AXE Method
The "AXE method" of electron counting is commonly used when applying the VSEPR theory. The A represents the central atom and always has an implied subscript one. The X represents the number of sigma bonds between the central atoms and outside atoms. Multiple covalent bonds (double, triple, etc.) count as one X. The E represents the number of lone electron pairs surrounding the central atom. The sum of X and E, known as the steric number, is also associated with the total number of hybridized orbitals used by valence bond theory.
Based on the steric number and distribution of X's and E's, VSEPR theory makes the predictions in the following tables. Note that the geometries are named according to the atomic positions only and not the electron arrangement. For example the description of AX2E1 as bent means that AX2 is a bent molecule without reference to the lone pair, although the lone pair helps to determine the geometry.
| Steric No. |
Basic geometry 0 lone pair |
1 lone pair | 2 lone pairs | 3 lone pairs |
|---|---|---|---|---|
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | 3) |
|||
| 6 | ||||
| 7 | 5) |
5) |
||
| 8 | (IF− 8) |
|||
| 9 | Tricapped trigonal prismatic (ReH2− 9) OR Capped square antiprismatic |
| Molecule Type | Shape | Electron arrangement† | Geometry‡ | Examples |
|---|---|---|---|---|
| AX2E0 | Linear | BeCl2, HgCl2, CO2 | ||
| AX2E1 | Bent | NO− 2, SO2, O3, CCl2 |
||
| AX2E2 | Bent | H2O, OF2 | ||
| AX2E3 | Linear | XeF2, I− 3, XeCl2 |
||
| AX3E0 | Trigonal planar | BF3, CO2− 3, NO− 3, SO3 |
||
| AX3E1 | Trigonal pyramidal | NH3, PCl3 | ||
| AX3E2 | T-shaped | ClF3, BrF3 | ||
| AX4E0 | Tetrahedral | CH4, PO3− 4, SO2− 4, ClO− 4, TiCl4, XeO4 |
||
| AX4E1 | Seesaw | SF4 | ||
| AX4E2 | Square planar | XeF4 | ||
| AX5E0 | Trigonal bipyramidal | PCl5 | ||
| AX5E1 | Square pyramidal | ClF5, BrF5, XeOF4 | ||
| AX5E2 | Pentagonal planar | XeF− 5 |
||
| AX6E0 | Octahedral | SF6, WCl6 | ||
| AX6E1 | Pentagonal pyramidal | XeOF− 5, IOF2− 5 |
||
| AX7E0 | Pentagonal bipyramidal | IF7 | ||
| AX8E0 | Square antiprismatic | IF− 8, ZrF4− 8, ReF− 8 |
||
| AX9E0 | Tricapped trigonal prismatic OR capped square antiprismatic |
ReH2− 9 |
When the substituent (X) atoms are not all the same, the geometry is still approximately valid, but the bond angles may be slightly different from the ones where all the outside atoms are the same. For example, the double-bond carbons in alkenes like C2H4 are AX3E0, but the bond angles are not all exactly 120°. Likewise, SOCl2 is AX3E1, but because the X substituents are not identical, the XAX angles are not all equal.
As a tool in predicting the geometry adopted with a given number of electron pairs, an often used physical demonstration of the principle of minimal electrostatic repulsion utilizes inflated balloons. Through handling, balloons acquire a slight surface electrostatic charge that results in the adoption of roughly the same geometries when they are tied together at their stems as the corresponding number of electron pairs. For example, five balloons tied together adopt the trigonal bipyramidal geometry, just as do the five bonding pairs of a PCl5 molecule (AX5) or the two bonding and three non-bonding pairs of a XeF2 molecule (AX2E3). The molecular geometry of the former is also trigonal bipyramidal, whereas that of the latter is linear.
Read more about this topic: VSEPR Theory
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