Chemistry 3730 Fall 2000 Assignment 5

Due: Friday, Nov. 10, 10:00a.m.

1.

The four lowest vibrational energy levels of NaI are 2.8368, 8.4883, 14.110 and 19.702zJ.¹ Calculate the bond stiffness, anharmonicity constant and dissociation energy of this molecule assuming that the effective potential is of the Morse form. Make sure to give units for all reported quantities. [10 marks]

Notes: Ideally, you would use a fitting procedure since you have more than the minimum amount of data required to determine the constants. To fit an equation in Maple, create two lists containing your x and y values. In this case, your y values are the energies so you could create the list of energies by

Evals := [2.8368,8.4883,14.110,19.702];

You must type

with(stats);

to load the statistics package. The fitting command is a little intricate so be careful to put in all the braces and parentheses exactly as shown below. Suppose that your x variable is called x and that your y variable is called y. The expression which relates x to y is given by a function yt(x). This function contains (say) three parameters which you want to fit called a, b and c. The lists of x and y values are held in lists called xvals and yvals. The fitting command is then

fit[leastsquare[[x,y],y=yt(x),{a,b,c}]]([xvals,yvals]);

Isotopic masses can be looked up on the NIST web site
http://physics.nist.gov/PhysRefData/contents.html. Note that you must use accurate values of the fundamental constants in this kind of exercise.  

2.

Compute the dissociation energy of NaI by a HyperChem calculation. Explain your computational procedure in sufficient detail to allow replication of your results. Compare your answer to the spectroscopic value derived in question 1. [10 marks]

3.

The absorption IR spectrum of dichloromethane is shown below:

Assign as many of the bands as possible to particular normal modes. [10 marks]

4.

Using the STO-3G^* basis set, find all minimum energy structures of 1,2-difluoroethane. For each structure, record the energy and F-C-C-F dihedral angle. Also find the transition states separating these minima. Present your results in the form of a diagram showing the energies of the minima and transition states as a function of dihedral angle. [10 marks]

Note: To get consistent results when measuring dihedral angles in HyperChem, it is important always to take the atoms in the same order. HyperChem numbers atoms when it builds a molecule. To see these numbers, select Number from the Label dialog. Then make sure to always drag over the atoms which define your dihedral angle in the same numerical order.

Using ghost atoms to avoid basis set superposition errors

Molecular orbitals are built up from approximate atomic orbitals in ab initio calculations. During these calculations, the basis functions associated with one atom are, to a certain extent, used to compute the orbitals of the other. Accordingly, we cannot compare the results of molecular orbital calculations directly to those of calculations for the corresponding atoms unless we correct for this effect. The proper way to do this is to use a ``ghost atom'' which has basis functions, but no nucleus or electrons.

Here is how to use ghost atoms in HyperChem:

1.

Optimize the geometry of the parent molecule and save the results to a file.

2.

Select the atom or atoms to convert to ghost atoms.

3.

Choose Name Selection from the Select menu. Name the selected atoms ``ghost-atoms''.

4.

Unselect the atom(s) by right-clicking on the HyperChem workspace.

5.

Go into the ab initio setup menu. In the advanced options dialog, enable ghost atoms. Go into the options dialog and check that the charge and spin multiplicity are correctly set for the molecular fragment you wish to study.

6.

Do a single-point calculation.

7.

If you want to repeat the procedure with different ghost atoms, it is easiest to load your original molecule into your HyperChem session than to try to undo the selection.

Footnotes

...zJ.¹

z is the SI prefix corresponding to a multiple of 10^-21, pronounced ``zepto''.