Part I:
Using the data provided on the webvista site in the file marked vdw.txt, try to develop a mathematical equation for the vdW potential we discussed in class, U(x), that best fits the data. There are 4 columns. Column 1 is the inter-atomic separation, x. Column 2 is the total potential (the one you should try to model. Columns 3 and 4 are the repulsive and attractive components respectively (that is, col2 = col3+col4). So, try to build a separate equation for each of col 3 and col 4, then the sum gives col 2. That is, U(x) = Uattractive + Urepulsive. Remember, U=f(x), you also need to include two parameters: εvdw and σvdw. Here is the graph:
Here are some hints:
- An attractive potential energy should be a negative one.
- A repulsive potential energy should be a positive one.
- Both parts should be multiplied by 4εvdw
- Both parts should have σvdw raised to some power (not necessarily the same for each part)
- Both parts should have x raised to some power (not necessarily the same for each part)
- There is nothing more complicated than multiplication, division, and exponents.
- This is data for water so use εvdw = 0.650 and σvdw = 0.316
- Start by cutting and pasting the data into Excel, then use Excel to generate the data for your function and see how my data and yours compare. If they don't, then modify your functional form and replot, etc, etc, etc
- Do your best, and pay attention to how different functional forms behave.
- Don't worry if you can't get it, this is a hard problem. I'm more interested in seeing your wrong answer then I am in your finding the correct answer on the web, from a friend, etc...
You should turn in 1) your equation and 2) a print out with an overlay of my data and your data (all 3 curves from the graph above)
