Ammonia provides a particularly simple example of the dependence of vibrational frequencies on the atomic masses and of the use of vibrational frequencies to distinguish between a stable molecule and a transition state. First examine the vibrational spectrum of pyramidal ammonia (“ammonia” on the pre-calculated Spartan file).

a. How many vibrational frequencies are there? How does this number relate to the number of atoms? Are all frequencies real numbers or are one or more imaginary numbers? Describe the motion associated with each frequency and characterize each as being primarily bond stretching, angle bending, or a combination of the two. Is bond stretching or angle bending easier? Do the stretching motions each involve a single NH bond or do they involve combinations of two or three bonds? 

b. Next, consider changes to the vibrational frequencies of ammonia as a result of substituting deuteriums for hydrogens (“perdeutero-ammonia” on the pre-calculated Spartan file). Are the frequencies in ND₃ larger, smaller, or unchanged from those in NH₃? Are any changes greater for motions that are primarily bond stretching or motions that are primarily angle bending?

c. Finally, examine the vibrational spectrum of an ammonia molecule that has been constrained to a planar geometry (“planar ammonia” on the Spartan download). Are all the frequencies real numbers? If not, describe the motions associated with any imaginary frequencies and relate them to the corresponding motion(s) in the pyramidal equilibrium form.