1. Plotting mathematical functions CSC 1521

2. Scenario CSC 1522

3. Domain We need to know the desired starting and ending values of the variable. Our variable is r the distance between the atoms, and we will start by looking at the function starting at r=0.2 and ending at r=1.0 (nanometers). Next we must decide on the intermediate values between 0.2 and 1.0. Let us go up by 0.001’s. CSC 1523

4. Make a place for the parameters at the top, start the set of r values at 0.2 and enter a formula like =A6+0.001. Copy that down until you get to the desired ending value CSC 1524

5. Enter the formula for the potential, something like =4*B$2*((B$3/A6)^12-(B$3/A6)^6). Note the use of absolute addressing (dollar signs) with the parameters. CSC 1525

6. Make an XY Scatter Graph of the data and also find its minimum CSC 1526

7. Scale the y axis to vary from -1 to 2. Scale the x axis to vary from 0 to 1. CSC 1527

8. Create columns for the average consecutive r value =AVERAGE(A6:A7) and the Approximate derivative = (B7-B6)/(A7-A6) (Note it’s rise over run.) CSC 1528

9. Here we are just testing an idea from calculus that the minimum occurs where the derivative changes sign (is zero) CSC 1529

10. Change the ε parameter controls the depth of the “well” CSC 15210

11. The σ parameter controls the r-value at which the minimum occurs CSC 15211

12. References http://polymer.bu.edu/Wasser/robert/work/n ode8.html CSC 15212