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The 18-electron rule is a rule used primarily for predicting formulae for stable metal complexes. The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals, which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that, the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period. The rule and its exceptions are similar to the application of the octet rule to main group elements. The rule is not helpful for complexes of metals that are not transition metals, and in fact the majority of transition metal complexes violate the rule. The rule was first proposed by American chemist Irving Langmuir in 1921.

Applicability of the 18-electron rule
Although the majority of metal complexes do not satisfy the 18-electron rule, the rule usefully predicts the formulae for low-spin complexes of the Cr, Mn, Fe, and Co triads. Well-known examples include ferrocene, iron pentacarbonyl, chromium carbonyl, and nickel carbonyl.

Ligands in a complex determine the applicability of the 18-electron rule. In general, complexes that obey the rule are composed at least partly of π-acid ligands. This kind of ligand exerts a very strong ligand field, which lowers the energies of the resultant molecular orbitals and thus favorably occupied. Typical ligands include olefins, phosphines, and CO. Complexes of π-acids typically feature metal in a low-oxidation state. The relationship between oxidation state and the nature of the ligands is rationalized within the framework of π backbonding.

Consequences for reactivity
Compounds that obey the 18 VE rule are typically "exchange inert." Examples include [Co(NH3)5Cl]2+, Mo(CO)6, and [Fe(CN)6]4-. In such cases, in general ligand exchange occurs via dissociative substitution mechanisms, wherein the rate of reaction is determined by the rate of dissociation of a ligand. On the other hand, 18-electron compounds can be highly reactive toward electrophiles such as protons, and such reactions are associative in mechanism, being acid-base reactions.

Complexes with fewer than 18 valence electrons tend to show enhanced reactivity. Thus, the 18-electron rule is often a recipe for non-reactivity in either a stoichiometric or a catalytic sense.

Alternative analysis
In the prevalent LF analysis, the valence p orbitals on the metal participate in metal-ligand bonding, albeit weakly. Some new theoretical treatments do not count the metal p-orbitals in metal-ligand bonding, although these orbitals are still included as polarization functions. This results in a 12-electron rule which accommodates all low-spin complexes including linear 14e complexes such as Tollen's reagent and square planar 16e complexes as well as implies that such transition metal complexes are hypervalent, but has yet to be adopted by the general chemistry community.

Counting for the 18-electron rule
There are two methods used to count electrons, method A and Method B.

Method A: Determine the oxidation state of the metal and deduce the number of d electrons, then add the d electrons and the ligands together.

Method B: Ignore formal oxidation state, assume it 0, and count the electrons from the ligands.

Example: ClMn(CO)5

Common ligands and their contributions to both methods of counting is shown in the table below.

Table found in Miessler text.

Oxidation
When determining the oxidation state of the metal, the ligands are the most important factor. For complexes with charged ligands the oxidation state of the metal can be calculated from the molecules formal charge, the charge would need to balance out the ligands charge to result in the formal charge of the molecule. For complexes with neutral ligands, the oxidation state is equal to the formal charge of the molecule.


 * Ex: CrCl3 the oxidation state of Cr is 3+ to balance with the 3(Cl-) ligands.


 * Ex2: [Fe(CO)6]2+ the oxidation of Fe is 2+ because the ligands are neutral and the formal charge is 2+.


 * A few common ligand charges would be: Halogens -1 charge; CO is a neutral ligand; CN -1 charge; NO +1 or -1 charge.

Eta
“eta-x” was originally developed to indicate how many contiguous donor atoms of a p-system were coordinated to a metal center. Hapticity is another word used to describe the bonding mode of a ligand to a metal center. An h5-cyclopentadienyl ligand, for example, has all five carbons of the ring bonding to the transition metal center.

Kappa
“kappa-x” was developed to indicate how many non-contiguous donor atoms of a ligand system were coordinated to a metal center. This usually refers to non-carbon donor atoms, but can include carbons.for example,a k1-dppe (Ph2PCH2CH2PPh2) ligand has only one of the two phosphorus donors bonded to the transition metal center.

Mu
“mu-x” is the nomenclature used to indicate the presence of a bridging ligand between two or more metal centers. The x refers to the number of metal centers being bridged by the ligand. Usually most authors omit x = 2 and just use m to indicate that the ligand is bridging the simplest case of two metals.

Exceptions to the 18-electron rule
π-donor or σ-donor ligands with small intractions with the metal orbitals lead to a weak ligand field which increases the energies of t2g orbitals. These molecular orbitals become non-bonding or weakly anti-bonding orbitals (small Δoct). Therefore, addition or removal of electron has little effect on complex stability. In this case, there is no restriction on the number of d-electrons and complexes with 12 -22 electrons are possible. Small Δoct makes filling eg* possible ( > 18e-) and π-donor ligands can make t2g antibonding ( < 18 e-). These types of ligand are located in low to medium of the spectrochemical series. For example: [TiF6]2- (Ti4+, d0, 12 e), [Co(NH3)6]3+ (Co3+, d6, 18 e), [Cu(OH2)6]2+ (Cu2+, d9, 21 e) In tems of metal ions, Δoct increases down a group as well as increasing oxidation number. Strong ligand fields lead to low-spin complexes which cause some exceptions to 18-electron rule.

