22.3.2: ii. Exercises

• • Contributed by Jack Simons
• Professor Emeritus and Henry Eyring Scientist (Chemistry) at University of Utah

Q1

Show that the configuration (determinant) corresponding to the $$Li^+ 1s(\alpha )1s(\alpha )$$ state vanishes.

Q2

Construct the 3 triplet and 1 singlet wavefunctions for the $$Li^+ 1s^12s^1$$ configuration. Show that each state is a proper eigenfunction of $$S^2 \text{ and } S_z$$ (use raising and lowering operators for $$S^2$$)

Q3

Construct wavefunctions for each of the following states of $$CH_2:$$
\begin{align} &a.) & ^1B_1(1_{a1}^22_{a1}^21_{b2}^23_{a1}^11_{b1}^1) \\ &b.) & ^3B_1(1_{a1}^22_{a1}^21_{b2}^23_{a1}^11_{b1}^1) \\ & c.) & ^1A_1(1_{a1}^22_{a1}^21_{b2}^23_{a1}^2) \end{align}

Q4

Construct wavefunctions for each state of the $$1\sigma^22\sigma^23\sigma^21\pi^2$$ configuration of NH.

Q5

Construct wavefunctions for each state of the $$1s^12s^13s^1$$ configuration of Li.

Q6

Determine all term symbols that arise from the $$1s^22s^22p^23d^1$$ configuration of the excited N atom.

Q7

Calculate the energy (using Slater Condon rules) associated with the ep valence electrons for the following states of the C atom.

i. $$^3P(M_L=1,M_S=1),$$
ii. $$^3P(M_L=0,M_S=0),$$
iii. $$^1S(M_L=0, M_S=0), \text{ and }$$
iv. $$^1D(M_L=0, M_S=0)$$.

Q8

Calculate the energy (using Slater Condon rules) associated with the $$\pi$$ valence electrons for the following states of the NH molecule.
i. $$^1\Delta (M_L=2, M_S=0),$$
ii. $$^1\Sigma (M_L=0, M_S=0), \text{ and }$$
iii. $$^3\Sigma (M_L=0, M_S=0).$$