Oxidation state

In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to other atoms are fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. Conceptually, the oxidation state may be positive, negative or zero. Beside nearly-pure ionic bonding, many covalent bonds exhibit a strong ionicity, making oxidation state a useful predictor of charge.

The oxidation state of an atom does not represent the "real" charge on that atom, or any other actual atomic property. This is particularly true of high oxidation states, where the ionization energy required to produce a multiply positive ion is far greater than the energies available in chemical reactions. Additionally, the oxidation states of atoms in a given compound may vary depending on the choice of electronegativity scale used in their calculation. Thus, the oxidation state of an atom in a compound is purely a formalism. It is nevertheless important in understanding the nomenclature conventions of inorganic compounds. Also, several observations regarding chemical reactions may be explained at a basic level in terms of oxidation states.

Oxidation states are typically represented by integers which may be positive, zero, or negative. In some cases, the average oxidation state of an element is a fraction, such as ⁠8/3⁠ for iron in magnetite Fe₃O₄ (see below). The highest known oxidation state is reported to be +9, displayed by iridium in the tetroxoiridium(IX) cation (IrO+4). It is predicted that even a +10 oxidation state may be achieved by platinum in tetroxoplatinum(X), PtO2+4. The lowest oxidation state is −5, as for boron in Al₃BC and gallium in pentamagnesium digallide (Mg₅Ga₂).

In Stock nomenclature, which is commonly used for inorganic compounds, the oxidation state is represented by a Roman numeral placed after the element name inside parentheses or as a superscript after the element symbol, e.g. Iron(III) oxide.

The term oxidation was first used by Antoine Lavoisier to signify the reaction of a substance with oxygen. Much later, it was realized that the substance, upon being oxidized, loses electrons, and the meaning was extended to include other reactions in which electrons are lost, regardless of whether oxygen was involved. The increase in the oxidation state of an atom, through a chemical reaction, is known as oxidation; a decrease in oxidation state is known as a reduction. Such reactions involve the formal transfer of electrons: a net gain in electrons being a reduction, and a net loss of electrons being oxidation. For pure elements, the oxidation state is zero.

Overview

Oxidation numbers are assigned to elements in a molecule such that the overall sum is zero in a neutral molecule. The number indicates the degree of oxidation of each element caused by molecular bonding. In ionic compounds, the oxidation numbers are the same as the element's ionic charge. Thus for KCl, potassium is assigned +1 and chlorine is assigned -1. The complete set of rules for assigning oxidation numbers are discussed in the following sections.

Oxidation numbers are fundamental to the chemical nomenclature of ionic compounds. For example, Cu compounds with Cu oxidation state +2 are called cupric and those with state +1 are cuprous.^: 172 The oxidation numbers of elements allow predictions of chemical formula and reactions, especially oxidation-reduction reactions. The oxidation numbers of the most stable chemical compounds follow trends in the periodic table.^: 140

IUPAC definition

International Union of Pure and Applied Chemistry (IUPAC) has published a "Comprehensive definition of oxidation state (IUPAC Recommendations 2016)". It is a distillation of an IUPAC technical report: "Toward a comprehensive definition of oxidation state". According to the IUPAC Gold Book: "The oxidation state of an atom is the charge of this atom after ionic approximation of its heteronuclear bonds." The term oxidation number is nearly synonymous.

The ionic approximation means extrapolating bonds to ionic. Several criteria were considered for the ionic approximation:

1. Extrapolation of the bond's polarity;
   1. from the electronegativity difference,
   2. from the dipole moment, and
   3. from quantum‐chemical calculations of charges.
2. Assignment of electrons according to the atom's contribution to the bonding Molecular orbital (MO) or the electron's allegiance in a LCAO–MO model.

In a bond between two different elements, the bond's electrons are assigned to its main atomic contributor typically of higher electronegativity; in a bond between two atoms of the same element, the electrons are divided equally. Most electronegativity scales depend on the atom's bonding state, which makes the assignment of the oxidation state a somewhat circular argument. For example, some scales may turn out unusual oxidation states, such as −6 for platinum in PtH2−4, for Pauling and Mulliken scales. The dipole moments would, sometimes, also turn out abnormal oxidation numbers, such as in CO and NO, which are oriented with their positive end towards oxygen. Therefore, this leaves the atom's contribution to the bonding MO, the atomic-orbital energy, and from quantum-chemical calculations of charges, as the only viable criteria with cogent values for ionic approximation. However, for a simple estimate for the ionic approximation, we can use Allen electronegativities, as only that electronegativity scale is truly independent of the oxidation state, as it relates to the average valence‐electron energy of the free atom:

v t e 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)

Determination

While introductory levels of chemistry teaching use postulated oxidation states, the IUPAC recommendation and the Gold Book entry list two entirely general algorithms for the calculation of the oxidation states of elements in chemical compounds.

Simple approach without bonding considerations

Introductory chemistry uses postulates: the oxidation state for an element in a chemical formula is calculated from the overall charge and postulated oxidation states for all the other atoms.

A simple example is based on two postulates,

1. OS = +1 for hydrogen
2. OS = −2 for oxygen

where OS stands for oxidation state. This approach yields correct oxidation states in oxides and hydroxides of any single element, and in acids such as sulfuric acid (H₂SO₄) or dichromic acid (H₂Cr₂O₇). Its coverage can be extended either by a list of exceptions or by assigning priority to the postulates. The latter works for hydrogen peroxide (H₂O₂) where the priority of rule 1 leaves both oxygens with oxidation state −1.

Additional postulates and their ranking may expand the range of compounds to fit a textbook's scope. As an example, one postulatory algorithm from many possible; in a sequence of decreasing priority:

1. An element in a free form has OS = 0.
2. In a compound or ion, the sum of the oxidation states equals the total charge of the compound or ion.
3. Fluorine in compounds has OS = −1; this extends to chlorine and bromine only when not bonded to a lighter halogen, oxygen or nitrogen.
4. Group 1 and group 2 metals in compounds have OS = +1 and +2, respectively.
5. Hydrogen has OS = +1 but adopts −1 when bonded as a hydride to metals or metalloids.
6. Oxygen in compounds has OS = −2 but only when not bonded to oxygen (e.g. in peroxides) or fluorine.

This set of postulates covers oxidation states of fluorides, chlorides, bromides, oxides, hydroxides, and hydrides of any single element. It covers all oxoacids of any central atom (and all their fluoro-, chloro-, and bromo-relatives), as well as salts of such acids with group 1 and 2 metals. It also covers iodides, sulfides, and similar simple salts of these metals.

Algorithm of assigning bonds

This algorithm is performed on a Lewis structure (a diagram that shows all valence electrons). Oxidation state equals the charge of an atom after each of its heteronuclear bonds has been assigned to the more electronegative partner of the bond (except when that partner is a reversibly bonded Lewis-acid ligand) and homonuclear bonds have been divided equally:

where each "—" represents an electron pair (either shared between two atoms or solely on one atom), and "OS" is the oxidation state as a numerical variable.

After the electrons have been assigned according to the vertical red lines on the formula, the total number of valence electrons that now "belong" to each atom is subtracted from the number N of valence electrons of the neutral atom (such as 5 for nitrogen in group 15) to yield that atom's oxidation state.

This example shows the importance of describing the bonding. Its summary formula, HNO₃, corresponds to two structural isomers; the peroxynitrous acid in the above figure and the more stable nitric acid. With the formula HNO₃, the simple approach without bonding considerations yields −2 for all three oxygens and +5 for nitrogen, which is correct for nitric acid. For the peroxynitrous acid, however, both oxygens in the O–O bond have OS = −1, and the nitrogen has OS = +3, which requires a structure to understand.

Organic compounds are treated in a similar manner; exemplified here on functional groups occurring in between methane (CH₄) and carbon dioxide (CO₂):

Analogously for transition-metal compounds; CrO(O₂)₂ on the left has a total of 36 valence electrons (18 pairs to be distributed), and hexacarbonylchromium (Cr(CO)₆) on the right has 66 valence electrons (33 pairs):

A key step is drawing the Lewis structure of the molecule (neutral, cationic, anionic): Atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule (a sort of "skeletal" structure), and the remaining valence electrons are distributed such that sp atoms obtain an octet (duet for hydrogen) with a priority that increases in proportion with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders (the full set of which is called the resonance formulas). Consider the sulfate anion (SO2−4) with 32 valence electrons; 24 from oxygens, 6 from sulfur, 2 of the anion charge obtained from the implied cation. The bond orders to the terminal oxygens do not affect the oxidation state so long as the oxygens have octets. Already the skeletal structure, top left, yields the correct oxidation states, as does the Lewis structure, top right (one of the resonance formulas):

The bond-order formula at the bottom is closest to the reality of four equivalent oxygens each having a total bond order of 2. That total includes the bond of order ⁠1/2⁠ to the implied cation and follows the 8 − N rule requiring that the main-group atom's bond-order total equals 8 − N valence electrons of the neutral atom, enforced with a priority that proportionately increases with electronegativity.

This algorithm works equally for molecular cations composed of several atoms. An example is the ammonium cation of 8 valence electrons (5 from nitrogen, 4 from hydrogens, minus 1 electron for the cation's positive charge):

Drawing Lewis structures with electron pairs as dashes emphasizes the essential equivalence of bond pairs and lone pairs when counting electrons and moving bonds onto atoms. Structures drawn with electron dot pairs are of course identical in every way:

The algorithm's caveat

The algorithm contains a caveat, which concerns rare cases of transition-metal complexes with a type of ligand that is reversibly bonded as a Lewis acid (as an acceptor of the electron pair from the transition metal); termed a "Z-type" ligand in Green's covalent bond classification method. The caveat originates from the simplifying use of electronegativity instead of the MO-based electron allegiance to decide the ionic sign. One early example is the O₂S−RhCl(CO)(PPh₃)₂ complex with sulfur dioxide (SO₂) as the reversibly-bonded acceptor ligand (released upon heating). The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of rhodium and sulfur, yielding oxidation state +1 for rhodium:

Algorithm of summing bond orders

This algorithm works on Lewis structures and bond graphs of extended (non-molecular) solids:

Oxidation state is obtained by summing the heteronuclear-bond orders at the atom as positive if that atom is the electropositive partner in a particular bond and as negative if not, and the atom’s formal charge (if any) is added to that sum. The same caveat as above applies.

Applied to a Lewis structure

An example of a Lewis structure with no formal charge,

illustrates that, in this algorithm, homonuclear bonds are simply ignored (the bond orders are in blue).

