Root-mean-square deviation of atomic positions

Okay kiddo, imagine you have a group of people standing in a line. Now, we want to know how much they’re moving from where they started, you know, maybe they're in a game or something. To figure that out, we measure how far each person has moved away from where they started.

But here’s the tricky part - some people may have moved a lot, and some may have moved just a tiny bit. So just measuring the distance from where they started won't be very helpful. We want to figure out how much everyone has moved in total.

To do that, we can use something called the root-mean-square deviation of atomic positions. It's like a fancy math formula that helps us make sense of all the movements.

First, we take the total distance each person has moved from their starting position and we square it (which means we multiply it by itself - think of it like doing a jump with your feet and then doing it again). We do this for every person in the line and add up all the results.

Next, we take the total number of people and divide the sum by that number. This gives us the average of all the squared distances that everybody moved from their original position.

And finally, we take the square root of that average.

This new number we get is the root-mean-square deviation of atomic positions. It tells us how much everyone has moved from their starting position on average, which is an important thing to know in figuring out if they're all still in the game or if someone is cheating.

So there you have it, kiddo! The root-mean-square deviation of atomic positions is a way to measure how much a group of people (or atoms, in science) have moved from their starting position. This helps us figure out if everyone is still playing by the rules or not.