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• Effective Atomic Number Calculation
• Effective Atomic Number Calculator
• How To Calculate Effective Atomic Number
• Chemistry Atomic Structure Worksheet Answers

Learning Objectives

THE EFFECTIVE ATOMIC NUMBER This gives E = no(aAZ1 + aBZ-1 +.) (8) where no is the total number of electrons per cubic centimeter, and aA, aB is the fraction of the total number of electrons belonging to atoms with atomic number ZA, ZB, etc. The effective atomic number can now be defined: ZI = (aAZZ-1 + aBZB1 +. )1/(-1) (9) and the atomic weight. Calculate effective atomic number of iron in Fe(CN)64− complex ion. Maharashtra State Board HSC Science (Electronics) 12th Board Exam. Question Papers 164. Textbook Solutions 10906. Important Solutions 3209. Question Bank Solutions 11430. Concept Notes & Videos 429.

In this lecture you will learn the following

• Have an insight about the stability of the transition metal complexes with respect to their total valence electron count.
• Be aware of the transition metal complexes that obey or do not obey the 18 Valence Electron Rule.
• Have an appreciation of the valence electron count in the transition metal organometallic complexes that arise out of the metal-ligand orbital interactions.

The transition metal organometallic compounds exhibit diverse structural variations that manifest in different chemical properties. Many of these transition metal organometallic compounds are primarily of interest from the prospectives of chemical catalysis. Unlike the main group organometallic compounds, which use mainly ns and np orbitals in chemical bonding, the transition metal compounds regularly use the (n−1)d, ns and np orbitals for chemical bonding (Figure 1). Partial filling of these orbitals thus render these metal centers both electron donor and electron acceptor abilities, thus allowing them to participate in σ-donor/π-acceptor synergic interactions with donor-acceptor ligands like carbonyls, carbenes, arenes, isonitriles and etc,.

The 18 Valence Electron (18 VE) Rule or The Inert Gas Rule or The Effective Atomic Number (EAN) Rule: The 18-valence electron (VE) rule states that thermodynamically stable transition metal compounds contain 18 valence electrons comprising of the metal d electrons plus the electrons supplied by the metal bound ligands. The counting of the 18 valence electrons in transition metal complexes may be obtained by following either of the two methods of electron counting, (i). the ionic method and (ii). the neutral method. Please note that a metal-metal bond contributes one electron to the total electron count of the metal atom. A bridging ligand donates one electron towards bridging metal atom.

Example 1: Ferrocene Fe(C₅H₅)₂

Example 2. Mn₂(CO)₁₀

Chrome store. Transition metal organometallic compounds mainly belong to any of the three categories.

1. Class I complexes for which the number of valence electrons do not obey the 18 VE rule.
2. Class II complexes for which the number of valence electrons do not exceed 18.
3. Class III complexes for which the valence electrons exactly obey the 18 VE rule.

The guiding principle which governs the classification of transition metal organometallic compounds is based on the premise that the antibonding orbitals should not be occupied; the nonbonding orbitals may be occupied while the bonding orbitals should be occupied.

Class I:
In class I complexes, the Δ_o splitting is small and often applies to 3d metals and σ ligands at lower end of the spectrochemical series. In this case the t_2g orbital is nonbonding in nature and may be occupied by 0−6 electrons (Figure 2). The e_g* orbital is weakly antibonding and may be occupied by 0−4 electrons. As a consequence, 12−22 valence electron count may be obtained for this class of compounds. Owing to small Δ_tetr splitting energy, the tetrahedral transition metal complexes also belongs to this class.

Class II:
In class II complexes, the Δ_o splitting is relatively large and is applicable to 4d and 5d transition metals having high oxidation state and for σ ligands in the intermediate and upper range of the spectrochemical series. In this case, the t_2gorbital is essentially nonbonding in nature and can be filled by 0−6 electrons (Figure 3). The e_g* orbital is strongly antibonding and is not occupied at all. Consequently, the valence shell electron count of these type of complexes would thus be 18 electrons or less.

Class III:
In class III complexes, the Δ_o splitting is the largest and is applicable to good σ donor and π acceptor ligands like CO, PF₃, olefins and arenes located at the upper end of the spectrochemical series. The t_2gorbital becomes bonding owing to interactions with ligand orbitals and should be occupied by 6 electrons. The e_g* orbital is strongly antibonding and therefore remains unoccupied.

Problems

State the oxidation state of the metal and the total valence electron count of the following species.