Carbon monoxide exemplifies a Lewis structure with formal charges:

To obtain the oxidation states, the formal charges are summed with the bond-order value taken positively at the carbon and negatively at the oxygen.

Applied to molecular ions, this algorithm considers the actual location of the formal (ionic) charge, as drawn in the Lewis structure. As an example, summing bond orders in the ammonium cation yields −4 at the nitrogen of formal charge +1, with the two numbers adding to the oxidation state of −3:

The sum of oxidation states in the ion equals its charge (as it equals zero for a neutral molecule).

Also in anions, the formal (ionic) charges have to be considered when nonzero. For sulfate this is exemplified with the skeletal or Lewis structures (top), compared with the bond-order formula of all oxygens equivalent and fulfilling the octet and 8 − N rules (bottom):

Applied to bond graph

A bond graph in solid-state chemistry is a chemical formula of an extended structure, in which direct bonding connectivities are shown. An example is the AuORb₃ perovskite, the unit cell of which is drawn on the left and the bond graph (with added numerical values) on the right:

We see that the oxygen atom bonds to the six nearest rubidium cations, each of which has 4 bonds to the auride anion. The bond graph summarizes these connectivities. The bond orders (also called bond valences) sum up to oxidation states according to the attached sign of the bond's ionic approximation (there are no formal charges in bond graphs).

Determination of oxidation states from a bond graph can be illustrated on ilmenite, FeTiO₃. We may ask whether the mineral contains Fe²⁺ and Ti⁴⁺, or Fe³⁺ and Ti³⁺. Its crystal structure has each metal atom bonded to six oxygens and each of the equivalent oxygens to two irons and two titaniums, as in the bond graph below. Experimental data show that three metal-oxygen bonds in the octahedron are short and three are long (the metals are off-center). The bond orders (valences), obtained from the bond lengths by the bond valence method, sum up to 2.01 at Fe and 3.99 at Ti; which can be rounded off to oxidation states +2 and +4, respectively:

Balancing redox

Oxidation states can be useful for balancing chemical equations for oxidation-reduction (or redox) reactions, because the changes in the oxidized atoms have to be balanced by the changes in the reduced atoms. For example, in the reaction of acetaldehyde with Tollens' reagent to form acetic acid (shown below), the carbonyl carbon atom changes its oxidation state from +1 to +3 (loses two electrons). This oxidation is balanced by reducing two Ag⁺ cations to Ag⁰ (gaining two electrons in total).

An inorganic example is the Bettendorf reaction using tin dichloride (SnCl₂) to prove the presence of arsenite ions in a concentrated HCl extract. When arsenic(III) is present, a brown coloration appears forming a dark precipitate of arsenic, according to the following simplified reaction:

2 As³⁺ + 3 Sn²⁺ → 2 As⁰ + 3 Sn⁴⁺

Here three tin atoms are oxidized from oxidation state +2 to +4, yielding six electrons that reduce two arsenic atoms from oxidation state +3 to 0. The simple one-line balancing goes as follows: the two redox couples are written down as they react;

As³⁺ + Sn²⁺ ⇌ As⁰ + Sn⁴⁺

One tin is oxidized from oxidation state +2 to +4, a two-electron step, hence 2 is written in front of the two arsenic partners. One arsenic is reduced from +3 to 0, a three-electron step, hence 3 goes in front of the two tin partners. An alternative three-line procedure is to write separately the half-reactions for oxidation and reduction, each balanced with electrons, and then to sum them up such that the electrons cross out. In general, these redox balances (the one-line balance or each half-reaction) need to be checked for the ionic and electron charge sums on both sides of the equation being indeed equal. If they are not equal, suitable ions are added to balance the charges and the non-redox elemental balance.

Appearances

Nominal oxidation states

A nominal oxidation state is a general term with two different definitions:

• Electrochemical oxidation state^: 1060 represents a molecule or ion in the Latimer diagram or Frost diagram for its redox-active element. An example is the Latimer diagram for sulfur at pH 0 where the electrochemical oxidation state +2 for sulfur puts HS
  ₂O⁻
  ₃ between S and H₂SO₃:

• Systematic oxidation state is chosen from close alternatives as a pedagogical description. An example is the oxidation state of phosphorus in H₃PO₃ (structurally diprotic HPO(OH)₂) taken nominally as +3, while Allen electronegativities of phosphorus and hydrogen suggest +5 by a narrow margin that makes the two alternatives almost equivalent:

Both alternative oxidation numbers for phosphorus make chemical sense, depending on which chemical property or reaction is emphasized. By contrast, a calculated alternative, such as the average (+4) does not.

Ambiguous oxidation states

Lewis formulae are rule-based approximations of chemical reality, as are Allen electronegativities. Still, oxidation states may seem ambiguous when their determination is not straightforward. If only an experiment can determine the oxidation state, the rule-based determination is ambiguous (insufficient). There are also truly dichotomous values that are decided arbitrarily.

Oxidation-state determination from resonance formulas

Seemingly ambiguous oxidation states are derived from a set of resonance formulas of equal weights for a molecule having heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8 − N rule.^: 1027 An example is S₂N₂ where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 for the two sulfur atoms, which average to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

A physical measurement is needed to determine oxidation state

• when a non-innocent ligand is present, of hidden or unexpected redox properties that could otherwise be assigned to the central atom. An example is the nickel dithiolate complex, Ni(S
  ₂C
  ₂H
  ₂)²⁻
  ₂.^{: 1056–1057}
• when the redox ambiguity of a central atom and ligand yields dichotomous oxidation states of close stability, thermally induced tautomerism may result, as exemplified by manganese catecholate, Mn(C₆H₄O₂)₃.^{: 1057–1058} Assignment of such oxidation states requires spectroscopic, magnetic or structural data.
• when the bond order has to be ascertained along with an isolated tandem of a heteronuclear and a homonuclear bond. An example is thiosulfate S
  ₂O²⁻
  ₃ having two possible oxidation states (bond orders are in blue and formal charges in green):

The S–S distance measurement in thiosulfate is needed to reveal that this bond order is very close to 1, as in the formula on the left.

Ambiguous/arbitrary oxidation states

• when the electronegativity difference between two bonded atoms is very small (as in H₃PO₃). Two almost equivalent pairs of oxidation states, arbitrarily chosen, are obtained for these atoms.
• when an electronegative p-block atom forms solely homonuclear bonds, the number of which differs from the number of two-electron bonds suggested by rules. Examples are homonuclear finite chains like N⁻
  ₃ (the central nitrogen connects two atoms with four two-electron bonds while only three two-electron bonds are required by the 8 − N rule^: 1027) or I⁻
  ₃ (the central iodine connects two atoms with two two-electron bonds while only one two-electron bond fulfills the 8 − N rule). A sensible approach is to distribute the ionic charge over the two outer atoms. Such a placement of charges in a polysulfide S²⁻
  _n (where all inner sulfurs form two bonds, fulfilling the 8 − N rule) follows already from its Lewis structure.
• when the isolated tandem of a heteronuclear and a homonuclear bond leads to a bonding compromise in between two Lewis structures of limiting bond orders. An example is N₂O:

The typical oxidation state of nitrogen in N₂O is +1, which also obtains for both nitrogens by a molecular orbital approach. The formal charges on the right comply with electronegativities, which implies an added ionic bonding contribution. Indeed, the estimated N−N and N−O bond orders are 2.76 and 1.9, respectively, approaching the formula of integer bond orders that would include the ionic contribution explicitly as a bond (in green):

Conversely, formal charges against electronegativities in a Lewis structure decrease the bond order of the corresponding bond. An example is carbon monoxide with a bond-order estimate of 2.6.

Fractional oxidation states

Fractional oxidation states are often used to represent the average oxidation state of several atoms of the same element in a structure. For example, the formula of magnetite is Fe
₃O
₄, implying an average oxidation state for iron of +⁠8/3⁠.^: 81–82 However, this average value may not be representative if the atoms are not equivalent. In a Fe
₃O
₄ crystal below 120 K (−153 °C), two-thirds of the cations are Fe³⁺
and one-third are Fe²⁺
, and the formula may be more clearly represented as FeO·Fe
₂O
₃.

Likewise, propane, C
₃H
₈, has been described as having a carbon oxidation state of −⁠8/3⁠. Again, this is an average value since the structure of the molecule is H
₃C−CH
₂−CH
₃, with the first and third carbon atoms each having an oxidation state of −3 and the central one −2.

An example with true fractional oxidation states for equivalent atoms is potassium superoxide, KO
₂. The diatomic superoxide ion O⁻
₂ has an overall charge of −1, so each of its two equivalent oxygen atoms is assigned an oxidation state of −⁠1/2⁠. This ion can be described as a resonance hybrid of two Lewis structures, where each oxygen has an oxidation state of 0 in one structure and −1 in the other.

For the cyclopentadienyl anion C
₅H⁻
₅, the oxidation state of C is −1 + −⁠1/5⁠ = −⁠6/5⁠. The −1 occurs because each carbon is bonded to one hydrogen atom (a less electronegative element), and the −⁠1/5⁠ because the total ionic charge of −1 is divided among five equivalent carbons. Again this can be described as a resonance hybrid of five equivalent structures, each having four carbons with oxidation state −1 and one with −2.

Examples of fractional oxidation states for carbon

Oxidation state	Example species
−⁠6/5⁠	C 5H^− 5
−⁠6/7⁠	C 7H^+ 7
+⁠3/2⁠	C 4O^2− 4

Finally, fractional oxidation numbers are not used in the chemical nomenclature.^: 66 For example the red lead Pb
₃O
₄ is represented as lead(II,IV) oxide, showing the oxidation states of the two nonequivalent lead atoms.

Elements with multiple oxidation states

Most elements have more than one possible oxidation state. For example, carbon has nine possible integer oxidation states from −4 to +4:

Integer oxidation states of carbon

Oxidation state	Example compound
−4	CH 4
−3	C 2H 6
−2	C 2H 4, CH 3Cl
−1	C 2H 2, C 6H 6, (CH 2OH) 2
0	HCHO, CH 2Cl 2
+1	OCHCHO, CHCl 2CHCl 2
+2	HCOOH, CHCl 3
+3	HOOCCOOH, C 2Cl 6
+4	CCl 4, CO 2

Oxidation state in metals

Many compounds with luster and electrical conductivity maintain a simple stoichiometric formula, such as the golden TiO, blue-black RuO₂ or coppery ReO₃, all of obvious oxidation state. Ultimately, assigning the free metallic electrons to one of the bonded atoms is not comprehensive and can yield unusual oxidation states. Examples are the LiPb and Cu
₃Au ordered alloys, the composition and structure of which are largely determined by atomic size and packing factors. Should oxidation state be needed for redox balancing, it is best set to 0 for all atoms of such an alloy.