16e complexes
A popular class of complexes that violate the 18e rule are the 16e complexes with d8 configurations. All high-spin d8metal ions are octahedral (or tetrahedral), but the low-spin d8 metal ions are all square planar (Jahn-Teller distortion). Important examples of square-planar low-spin d8 metal Ions are Ni(II), Pd(II), and Pt(II). At picture below is shown the splitting of the d sub-shell in low-spin square-planar complexes. Examples are especially prevalent for derivatives of the cobalt and nickel triads. Such compounds are typically square-planar. The most famous example is Vaska's complex (IrCl(CO)(PPh3)2), [PtCl4]2 &minus;, and Zeise's salt [PtCl3(η2-C2H4)]&minus;. In such complexes, the dz 2 orbital is doubly occupied and nonbonding.


 * [[Image:Chem507f09sqvstet2.png]]

Many catalytic cycles operate via complexes that alternate between 18e and square-planar 16 configurations. Examples include Monsanto acetic acid synthesis, hydrogenations, hydroformylations, olefin isomerizations, and some alkene polymerizations.

Other violations can be classified according to the kinds of ligands on the metal center.

14e complexes
A d10 transition metal complex with only 2 ligands can form 14 electron complexes. Sterically large ligands encourage this coordination number.

For d10 complexes, a relatively small energy difference between the d, s and p orbitals results in extensive hybridization between the dz2, s and pz orbitals. 14-electron complexes are more common for group 11 (Cu, Ag, Au) than group 12 (Zn, Cd, Hg) because the energy difference between the d, s and p-orbitals is smaller for group 11.

Examples: [Ag(CN)2]-, [Ag(NH3)2]+, [Cu(NH3)2]+, [(R3P)AuCl], [HgMe2], [CdMe2], [ZnMe2]

These complexes are active and could be a real catalyst. They have two vacant sites that could be further occupied by other molecules. The utilization of the neutral 14-electron complex, in organic and polymer chemistry is now pervasive.

Bulky ligands
Bulky ligands can preclude the approach of the full complement of ligands that would allow the metal to achieve the 18 electron configuration. Examples: Sometimes such complexes engage in agostic interactions with the hydrocarbon framework of the bulky ligand. For example:
 * Ti(neopentyl)4 (8 VE)
 * Cp*2Ti(C2H4) (16 VE)
 * V(CO)6 (17 VE)
 * Cp*Cr(CO)3 (17 VE)
 * Pt(PtBu3)2 (14 VE)
 * Co(norbornyl)4 (13 VE)
 * [FeCp2]+ (17 VE)
 * W(CO)3[P(C6H11)3]2 has 16 VE but has a short bonding contact between one C-H bond and the W center.
 * Cp(PMe3)V(CHCMe3) (14 VE, diamagnetic) has a short V-H bond with the 'alkylidene-H', so the description of the compound is somewhere between Cp(PMe3)V(CHCMe3) and Cp(PMe3)V(H)(CCMe3).

High-spin complexes
High-spin metal complexes have singly occupied orbitals and may not have any empty orbitals into which ligands could donate electron density. In general, there are few or no π-acidic ligands in the complex. These singly occupied orbitals can combine with the singly occupied orbitals of radical ligands (e.g., oxygen), or addition of a strong field ligand can cause electron-pairing, thus creating a vacant orbital that it can donate into. Examples: Complexes containing strongly pi-donating ligands often violate the 18-electron rule. These ligands include fluoride (F&minus;), oxide (O2 &minus;), nitride (N3 &minus;), alkoxide (RO&minus;), and imide (oxide (RN2 &minus;). Examples: In the latter case, there is substantial donation of the nitrogen lone pairs to the Mo (so the compound could also be described as a 16 VE compound). This can be seen from the short Mo-N bond length, and from the angle Mo - N - C(R), which is nearly 180°. Counter-examples: In these cases, the M=O bonds are "pure" double bonds (i.e., no donation of the lone pairs of the oxygen to the metal), as reflected in the relatively long bond distances.
 * CrCl3(THF)3 (15 VE)
 * [Mn(H2O)6]2+ (17 VE)
 * [Cu(H2O)6]2+ (21 VE, see comments below)
 * [CrO4]2 &minus; (16 VE)
 * Mo(=NR)2Cl2 (12 VE)
 * trans-WO2(Me2PCH2CH2PMe2)2 (18 VE)
 * Cp*ReO3 (18 VE)

Pi-donating ligands
Ligands where the coordinating atom bear nonbonding lone pairs often stabilize unsaturated complexes. Metal amides and alkoxides often violate the 18e rule.

Combinations of effects
The above factors can sometimes combine. Examples include
 * Cp*VOCl2 (14 VE)
 * TiCl4 (8 VE)

Higher electron counts
Some complexes have more than 18 electrons. Examples: Often, cases where complexes have more than 18 valence electrons are attributed to electrostatic forces - the metal attracts ligands to itself to try to counterbalance its positive charge, and the number of electrons it ends up with is unimportant. In the case of the metallocenes, the chelating nature of the cyclopentadienyl ligand stabilizes its bonding to the metal. Somewhat satisfying are the two following observations: (i) cobaltocene is a strong electron donor, readily forming the 18-electron cobaltocenium cation and (ii) nickelocene tends to react with substrates to give 18-electron complexes, e.g. CpNiCl(PR3) and free CpH.
 * Cobaltocene (19 VE)
 * Nickelocene (20 VE)
 * The hexaaqua copper(II) ion [Cu(H2O)6]2+ (21 VE)