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发布日期:2021年09月20日
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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.


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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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