Linear

An example of linear geometry is provided below of the molecule Xenon Difluoride (XeF₂). Recall that linear is the geometry where the molecule looks like a line.

XeF₂:

Square Planar

Square planar is the geometry where the molecule looks like it is a square plane. An example of the molecule Xenon Tetrafluoride (XeF₄) is provided below.

XeF₄:

Tetrahedral

Tetrahedral is the geometry where the molecule looks like a pyramid. An example of the molecule Methane (CH₄) is provided below.

CH₄:

Octahedral

Octahedral is the geometry where the bases of two pyramids are stuck together. Alternatively, it can also be though as where the center consists of a square plane with a ligand sticking out above it and another ligand sticking out below it. An example of the molecule Sulfur Hexafluoride (SF6) is provided below. A quick note on octahedral geometry: sometimes an octahedral molecule may contain polydentate ligands. Polydentate ligands are ligands that "bite" the central atom in several locations. In other words, polydentate ligands have the ability to form more than one bond with the central metal, unlike other ligands. An example of a polydentate ligand is ethylenediamine, a bidentate ligand, which is abbreviated as en. 

SF₆:

Cis-Trans Isomers

Cis-Trans Isomers are isomers that differ in the arrangement of 2 ligands in square planar and octahedral geometry. Cis isomers are isomers where the two ligands are 90 degrees apart from one another in relation to the central molecule. This is because Cis isomers have a bond angle of 90^o, between two same atoms. Trans isomers, on the other hand, are isomers where the two ligands are on opposite sides in a molecule because trans isomers have a bond angle of 180^o, between the two same atoms. When naming cis or trans isomers, the name begins either with cis or trans, whichever applies, followed by a hyphen and then the name of a molecule. For example a cis isomer of CoCl₂F₂ would be called cis-CoCl₂F₂. Finally, the last thing to keep in mind when examining cis and trans isomers is that only square planar and octahedral geometries can have cis or trans isomers. Examples of both isomers are provided below.

Tetrahedral Cis Isomers

CoCl₂F₂:

(Color scheme: pink=cobalt, blue=fluorine, green=chlorine)

This above is an example of the molecule cis-CoCl₂F₂ or cis-dichlorodifluorocobalt (IV). The molecule pictured above is a cis isomer because both fluorine and chlorine ligands, respectively, are on the same side of the molecule. Additionally, one can approximate that the bond angle between each of the chlorine atoms and between each of the fluorine atoms is 90^o.

Tetrahedral Trans Isomers

CoCl₂F₂:

(Color scheme: pink=cobalt, blue=fluorine, green=chlorine)

(Note, the differences in the length of the bond between the two pictures are not intentional and have nothing to do with cis-trans isomerism)

This above is an example of the molecule trans-CoCl₂F₂ or trans-dichlorodifluorocobalt (IV).

We know the above molecule is a trans isomer because the two same chlorine atoms and the two same fluorine atoms are opposite each other. Furthermore, the bond angle between the two chlorine atoms and between the two fluorine atoms is 180^o. The above examples were all for square planar geometry but as the examples below illustrate, cis-trans isomerism can also occur in octahedral geometry. Both the molecules below are isomers of the molecule SCl₂F₄ (color scheme: yellow=sulfur, blue=fluorine, green=chlorine).

Octahedral cis Isomers

SCl₂F₄:

We know this isomer above is a cis isomer because both the chlorine ligands are on the same side and the bond angle between the chlorine atoms appears to be 90^o. 

Octahedral Trans Isomers

SCl₂F₄:

We know this isomer above is a trans isomer because the chlorine ligands are on opposite sides and the bond angle between the chlorine atoms is 180^o. All other isomers are essentially just rotations of these two isomers. Once again when trying to find cis and trans isomers look at the arrangement of the ligands. If two same ligands are on the same side, it is a cis isomer and if the ligands are on opposite sides, it is a trans isomer. Another way to tell the isomers apart is the bond angles: cis isomers have a 90^o bond angle whereas trans isomers have a 180^o bond angle.

Mer-Fac Isomers

Mer-Fac isomers are easier to notice than cis-trans isomers in the sense that they only exist in octahedral geometry. Just like cis-trans isomers, mer-fac isomers are determined based on whether or not the ligands exist on the same side. Instead of dealing with 2 ligands, mer-fac isomers deal with 3 ligands. If the 3 ligands are all on the same side, the isomer is called a fac-isomer. Another way to identify fac isomers is to look at the bond angle between the ligands because fac isomers have a 90^o bond angle between each of the 3 atoms. The mer isomer on the other hand is where only 2 of the 3 ligands are on the same side. In mer isomers, there exists a 90^o-90^o-180^o bond angle between the 3 same ligands. In terms of nomenclature, mer-fac isomers follow the same rule as cis-trans isomers where you put the isomer type, followed by a hyphen, followed by the molecular formula. Examples have been provided below.

Fac Isomers Example

Below is an example of the fac isomer, fac-CoCl₃F₃:

(note the color scheme: pink=cobalt, green=chlorine, blue=fluorine)

2d version:

Through the 2d version, it is easier to see how the ligands are all on the same side. Nonetheless, in the 3D version, one can observe that the bond angle between the 3 same ligands is 90^o, thus making this isomer a fac-isomer.

