# Is plane of symmetry a necessary and sufficient condition for optical inactivity in coordination compounds? [closed]

In organic chemistry, we have to check for all three types of symmetry in a compound to check its chirality, ie, plane, alternate axis and centre of symmetry. But in coordination compounds, do we need to check all the symmetries to check its chirality? The ligands are supposed to be achiral. The difference between the two being that in coordination compounds only one "chiral" center is present but in organic compounds it can be more than one.

All the achiral coordination compounds of any coordination number which I have come across have a plane of symmetry. But for those which don't have, I have to check whether it's image coincides with itself or not. So, is plane of symmetry a necessary and sufficient condition for achirality of coordination compounds?

This thing is necessary for my purpose, as I have to solve problems in limited time, so I cannot use the orignal method always.

• – Karsten Theis Sep 28 '20 at 11:44
• I remember my coordination chemistry professor at uni drawing a tetracoordinating chelate ligand with a central metal on the blackboard. The tetrahedral complex had improper rotation (which we spent two minutes proving by him drawing the mirror image). It was thus achiral. Alas, it’s not mentioned on his webpages … – Jan Sep 29 '20 at 12:10
• Does this answer your question? What is the perfect definition for chirality? – Tyberius Oct 8 '20 at 17:55

The number $$\pi$$ for bowhead whales is still 3.1415... Same thing here.

Chirality of coordination compounds is the same thing as chirality of organic compounds. If all your symmetry elements are just rotations, you have it; if some are improper rotations, then you don't. It is as simple as that, and is not going to be any simpler.

Can you just check for the planes and call it a day? Well, you kinda can, and that will do, until you come across a compound which doesn't have a plane, but still is achiral because of some other symmetry element.

Are there such compounds? Well, that's like asking whether there is a place on Earth where three bricks stand on top of each other. You may google long and hard, or you may apply for a travel grant to visit countries with rich traditions of brickwork masonry... or you may just take three bricks and put them on top of each other. That's it; problem solved.

Here are my bricks. I claim that the tetrahedral $$\ce{[Zn(NH3)4}]^{2+}$$ has an inversion axis $$\bar4$$ and hence is achiral. You may point out that it has a plane as well. Fine. Let's give it some substituents: change each ligand to $$\ce{N(CH3)3}$$. What? Does it still have a plane, given that everything which rotates is rotated to the appropriate position? Fine. Let's give it different substituents. Change each ligand to $$\ce{CH3NHC2H5}$$. Where is the plane now?

So it goes.

† There was an old anecdote about an even more old paper on biophysics which was said to include some volume calculations and some crude approximations of a whale as a cylinder, then of course the number $$\pi$$ showed up, followed by the hilarious phrase along the lines of "The number $$\pi$$ for bowhead whales is about 3.14".

• But the chirality introduced due to ethyl methyl amine is because of the chirality of the ligands and not because of the arrangement of different ligands around the central atom. I have assumed the ligands as non chiral. – siddharth kalra Sep 28 '20 at 13:26
• @siddharthkalra If the ligands are chemically different, because you arrange around a central ion $\ce{M^{4+}}$ at once $\ce{F-}$ and $\ce{Cl-}$ and $\ce{Br-}$ and $\ce{I-}$, than the complex is chiral even if the ligands are not. Well if the four are chemically different like methyl, ethyl, propyl, ... (which includes the «if at least one them is chiral»), the complex is chiral, too. – Buttonwood Sep 28 '20 at 17:13

No. A plane of symmetry is a sufficient, but not necessary criterion to exclude optical activity of a molecular compound. Equally sufficient, but not necessary criterion for the absence of chirality is the presence of a centre of inversion. Note that you probe for these criteria independent from each other the whole molecule.

An easier example of organic molecules suitable for the first criterion is (2R,3S)-tartaric acid - equally known as meso-compound - where you may draw a mirror plane across the molecule even if you have two examples of atom centred chirality in the molecule present. (It is not good to call the stereogenic atoms «chiral atoms». Beside atom centred chirality, there equally are helical and axial chirality, too.)

By training, you are going to identify these compounds by inspection of their formulae:

(credit)

Don't hesitate to build models of the molecule in question and to redraw the structure formulae like the following to get more familiar with the topic:

(credit)

Only the two first columns of the four depict a mesocompound.

• But I was talking about coordination compounds having only one central metal atom and having non chiral ligands. I am fine with chirality in organic compounds. I just wanted to ask if there is any shorter method to check chirality in such coordination compounds by just checking plane of symmetry, as all the coordination compounds I have come across have a plane of symmetry if they are achiral. – siddharth kalra Sep 28 '20 at 13:32
• @siddharthkalra No. As stated, you probe the molecule / complex for a mirror plane which either is positive (is present), or negative (is absent). And you probe the molecule for the presence / absence of a centre of inversion. The order of testing them may be formalized in a flowchart (like here) if aiming to determine the point group of the object (e.g., IR spectroscopy), but neither one of the two tests is a necessary and sufficient condition for the other to yield either answer. – Buttonwood Sep 28 '20 at 17:18