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Analyzing Mathematical Functions for Distance Between Atoms: A CSC 152 Scenario

Explore plotting and analyzing mathematical functions related to the distance between atoms in a CSC 152 scenario. Learn how to set parameters, calculate potential, create graphs, find minima, and test calculus concepts using Excel. References provided for further reading.

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Analyzing Mathematical Functions for Distance Between Atoms: A CSC 152 Scenario

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  1. Plotting mathematical functions CSC 152

  2. Scenario CSC 152

  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 152

  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 152

  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 152

  6. Make an XY Scatter Graph of the data and also find its minimum CSC 152

  7. Scale the y axis to vary from -1 to 2. Scale the x axis to vary from 0 to 1. CSC 152

  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 152

  9. Here we are just testing an idea from calculus that the minimum occurs where the derivative changes sign (is zero) CSC 152

  10. Change the ε parameter controls the depth of the “well” CSC 152

  11. The σ parameter controls the r-value at which the minimum occurs CSC 152

  12. References • http://polymer.bu.edu/Wasser/robert/work/node8.html CSC 152

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