List of oxidation states of the elements

This is a list of known oxidation states of the chemical elements, excluding nonintegral values. The most common states appear in bold. The table is based on that of Greenwood and Earnshaw, with additions noted. Every element exists in oxidation state 0 when it is the pure non-ionized element in any phase, whether monatomic or polyatomic allotrope. The column for oxidation state 0 only shows elements known to exist in oxidation state 0 in compounds.

  Noble gas

+1 Bold values are main oxidation states

v t e Oxidation states of the elements
Element			Negative states						Positive states									Group	Notes
			−5	−4	−3	−2	−1	0	+1	+2	+3	+4	+5	+6	+7	+8	+9
Z
1	hydrogen	H					−1		+1									1
2	helium	He						0										18	0
3	lithium	Li					−1		+1									1
4	beryllium	Be							+1	+2								2
5	boron	B	−5				−1	0	+1	+2	+3							13
6	carbon	C		−4	−3	−2	−1	0	+1	+2	+3	+4						14
7	nitrogen	N			−3	−2	−1	0	+1	+2	+3	+4	+5					15
8	oxygen	O				−2	−1	0	+1	+2								16
9	fluorine	F					−1											17
10	neon	Ne						0										18	0
11	sodium	Na					−1	0	+1									1
12	magnesium	Mg						0	+1	+2								2
13	aluminium	Al				−2	−1	0	+1	+2	+3							13
14	silicon	Si		−4	−3	−2	−1	0	+1	+2	+3	+4						14
15	phosphorus	P			−3	−2	−1	0	+1	+2	+3	+4	+5					15
16	sulfur	S				−2	−1	0	+1	+2	+3	+4	+5	+6				16
17	chlorine	Cl					−1		+1	+2	+3	+4	+5	+6	+7			17
18	argon	Ar						0										18	0
19	potassium	K					−1		+1									1
20	calcium	Ca							+1	+2								2
21	scandium	Sc						0	+1	+2	+3							3
22	titanium	Ti				−2	−1	0	+1	+2	+3	+4						4
23	vanadium	V			−3		−1	0	+1	+2	+3	+4	+5					5
24	chromium	Cr		−4		−2	−1	0	+1	+2	+3	+4	+5	+6				6
25	manganese	Mn			−3	−2	−1	0	+1	+2	+3	+4	+5	+6	+7			7
26	iron	Fe				−2	−1	0	+1	+2	+3	+4	+5	+6	+7			8
27	cobalt	Co			−3		−1	0	+1	+2	+3	+4	+5					9
28	nickel	Ni				−2	−1	0	+1	+2	+3	+4						10
29	copper	Cu				−2	−1	0	+1	+2	+3	+4						11
30	zinc	Zn				−2		0	+1	+2								12	^?
31	gallium	Ga	−5	−4	−3	−2	−1	0	+1	+2	+3							13
32	germanium	Ge		−4	−3	−2	−1	0	+1	+2	+3	+4						14
33	arsenic	As			−3	−2	−1	0	+1	+2	+3	+4	+5					15
34	selenium	Se				−2	−1	0	+1	+2	+3	+4	+5	+6				16	^?
35	bromine	Br					−1		+1	+2	+3	+4	+5		+7			17
36	krypton	Kr							+1	+2								18	^?
37	rubidium	Rb					−1		+1									1
38	strontium	Sr							+1	+2								2
39	yttrium	Y						0	+1	+2	+3							3	^?
40	zirconium	Zr				−2		0	+1	+2	+3	+4						4
41	niobium	Nb			−3		−1	0	+1	+2	+3	+4	+5					5
42	molybdenum	Mo		−4		−2	−1	0	+1	+2	+3	+4	+5	+6				6
43	technetium	Tc					−1		+1	+2	+3	+4	+5	+6	+7			7
44	ruthenium	Ru				−2			+1	+2	+3	+4	+5	+6	+7	+8		8
45	rhodium	Rh			−3		−1	0	+1	+2	+3	+4	+5	+6	+7			9
46	palladium	Pd						0	+1	+2	+3	+4	+5					10
47	silver	Ag				−2	−1	0	+1	+2	+3							11
48	cadmium	Cd				−2			+1	+2								12
49	indium	In	−5			−2	−1	0	+1	+2	+3							13
50	tin	Sn		−4	−3	−2	−1	0	+1	+2	+3	+4						14
51	antimony	Sb			−3	−2	−1	0	+1	+2	+3	+4	+5					15	^?
52	tellurium	Te				−2	−1	0	+1	+2	+3	+4	+5	+6				16	^?
53	iodine	I					−1		+1	+2	+3	+4	+5	+6	+7			17	^?
54	xenon	Xe						0		+2		+4		+6		+8		18
55	caesium	Cs					−1		+1									1
56	barium	Ba							+1	+2								2
57	lanthanum	La						0	+1	+2	+3							f-block groups
58	cerium	Ce								+2	+3	+4						f-block groups
59	praseodymium	Pr						0	+1	+2	+3	+4	+5					f-block groups	^?
60	neodymium	Nd						0		+2	+3	+4						f-block groups
61	promethium	Pm								+2	+3							f-block groups	^?
62	samarium	Sm						0	+1	+2	+3							f-block groups
63	europium	Eu						0		+2	+3							f-block groups	0
64	gadolinium	Gd						0	+1	+2	+3							f-block groups
65	terbium	Tb						0	+1	+2	+3	+4						f-block groups
66	dysprosium	Dy						0		+2	+3	+4						f-block groups
67	holmium	Ho						0		+2	+3							f-block groups
68	erbium	Er						0		+2	+3							f-block groups
69	thulium	Tm						0	+1	+2	+3							f-block groups
70	ytterbium	Yb						0	+1	+2	+3							f-block groups
71	lutetium	Lu						0		+2	+3							3
72	hafnium	Hf				−2		0	+1	+2	+3	+4						4
73	tantalum	Ta			−3		−1	0	+1	+2	+3	+4	+5					5
74	tungsten	W		−4		−2	−1	0	+1	+2	+3	+4	+5	+6				6
75	rhenium	Re			−3		−1	0	+1	+2	+3	+4	+5	+6	+7			7
76	osmium	Os		−4		−2	−1	0	+1	+2	+3	+4	+5	+6	+7	+8		8	^?
77	iridium	Ir			−3	−2	−1	0	+1	+2	+3	+4	+5	+6	+7	+8	+9	9	^?
78	platinum	Pt			−3	−2	−1	0	+1	+2	+3	+4	+5	+6				10	^?
79	gold	Au			−3	−2	−1	0	+1	+2	+3		+5					11	^?
80	mercury	Hg				−2			+1	+2								12
81	thallium	Tl	−5			−2	−1		+1	+2	+3							13	^?
82	lead	Pb		−4		−2	−1	0	+1	+2	+3	+4						14	^?
83	bismuth	Bi			−3	−2	−1	0	+1	+2	+3	+4	+5					15	^?
84	polonium	Po				−2				+2		+4	+5	+6				16
85	astatine	At					−1		+1		+3		+5		+7			17
86	radon	Rn								+2				+6				18	^?
87	francium	Fr							+1									1
88	radium	Ra								+2								2
89	actinium	Ac									+3							f-block groups
90	thorium	Th					−1		+1	+2	+3	+4						f-block groups	^?
91	protactinium	Pa								+2	+3	+4	+5					f-block groups	^?
92	uranium	U					−1		+1	+2	+3	+4	+5	+6				f-block groups	^?
93	neptunium	Np								+2	+3	+4	+5	+6	+7			f-block groups	^?
94	plutonium	Pu								+2	+3	+4	+5	+6	+7	+8		f-block groups	, ^?
95	americium	Am								+2	+3	+4	+5	+6	+7			f-block groups
96	curium	Cm									+3	+4	+5	+6				f-block groups
97	berkelium	Bk								+2	+3	+4	+5					f-block groups	^?
98	californium	Cf								+2	+3	+4	+5					f-block groups
99	einsteinium	Es								+2	+3	+4						f-block groups
100	fermium	Fm								+2	+3							f-block groups
101	mendelevium	Md								+2	+3							f-block groups
102	nobelium	No								+2	+3							f-block groups
103	lawrencium	Lr									+3							3
104	rutherfordium	Rf									+3	+4						4
105	dubnium	Db									+3	+4	+5					5
106	seaborgium	Sg									+3	+4	+5	+6				6
107	bohrium	Bh									+3	+4	+5		+7			7
108	hassium	Hs									+3	+4		+6		+8		8
109	meitnerium	Mt							+1		+3			+6				9
110	darmstadtium	Ds								+2		+4		+6				10
111	roentgenium	Rg					−1				+3		+5					11
112	copernicium	Cn								+2		+4						12
113	nihonium	Nh																13
114	flerovium	Fl																14
115	moscovium	Mc																15
116	livermorium	Lv				−2						+4						16
117	tennessine	Ts					−1						+5					17
118	oganesson	Og					−1		+1	+2		+4		+6				18

Early forms (octet rule)

A figure with a similar format was used by Irving Langmuir in 1919 in one of the early papers about the octet rule. The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule.

Use in nomenclature

The oxidation state in compound naming for transition metals and lanthanides and actinides is placed either as a right superscript to the element symbol in a chemical formula, such as Fe^III or in parentheses after the name of the element in chemical names, such as iron(III). For example, Fe
₂(SO
₄)
₃ is named iron(III) sulfate and its formula can be shown as Fe^III
₂(SO
₄)
₃. This is because a sulfate ion has a charge of −2, so each iron atom takes a charge of +3.

History of the oxidation state concept

Early days

Oxidation itself was first studied by Antoine Lavoisier, who defined it as the result of reactions with oxygen (hence the name). The term has since been generalized to imply a formal loss of electrons. Oxidation states, called oxidation grades by Friedrich Wöhler in 1835, were one of the intellectual stepping stones that Dmitri Mendeleev used to derive the periodic table.William B. Jensen gives an overview of the history up to 1938.

