Background

Atoms form bonds (stick to each other) because there are long range attractive forces that pull the atoms together. However, there are short range repulsive forces which cause the atoms to repel each other when they get too close. A common way to think about this is to imagine the atoms are connected by a simple spring. The spring has a natural length it wants to be at, so if you move the atoms closer than that, the spring is compressed creating a repulsive force. When the spring is stretched, it tries to pull that atoms back together. Either way, the potential energy of the atoms are increased, and they naturally want to move back to the equilibrium position of lowest energy. The following Wikipedia page has a nice description: https://en.wikipedia.org/wiki/Morse_potential (Links to an external site.)Links to an external site.. Read up through the "Potential energy function" portion for a nice description.

Assignment

The Morse potential is a famous equation for approximating the potential energy of two atoms as a function of separation distance. It is given in Equation 3 in a paper by H. Hulburt and J. Hirshchfelder, (hulburt_JChemPhys_1941_v9). Table 1 in the Hulburt paper gives values for the different parameters of the Morse Potential. Note that the unit on the separation distance column is the (angstrom). 1 = 10-10 m. Your assignment is to write a script to generate plots of Morse potentials for at least twelve of the diatomic molecules in Table 1 of the Hulbert paper in order to compare them. Additionally, include a horizontal, dashed line to show the dissociation energy for each potential function.

You decide what the best way to compare them is. Plot the curves in 3D separated from one another on the third axis? Subplots? Two y-axes? All plots in one figure? Metal hydrides in one figure, Hydrogen halides in another? You determine what is best. Be sure to format and clearly label all plots including each curve.

Finally, report any interesting trends you happen to notice, if any, in 750 words or less. If there is a good way to show a trend using a plot, bar graph, etc., do that. Also include the plots of the potentials. For example, are there trends for the dissociation energies or equilibrium separation distances? See what you can find. Upload your MATLAB script as a .m file and your report as a .pdf file.

Background

Atoms form bonds (stick to each other) because there are long range attractive forces that pull the atoms together. However, there are short range repulsive forces which cause the atoms to repel each other when they get too close. A common way to think about this is to imagine the atoms are connected by a simple spring. The spring has a natural length it wants to be at, so if you move the atoms closer than that, the spring is compressed creating a repulsive force. When the spring is stretched, it tries to pull that atoms back together. Either way, the potential energy of the atoms are increased, and they naturally want to move back to the equilibrium position of lowest energy. The following Wikipedia page has a nice description: https://en.wikipedia.org/wiki/Morse_potential (Links to an external site.)Links to an external site.. Read up through the "Potential energy function" portion for a nice description.

Assignment

The Morse potential is a famous equation for approximating the potential energy of two atoms as a function of separation distance. It is given in Equation 3 in a paper by H. Hulburt and J. Hirshchfelder, (hulburt_JChemPhys_1941_v9). Table 1 in the Hulburt paper gives values for the different parameters of the Morse Potential. Note that the unit on the separation distance column is the (angstrom). 1 = 10-10 m. Your assignment is to write a script to generate plots of Morse potentials for at least twelve of the diatomic molecules in Table 1 of the Hulbert paper in order to compare them. Additionally, include a horizontal, dashed line to show the dissociation energy for each potential function.

You decide what the best way to compare them is. Plot the curves in 3D separated from one another on the third axis? Subplots? Two y-axes? All plots in one figure? Metal hydrides in one figure, Hydrogen halides in another? You determine what is best. Be sure to format and clearly label all plots including each curve.

Finally, report any interesting trends you happen to notice, if any, in 750 words or less. If there is a good way to show a trend using a plot, bar graph, etc., do that. Also, include the plots of the potentials. For example, are there trends for the dissociation energies or equilibrium separation distances? See what you can find. Upload your MATLAB script as a .m file and your report as a .pdf file.