Mer Isomers Example

Below is an example of the mer isomer, mer-CoCl₃F₃:

(note the color scheme: pink=cobalt, green=chlorine, blue=fluorine)

2d version:

Its hard to tell in the 3D version but in the 2D version, one can easily tell how the same ligands are not on the same side. Additionally, one can approximate that the bond angle between the three chlorine atoms and between the three fluorine atoms is 90^o-90^o-180^o, thus making the above molecule a mer isomer.

Plane of Symmetry Method

The plane of symmetry method uses symmetry, as it's name indicates, to identify optical isomers. In this method, one tries to see if such a plane exists which when cut through the coordinate compound produces two exact images. In other words, one looks for the existence of a plane of symmetry within the coordinate compound. If a plane of symmetry exists, then no optical isomers exist. On the other hand, if there is no plane of symmetry, the coordinate compound has optical isomers. Furthermore, if a plane of symmetry exists around the central atom, then that molecule is called achiral but if a plane of symmetry does not exist around the central molecule, then that molecule has chiral center.

Mirror Images Method

The mirror images method uses a mirror image of the molecule to determined whether optical isomers exist or not. If the mirror image can be rotated in such a way that it looks identical to the original molecule, then the molecule is said to be superimposable and has no optical isomers. On the other hand, if the mirror image cannot be rotated in any way such that it looks identical to the original molecule, then the molecule is said to be non-superimposable and the molecule has optical isomers. Once again, if the mirror image is superimposable, then no optical isomers but if the mirror image is non-superimposable, then optical isomers exist.

Non-superimposable means the structure cannot be rotated in a way that one can be put on top of another. This means that no matter how the structure is rotated, it cannot be put on top of another with all points matching. An example of this is your hands. Both left and right hands are identical, but they cannot be put on top of each other with all points matching. 

Consider the tetrahedral molecule, CHBrClF (note the color scheme: grey=carbon, white=hydrogen, green=chlorine, blue=fluorine, red=bromine)

Is this molecule optically active? In other words, does this molecule have optical isomers?

First take the Mirror-image method. The mirror image of the molecule is:

Note that this mirror image is not superimposable. In other words, the mirror image above cannot be rotated in any such way that it looks identical to the original molecule. Remember, if the mirror image is not superimposable, then optical isomers exist. Thus we know that this molecule has optical isomers.

Let's try approaching this problem using the symmetry method. If we take the original molecule and draw an axis or plane of symmetry down the middle, this is what we get:

Since the left side is not identical to the right, this molecule does not have a symmetrical center and thus can be called chiral. Additionally, because it does not have a symmetrical center, we can conclude that this molecule has optical isomers. In general, when dealing with a tetrahedral molecule that has 4 different ligands, optical isomers will exist most of the time.

No matter which method you use, the answer will end up being the same.

This time we will be analyzing the octahedral compound FeCl₃F₃ (note the color scheme: orange=iron, blue=fluorine, green=chlorine):

If we try to attempt this problem using the mirror image method, we notice that the mirror image is essentially identical to the original molecule. In other words, the mirror image can be placed on top of the original molecule and is thus superimposable. Since the mirror image is superimposable, this molecule does not have any optical isomers. Let's attempt this same problem using the symmetry method. If we draw an axis or plane of symmetry, this is what we get:

Since the left side is identical to the right side, this molecule has a symmetrical center and is an achiral molecule. Thus, it has no optical isomers. 

What is a polarimeter?

A polarimeter is a cylinder tube which a single ray of light can be shot through. Another way to distinguish whether a molecule is chiral or achiral is to shine light through that molecule. If no light passes that molecule then the molecule is achiral and does not have optical isomers. On the other hand, if light passes through the molecule, it is chiral and has optical isomers. Another interesting fact about optical isomers is that they have the ability to polarize and rotate light passed through them. These type of optical isomers are classified based on how they rotate the light. If the isomer rotates the light in the left direction, then it is called levorotatory. If the isomer rotates the light in the right direction, then it is called dextrorotatory. Often times, certain drugs or proteins also depend on stereoisomers for function because only one correct stereoisomer of the molecule can function effectively as the drug or protein.

Answers

1) MnCl₂F₂ has no geometric isomers because recall that tetrahedral molecules do not have geometric isomers.

2) The molecule, FeBr₂I₂ pictured in problem 3 is a cis isomer, or cis-FeBr₂I₂, because both the Br and I ligands are on the same side. There is one more stereoisomer for this molecule: trans-FeBr₂I₂, pictured below:

3) This molecule has two isomers: mer-CrF₃I₃ and fac-CrF₃I₃, both are pictured below. The mer isomer is where the ligands are not on the same plane and there exists a 90-90-180 degree bond angle between the 3 same ligands. The fac isomer is where the ligands are on the same plane and there exists a 90-90-90 degree bond angle between the 3 same ligands.

fac-CrF₃I₃:

mer-CrF₃I₃:

4) A dextrorotatory optical isomer is a isomer that can rotate light in the right direction. A levorotatory optical isomer on the other hand is a isomer that can rotate light in the left direction.

5) In the molecule Fe(en)3, recall that the en ligand, ethylenediamine is a bidentate ligand. The 2D structure of this molecule is shown below:

Note, the black lines represent the bonds and the blue lines represent the bonds ethylenediamine binds to. Using either the symmetry method or the mirror image method, one can observe that this molecule has a chiral center and that the mirror image is not superimposable on the original molecule. Thus, this molecule is optically active because it has optical isomers.

6) True. Octahedral geometry as well as square planar geometry can have cis-trans isomers. The only geometry that cannot have cis-trans isomers is tetrahedral.