Use in nomenclature

When it was realized that some metals form two different binary compounds with the same nonmetal, the two compounds were often distinguished by using the ending -ic for the higher metal oxidation state and the ending -ous for the lower. For example, FeCl₃ is ferric chloride and FeCl₂ is ferrous chloride. This system is not very satisfactory (although sometimes still used) because different metals have different oxidation states which have to be learned: ferric and ferrous are +3 and +2 respectively, but cupric and cuprous are +2 and +1, and stannic and stannous are +4 and +2. Also, there was no allowance for metals with more than two oxidation states, such as vanadium with oxidation states +2, +3, +4, and +5.^: 84

This system has been largely replaced by one suggested by Alfred Stock in 1919 and adopted by IUPAC in 1940. Thus, FeCl₂ was written as iron(II) chloride rather than ferrous chloride. The Roman numeral II at the central atom came to be called the "Stock number" (now an obsolete term), and its value was obtained as a charge at the central atom after removing its ligands along with the electron pairs they shared with it.^: 147

Development towards the current concept

The term "oxidation state" in English chemical literature was popularized by Wendell Mitchell Latimer in his 1938 book about electrochemical potentials. He used it for the value (synonymous with the German term Wertigkeit) previously termed "valence", "polar valence" or "polar number" in English, or "oxidation stage" or indeed the "state of oxidation". Since 1938, the term "oxidation state" has been connected with electrochemical potentials and electrons exchanged in redox couples participating in redox reactions. By 1948, IUPAC used the 1940 nomenclature rules with the term "oxidation state", instead of the originalvalency. In 1948 Linus Pauling proposed that oxidation number could be determined by extrapolating bonds to being completely ionic in the direction of electronegativity. A full acceptance of this suggestion was complicated by the fact that the Pauling electronegativities as such depend on the oxidation state and that they may lead to unusual values of oxidation states for some transition metals. In 1990 IUPAC resorted to a postulatory (rule-based) method to determine the oxidation state. This was complemented by the synonymous term oxidation number as a descendant of the Stock number introduced in 1940 into the nomenclature. However, the terminology using "ligands"^: 147 gave the impression that oxidation number might be something specific to coordination complexes. This situation and the lack of a real single definition generated numerous debates about the meaning of oxidation state, suggestions about methods to obtain it and definitions of it. To resolve the issue, an IUPAC project (2008-040-1-200) was started in 2008 on the "Comprehensive Definition of Oxidation State", and was concluded by two reports and by the revised entries "Oxidation State" and "Oxidation Number" in the IUPAC Gold Book. The outcomes were a single definition of oxidation state and two algorithms to calculate it in molecular and extended-solid compounds, guided by Allen electronegativities that are independent of oxidation state.

See also

• Electronegativity
• Electrochemistry
• Atomic orbital
• Atomic shell
• Quantum numbers
  • Azimuthal quantum number
  • Principal quantum number
  • Magnetic quantum number
  • Spin quantum number
• Aufbau principle
  • Wiswesser's rule
• Ionization energy
• Electron affinity
• Ionic potential
• Ions
  • Cations and Anions
  • Polyatomic ions
• Covalent bonding
• Metallic bonding
• Hybridization

