Oxidation State, A Long‐Standing Issue!
2015; Wiley; Volume: 54; Issue: 16 Linguagem: Inglês
10.1002/anie.201407561
ISSN1521-3773
Autores Tópico(s)Radioactive element chemistry and processing
ResumoWhat 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 NN 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 alone dictates the oxidation states. The algorithm is named DIA (direct ionic approximation) in Ref. 14: Atoms are assigned octets according to their decreasing electronegativity until all the available valence electrons are used up. The atom charges then represent the oxidation states. Typical DIA-friendly species are homoleptic binaries of at least one sp element (Figure 3): CO, HF2−, NO3−, NO2, NH4+, CrO42−, BF4−, SF6, SnCl62−, CuCl42−, RuO4, AuI4−…; or solids with a homoleptic periodic bonding unit: KBr, SiC, AlCl3, SnCl2, etc. DIA of compounds of three or more elements may become ambiguous, with the limitations discussed in Appendix D of Ref. 14. Oxidation states (in red) in CO and HF2− from DIA (direct ionic approximation) performed on a summary formula by distributing valence electrons (here drawn in pairs) into octets according to decreasing electronegativity. These algorithms work on Lewis formulas that display all the valence electrons: Bonds are assigned to the more negative bond partner identified by ionic approximation. The resulting atom charges then represent the oxidation state (Figure 4). As only homonuclear bonds are divided (equally), the correct bond multiplicity is essential only between those pairs of atoms of the same element that appear asymmetrical within the segment of the pair's bonds, including the sign of their ionic approximation: Whereas the OO bond order in Figure 4 would not matter so long as the -OO- segment were kept symmetrical, the NN bond order in an N2O Lewis formula always matters. Oxidation states (in red) in peroxynitrous acid, obtained by assigning bonds to more electronegative partners on Lewis formula with all valence-electron pairs drawn (dashes). An example of the exception to the rule of ionic approximation according to electronegativity is [(C5H5)(CO)2FeB(C6H5)3]23 on the right-hand side of Figure 5. Despite the higher electronegativity of B, the Lewis-basic Fe atom keeps the electrons it donated to bond triphenylborane. When B is replaced by Al24 (Figure 5 left), the same principle applies, now in line with the Fe and Al electronegativities. The weak donor–acceptor bonds in these two adducts are the telltale sign of the reversibility criterion of Haaland,21 suggested in Ref. 14 to identify cases of electron allegiance against electronegativity such as the one on the right-hand side of Figure 5. Oxidation states (in red) by assigning a metal–metal bond according to the atoms' contributions to the bonding MO. An assignment according to the electronegativity needs to invoke the caveat of a Lewis-basic atom with electronegativity lower than the Lewis-acidic one (in the formula on the right). This algorithm is tailored to bond graphs. A bond graph represents the infinite periodic network of an extended solid.25, 26 It is constructed on a stoichiometric formula of the network's repetitive unit, with atom symbols distributed such that a straight line is drawn for each instance of an atom's bonding connectivity. Each line carries its own specific bond order. To obtain the oxidation state, a sum is calculated at each atom, of the orders of its bonds weighted by their ionic sign at that atom. Such an "ionized bond order sum", iBOS, then equals the atom's oxidation state. Figure 6 explains this on the AuORb3 perovskite-type structure27 with bond orders according to the 8+N rule at Rb, 8−N rule at O, and the 12−N rule at Au. The unit cell and coordination polyhedra of the AuORb3 perovskite with its bond graph of ideal bond orders (values in blue) obtained from the 8−N rule for O, the 8+N rule for Rb, and the 12−N rule for Au. The bond orders are shown with signs, which sum up at each atom to yield that atom's oxidation state (in red). The 8+N rule: An electropositive sp atom with N valence electrons forms N two-electron bonds with atoms of higher electronegativity. The rule concerns alkali metals and alkaline-earth metals. The 8 in its name symbolizes the preceding noble-gas shell. The 8−N rule: An electronegative sp atom with N valence electrons tends to form 8−N but not more than