Computational Chemistry 1.7 - Covalent Radius

Short lecture on the covalent radii of atoms.
The covalent radius is an effective size of an atom, outside of which it does not participate in chemical bonds. If the distance between two atoms is within the sum of their covalent radii multiplied by a threshold factor, they are considered to be bonded to one another.
Notes Slide: i.imgur.com/L70Niwo.png
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[@OtakuConfeiteiro]

Hey I"m staring my Ph.D in computational chemistry and your videos are helping me so much. Tanks man.

[@TMPChem]

Hi Daniel. Good luck with everything moving forward. Questions are always welcome on the video for a given topic.

[@bonbonpony]

So are the bonds stored in a PDF file too or just the positions of atoms? As for checking all possible pairs: wouldn't it be faster to divide the space into octants, and those octants into smaller octants, etc., and save those atoms' positions in an octree? This should drastically reduce the number of atoms to check, because atoms that are too far will already be in different octree branches, so all you need to check is a bunch of siblings in the tree.

[@rmiller415]

It would be really awesome if you added the github path name for the files you use in your videos.

[@TMPChem]

The reason I'm hesitant to add full paths to videos is that once uploaded videos are immutable (especially since KZbin removed the ability to add annotations in March 2017). If I ever decide to change the directory structure of the GitHub project, the video would contain unfixable broken links. This has happened before when I changed the structure in the previous version. I think the directory structure is self-explanatory enough given the project link that providing the GitHub link in the description and on the channel page is a sufficient amount of direction.

[@amritasharma3392]

I didn't get the n(n+1)/2 relation

[@TMPChem]

Imagine a room full of people where everyone shakes hands with everyone else exactly once. How many handshakes took place? If there is 1 person, 0 handshakes. For 2 people, 1 handshake. 3 -> 3. 4 -> 6. 5 -> 10. 6 -> 15. And the pattern continues. The formula that predict the number of handshakes between N people is N(N-1)/2. This is also the number of unique pairwise interactions between particles. If we have N particles there are N(N-1)/2 pairwise interactions. N(N-1)/2 = N^2 / 2 - N/2. As N gets very large, the linear term doesn't matter and the quadratic term dominates the number of pairwise interactions. In algorithmic analysis, this scaling, or "asymptotic complexity" would be described as O(N^2), i.e. the computing resources needed to compute all interatomic distances scales as the number of atoms squared.

[@amritasharma3392]

Hey, thanks for the reply, so in ethane, there are 8 atoms, so does that mean it will have 8*7/2=28 bonds?

[@TMPChem]

If all atoms were bonded to all other atoms, there would be 8*(8-1)/2 = 28 bonds. So the program inside the pairwise double loop of the bond graph function checked all 28 interatomic distances, and determined that only 7 of them were within the necessary cutoff distance to be considered a chemical bond. The other 21 interatomic pairs were too far apart.

[@amritasharma3392]

Ohh that's a really nice explanation. Thank you:)

[@zamzamali4842]

awesome explanation!

[@pnarempire9837]

I didn't see it clearly .I don't know what happen maybe due to low quality video or....