How can I find chiral centers in ring structures?

Here's one way to do it.

Assume that you have to find the chiral centres in 3-aminocyclohexanol.

Here are the steps to find the chiral centres.

Step 1: Ignore all atoms that cannot be chiral centres.

These include ##"CH"_2, "CH"_3##, and ##"NH"_2## groups, oxygens, halogens, and any atom that is part of a double or triple bond.

That eliminates every atom except ##"C-1"## and ##"C-3"## of the ring.

Step 2: For the remaining atoms, check if there are four different groups attached to that atom.

Two groups can appear to be the same if you look only at the first attached atom.

You may have to keep going to check if they are really the same or are different.

##bb"C-1"##

The four atoms directly attached to ##"C-1"## are ##"O, C-2, C-6"## and ##"H"##.

We have to go one atom further out to see if ##"C-2"## and ##"C-6"## are different.

##"C-2"## is attached to ##"C-3, H"##, and ##"H"##. We write it as ##"C-2(C,H,H)"##, with the elements in parentheses listed in order of decreasing atomic number.

##"C-6"## is attached to ##"C-5, H"##, and ##"H"##. We write it as ##"C-5(C,H,H)"##,

So ##"C-2"## and ##"C-6"## are still the same.

We must go one atom further out to decide between ##"C-3"## and ##"C-5"##.

We list ##"C-3"## as ##"C-3(N,C,H)"##.

##"C-5"## is ##"C-5(C,H,H)"##

These are definitely different, so ##"C-1"## has four different groups, and ##"C-1"## is a chiral centre.

##bb"C-3"##

The four atoms attached to ##"C-3"## are ##"N, C-2, C-4"##, and ##"H"##.

We have to go one atom further out to see if ##"C-2"## and ##"C-4"## are different.

##"C-2"## is attached to ##"C-1, H"##, and ##"H"##. We write it as ##"C-2(C,H,H)"##.

##"C-4"## is attached to ##"C-5, H"##, and ##"H"##. We write it as ##"C-4(C,H,H)"##.

##"C-2"## and ##"C-4"## are the same.

We must go one atom further out to decide between ##"C-1"## and ##"C-5"##.

We list ##"C-1"## as ##"C-1(O,C,H)"##.

##"C-5"## is ##"C-5(C,H,H)"##.

These are definitely different, so ##"C-3"## has four different groups, and ##"C-3"## is a chiral centre.

Here’s a video on finding chiral centres.