1. V(C₂O₄)₃³⁻

Ans: +3 and 14 2. Mn(acac)₃ Ans: +3 and 16 3. W(CN)₈³⁻ Ans: +5 and 17 4. CpMn(CO)₃ Ans: 0 and 18 5. Fe₂(CO)₉ Ans: 0 and 18 Self Assessment test

State the oxidation state of the metal and the total valence electron count of the following species.

1. TiF₆^2-

Ans: +4 and 12 2. Ni(en)₃²⁺ Ans: +2 and 20 3. Cu(NH₃)₆²⁺ Ans: +2 and 21 4. W(CN)₈^4- Ans: +4 and 18 5. CH₃Co(CO)₄ Ans: 0 and 18

Summary

The transition metal complexes may be classified into the following three types. (i). The ones that do not obey the 18 valence electron rule are of class I type (ii). the ones that do not exceed the 18 valence electron rule are of class II and (iii). the ones that strictly follow the 18 valence electron rule. Depending upon the interaction of the metal orbitals with the ligand orbitals and also upon the nature of the ligand position in spectrochemical series, the transition metal organometallic compounds can form into any of the three categories.

The 18-electron rule is used primarily for predicting and rationalizing formulae for stable metal complexes, especially organometallic compounds. The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals (one s orbital, three p orbitals and five d 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 has 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.

This rule applies primarily to organometallic compounds, and the 18 electrons come from the 9 available orbitals in d orbital elements (1 s orbital, 3 p orbitals, and 5 d orbitals). The rule is not helpful for complexes of metals that are not transition metals, and interesting or useful transition metal complexes will violate the rule because of the consequences deviating from the rule bears on reactivity. If the molecular transition metal complex has an 18 electron count, it is called saturated. This means that additional ligands cannot bind to the transition metal because there are no empty low-energy orbitals for incoming ligands to coordinate. If the molecule has less than 18 electrons, then it is called unsaturated and can bind additional ligands.

Electron counting

Two methods are commonly employed for electron counting:

1. Neutral atom method: Metal is taken as in zero oxidation state for counting purpose
2. Oxidation state method: We first arrive at the oxidation state of the metal by considering the number of anionic ligands present and overall charge of the complex

To count electrons in a transition metal compound:

1. Determine the oxidation state of the transition metal and the resulting d-electron count.
   • Identify if there are any overall charges on the molecular complex.
   • Identify the charge of each ligand.
2. Determine the number of electrons from each ligand that are donated to the metal center.
3. Add up the electron counts for the metal and for each ligand.

Typically for most compounds, the electron count should add up to 18 electrons. However, there are many exceptions to the 18 electron rule, just like there are exceptions to the octet rule.

Reactivity

The 18 electron rule allows one to predict the reactivity of a certain compound. The associative mechanism means that there is an addition of a ligand while a dissociative mechanism means that there is a loss of a ligand. When the electron count is less than 18, a molecule will most likely undergo an associative reaction. For example: (C₂H₄)PdCl₂

• 16 electron count
• Would it more likely lose a C₂H₄ or gain a CO? Losing a C₂H₄ results in a 14 electron complex while gaining a CO gives an 18 electron complex. From the 18 electron rule, we will expect that the compound will more likely undergo an associative addition of CO.

Mac drivers for xp. Example (PageIndex{1}):

1. There is no overall charge on the molecule and there is one anionic ligand (CH₃^-)
   • The Re metal must have a positive charge that balances out the anionic ligand charge to equal the 0 overall molecular charge. Since there is a -1 charge contribution from the methyl ligand, the Re metal has a +1 charge.
   • Because the Re metal is in the +1 oxidation state, it is a d⁶ electron count. It would have been its regular d⁷ electron count if it had a neutral (0) oxidation state.
2. The CH₃^- ligand contributes 2 electrons. Each CO ligand contributes 2 electrons. Each PR₃ ligand contributes 2 electrons. The H2C=CH2 ligand contributes 2 electrons.
3. Adding up the electrons:
   • Re(1): 6 electrons
   • CH₃^-: 2 electrons
   • 2 x CO: 2 x 2 electrons = 4 electrons
   • 2 x PR₃: 2 x 2 electrons = 4 electrons
   • H₂C=CH₂: 2 electrons
   • Total: 18 electrons

In this example, the molecular compound has an 18 electron count, which means that all of its orbitals are filled and the compound is stable.