four two-electron bonds with atoms of equal or lower electronegativity. As an example, phosphorus with 5 valence electrons forms 3 two-electron bonds in the P4 tetrahedron, and nitrogen does the same in N2. In heteroatomic molecules, the 8−N rule is enforced by higher electronegativity. For example: In sulfur fluorides, the 8−N rule concerns fluorine. Bonds in SF2, SF4, and SF6 have all approximately the length of a single bond.28 In the series BF, CO, and N2, the full triple bond suggested by the octet rule only occurs in N2, whereas O and F force the bond order towards 2 and 1, respectively.29 The 8−N rule is not the same as the octet rule, as each can be violated independently: The Lewis formula of N2O can be drawn as |NN-O|, which has octets yet violates the 8−N rule on oxygen. Hydrogen obeys an analogous 2−N rule. The 12−N rule: An element having close to 12 dsp electrons in its outermost shells tends to lose those that exceed 12 or to gain in bonds those less than 12. While the first tendency (to form s2 cations) is magnified by other trends in the main groups of the periodic system, the second (to form s2 anions) is specific to Pt and Au, which in such compounds are called relativistic chalcogens and halogens, respectively.30 Oxidation state (in red) in carbon monoxide (left) and chromium hexacarbonyl (right) calculated from Lewis formulas of idealized bond orders (in blue) featuring nonzero formal charges (in black). In this expression, BVij and dij are the respective bond valence and distance of the atoms i and j, R0ij is the single-bond length between them, and B is a variable parameter often fixed to 0.37. Although for the best accuracy R0ij is a function of the coordination number and oxidation state of the "cation" for a given "anion" (fitted33, 34 to a set of such structures), a general approach35 lists two parameters for each atom, related to the size and electronegativity, from which R0ij is calculated for any atom pair i and j. As the oxidation state operates on integer electrons, a round off is required on the obtained bond valences/orders or on their ionized sums at an atom. We will now analyze WCl4 in Figure 8. The bond graph of its infinite chain has a W-W group and eight Cl atoms, with each W coordinating six Cl atoms by two single, two 3/4, and two 1/2 bonds, as estimated from experimental bond lengths36 in Ref. 14c. Participation of more than one p orbital at the Cl bridge above and below W-W makes its bond-order sum (1.5 at Cl) exceed the 8−N rule. A chain edge resembles locally a molecule, and such a Cl atom in a Lewis formula would carry a formal charge of 0.5+, compensated by 0.25− at each of the two W atoms it bridges. This feature can be seen in the bond graph in Figure 8. Top: A segment of the infinite WCl4 chain with alternate WW bonds. Bottom: Bond graph of the chain with idealized bond orders (in blue, rounded off bond-length to bond-valence calculations), which sum at each atom with the formal charges (in black) to the oxidation state of that atom (in red). The bond-valence approach to bond orders can also be used for finite species. An example is Cu5I72− 37 in Figure 9. One of the five Cu atoms bonds to four iodine atoms, while the remaining four Cu atoms bond three. Two of the seven iodine atoms bond to three Cu atoms and the remaining five only to two. The oxidation state is evaluated as a round off value of the positive and negative sums of bond valences calculated with Equation (2)] from bond distances dCuI in Ref. 37 and R0CuI=2.188 Å obtained from parameters in Ref. 35. As the CuCu bonds are not approximated to be ionic, only the CuI bonds are relevant besides the 2/7 bonds from each iodine atom to the cations omitted in Figure 9, which yields ionized bond valence sums of −1.05(4) per iodine and +1.07(2) per Cu atom. A round off yields a single oxidation state for each element in a nice demonstration of the Pauling's31 parsimony rule. Bond valences (in blue) in Cu5I72− and the sums of the ionized bond valence at the atoms (in pink) that yield the oxidation states (in red) upon rounding off. Blue sphere Cu, yellow sphere I. An example of an sp molecule shows another kind of bonding compromise: (C6H5)3PCP(C6H5)3. This extreme Lewis formula emphasizes the high order of the phosphorus-to-carbon bond because of the 8−N rule working for the more electronegative carbon atom. A bond order of 