Chemistry

Determining the Hybridization and Geometry of Bonded Atoms



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If that title didn't scare you away, you're either quite brave, curious, or a chemistry student. For those of you who are chemistry students, you may wish to skip down to the meat of the article, marked with a line of asterisks (*). If your chemistry skills have dwindled with time, or never formed in the first place, do read on.

To make compounds, atoms can connect to one another via a covalent bond. In covalent bonding, two electrons are shared between two atoms in each bond. In a lone atom, electrons are found in atomic orbitals regions of space which are calculated using probabilities and the Shroedinger Wave Equation. When bonding, the atomic orbitals are not in a favorable position to allow electron sharing. A mathematical mixing of the atomic orbitals (hybridization) creates a new set of hybrid orbitals that do allow electron sharing, and fit very well with observed chemical behavior. (Note that this is all theory, no one can see an orbital, but the math gives us a model that represents reality well.)

An excellent animated illustration of hybridization can be found at the following site:

http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/hybrv18.swf

Because the hybrid orbitals are arranged in three dimensional space, different geometric arrangements result from different types of hybridization. Often it is important to know the actual geometry of a molecule, or portion of a molecule, to predict how it will behave in certain situations. For this reason, chemists learn to quickly identify the hybridization and geometry. The key to both is to identify how many atoms are bonded to the atom in question, and how many unbonded (lone) pairs of electrons are still left in the atom's outermost (valence) shell. That sum dictates how many orbitals have been combined, and the geometry is then predicted using Valence Shell Electron Pair Repulsion (VSEPR) Theory a model based on the idea that electrons repel, so that bonds and lone pairs of electrons must orient themselves as far away from one another as possible.

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The first step in determining hybridization and geometry is to draw the Lewis Dot Structure for your molecule. (You'll have to look elsewhere for instructions on drawing Lewis Dot Structures http://web.chem.ucla.edu/~harding/lewisdots.html isn't too bad.)

Once you have your Lewis structure, count how many atoms are bonded to the atom you are interested in. Also count the number of lone pairs (valence shell only) of electrons on your atom of interest. Add together the two counts.

Hybridization is easy once you have your count. Remember the order in which atomic orbitals fill within an energy level? (s,p,p,p,d,d,d,d,d,f,f,f,f,f,f,f) The same order is used in constructing hybrid orbitals. If there are two bonded atoms and a lone pair, the count comes to three. Taking the first three orbitals (s,p,p) results in sp2 (the "2" indicates that two p orbitals were used) hybridization. Similarly, an atom with five atoms bonded to it and no lone pairs would need to have sp3d hybridization (from the first five orbitals: s,p,p,p,d). Going to extremes, an atom with six atoms bonded and one lone pair would need seven hybrid orbitals, resulting in sp3d3 hybridization. (Incidentally, the numbers in the "sp2", "sp3d", and "sp3d3" should be superscripted in proper notation, but plain text formatting requires certain adaptations.)

Once the number of bonded atoms and lone pairs is known, it is fairly straightforward to predict the arrangement that they must take around the central atom (the one you've been counting around). I'll just list those quickly, and then go into more detail.

atoms bonded
+ lone pairs ....................... geometry
0 .............. a point just the central atom (hydrogen ion)
1 .............. a line any two points define a line (diatomic hydrogen)
2 .............. a line the two things are at opposite ends
3 .............. a triangle the three things repel to ~120 degree angles, all in a plane
4 .............. a tetrahedron three dimensional now, ~ 109.5 degree angles
5 .............. a triangle, plus one up and one down from the plane of the triangle
6 .............. an octahedron ~ 90 degrees
7 .............. a mess a triangular prism (6) with the last sticking out of one face
8 .............. a cube
(I don't believe I've ever seen an 8, but VSEPR still predicts the geometry just fine.)

When discussing geometry, chemists are usually only interested in the shape formed by the bonded atoms, as a lone pair of electrons does not physically occupy much space comparatively. As a result, there are more geometric appearances. For example, if one atom is surrounded by two atoms and a lone pair, the total count is three. Those things will be arranged in a triangle, but since we don't "see" the lone pair, all that is observed is two atoms, attached roughly at 120 degrees, forming a "bent" geometry. For each of the higher counts, lone pairs also result in different apparent geometries. If you have a molecular modeling kit, you can easily see these by first making the atom with the full complement of attached atoms and lone pairs, and then removing the lone pairs. If you do not have a kit, a marshmallow and toothpicks can work wonders too. (Use the marshmallow as the central atom, and a toothpick for each atom or lone pair attached to it.)

Diagrams of geometries 2-6 can be found in a table at the following site:

http://en.wikipedia.org/wiki/VSEPR

Each geometry has a name, and they can be memorized fairly readily by the total count and number of lone pairs. In general, no one worries about zero or one, so we will skip them here as well. There are others which are usually left out as well, but we'll include them to show how VSEPR predicts even the non-observed geometries. Note that if all groups were electron pairs, the geometry would have to be that of a point. (Consider Noble gases, for instance.)

Count . Lone Pairs . Name .............. Notes
. 2 ....... 0 ..... linear
. 2 ....... 1 ..... linear ...... (this is often left out, but it fits acetylene / ethyne)
. 3 ....... 0 ..... trigonal planar
. 3 ....... 1 ..... bent
. 3 ....... 2 ..... linear ...... (usually ignored)
. 4 ....... 0 ..... tetrahedral
. 4 ....... 1 ..... triangular pyramid ..... three atoms angled down form the base
. 4 ....... 2 ..... bent
. 4 ....... 3 ..... linear ...... (usually ignored)
. 5 ....... 0 ..... trigonal bipyramid
. 5 ....... 1 ..... see saw ...... the electron pair is a part of the triangle, to
.................................. maximize its spacing from other atoms
. 5 ....... 2 ..... T shaped ... both electron pairs on the triangle
. 5 ....... 3 ..... linear
. 5 ....... 4 ..... linear ....... (ignored)
. 6 ....... 0 ..... octahedral
. 6 ....... 1 ..... square pyramid .... four atoms form a planar base, one is above
. 6 ....... 2 ..... square planar .... the electron pairs are on opposite sides
. 6 ....... 3 ..... T shaped .... the top of the "T" will be angled down
. 6 ....... 4 ..... linear ........ the four electron pairs are in a square
. 6 ....... 5 ..... linear ....... (ignored)
. 7 ....... 0 ..... irregular, but can be described as a triangular prism with an
................... additional point coming from one of the faces. To my knowledge,
................... this isn't observed, probably because cramming seven atoms around
................... one is just too crowded. It might be possible with the heavier
................... elements though, if a stable one is ever made. (ignored)
. 7 ....... 1 ..... distorted triangular prism ......... the electron pair juts out the face
. 7 ....... 2 ..... use your marshmallow, I really don't know (ignored)

For those of you who just want to print a list to memorize the common geometries:

Count . Lone Pairs . Name
. 2 ....... 0 ..... linear
. 3 ....... 0 ..... trigonal planar
. 3 ....... 1 ..... bent
. 4 ....... 0 ..... tetrahedral
. 4 ....... 1 ..... triangular pyramid
. 4 ....... 2 ..... bent
. 5 ....... 0 ..... trigonal bipyramid
. 5 ....... 1 ..... see saw
. 5 ....... 2 ..... T shaped
. 5 ....... 3 ..... linear
. 6 ....... 0 ..... octahedral
. 6 ....... 1 ..... square pyramid
. 6 ....... 2 ..... square planar
. 6 ....... 3 ..... T shaped
. 6 ....... 4 ..... linear

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