Example (PageIndex{2}): [M(CO)₇]⁺

The 18 electron rule can also be used to help identify an unknown transition metal in a compound. Take for example [M(CO)₇]⁺. To find what the unknown transition metal M is, simply work backwards:

1. 18 electrons
2. Each (CO) ligand contributes 2 electrons
   • 7 x 2 electrons = 14 electrons
3. 18 - 14 = 4 electrons
4. d⁴
5. M(I) oxidation state
6. The unknown metal M must be V, Vanadium

Example (PageIndex{3}): [Co(CO)₅]^z

Similarly to Example 2, the 18 electron rule can also be applied to determine the overall expected charge of an molecule. Take for example [Co(CO)₅]^z. To find the unknown charge z:

1. 18 electrons
2. Each CO ligand contributes 2 electrons
   1. 5 x 2 electrons = 10 electrons
3. Co is typically d⁹
4. 9 + 10 = 19 electrons
5. To satisfy the 18 electron rule, the [Co(CO)₅]^z compound must have a charge of z = +1.

Ligand Contributions

Below is a list of common organometallic ligands and their respective electron contributions.

Exceptions

Generally, the early transition metals (group 3 to 5) could have an electron count of 16 or less. Middle transition metals (group 6 to group 8) commonly have 18 electron count while late transition metals (group 9 to group 11) generally have 16 or lower electron count. When a structure has less than an 18 electron count, it is considered electron-deficient or coordinately unsaturated. This means that the compound has empty valence orbitals, making it electrophilic and extremely reactive. If a structure has 'too many electrons,' that means that not all of the bonds are covalent bonds, and thus some has to be ionic bonds. These bonds are weaker compared to covalent bonds. However, these organometallic compounds that have an electron count greater than 18 are fairly rare.

Effective Atomic Number Calculation

Summary

The 18-electron rule is similar to the octet rule for main group elements, something you might be more familiar with, and thus it may be useful to bear that in mind. So in a sense, there's not much more to it than 'electron bookkeeping'.

References

1. Pfenning, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: John Wiley & Sons, Inc. pp. 629–631. ISBN9781118973868.

Contributors and Attributions

• Wikipedia (CC-BY-SA-3.0)

The 18-electron rule is sometimes referred to as the effective atomic number or EAN rule.

What is EAN rule with example?

The sum of the electrons on the metal plus the electrons donated from the ligands was called the effective atomic number (EAN), and when it was equal to 36 (Kr), 54 (Xe) and 86 (Rn), the EAN rule is said to be obeyed.

Key points: Six σ-bonding interactions are possible in an octahedral complex and, when π acceptor ligands are present, bonding combinations can be made with the three orbitals of the t_2g set, leading to nine bonding MOs, and space for a total of 18 electrons.

In the 1920s, N.V. Sidgwick recognized that the metal atom in a simple metal carbonyl, such as [Ni(CO)₄], has the same valence electron count (18) as the noble gas that terminates the long period to which the metal belongs. Sidgwick coined the term ‘inert gas rule’ for this indication of stability, but it is now usually referred to as the 18–electron rule or EAN Rule.

It becomes readily apparent, however, that the 18-electron rule is not as uniformly obeyed for d-block organometallic compounds as the octet rule is obeyed for compounds of Period 2 elements and we need to look more closely at the bonding to establish the reasons for the stability of both the compounds that have the 18-electron configurations and those that do not.

The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals (one s orbitals, three p orbitals and five d orbitals), which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that the combination of these nine A.O.s with ligand orbitals creates nine M.O.s that are either metal-ligand bonding or non-bonding.

Effective Atomic Number Calculator

Which does not obey EAN rule?

Ligands (donor-acceptor ligands) like carbonyls, carbenes, arenes, isonitriles, etc. forms complexes that tend to follow the ean rule or the 18 electron rule.

Because the rule is obeyed with rather high frequency by organometallic compounds, especially those having carbonyl and nitrosyl ligands (π acceptor ligands), it has considerable usefulness as a tool for predicting formulas of stable compounds.

18 Electron Rule in Octahedral Complexes

Figure 22.1 shows the energy levels that arise when a strong-field ligand such as carbon monoxide bonds to a d-metal atom.

How To Calculate Effective Atomic Number

Carbon monoxide is a strong-field ligand, even though it is a poor σ donor because it can use its empty π* orbitals to act as a good π acceptor. In this picture of the bonding, the t_2g orbitals of the metal atom are no longer nonbonding, as they would be in the absence of π interactions, but are bonding.

The energy-level diagram shows six bonding MOs that result from the ligand–metal σ interactions, and three bonding MOs that result from π interactions. Thus up to 18 electrons can be accommodated in the nine bonding MOs.

Compounds that have this configuration are remarkably stable; for instance, the 18-electron [Cr(CO)₆] is a colourless, air-stable compound.

An indication of the size of the HOMO-LUMO gap (Δ_O) can be gained from a consideration of its lack of colour, which results from a lack of any electronic transitions in the visible region of the spectrum; that is, Δ_O is so large that such transitions are shifted to the UV.