References

1. Wang, G.; Zhou, M.; Goettel, G. T.; Schrobilgen, G. J.; Su, J.; Li, J.; Schlöder, T.; Riedel, S. (2014). "Identification of an iridium-containing compound with a formal oxidation state of IX". Nature. 514 (7523): 475–477. Bibcode:2014Natur.514..475W. doi:10.1038/nature13795. PMID 25341786. S2CID 4463905.
2. Yu, Haoyu S.; Truhlar, Donald G. (2016). "Oxidation State 10 Exists". Angewandte Chemie International Edition. 55 (31): 9004–9006. doi:10.1002/anie.201604670. PMID 27273799.
3. Schroeder, Melanie, Eigenschaften von borreichen Boriden und Scandium-Aluminium-Oxid-Carbiden (in German), p. 139, archived from the original on 2020-08-06, retrieved 2020-02-24
4. Siebring, B. R., Schaff, M. E. (1980). General Chemistry. United States: Wadsworth Publishing Company.
5. Gray, H. B., Haight, G. P. (1967). Basic Principles of Chemistry. Netherlands: W. A. Benjamin.
6. Karen, P.; McArdle, P.; Takats, J. (2016). "Comprehensive definition of oxidation state (IUPAC Recommendations 2016)". Pure Appl. Chem. 88 (8): 831–839. doi:10.1515/pac-2015-1204. hdl:10852/59520. S2CID 99403810.
7. Karen, P.; McArdle, P.; Takats, J. (2014). "Toward a comprehensive definition of oxidation state (IUPAC Technical Report)". Pure Appl. Chem. 86 (6): 1017–1081. doi:10.1515/pac-2013-0505.
8. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Oxidation state". doi:10.1351/goldbook.O04365
9. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Oxidation number". doi:10.1351/goldbook.O04363
10. Karen, Pavel (2015). "Oxidation State, A Long-Standing Issue!". Angewandte Chemie International Edition. 54 (16): 4716–4726. doi:10.1002/anie.201407561. PMC 4506524. PMID 25757151.
11. Hooydonk, G. Van (1974-05-01). "O n an Ionic Approximation to Chemical Bonding". Zeitschrift für Naturforschung A. 29 (5): 763–767. Bibcode:1974ZNatA..29..763H. doi:10.1515/zna-1974-0517. ISSN 1865-7109.
12. "Oxidation state". The IUPAC Compendium of Chemical Terminology: The Gold Book. 2009. doi:10.1351/goldbook.O04365. ISBN 978-0-9678550-9-7.
13. Muir, K. W.; Ibers, J. A. (1969). "The structure of chlorocarbonyl(sulfur dioxide)bis(triphenylphosphine)rhodium, (RhCl(CO)(SO2)(P(C6H5)3 2)". Inorg. Chem. 8 (9): 1921–1928. doi:10.1021/ic50079a024.
14. Jørgensen, C. K. (1966). "Electric Polarizability, Innocent Ligands and Spectroscopic Oxidation States". Structure and Bonding. Vol. 1. Berlin: Springer-Verlag. pp. 234–248.
15. "The Two-Electron Bond". Chemistry LibreTexts. June 25, 2016. Archived from the original on February 9, 2021. Retrieved September 1, 2020.
16. Martinie, R. J.; Bultema, J. J.; Wal, M. N. V.; Burkhart, B. J.; Griend, D. A. V.; DeCock, R. L. (2011). "Bond order and chemical properties of BF, CO, and N₂". J. Chem. Educ. 88 (8): 1094–1097. Bibcode:2011JChEd..88.1094M. doi:10.1021/ed100758t.
17. Petrucci, R. H.; Harwood, W. S.; Herring, F. G. (2002). General Chemistry (8th ed.). Prentice-Hall. ISBN 978-0-13-033445-9.^{[ISBN missing]}
18. Senn, M. S.; Wright, J. P.; Attfield, J. P. (2012). "Charge order and three-site distortions in the Verwey structure of magnetite" (PDF). Nature. 481 (7380): 173–6. Bibcode:2012Natur.481..173S. doi:10.1038/nature10704. hdl:20.500.11820/1b3bb558-52d5-419f-9944-ab917dc95f5e. PMID 22190035. S2CID 4425300. Archived (PDF) from the original on 2022-10-09.
19. Whitten, K. W.; Galley, K. D.; Davis, R. E. (1992). General Chemistry (4th ed.). Saunders. p. 147. ISBN 978-0-03-075156-1.^{[ISBN missing]}
20. Connelly, N. G.; Damhus, T.; Hartshorn, R. M.; Hutton, A. T. Nomenclature of Inorganic Chemistry (IUPAC Recommendations 2005) (PDF). RSC Publishing. Archived (PDF) from the original on 2022-10-09.
21. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. pp. 27–28. ISBN 978-0-08-037941-8.
22. Disodium helide, (Na⁺)₂He(e⁻)₂, has been synthesized at high pressure, see Dong, Xiao; Oganov, Artem R.; Goncharov, Alexander F.; Stavrou, Elissaios; Lobanov, Sergey; Saleh, Gabriele; Qian, Guang-Rui; Zhu, Qiang; Gatti, Carlo; Deringer, Volker L.; Dronskowski, Richard; Zhou, Xiang-Feng; Prakapenka, Vitali B.; Konôpková, Zuzana; Popov, Ivan A.; Boldyrev, Alexander I.; Wang, Hui-Tian (6 February 2017). "A stable compound of helium and sodium at high pressure". Nature Chemistry. 9 (5): 440–445. arXiv:1309.3827. Bibcode:2017NatCh...9..440D. doi:10.1038/nchem.2716. PMID 28430195. S2CID 20459726.
23. Li(–1) has been observed in the gas phase; see R. H. Sloane; H. M. Love (1947). "Surface Formation of Lithium Negative Ions". Nature. 159: 302–303. doi:10.1038/159302a0.
24. Boronski, Josef T.; Crumpton, Agamemnon E.; Wales, Lewis L.; Aldridge, Simon (2023-06-16). "Diberyllocene, a stable compound of Be(I) with a Be–Be bond". Science. 380 (6650): 1147–1149. Bibcode:2023Sci...380.1147B. doi:10.1126/science.adh4419. ISSN 0036-8075. PMID 37319227. S2CID 259166086.
25. Arrowsmith, Merle; Braunschweig, Holger; Celik, Mehmet Ali; Dellermann, Theresa; Dewhurst, Rian D.; Ewing, William C.; Hammond, Kai; Kramer, Thomas; Krummenacher, Ivo (2016). "Neutral zero-valent s-block complexes with strong multiple bonding". Nature Chemistry. 8 (9): 890–894. Bibcode:2016NatCh...8..890A. doi:10.1038/nchem.2542. PMID 27334631.
26. Gimferrer, Martí; Danés, Sergi; Vos, Eva; Yildiz, Cem B.; Corral, Inés; Jana, Anukul; Salvador, Pedro; Andrada, Diego M. (2022-06-07). "The oxidation state in low-valent beryllium and magnesium compounds". Chemical Science. 13 (22): 6583–6591. doi:10.1039/D2SC01401G. ISSN 2041-6539. PMC 9172369. PMID 35756523.
27. Be(I) is known in CpBeBeCp. While Be(0) is claimed to exist in bis(carbene) compounds, its existence has been questioned.
28. B(−5) has been observed in Al₃BC, see Schroeder, Melanie. "Eigenschaften von borreichen Boriden und Scandium-Aluminium-Oxid-Carbiden" (in German). p. 139.
29. B(−1) has been observed in magnesium diboride (MgB₂), see Keeler, James; Wothers, Peter (2014). Chemical Structure and Reactivity: An Integrated Approach. Oxford University Press. ISBN 9780199604135.
30. Braunschweig, H.; Dewhurst, R. D.; Hammond, K.; Mies, J.; Radacki, K.; Vargas, A. (2012). "Ambient-Temperature Isolation of a Compound with a Boron-Boron Triple Bond". Science. 336 (6087): 1420–2. Bibcode:2012Sci...336.1420B. doi:10.1126/science.1221138. PMID 22700924. S2CID 206540959.
31. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 28. ISBN 978-0-08-037941-8.
32. Zhang, K.Q.; Guo, B.; Braun, V.; Dulick, M.; Bernath, P.F. (1995). "Infrared Emission Spectroscopy of BF and AIF" (PDF). J. Molecular Spectroscopy. 170 (1): 82. Bibcode:1995JMoSp.170...82Z. doi:10.1006/jmsp.1995.1058.
33. Tetrazoles contain a pair of double-bonded nitrogen atoms with oxidation state 0 in the ring. A Synthesis of the parent 1H-tetrazole, CH₂N₄ (two atoms N(0)) is given in Henry, Ronald A.; Finnegan, William G. (1954). "An Improved Procedure for the Deamination of 5-Aminotetrazole". Journal of the American Chemical Society. 76 (1): 290–291. doi:10.1021/ja01630a086. ISSN 0002-7863.
34. Ne(0) has been observed in Cr(CO)₅Ne; see Perutz, Robin N.; Turner, James J. (August 1975). "Photochemistry of the Group 6 hexacarbonyls in low-temperature matrices. III. Interaction of the pentacarbonyls with noble gases and other matrices". Journal of the American Chemical Society. 97 (17): 4791–4800. doi:10.1021/ja00850a001.
35. The compound NaCl has been shown in experiments to exists in several unusual stoichiometries under high pressure, including Na₃Cl in which contains a layer of sodium(0) atoms; see Zhang, W.; Oganov, A. R.; Goncharov, A. F.; Zhu, Q.; Boulfelfel, S. E.; Lyakhov, A. O.; Stavrou, E.; Somayazulu, M.; Prakapenka, V. B.; Konôpková, Z. (2013). "Unexpected Stable Stoichiometries of Sodium Chlorides". Science. 342 (6165): 1502–1505. arXiv:1310.7674. Bibcode:2013Sci...342.1502Z. doi:10.1126/science.1244989. PMID 24357316. S2CID 15298372.
36. Mg(0) has been synthesized in a compound containing a Na₂Mg₂²⁺ cluster coordinated to a bulky organic ligand; see Rösch, B.; Gentner, T. X.; Eyselein, J.; Langer, J.; Elsen, H.; Li, W.; Harder, S. (2021). "Strongly reducing magnesium(0) complexes". Nature. 592 (7856): 717–721. Bibcode:2021Natur.592..717R. doi:10.1038/s41586-021-03401-w. PMID 33911274. S2CID 233447380
37. Bernath, P. F.; Black, J. H. & Brault, J. W. (1985). "The spectrum of magnesium hydride" (PDF). Astrophysical Journal. 298: 375. Bibcode:1985ApJ...298..375B. doi:10.1086/163620.. See also Low valent magnesium compounds.
38. Al(−2) has been observed in Sr₁₄[Al₄]₂[Ge]₃, see Wemdorff, Marco; Röhr, Caroline (2007). "Sr₁₄[Al₄]₂[Ge]₃: Eine Zintl-Phase mit isolierten [Ge]^4–- und [Al₄]^8–-Anionen / Sr₁₄[Al₄]₂[Ge]₃: A Zintl Phase with Isolated [Ge]^4–- and [Al₄]^8– Anions". Zeitschrift für Naturforschung B (in German). 62 (10): 1227. doi:10.1515/znb-2007-1001. S2CID 94972243.
39. Al(–1) has been reported in Na₅Al₅; see Haopeng Wang; Xinxing Zhang; Yeon Jae Ko; Andrej Grubisic; Xiang Li; Gerd Ganteför; Hansgeorg Schnöckel; Bryan W. Eichhorn; Mal-Soon Lee; P. Jena; Anil K. Kandalam; Boggavarapu Kiran; Kit H. Bowen (2014). "Aluminum Zintl anion moieties within sodium aluminum clusters". The Journal of Chemical Physics. 140 (5). doi:10.1063/1.4862989.
40. Unstable carbonyl of Al(0) has been detected in reaction of Al₂(CH₃)₆ with carbon monoxide; see Sanchez, Ramiro; Arrington, Caleb; Arrington Jr., C. A. (December 1, 1989). "Reaction of trimethylaluminum with carbon monoxide in low-temperature matrixes". American Chemical Society. 111 (25): 9110-9111. doi:10.1021/ja00207a023. OSTI 6973516.
41. Dohmeier, C.; Loos, D.; Schnöckel, H. (1996). "Aluminum(I) and Gallium(I) Compounds: Syntheses, Structures, and Reactions". Angewandte Chemie International Edition. 35 (2): 129–149. doi:10.1002/anie.199601291.
