Electron counting

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In chemistry, electron counting is a formalism for assigning a number of valence electrons to individual atoms in a molecule. It is used for classifying compounds and for explaining or predicting their electronic structure and bonding. [1] Many rules in chemistry rely on electron-counting:

Contents

Atoms are called "electron-deficient" when they have too few electrons as compared to their respective rules, or "hypervalent" when they have too many electrons. Since these compounds tend to be more reactive than compounds that obey their rule, electron counting is an important tool for identifying the reactivity of molecules. While the counting formalism considers each atom separately, these individual atoms (with their hypothetical assigned charge) do not generally exist as free species.

Counting rules

Two methods of electron counting are "neutral counting" and "ionic counting". Both approaches give the same result (and can therefore be used to verify one's calculation).

It is important, though, to be aware that most chemical species exist between the purely covalent and ionic extremes.

Neutral counting

E.g. in period 2: B, C, N, O, and F have 3, 4, 5, 6, and 7 valence electrons, respectively.
E.g. in period 4: K, Ca, Sc, Ti, V, Cr, Fe, Ni have 1, 2, 3, 4, 5, 6, 8, 10 valence electrons respectively.

Ionic counting

E.g. for a Fe2+ has 6 electrons
S2− has 8 electrons

Electrons donated by common fragments

LigandElectrons contributed
(neutral counting)		Electrons contributed
(ionic counting)		Ionic equivalent
X 12X−; X = F, Cl, Br, I
H 12H−
H 10H+
O 24O2−
N 36N3−
CO 22CO
NR3 22NR3; R = H, alkyl, aryl
CR2 24CR2−2
Ethylene 22C2H4
cyclopentadienyl 56C5H−5
benzene 66C6H6

"Special cases"

The numbers of electrons "donated" by some ligands depends on the geometry of the metal-ligand ensemble. An example of this complication is the M–NO entity. When this grouping is linear, the NO ligand is considered to be a three-electron ligand. When the M–NO subunit is strongly bent at N, the NO is treated as a pseudohalide and is thus a one electron (in the neutral counting approach). The situation is not very different from the η3 versus the η1 allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.

Examples

For a water molecule (H2O), using both neutral counting and ionic counting result in a total of 8 electrons.

This figure of the water molecule shows how the electrons are distributed with the covalent counting method. The red ones are the oxygen electrons, and the blue ones are electrons from the hydrogen atoms. Water molecule covalent counting.jpg
This figure of the water molecule shows how the electrons are distributed with the covalent counting method. The red ones are the oxygen electrons, and the blue ones are electrons from the hydrogen atoms.
Neutral counting
AtomElectrons contributedElectron count
H.1 electron x 22 electrons
O6 electrons6 electrons
Total = 8 electrons

The neutral counting method assumes each OH bond is split equally (each atom gets one electron from the bond). Thus both hydrogen atoms have an electron count of one. The oxygen atom has 6 valence electrons. The total electron count is 8, which agrees with the octet rule.

This figure of the water molecule shows how the electrons are distributed with the ionic counting method. The red ones are the oxygen electrons, and the blue ones are electrons from hydrogen. All electrons in the OH bonds belong to the more electronegative oxygen. Water molecule ionic countin.jpg
This figure of the water molecule shows how the electrons are distributed with the ionic counting method. The red ones are the oxygen electrons, and the blue ones are electrons from hydrogen. All electrons in the OH bonds belong to the more electronegative oxygen.
Ionic counting
AtomElectrons contributedElectron count
H+none0 electron
O2-8 electrons8 electrons
Total = 8 electrons

With the ionic counting method, the more electronegative oxygen will gain electrons donated by the two hydrogen atoms in the two OH bonds to become O2-. It now has 8 total valence electrons, which obeys the octet rule.

