustrated and oxidation states by have been An central atoms is in Ref. of in The is a for It tricky when the is bonded by the more electronegative atom as a Lewis of the discussed in Ref. is In this adduct, Au the bonding MO so that the this MO together with the of the electrons Au as an oxidation state of for the Au that is typical of with (Figure The Au because the Au the bond its and the is by the electrons of Au in the generic definition also for this oxidation state to the formula for a atom with N valence must also the bonding by the central atom. To the and avoid the above by the the or we by the as in where a bonding Au in the of the oxidation state all atoms is if in redox also the oxidation states and are for compounds with electrons atoms, as by several formulas with in long of bond in Lewis values of oxidation states would be obtained for bonding which does not Ref. 14 Appendix are with bonding such as are a related with of rules make a illustrated in Ref. with N2O does not On the and of are obtained for oxidation states in compounds such as and or in such as and or when oxidation states are such as in oxidation states also in where the charge is several equivalent atoms such as and are for bond-valence after the to bond-valence with values are to the of bonding when the of a bond is to an average of a of bonds. In an is for the to The generic definition in Ref. 14 oxidation state of a bonded atom its charge after ionic approximation”. bonds are extrapolated to be ionic, and the atom to negative is the one that more to the bonding MO. The heuristic MO in Figure 1 does that quantum-chemical calculations be to oxidation states. As discussed in Appendix C of Ref. 14, this carries an of because of the variety of and of the to this a MO approach use a that an atom reversibly contributing more to a MO or of a bond that with a that bonds are split This is illustrated with nitrogen in Figure by the we that a MO is in energy to one of its contributing receives the electrons upon ionic approximation. all the the oxidation states are obtained (Figure Oxidation states in nitrogen by assigning the electrons to the in a MO set from the orbital energies estimated with an A with a is in Figure such a one has to atoms that are or bonded together by MO. merely of a the approach in Figure the in Ref. Lewis formulas of Oxidation states in N2O by assigning the electrons to the in a MO set from an are A approach to the ionic approximation and oxidation states identifies the negative atom by Allen with the exception of the more electronegative atom bonded as a Lewis This approach in algorithms for of chemical formulas Lewis bond molecules, ions, and or of An of the and is in Table for on ionic approximation of terminal atoms summary number of valence electrons atom of the summary formula assigning bonds molecules or Lewis formula of the all bond pairs and if all bond pairs and pairs Lewis formula bond molecules or Lewis formula with all of the and for all atoms Lewis formula with or bond with all bonding as bond for all bond The definition IUPAC algorithms in Ref. while and some such as those of acceptor atoms with an electronegativity than the based on chemical definition does not the algorithms early on in the chemistry It be a the of where also his a the of as a and with and in the of was in a in He is an where electron lead to