The only way to accommodate more than 18 valence electrons in an octahedral complex with strong-field ligands is to use an antibonding orbital. As a result, such complexes are unstable, being particularly prone to electron loss and acting as reducing agents.

Compounds with fewer than 18 electrons will not necessarily be very unstable. However, such complexes will find it energetically favourable to acquire extra electrons by reaction and so populate their bonding MOs fully.

The bonding characteristic of the carbonyl ligand is replicated with other ligands, which are often poor σ donors but good π acceptors. Hence, octahedral organometallic compounds are most stable when they have a total of 18 valence electrons around their central metal ion.

How do I calculate effective atomic number of coordinate compounds?

Q: Do (a) [IrBr₂(CH₃)(CO)(PPh₃)₂] and (b) [Cr(η⁵-C₅H₅)(η⁶-C₆H₆)] obey the 18-electron rule?

Answer

(a) We start with the Ir atom (Group 9), which has nine valence electrons, then add in the electrons from the two Br atoms and the CH₃ group (each is a one-electron donor) and finally add in the electrons from the CO and PPh₃ (both are two-electron donors). Thus, the number of valence electrons on the metal atom is 9+ (3×1) + (3×2) =18.

(b) In a similar fashion, the Cr atom (Group 6) has six valence electrons, the η⁵-C₅H₅ ligand donates five electrons, and the η⁶-C₆H₆ ligand donates six, so the number of metal valence electrons is 6+5 + 6=17. This complex does not obey the 18-electron rule and is not stable. A related but stable 18-electron compound is [Cr(η⁶-C₆H₆)₂].

Problem on Effective Atomic Number Rule:

Self-test:Is [Mo(CO)₇] likely to be stable?

Assign the oxidation number and count the valence electrons on the metal atom in

(a) [IrBr₂(CH₃)(CO)(PPh₃)₂], (b) [Cr(η⁵-C₅H₅)(η⁶-C₆H₆)], and (c) [Mn(CO)₅]-.

Answer

(a) We treat the two Br groups and the CH₃ as three singly negatively charged two-electron donors and the CO and the two PPh₃ ligands as three two-electron donors, providing 12 electrons in all. Because the complex is neutral overall, the Group 9 Ir atom must have a charge of +3 (that is, have oxidation number +3) to balance the charge of the three anionic ligands, and thus contributes 9 -3 = 6 electrons. This analysis gives a total of 18 electrons for the Ir(III) complex.

(b) We treat the η⁵-C₅H₅ ligand as C₅H₅^– and thus it donates six electrons, with the η⁶-C₆H₆ ligand donating a further six. To maintain neutrality, the Group 6 Cr atom must have a charge of +1 (and an oxidation number of +1) and contributes 6- 1 =5 electrons. The total number of metal electrons is 12 + 5 =17 for a Cr(I) complex. As noted before, this complex does not obey the 18-electron rule and is unlikely to be stable.

(c) We treat each CO ligand as neutral and contributing two electrons, giving 10 electrons. The overall charge of the complex is -1; because all the ligands are neutral, we consider this charge to reside formally on the metal atom, giving it an oxidation number of -1. The Group 7 Mn atom thus contributes 7+ 1 electrons, giving a total of 18 for a Mn(-1) complex.

Self-test:What is the electron count for, and oxidation number of, platinum in the anion of Zeise’s salt, [Pt(CH₂=CH₂)Cl₃]^– ? Treat CH₂=CH₂ as a neutral two-electron donor.

Some EAN Rule FAQs

What is EAN rule with example?

EAN rule stands for the effective atomic number rule. This rule is also referred to as '18 electron rule'. The sum of the electrons on the metal atom plus the electrons donated from the ligands is called the effective atomic number and when it is equal to 36 (Xe), 54 (Kr) and 86 (Rn), then the EAN rule is said to be obeyed. One example is Hexaamminecobalt(III) in which Co3+ donates 6 electrons and the 6 NH3 ligands donate 12 electrons. Thus, the total number of valence electrons on the metal atom is 6 + 12 = 18 electrons.

How is EAN value calculated?

EAN = (atomic number of the metal atom) – (the oxidation state of the central metal atom ) + (the number of electrons donated by the ligands to the metal atom EAN= Z metal – (ox.state of the metal) + 2(coordination number of the metal atom).

What is Sidgwick theory?

Chemistry Atomic Structure Worksheet Answers

In 1940 Sidgwick and Powell reviewed the structures of molecules then known. They suggested that for molecules and ions that only contain single bonds, the approximate shape can be predicted from the number of electron pairs in the outer or valence shell of the central atom.