1.9 is calculated as above from the distance38, 39 of 1.63 Å. As the PCP angle is not 180° but only 134°,39 the 8−N rule is somewhat violated due to the only small difference in the electronegativity of P and C, and it is clear that this bond has a strong ionic contribution from the formal charges 1+, 2−, and 1+ that would appear on the PCP segment if σ bonded. As these charges comply with the electronegativity, the bond strengthens and becomes a40 "sort of double bond". When this ionocovalent interaction is drawn with two full dashes as above, the formula loses its formal charges, and the oxidation states equal directly to the sums of the ionized bond order: −4 at the carbon and +5 at the phosphorus atom. That makes sense redox-wise within the molecule41 as well as in its full42, 43 synthesis. Given the bond strength, the Haaland criterion is unlikely to apply in this case. An example of an sp cluster is As4S4. It occurs as two different molecules, where both elements maintain the 8−N rule (an electron-precise cluster). This information is sufficient to obtain their oxidation states by sums of the ionized bond orders (Figure 10). Oxidation states (in red) obtained by summing the bond orders (in blue) in two σ-bonded As4S4 clusters that maintain the 8−N rule. A cluster where the 8−N rule is weakened due to steric compromise is S4N4. It is the same as on the left side of Figure 10, except that N replaces S while S replaces As. Neither atom complies with the 8−N rule, which would require formation of three short two-electron bonds from the small N to the bulky S atom. As the bond lengths and angles in solid S4N444 are irregular, data for gaseous S4N445 are considered here: The molecule has a sulfur tetrahedron with a 2m point symmetry and bond lengths of 2.666 and 2.725 Å, far longer than a single bond of 2.055 Å.46 One approach to sensible oxidation states is to neglect these weak S-S interactions and consider S4N4 a cyclic tetramer with an SN summary formula, to which DIA applies to yield +3 and −3 for the oxidation states. Bond-based algorithms give the same result (Figure 11) on a symmetrical Lewis formula with 22 electron pairs, by considering the SNS bond angle of 105.3(7)° is tetrahedral and complemented by two lone pairs of electrons at N, with each S atom forming one single bond to another S atom (with a 1− formal charge at N and 1+ charge at S). The reality is somewhere in between these two simplifications: The SN bond valence calculated with parameters from Ref. 35 with a SN bond length of 1.623(4) Å45 is 1.40(2)—more than the single bond of the Lewis formula but not quite the 1.50 required by the 8−N rule. The similarly calculated sum of the homonuclear bond valence at each S atom of the tetrahedron is about 0.5, half of the 1.00 generated by the single bond in the Lewis formula. Oxidation states evaluated on formulas approximating S4N4: a periodic unit of a ring (left; neglecting the weak bonds among the sulfur atoms in the real compound) and a Lewis formula of octets (middle and right; approximating the tetrahedral sulfur cluster with two SS bonds). For our S4N4 example above, we obtain VECA=11. The three electrons in excess of eight remain at the S atom as one SS bond and one lone pair per S atom in our Lewis formula; in reality this is somewhat violated, since electronegativity makes sulfur enforce the 8−N rule almost as strongly as nitrogen. When there is sufficient difference in electronegativity, bonding predictions with the generalized 8−N rule are precise. Consider GaSe with VECA=9: The single electron in excess of 8 would remain on Ga, thereby forming single-bonded GaGa dumbbells. That is indeed the case, and the oxidation states in GaSe are evaluated by summing bond orders in Figure 12. Unit cell of GaSe with one full Ga coordination shown (left, two of the three coordinated Se atoms are outside the unit cell) and the oxidation states determined from its bond graph (right). The bond order dictated by the 8−N rule is listed above the three connectivity lines. Below them, the bond valence is listed, calculated from the bond length determined50 by X-ray diffraction. Boranes of general formula BbHhc (b>4, c≤0) are sp clusters that are not electron-precise (the skeleton bonds are not single bonds). When all the B atoms are equivalent, the oxidation state can be evaluated by DIA on a repeat unit, such as BH(1/3)− with 