42. Tyte, D. C. (1964). "Red (B2Π–A2σ) Band System of Aluminium Monoxide". Nature. 202 (4930): 383. Bibcode:1964Natur.202..383T. doi:10.1038/202383a0. S2CID 4163250.
43. "New Type of Zero-Valent Tin Compound". Chemistry Europe. 27 August 2016.
44. Ram, R. S.; et al. (1998). "Fourier Transform Emission Spectroscopy of the A2D–X2P Transition of SiH and SiD" (PDF). J. Mol. Spectr. 190 (2): 341–352. doi:10.1006/jmsp.1998.7582. PMID 9668026.
45. Wang, Yuzhong; Xie, Yaoming; Wei, Pingrong; King, R. Bruce; Schaefer, Iii; Schleyer, Paul v. R.; Robinson, Gregory H. (2008). "Carbene-Stabilized Diphosphorus". Journal of the American Chemical Society. 130 (45): 14970–1. doi:10.1021/ja807828t. PMID 18937460.
46. Ellis, Bobby D.; MacDonald, Charles L. B. (2006). "Phosphorus(I) Iodide: A Versatile Metathesis Reagent for the Synthesis of Low Oxidation State Phosphorus Compounds". Inorganic Chemistry. 45 (17): 6864–74. doi:10.1021/ic060186o. PMID 16903744.
47. Ar(0) has been observed in argon fluorohydride (HArF) and ArCF₂²⁺, see Lockyear, J.F.; Douglas, K.; Price, S.D.; Karwowska, M.; et al. (2010). "Generation of the ArCF₂²⁺ Dication". Journal of Physical Chemistry Letters. 1: 358. doi:10.1021/jz900274p.
48. John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
49. Krieck, Sven; Görls, Helmar; Westerhausen, Matthias (2010). "Mechanistic Elucidation of the Formation of the Inverse Ca(I) Sandwich Complex [(thf)3Ca(μ-C6H3-1,3,5-Ph3)Ca(thf)3] and Stability of Aryl-Substituted Phenylcalcium Complexes". Journal of the American Chemical Society. 132 (35): 12492–12501. doi:10.1021/ja105534w. PMID 20718434.
50. Cloke, F. Geoffrey N.; Khan, Karl & Perutz, Robin N. (1991). "η-Arene complexes of scandium(0) and scandium(II)". J. Chem. Soc., Chem. Commun. (19): 1372–1373. doi:10.1039/C39910001372.
51. Smith, R. E. (1973). "Diatomic Hydride and Deuteride Spectra of the Second Row Transition Metals". Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences. 332 (1588): 113–127. Bibcode:1973RSPSA.332..113S. doi:10.1098/rspa.1973.0015. S2CID 96908213.
52. McGuire, Joseph C.; Kempter, Charles P. (1960). "Preparation and Properties of Scandium Dihydride". Journal of Chemical Physics. 33 (5): 1584–1585. Bibcode:1960JChPh..33.1584M. doi:10.1063/1.1731452.
53. Ti(-2) is known in Ti(CO)2−6; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
54. Jilek, Robert E.; Tripepi, Giovanna; Urnezius, Eugenijus; Brennessel, William W.; Young, Victor G. Jr.; Ellis, John E. (2007). "Zerovalent titanium–sulfur complexes. Novel dithiocarbamato derivatives of Ti(CO)₆:[Ti(CO)₄(S₂CNR₂)]⁻". Chem. Commun. (25): 2639–2641. doi:10.1039/B700808B. PMID 17579764.
55. Andersson, N.; et al. (2003). "Emission spectra of TiH and TiD near 938 nm". J. Chem. Phys. 118 (8): 10543. Bibcode:2003JChPh.118.3543A. doi:10.1063/1.1539848.
56. V(–3) is known in V(CO)3−5; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
57. V(0) is known in V(CO)₆; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
58. Cr(–4) is known in Na₄Cr(CO)₄; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
59. Cr(0) is known in Cr(CO)₆; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
60. Mn(–2) is known in Mn(cod)2−2; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
61. Ram, R. S.; Bernath, P. F. (2003). "Fourier transform emission spectroscopy of the g⁴Δ–a⁴Δ system of FeCl". Journal of Molecular Spectroscopy. 221 (2): 261. Bibcode:2003JMoSp.221..261R. doi:10.1016/S0022-2852(03)00225-X.
62. Demazeau, G.; Buffat, B.; Pouchard, M.; Hagenmuller, P. (1982). "Recent developments in the field of high oxidation states of transition elements in oxides stabilization of six-coordinated Iron(V)". Zeitschrift für anorganische und allgemeine Chemie. 491: 60–66. doi:10.1002/zaac.19824910109.
63. Lu, J.; Jian, J.; Huang, W.; Lin, H.; Li, J; Zhou, M. (2016). "Experimental and theoretical identification of the Fe(VII) oxidation state in FeO₄⁻". Physical Chemistry Chemical Physics. 18 (45): 31125–31131. Bibcode:2016PCCP...1831125L. doi:10.1039/C6CP06753K. PMID 27812577.
64. Co(–3) is known in Na₃Co(CO)₃; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
65. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. pp. 1117–1119. ISBN 978-0-08-037941-8.
66. Ni(–2) is known in Ni(COD)2−2; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
67. Ni(0) is known in Ni(CO)₄; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
68. Pfirrmann, Stefan; Limberg, Christian; Herwig, Christian; Stößer, Reinhard; Ziemer, Burkhard (2009). "A Dinuclear Nickel(I) Dinitrogen Complex and its Reduction in Single-Electron Steps". Angewandte Chemie International Edition. 48 (18): 3357–61. doi:10.1002/anie.200805862. PMID 19322853.
69. Carnes, Matthew; Buccella, Daniela; Chen, Judy Y.-C.; Ramirez, Arthur P.; Turro, Nicholas J.; Nuckolls, Colin; Steigerwald, Michael (2009). "A Stable Tetraalkyl Complex of Nickel(IV)". Angewandte Chemie International Edition. 48 (2): 290–4. doi:10.1002/anie.200804435. PMID 19021174.
70. Cu(−2) have been observed as dimeric anions [Cu₄]^2– in La₂Cu₂In; see Changhoon Lee; Myung-Hwan Whangbo (2008). "Late transition metal anions acting as p-metal elements". Solid State Sciences. 10 (4): 444–449. Bibcode:2008SSSci..10..444K. doi:10.1016/j.solidstatesciences.2007.12.001.
71. Jackson, Ross A.; Evans, Nicholas J.; Babula, Dawid J.; Horsley Downie, Thomas M.; Charman, Rex S. C.; Neale, Samuel E.; Mahon, Mary F.; Liptrot, David J. (2025-01-28). "Nucleophilicity at copper(-I) in a compound with a Cu–Mg bond". Nature Communications. 16 (1). doi:10.1038/s41467-025-56544-z. ISSN 2041-1723. PMC 11775243. PMID 39875432.
72. Moret, Marc-Etienne; Zhang, Limei; Peters, Jonas C. (2013). "A Polar Copper–Boron One-Electron σ-Bond". J. Am. Chem. Soc. 135 (10): 3792–3795. doi:10.1021/ja4006578. PMID 23418750.
73. Zn(−2) have been observed (as dimeric and monomeric anions; dimeric ions were initially reported to be [T–T]²⁻, but later shown to be [T–T]⁴⁻ for all these elements) in Ca₅Zn₃ (structure (AE²⁺)₅(T–T)⁴⁻T²⁻⋅4e⁻); see Changhoon Lee; Myung-Hwan Whangbo (2008). "Late transition metal anions acting as p-metal elements". Solid State Sciences. 10 (4): 444–449. Bibcode:2008SSSci..10..444K. doi:10.1016/j.solidstatesciences.2007.12.001. and Changhoon Lee; Myung-Hwan Whangbo; Jürgen Köhler (2010). "Analysis of Electronic Structures and Chemical Bonding of Metal-rich Compounds. 2. Presence of Dimer (T–T)^4– and Isolated T^2– Anions in the Polar Intermetallic Cr₅B₃-Type Compounds AE₅T₃ (AE = Ca, Sr; T = Au, Ag, Hg, Cd, Zn)". Zeitschrift für Anorganische und Allgemeine Chemie. 636 (1): 36–40. doi:10.1002/zaac.200900421.
74. Zn(I) has been reported in decamethyldizincocene; see Resa, I.; Carmona, E.; Gutierrez-Puebla, E.; Monge, A. (2004). "Decamethyldizincocene, a Stable Compound of Zn(I) with a Zn-Zn Bond". Science. 305 (5687): 1136–8. Bibcode:2004Sci...305.1136R. doi:10.1126/science.1101356. PMID 15326350. S2CID 38990338.
75. Hofmann, Patrick (1997). Colture. Ein Programm zur interaktiven Visualisierung von Festkörperstrukturen sowie Synthese, Struktur und Eigenschaften von binären und ternären Alkali- und Erdalkalimetallgalliden (PDF) (Thesis) (in German). PhD Thesis, ETH Zurich. p. 72. doi:10.3929/ethz-a-001859893. hdl:20.500.11850/143357. ISBN 978-3728125972.
76. Ga(−3) has been observed in LaGa, see Dürr, Ines; Bauer, Britta; Röhr, Caroline (2011). "Lanthan-Triel/Tetrel-ide La(Al,Ga)_x(Si,Ge)_1-x. Experimentelle und theoretische Studien zur Stabilität intermetallischer 1:1-Phasen" (PDF). Z. Naturforsch. (in German). 66b: 1107–1121.
77. Ga(−1) has been observed in LiGa; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1185. ISBN 9783110206845.
78. Ga(0) is known in gallium monoiodide; see Widdifield, Cory M.; Jurca, Titel; Richeson, Darrin S.; Bryce, David L. (2012-03-16). "Using 69/71Ga solid-state NMR and 127I NQR as probes to elucidate the composition of "GaI"". Polyhedron. 35 (1): 96–100. doi:10.1016/j.poly.2012.01.003. ISSN 0277-5387.
79. Ge(−1), Ge(−2), Ge(−3), and Ge(–4) have been observed in germanides; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (1995). "Germanium". Lehrbuch der Anorganischen Chemie (in German) (101 ed.). Walter de Gruyter. pp. 953–959. ISBN 978-3-11-012641-9.
80. "New Type of Zero-Valent Tin Compound". Chemistry Europe. 27 August 2016.
81. As(−2) has been observed in CaAs; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 829. ISBN 9783110206845.
82. As(−1) has been observed in LiAs; see Reinhard Nesper (1990). "Structure and chemical bonding in zintl-phases containing lithium". Progress in Solid State Chemistry (1): 1–45. doi:10.1016/0079-6786(90)90006-2.
83. Abraham, Mariham Y.; Wang, Yuzhong; Xie, Yaoming; Wei, Pingrong; Shaefer III, Henry F.; Schleyer, P. von R.; Robinson, Gregory H. (2010). "Carbene Stabilization of Diarsenic: From Hypervalency to Allotropy". Chemistry: A European Journal. 16 (2): 432–5. doi:10.1002/chem.200902840. PMID 19937872.
84. Ellis, Bobby D.; MacDonald, Charles L. B. (2004). "Stabilized Arsenic(I) Iodide: A Ready Source of Arsenic Iodide Fragments and a Useful Reagent for the Generation of Clusters". Inorganic Chemistry. 43 (19): 5981–6. doi:10.1021/ic049281s. PMID 15360247.
85. As(IV) has been observed in (As(OH)₄) and HAsO⁻; see Kläning, Ulrik K.; Bielski, Benon H. J.; Sehested, K. (1989). "Arsenic(IV). A pulse-radiolysis study". Inorganic Chemistry. 28 (14): 2717–24. doi:10.1021/ic00313a007.