neutral counting: C contributes 4 electrons, each H radical contributes one each: 4 + 4 × 1 = 8 valence electrons
ionic counting: C4− contributes 8 electrons, each proton contributes 0 each: 8 + 4 × 0 = 8 electrons.
Similar for H:
neutral counting: H contributes 1 electron, the C contributes 1 electron (the other 3 electrons of C are for the other 3 hydrogens in the molecule): 1 + 1 × 1 = 2 valence electrons.
ionic counting: H contributes 0 electrons (H+), C4− contributes 2 electrons (per H), 0 + 1 × 2 = 2 valence electrons
conclusion: Methane follows the octet-rule for carbon, and the duet rule for hydrogen, and hence is expected to be a stable molecule (as we see from daily life)
neutral counting: S contributes 6 electrons, each hydrogen radical contributes one each: 6 + 2 × 1 = 8 valence electrons
ionic counting: S2− contributes 8 electrons, each proton contributes 0: 8 + 2 × 0 = 8 valence electrons
conclusion: with an octet electron count (on sulfur), we can anticipate that H2S would be pseudo-tetrahedral if one considers the two lone pairs.
neutral counting: S contributes 6 electrons, each chlorine radical contributes one each: 6 + 2 × 1 = 8 valence electrons
ionic counting: S2+ contributes 4 electrons, each chloride anion contributes 2: 4 + 2 × 2 = 8 valence electrons
conclusion: see discussion for H2S above. Both SCl2 and H2S follow the octet rule - the behavior of these molecules is however quite different.
neutral counting: S contributes 6 electrons, each fluorine radical contributes one each: 6 + 6 × 1 = 12 valence electrons
ionic counting: S6+ contributes 0 electrons, each fluoride anion contributes 2: 0 + 6 × 2 = 12 valence electrons
conclusion: ionic counting indicates a molecule lacking lone pairs of electrons, therefore its structure will be octahedral, as predicted by VSEPR. One might conclude that this molecule would be highly reactive - but the opposite is true: SF6 is inert, and it is widely used in industry because of this property.
The geometry of cis-Dichlorobis(bipyridine)ruthenium(II). RuCl2(bpy)2.jpg
The geometry of cis-Dichlorobis(bipyridine)ruthenium(II).

RuCl2(bpy)2 is an octahedral metal complex with two bidentate 2,2′-Bipyridine (bpy) ligands and two chloride ligands.

Neutral counting
Metal/ligandElectrons contributedElectron count
Ru(0)d8 (8 d electrons)8 electrons
bpy4 electrons x 28 electrons
Cl .1 electron x 22 electrons
Total = 18 electrons

In the neutral counting method, the Ruthenium of the complex is treated as Ru(0). It has 8 d electrons to contribute to the electron count. The two bpy ligands are L-type ligand neutral ligands, thus contributing two electrons each. The two chloride ligands hallides and thus 1 electron donors, donating 1 electron each to the electron count. The total electron count of RuCl2(bpy)2 is 18.

Ionic counting
metal/ligandelectrons contributednumber of electrons
Ru(II)d6 (6 d electrons)6 electrons
bpy4 electrons x 28 electrons
Cl-2 electrons x 24 electrons
Total = 18 electrons

In the ionic counting method, the Ruthenium of the complex is treated as Ru(II). It has 6 d electrons to contribute to the electron count. The two bpy ligands are L-type ligand neutral ligands, thus contributing two electrons each. The two chloride ligands are anionic ligands, thus donating 2 electrons each to the electron count. The total electron count of RuCl2(bpy)2 is 18, agreeing with the result of neural counting.

neutral counting: Ti contributes 4 electrons, each chlorine radical contributes one each: 4 + 4 × 1 = 8 valence electrons
ionic counting: Ti4+ contributes 0 electrons, each chloride anion contributes two each: 0 + 4 × 2 = 8 valence electrons
conclusion: Having only 8e (vs. 18 possible), we can anticipate that TiCl4 will be a good Lewis acid. Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.
neutral counting: Fe contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
ionic counting: Fe(0) contributes 8 electrons, each CO contributes 2 each: 8 + 2 × 5 = 18 valence electrons
conclusions: this is a special case, where ionic counting is the same as neutral counting, all fragments being neutral. Since this is an 18-electron complex, it is expected to be isolable compound.
neutral counting: Fe contributes 8 electrons, the 2 cyclopentadienyl-rings contribute 5 each: 8 + 2 × 5 = 18 electrons
ionic counting: Fe2+ contributes 6 electrons, the two aromatic cyclopentadienyl rings contribute 6 each: 6 + 2 × 6 = 18 valence electrons on iron.
conclusion: Ferrocene is expected to be an isolable compound.


See also

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References

  1. ↑ Parkin, Gerard (2006). "Valence, Oxidation Number, and Formal Charge: Three Related but Fundamentally Different Concepts". Journal of Chemical Education. 83 (5): 791. Bibcode:2006JChEd..83..791P. doi:10.1021/ed083p791. ISSN   0021-9584 . Retrieved 2009-11-10.
  2. ↑ Rasmussen, Seth C. (March 2015). "The 18-electron rule and electron counting in transition metal compounds: theory and application". ChemTexts. 1 (1). doi:10.1007/s40828-015-0010-4. ISSN   2199-3793.
  3. ↑ Green, M. L. H. (1995-09-20). "A new approach to the formal classification of covalent compounds of the elements". Journal of Organometallic Chemistry . 500 (1–2): 127–148. doi:10.1016/0022-328X(95)00508-N. ISSN   0022-328X.
  4. ↑ Green, M. L. H. (1995-09-20). "A new approach to the formal classification of covalent compounds of the elements". Journal of Organometallic Chemistry. 500 (1): 127–148. doi:10.1016/0022-328X(95)00508-N. ISSN   0022-328X.
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