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_ N_Where's the Math in Mathmol?_
    
 Table of Contents
  Introductory Comments
  What is Molecular Modeling?
  Why is Molecular Modeling Important?
  What do some common molecules look like?
  Where's the Math?
  Carbon 3 Ways
  Carbon Compounds
  Water and Ice
  Water and Ice pt.II
  How to view structures in class or at home
  MathMol Library of Structures.
  Tutorial 1: 1-Dimension, 2-Dimensions, 3-Dimensions...
  Tutorial2: The Geometry of 2 Dimensions..
  Tutorial3: The Geometry of 3- Dimensions
  Tutorial4: The Geometry of Molecules.
  Appendix1: Scientific Notation
  Appendix 2: Mass
  Appendix3: Volume
  Appendix4: Density
 

Part II -Mathematical Relationships

Part I -Geometry
Part III- Overview of MathMol Tutorials

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A line is a set of points described by an equation which may be written in the form y=mx+b where the constant m is the slope of the line and b represents its y intercept. As x varies y varies. In the figure above, as the temperature (T) of the system varies, the kinetic energy (E) of the molecule varies. The line describes the equation E=kT where k is the slope of the line.

The set of points which satisfy the equation y=1/x is a hyperbola. As x varies y varies inversely. As x becomes smaller y becomes larger. The movie above shows two particles of opposite charge attracted to each other. The relationship between coulombic energy and distance is an inverse relationship. The coulombic energy between the two particles varies with -1/r, where r is the distance separating their center of masses. In the movie notice that as r gets smaller, the potential energy becomes more negative.


Cliick right mouse button over image-->play (repeat to stop)

The movie above shows that the torsion bond energy of a molecule can be modeled by a periodic function.

 

Continue to part III


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