86. Se(−1) has been observed in diselenides(Se2−2, such as (Na₂Se₂); see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 829. ISBN 9783110206845. and H. Föppl; E. Busmann; F.-K. Frorath (1962). "Die Kristallstrukturen von α-Na2S2 und K2S2, β-Na2S2 und Na2Se2". Zeitschrift für anorganische und allgemeine Chemie (in German). 314 (1): 12–20. doi:10.1002/zaac.19623140104.
87. A Se(0) atom has been identified using DFT in [ReOSe(2-pySe)₃]; see Cargnelutti, Roberta; Lang, Ernesto S.; Piquini, Paulo; Abram, Ulrich (2014). "Synthesis and structure of [ReOSe(2-Se-py)3]: A rhenium(V) complex with selenium(0) as a ligand". Inorganic Chemistry Communications. 45: 48–50. doi:10.1016/j.inoche.2014.04.003. ISSN 1387-7003.
88. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 978-0-08-037941-8.
89. Se(III) has been observed in Se₂NBr₃; see Lau, Carsten; Neumüller, Bernhard; Vyboishchikov, Sergei F.; Frenking, Gernot; Dehnicke, Kurt; Hiller, Wolfgang; Herker, Martin (1996). "Se₂NBr₃, Se₂NCl₅, Se₂NCl⁻₆: New Nitride Halides of Selenium(III) and Selenium(IV)". Chemistry: A European Journal. 2 (11): 1393–1396. doi:10.1002/chem.19960021108.
90. Br(II) is known to occur in bromine monoxide radical; see Kinetics of the bromine monoxide radical + bromine monoxide radical reaction
91. Rb(–1) is known in ; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
92. Colarusso, P.; Guo, B.; Zhang, K.-Q.; Bernath, P. F. (1996). "High-Resolution Infrared Emission Spectrum of Strontium Monofluoride" (PDF). J. Molecular Spectroscopy. 175 (1): 158. Bibcode:1996JMoSp.175..158C. doi:10.1006/jmsp.1996.0019.
93. Yttrium and all lanthanides except Ce and Pm have been observed in the oxidation state 0 in bis(1,3,5-tri-t-butylbenzene) complexes, see Cloke, F. Geoffrey N. (1993). "Zero Oxidation State Compounds of Scandium, Yttrium, and the Lanthanides". Chem. Soc. Rev. 22: 17–24. doi:10.1039/CS9932200017. and Arnold, Polly L.; Petrukhina, Marina A.; Bochenkov, Vladimir E.; Shabatina, Tatyana I.; Zagorskii, Vyacheslav V.; Cloke (2003-12-15). "Arene complexation of Sm, Eu, Tm and Yb atoms: a variable temperature spectroscopic investigation". Journal of Organometallic Chemistry. 688 (1–2): 49–55. doi:10.1016/j.jorganchem.2003.08.028.
94. Zr(–2) is known in Zr(CO)2−6; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
95. Zr(0) occur in (η⁶-(1,3,5-^tBu)₃C₆H₃)₂Zr and [(η⁵-C₅R₅Zr(CO)₄]⁻, see Chirik, P. J.; Bradley, C. A. (2007). "4.06 - Complexes of Zirconium and Hafnium in Oxidation States 0 to ii". Comprehensive Organometallic Chemistry III. From Fundamentals to Applications. Vol. 4. Elsevier Ltd. pp. 697–739. doi:10.1016/B0-08-045047-4/00062-5. ISBN 9780080450476.
96. Calderazzo, Fausto; Pampaloni, Guido (January 1992). "Organometallics of groups 4 and 5: Oxidation states II and lower". Journal of Organometallic Chemistry. 423 (3): 307–328. doi:10.1016/0022-328X(92)83126-3.
97. Ma, Wen; Herbert, F. William; Senanayake, Sanjaya D.; Yildiz, Bilge (2015-03-09). "Non-equilibrium oxidation states of zirconium during early stages of metal oxidation". Applied Physics Letters. 106 (10). Bibcode:2015ApPhL.106j1603M. doi:10.1063/1.4914180. hdl:1721.1/104888. ISSN 0003-6951.
98. Nb(–3) occurs in Cs₃Nb(CO)₅; see John E. Ellis (2003). "Metal Carbonyl Anions:  from [Fe(CO)₄]₂⁻ to [Hf(CO)₆]₂⁻ and Beyond†". Organometallics. 22 (17): 3322–3338. doi:10.1021/om030105l.
99. Nb(0) and Nb(I) has been observed in Nb(bpy)₃ and CpNb(CO)₄, respectively; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1554. ISBN 9783110206845.
100. Mo(–4) occurs in Na₄Mo(CO)₄; see John E. Ellis (2003). "Metal Carbonyl Anions:  from [Fe(CO)₄]₂⁻ to [Hf(CO)₆]₂⁻ and Beyond†". Organometallics. 22 (17): 3322–3338. doi:10.1021/om030105l.
101. Mo(0) occurs in molybdenum hexacarbonyl; see John E. Ellis (2003). "Metal Carbonyl Anions:  from [Fe(CO)₄]₂⁻ to [Hf(CO)₆]₂⁻ and Beyond†". Organometallics. 22 (17): 3322–3338. doi:10.1021/om030105l.
102. Ellis J E. Highly Reduced Metal Carbonyl Anions: Synthesis, Characterization, and Chemical Properties. Adv. Organomet. Chem, 1990, 31: 1-51.
103. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 1140. ISBN 978-0-08-037941-8.
104. Rh(VII) is known in the RhO₃⁺ cation, see Da Silva Santos, Mayara; Stüker, Tony; Flach, Max; Ablyasova, Olesya S.; Timm, Martin; von Issendorff, Bernd; Hirsch, Konstantin; Zamudio‐Bayer, Vicente; Riedel, Sebastian; Lau, J. Tobias (2022). "The Highest Oxidation State of Rhodium: Rhodium(VII) in [RhO3]+". Angew. Chem. Int. Ed. 61 (38): e202207688. doi:10.1002/anie.202207688. PMC 9544489. PMID 35818987.
105. Pd(I) is known in [Pd₂]²⁺ compounds; see Christoph Fricke; Theresa Sperger; Marvin Mendel; Franziska Schoenebeck (2020). "Catalysis with Palladium(I) Dimers". Angewandte Chemie International Edition. 60 (7). doi:10.1002/anie.202011825.
106. Pd(III) has been observed; see Powers, D. C.; Ritter, T. (2011). "Palladium(III) in Synthesis and Catalysis" (PDF). Higher Oxidation State Organopalladium and Platinum Chemistry. Topics in Organometallic Chemistry. Vol. 35. pp. 129–156. Bibcode:2011hoso.book..129P. doi:10.1007/978-3-642-17429-2_6. ISBN 978-3-642-17428-5. PMC 3066514. PMID 21461129. Archived from the original (PDF) on June 12, 2013.
107. Palladium(V) has been identified in complexes with organosilicon compounds containing pentacoordinate palladium; see Shimada, Shigeru; Li, Yong-Hua; Choe, Yoong-Kee; Tanaka, Masato; Bao, Ming; Uchimaru, Tadafumi (2007). "Multinuclear palladium compounds containing palladium centers ligated by five silicon atoms". Proceedings of the National Academy of Sciences. 104 (19): 7758–7763. doi:10.1073/pnas.0700450104. PMC 1876520. PMID 17470819.
108. Ag(−2) have been observed as dimeric and monomeric anions in Ca₅Ag₃, (structure (Ca²⁺)₅(Ag–Ag)⁴⁻Ag²⁻⋅4e⁻); see Changhoon Lee; Myung-Hwan Whangbo; Jürgen Köhler (2010). "Analysis of Electronic Structures and Chemical Bonding of Metal-rich Compounds. 2. Presence of Dimer (T–T)^4– and Isolated T^2– Anions in the Polar Intermetallic Cr₅B₃-Type Compounds AE₅T₃ (AE = Ca, Sr; T = Au, Ag, Hg, Cd, Zn)". Zeitschrift für Anorganische und Allgemeine Chemie. 636 (1): 36–40. doi:10.1002/zaac.200900421.
109. The Ag⁻ ion has been observed in metal ammonia solutions: see Tran, N. E.; Lagowski, J. J. (2001). "Metal Ammonia Solutions: Solutions Containing Argentide Ions". Inorganic Chemistry. 40 (5): 1067–68. doi:10.1021/ic000333x.
110. Ag(0) has been observed in carbonyl complexes in low-temperature matrices: see McIntosh, D.; Ozin, G. A. (1976). "Synthesis using metal vapors. Silver carbonyls. Matrix infrared, ultraviolet-visible, and electron spin resonance spectra, structures, and bonding of silver tricarbonyl, silver dicarbonyl, silver monocarbonyl, and disilver hexacarbonyl". J. Am. Chem. Soc. 98 (11): 3167–75. doi:10.1021/ja00427a018.
111. Cd(−2) have been observed (as dimeric and monomeric anions; dimeric ions were initially reported to be [T–T]²⁻, but later shown to be [T–T]⁴⁻) in Sr₅Cd₃; see Changhoon Lee; Myung-Hwan Whangbo; Jürgen Köhler (2010). "Analysis of Electronic Structures and Chemical Bonding of Metal-rich Compounds. 2. Presence of Dimer (T–T)^4– and Isolated T^2– Anions in the Polar Intermetallic Cr₅B₃-Type Compounds AE₅T₃ (AE = Ca, Sr; T = Au, Ag, Hg, Cd, Zn)". Zeitschrift für Anorganische und Allgemeine Chemie. 636 (1): 36–40. doi:10.1002/zaac.200900421.
112. Cd(I) has been observed in cadmium(I) tetrachloroaluminate (Cd₂(AlCl₄)₂); see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (1985). "Cadmium". Lehrbuch der Anorganischen Chemie (in German) (91–100 ed.). Walter de Gruyter. pp. 1056–1057. ISBN 978-3-11-007511-3.
113. Guloy, A. M.; Corbett, J. D. (1996). "Synthesis, Structure, and Bonding of Two Lanthanum Indium Germanides with Novel Structures and Properties". Inorganic Chemistry. 35 (9): 2616–22. doi:10.1021/ic951378e. PMID 11666477.
114. In(−2) has been observed in Na₂In, see [1], p. 69.
115. In(−1) has been observed in NaIn; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1185. ISBN 9783110206845.
116. Unstable In(0) carbonyls and clusters have been detected, see [2], p. 6.
117. Sn(−3) has been observed in [Sn₂]⁶⁻, e.g. in (Ba₂)⁴⁺(Mg₄)⁸⁺Sn⁴⁻(Sn₂)⁶⁻Sn²⁻ (with square (Sn²⁻)_n sheets), see Papoian, Garegin A.; Hoffmann, Roald (2000). "Hypervalent Bonding in One, Two, and Three Dimensions: Extending the Zintl–Klemm Concept to Nonclassical Electron-Rich Networks". Angew. Chem. Int. Ed. 2000 (39): 2408–2448. doi:10.1002/1521-3773(20000717)39:14<2408::aid-anie2408>3.0.co;2-u. PMID 10941096. Retrieved 2015-02-23.
118. Sn(−2) has been observed in SrSn; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1007. ISBN 9783110206845.
119. Sn(−1) has been observed in CsSn; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1007. ISBN 9783110206845.
120. "New Type of Zero-Valent Tin Compound". Chemistry Europe. 27 August 2016.
121. "HSn". NIST Chemistry WebBook. National Institute of Standards and Technology. Retrieved 23 January 2013.
122. "SnH3". NIST Chemistry WebBook. National Institure of Standards and Technology. Retrieved 23 January 2013.
123. Sb(−2) and Sb(−1) has been observed in [Sb₂]⁴⁻ and ¹_∞[Sb_n]ⁿ⁻, respectively; see Boss, Michael; Petri, Denis; Pickhard, Frank; Zönnchen, Peter; Röhr, Caroline (2005). "Neue Barium-Antimonid-Oxide mit den Zintl-Ionen [Sb]³⁻, [Sb₂]⁴⁻ und ¹_∞[Sb_n]ⁿ⁻ / New Barium Antimonide Oxides containing Zintl Ions [Sb]³⁻, [Sb₂]⁴⁻ and ¹_∞[Sb_n]ⁿ⁻". Zeitschrift für Anorganische und Allgemeine Chemie (in German). 631 (6–7): 1181–1190. doi:10.1002/zaac.200400546.
124. Anastas Sidiropoulos (2019). "Studies of N-heterocyclic Carbene (NHC) Complexes of the Main Group Elements" (PDF). p. 39. doi:10.4225/03/5B0F4BDF98F60. S2CID 132399530.