4 1/3 electrons for B6H62−. The unit's hydrogen atom obtains 2 electrons (2−N rule), thereby leaving 2 1/3 electrons at B, which means that OSB=+2/3 (still counting whole electrons; 2 per 3 atoms). Generalizing that OSH=−1, charge balance yields (h+c)/b for the average boron oxidation state in BbHhc. To resolve individual boron oxidation states, Wade–Mingos rules51–54 are applied first: As an example, B6H10 has 14 valence-electron pairs of which 6 are in BH single bonds, 1 always is in a radial-skeletal MO, and the remaining 7, in the tangential skeletal MOs, form a 7-vertex parent deltahedron (pentagonal bipyramid), of which one vertex is "missing" in B6H10 (a nido-borane; Figure 13). Its B atoms are not all equivalent. The five basal boron atoms are bonded to nine hydrogen atoms that maintain the 2−N rule. Summation of the bond orders with a positive sign yields an oxidation state of +2 for three of these B atoms (those in front) and +3/2 for the remaining two. The apical B atom has an oxidation state of +1 arising from one single bond to H. The nido-borane B6H10. When bonding and antibonding orbitals/bands overlap in a metal, we are no longer entitled to make the ionic extrapolations as in Figure 1. However, there are simple metallic compounds with obvious oxidation states, such as the golden TiO, dark RuO2, or silvery ReO3. Some sp elements also form stoichiometric metallic compounds: Ba3Si4 obeys the Zintl concept47 in that it forms butterfly-shaped Si46− anions, in which two Si atoms have two bonds and two Si atoms three bonds to each other according to the generalized 8−N rule, but the compound is weakly metallic.55 Ultimately, the assignment of conducting electrons to one of the two bonded atoms has its limits. An indication of the problem is an unexpected electron configuration or an unexpected bonding pattern. The former is exemplified by the AuNCa3 perovskite56 (Figure 14), where neglecting its metallic character suggests Au3− anions, for which there is no support in theory. The latter may be illustrated on two platinides: red transparent Cs2Pt57 and58 black BaPt. In line with the 12−N rule, Cs2Pt contains isolated Pt2− anions—a relativistic sulfide. However, BaPt does not have such anions; it has chains of Pt as if there were a deficit of electrons at the Pt atom. This means that some electrons left Pt2− to make BaPt metallic, and it is this deficit that is compensated by forming PtPt bonds. If these PtPt bonds were single bonds, their chain would be a neutral relativistic sulfur and BaPt would be built of Ba2+, 2e−, and Pt in infinite chains. As BaPt appears formally stoichiometric, the +2 oxidation state for Ba leaves Pt with −2, which does not comply with the actual bonding. Bond graph for the metallic perovskite AuNCa3, in which summing bond orders (in blue) of N and Ca, obtained from 8−N and 8+N rules, respectively, yields an invalid oxidation state for Au. Unsatisfactory oxidation states are also obtained when DIA is applied to ordered alloys with compositions and structures dictated largely by the size, such as LiPb or Cu3Au, where the 8−N or 12−N rules for the most electronegative element are not valid. If an oxidation state is needed to balance redox equations, it is best considered zero for all elements. The applications of oxidation state in chemistry are wide, and one value does not always fit all. In systematic descriptive chemistry, the oxidation state sorts out compounds of an element; in electrochemistry, it represents the electrochemically relevant compound or ion in Latimer diagrams and Frost diagrams of standard (reduction) potentials. Such purpose-oriented oxidation states that differ from those by definition may be termed nominal, here "systematic" and "electrochemical". An example of both is thiosulfate. Its structural properties59 suggest that all its terminal atoms carry some of the anion charge, even if the SS and SO bond orders are not entirely equal. The SS bond distance of 2.025 Å59 is shorter than the single bond of 2.055 Å46 in crystalline S8 or 2.056 Å60 in H2S2 gas, but substantially longer than the double bond of 1.883 Å61, 62 in S2O or 1.889 Å63 in S2. Although the single SS bond is the closest approximation, two limiting Lewis formulas are considered in Figure 15. Oxidation states in thiosulfate by assignment of bonds and by summing bond orders on two limiting Lewis formulas (in which the author chose to draw bonds to unexpressed cations to avoid formal charges) with a sulfur–sulfur single bond (left), double bond (right). The formula on the left provides oxidation state −1 at the terminal sulfur atom, reminiscent of the value in peroxides. The formula on right suggests oxidation states that at times are used for a Lewis acid–base interpretation of the synthesis reaction S + SO32−=S2O32−, making it a nonredox process. This is not necessarily an advantage, as this reaction in an aqueous environment is well-described with half-reaction standard potentials that utilize the average sulfur oxidation state +2, which represents thiosulfate in Latimer and Frost diagrams—an electrochemical oxidation state. The only route to unambiguous oxidation states for both S atoms in thiosulfate would be to resolve the SS bond polarity, as in some textbooks: the terminal sulfur has −2, the central sulfur +6, independent of their bond order and emphasizing the similarity of the O and S ligands—a systematic oxidation state. Jørgensen64, 65 coined the adjective "non-innocent" for redox-active ligands that render the oxidation state of the central atom less obvious. Additional information from diffraction, spectra, or magnetic measurements is needed. Of the many examples,66–68 the simplest non-innocent ligand is molecular H2. Complexes with molecular H2 resemble hapto complexes of olefins or aromatic hydrocarbons, except that H2 only has a σ bond. Despite this, H2 attaches to metal cations even in the gas phase, free of solvents, substrates, and intervening atoms, as elaborated in a recent review69 by Bieske and co-workers. An intriguing ambiguity arises: with some metal ions, the atoms of the H2 molecule remain bonded to each other, while with others they form a dihydride. Crabtree70 attributes this to the central transition-metal atom having both empty and filled d orbitals: The former participate in the three-center bonding MO that binds the H2 moiety while the latter sabotage this by back donation into the empty antibonding MO of H2. The two extreme outcomes are presented schematically in Figure 16. Two extremes of an H2 adduct with a generic metal atom M. In 1984, Kubas et al.71 synthesized the first transition-metal complex with an H2 ligand, the yellow [W(CO)3(η2-H2){P(C6H11)3}2], by precipitating it from a solution of [W(CO)3{P(C6H11)3}2] in toluene with H2 gas. An example of the hydride formation is [Ir(CO)Cl(H)2{P(C6H5)3}2],72, 73 obtained from H2 and the square-planar [Ir(CO)Cl{P(C6H5)3}2],74 also known as Vaska's complex. Both types of bonded hydrogen occur in [Ru(H)2(η2-H2)2{P(C5H9)3}2],75 the oxidation states of which are evaluated in Figure 17. Oxidation states (in red) of hydrogen and ruthenium in [RuH2(η2-H2)2{P(C5H9)3}2],75 obtained by assigning bonds onto the electronegative partner (left) and by summing ionized bond orders (right). The octahedral complex in Figure 17 is stabilized by the d6 electronic configuration and the 18-plet on Ru. While the two cis-hydride anions are 2.13 Å apart, the HH distance in the H2 ligand is 0.83 Å (0.09 Å longer than in H2 gas). Its bond order is 0.78, a little more than 2/3 for a three-center bond of equal partners, and this can be attributed to the 2−N rule working for the more electronegative hydrogen atom. A review by Morris76 of iron-group H2 complexes shows that the HH bond distances vary, up to about 1.60 Å for the largest Os,77 and also depend on the ligand trans to H2: When that ligand is an electron-rich sp atom, such as oxygen or a halogen78 capable of strong π donation to the central atom, the HH distance is long. When that ligand is π-acidic, such as CO, or when it is electron-poor, the HH distance is short.76 The distance increases with the extent of back donation from the central atom into the σ* MO of H2, as controlled by the metal's size and by the trans ligand. By our oxidation-state definition, the back-bonding metal atom gets its electrons back because it is the main contributor to this additional metal–ligand bonding interaction, which is antibonding with respect to the HH bond. Allen electronegativities also yield zero for the oxidation state of all such η2 hydrogen atoms. Perhaps the best known nitrosyl complex is nitroprusside. While CN in [Fe(CN)5NO]2− is easy, NO offers three alternatives f
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