125. Sb(I) have been observed in organoantimony compounds; see Šimon, Petr; de Proft, Frank; Jambor, Roman; Růžička, Aleš; Dostál, Libor (2010). "Monomeric Organoantimony(I) and Organobismuth(I) Compounds Stabilized by an NCN Chelating Ligand: Syntheses and Structures". Angewandte Chemie International Edition. 49 (32): 5468–5471. doi:10.1002/anie.201002209. PMID 20602393.
126. Sb(IV) has been observed in [SbCl₆]²⁻, see Nobuyoshi Shinohara; Masaaki Ohsima (2000). "Production of Sb(IV) Chloro Complex by Flash Photolysis of the Corresponding Sb(III) and Sb(V) Complexes in CH3CN and CHCl3". Bulletin of the Chemical Society of Japan. 73 (7): 1599–1604. doi:10.1246/bcsj.73.1599.
127. I(II) is known to exist in monoxide (IO); see Nikitin, I V (31 August 2008). "Halogen monoxides". Russian Chemical Reviews. 77 (8): 739–749. Bibcode:2008RuCRv..77..739N. doi:10.1070/RC2008v077n08ABEH003788. S2CID 250898175.
128. Xe(0) has been observed in tetraxenonogold(II) (AuXe₄²⁺).
129. Harding, Charlie; Johnson, David Arthur; Janes, Rob (2002). Elements of the p block. Great Britain: Royal Society of Chemistry. pp. 93–94. ISBN 0-85404-690-9.
130. Dye, J. L. (1979). "Compounds of Alkali Metal Anions". Angewandte Chemie International Edition. 18 (8): 587–598. doi:10.1002/anie.197905871.
131. Xu, Wei; Lerner, Michael M. (2018). "A New and Facile Route Using Electride Solutions to Intercalate Alkaline Earth Ions into Graphite". Chemistry of Materials. 30 (19): 6930–6935. doi:10.1021/acs.chemmater.8b03421. S2CID 105295721.
132. La(I), Pr(I), Tb(I), Tm(I), and Yb(I) have been observed in MB₈⁻ clusters; see Li, Wan-Lu; Chen, Teng-Teng; Chen, Wei-Jia; Li, Jun; Wang, Lai-Sheng (2021). "Monovalent lanthanide(I) in borozene complexes". Nature Communications. 12 (1): 6467. doi:10.1038/s41467-021-26785-9. PMC 8578558. PMID 34753931.
133. Chen, Xin; et al. (2019-12-13). "Lanthanides with Unusually Low Oxidation States in the PrB₃^– and PrB₄^– Boride Clusters". Inorganic Chemistry. 58 (1): 411–418. doi:10.1021/acs.inorgchem.8b02572. PMID 30543295. S2CID 56148031.
134. All the lanthanides, except Pm, in the +2 oxidation state have been observed in organometallic molecular complexes, see Lanthanides Topple Assumptions and Meyer, G. (2014). "All the Lanthanides Do It and Even Uranium Does Oxidation State +2". Angewandte Chemie International Edition. 53 (14): 3550–51. doi:10.1002/anie.201311325. PMID 24616202.. Additionally, all the lanthanides (La–Lu) form dihydrides (LnH₂), dicarbides (LnC₂), monosulfides (LnS), monoselenides (LnSe), and monotellurides (LnTe), but for most elements these compounds have Ln³⁺ ions with electrons delocalized into conduction bands, e. g. Ln³⁺(H⁻)₂(e⁻).
135. SmB₆⁻ cluster anion has been reported and contains Sm in rare oxidation state of +1; see Paul, J. Robinson; Xinxing, Zhang; Tyrel, McQueen; Kit, H. Bowen; Anastassia, N. Alexandrova (2017). "SmB₆^– Cluster Anion: Covalency Involving f Orbitals". J. Phys. Chem. A 2017,^? 121,^? 8,^? 1849–1854. 121 (8): 1849–1854. doi:10.1021/acs.jpca.7b00247. PMID 28182423. S2CID 3723987..
136. Hf(–2) occurs in Hf(CO)₆²⁻; see John E. Ellis (2003). "Metal Carbonyl Anions:  from [Fe(CO)₄]₂⁻ to [Hf(CO)₆]₂⁻ and Beyond†". Organometallics. 22 (17): 3322–3338. doi:10.1021/om030105l.
137. Hf(0) occur in (η⁶-(1,3,5-^tBu)₃C₆H₃)₂Hf and [(η⁵-C₅R₅Hf(CO)₄]⁻, see Chirik, P. J.; Bradley, C. A. (2007). "4.06 - Complexes of Zirconium and Hafnium in Oxidation States 0 to ii". Comprehensive Organometallic Chemistry III. From Fundamentals to Applications. Vol. 4. Elsevier Ltd. pp. 697–739. doi:10.1016/B0-08-045047-4/00062-5. ISBN 9780080450476.
138. Hf(I) has been observed in hafnium monobromide (HfBr), see Marek, G.S.; Troyanov, S.I.; Tsirel'nikov, V.I. (1979). "Кристаллическое строение и термодинамические характеристики монобромидов циркония и гафния / Crystal structure and thermodynamic characteristics of monobromides of zirconium and hafnium". Журнал неорганической химии / Russian Journal of Inorganic Chemistry (in Russian). 24 (4): 890–893.
139. Ta(–3) occurs in Ta(CO)₅³⁻; see John E. Ellis (2003). "Metal Carbonyl Anions:  from [Fe(CO)₄]₂⁻ to [Hf(CO)₆]₂⁻ and Beyond†". Organometallics. 22 (17): 3322–3338. doi:10.1021/om030105l.
140. Ta(0) is known in Ta(CNDipp)₆; see Khetpakorn Chakarawet; Zachary W. Davis-Gilbert; Stephanie R. Harstad; Victor G. Young Jr.; Jeffrey R. Long; John E. Ellis (2017). "Ta(CNDipp)6: An Isocyanide Analogue of Hexacarbonyltantalum(0)". Angewandte Chemie International Edition. 56 (35): 10577–10581. doi:10.1002/anie.201706323. Additionally, Ta(0) has also been previously reported in Ta(bipy)₃, but this has been proven to contain Ta(V).
141. Ta(I) has been observed in CpTa(CO)₄; see Holleman, Arnold F.; Wiberg, Egon; Wiberg, Nils (2008). Lehrbuch der Anorganischen Chemie (in German) (102 ed.). Walter de Gruyter. p. 1554. ISBN 9783110206845.
142. W(−4) is known in W(CO)4−4; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
143. W(0) is known in W(CO)₆; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
144. Re(0) is known in Re₂(CO)₁₀; see John E. Ellis (2006). "Adventures with Substances Containing Metals in Negative Oxidation States". Inorganic Chemistry. 45 (8). doi:10.1021/ic052110i.
145. Wang, Guanjun; Zhou, Mingfei; Goettel, James T.; Schrobilgen, Gary G.; Su, Jing; Li, Jun; Schlöder, Tobias; Riedel, Sebastian (2014). "Identification of an iridium-containing compound with a formal oxidation state of IX". Nature. 514 (7523): 475–477. Bibcode:2014Natur.514..475W. doi:10.1038/nature13795. PMID 25341786. S2CID 4463905.
146. Mézaille, Nicolas; Avarvari, Narcis; Maigrot, Nicole; Ricard, Louis; Mathey, François; Le Floch, Pascal; Cataldo, Laurent; Berclaz, Théo; Geoffroy, Michel (1999). "Gold(I) and Gold(0) Complexes of Phosphinine‐Based Macrocycles". Angewandte Chemie International Edition. 38 (21): 3194–3197. doi:10.1002/(SICI)1521-3773(19991102)38:21<3194::AID-ANIE3194>3.0.CO;2-O. PMID 10556900.
147. Brauer, G.; Haucke, W. (1936-06-01). "Kristallstruktur der intermetallischen Phasen MgAu und MgHg". Zeitschrift für Physikalische Chemie. 33B (1): 304–310. doi:10.1515/zpch-1936-3327. ISSN 2196-7156. MgHg then lends itself to an oxidation state of +2 for Mg and -2 for Hg because it consists entirely of these polar bonds with no evidence of electron unpairing. (translated)
148. Dong, Z.-C.; Corbett, J. D. (1996). "Na₂₃K₉Tl_15.3: An Unusual Zintl Compound Containing Apparent Tl₅⁷⁻, Tl₄⁸⁻, Tl₃⁷⁻, and Tl⁵⁻ Anions". Inorganic Chemistry. 35 (11): 3107–12. doi:10.1021/ic960014z. PMID 11666505.
149. Pb(0) carbonyls have been observered in reaction between lead atoms and carbon monoxide; see Ling, Jiang; Qiang, Xu (2005). "Observation of the lead carbonyls Pb_nCO (n=1–4): Reactions of lead atoms and small clusters with carbon monoxide in solid argon". The Journal of Chemical Physics. 122 (3): 034505. 122 (3): 34505. Bibcode:2005JChPh.122c4505J. doi:10.1063/1.1834915. ISSN 0021-9606. PMID 15740207.
150. Bi(0) state exists in a N-heterocyclic carbene complex of dibismuthene; see Deka, Rajesh; Orthaber, Andreas (May 9, 2022). "Carbene chemistry of arsenic, antimony, and bismuth: origin, evolution and future prospects". Royal Society of Chemistry. 51 (22): 8540–8556. doi:10.1039/d2dt00755j. PMID 35578901. S2CID 248675805.
151. Thayer, John S. (2010). "Relativistic Effects and the Chemistry of the Heavier Main Group Elements". Relativistic Methods for Chemists. Challenges and Advances in Computational Chemistry and Physics. 10: 78. doi:10.1007/978-1-4020-9975-5_2. ISBN 978-1-4020-9974-8.
152. Th(-I) and U(-I) have been detected in the gas phase as octacarbonyl anions; see Chaoxian, Chi; Sudip, Pan; Jiaye, Jin; Luyan, Meng; Mingbiao, Luo; Lili, Zhao; Mingfei, Zhou; Gernot, Frenking (2019). "Octacarbonyl Ion Complexes of Actinides [An(CO)₈]^+/− (An=Th, U) and the Role of f Orbitals in Metal–Ligand Bonding". Chemistry (Weinheim an der Bergstrasse, Germany). 25 (50): 11772–11784. 25 (50): 11772–11784. doi:10.1002/chem.201902625. ISSN 0947-6539. PMC 6772027. PMID 31276242.
153. Morss, L.R.; Edelstein, N.M.; Fuger, J., eds. (2006). The Chemistry of the Actinide and Transactinide Elements (3rd ed.). Netherlands: Springer. ISBN 978-9048131464.
154. Np(II), (III) and (IV) have been observed, see Dutkiewicz, Michał S.; Apostolidis, Christos; Walter, Olaf; Arnold, Polly L (2017). "Reduction chemistry of neptunium cyclopentadienide complexes: from structure to understanding". Chem. Sci. 8 (4): 2553–2561. doi:10.1039/C7SC00034K. PMC 5431675. PMID 28553487.
155. Kovács, Attila; Dau, Phuong D.; Marçalo, Joaquim; Gibson, John K. (2018). "Pentavalent Curium, Berkelium, and Californium in Nitrate Complexes: Extending Actinide Chemistry and Oxidation States". Inorg. Chem. 57 (15). American Chemical Society: 9453–9467. doi:10.1021/acs.inorgchem.8b01450. OSTI 1631597. PMID 30040397. S2CID 51717837.
156. Domanov, V. P.; Lobanov, Yu. V. (October 2011). "Formation of volatile curium(VI) trioxide CmO₃". Radiochemistry. 53 (5). SP MAIK Nauka/Interperiodica: 453–6. doi:10.1134/S1066362211050018. S2CID 98052484.
157. Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. p. 1265. ISBN 978-0-08-037941-8.
158. Hoffman, Darleane C.; Lee, Diana M.; Pershina, Valeria (2006). "Transactinides and the future elements". In Morss; Edelstein, Norman M.; Fuger, Jean (eds.). The Chemistry of the Actinide and Transactinide Elements (3rd ed.). Dordrecht, The Netherlands: Springer Science+Business Media. ISBN 978-1-4020-3555-5.
159. Thayer, John S. (2010). "Relativistic Effects and the Chemistry of the Heavier Main Group Elements". Relativistic Methods for Chemists. Challenges and Advances in Computational Chemistry and Physics. 10: 83. doi:10.1007/978-1-4020-9975-5_2. ISBN 978-1-4020-9974-8.