BeH₂ is linear, whereas CH₂ with two additional electrons and H₂O with four additional electrons are both bent to a similar degree. Could these changes in geometry have been anticipated by examining the shapes of the bonding molecular orbitals?

a. Perform a series of geometry optimizations on BeH₂ with the bond angle constrained at 90°, 100°, 110°, . . . , 180° (10 optimizations in total). Use the HF/6 31G* model. Plot the total energy, along with the HOMO and LUMO energies versus bond angle. Also, display the HOMO and LUMO for one of your structures of intermediate bond angle.

Does the energy of the HOMO of BeH₂ increase (more positive) or decrease in going from a bent to a linear structure, or does it remain constant, or is the energy at a minimum or maximum somewhere between? Rationalize your result by reference to the shape and nodal structure of the HOMO. Given that BeH₂ has only two valence electrons (in the HOMO), would you expect the molecule to be linear or bent? Is your conclusion consistent with the total energy curve you plotted?

Does the energy of the LUMO of BeH₂ increase or decrease with increase in bond angle, or does it remain constant, or is the energy at a minimum or maximum somewhere between? Rationalize your result by reference to the shape and nodal structure of the LUMO. What do you anticipate would happen to the geometry of BeH₂ as electrons are added to the LUMO? Take a guess at the structure of BH^•₂ (one electron added to the LUMO) and singlet CH₂ (two electrons added to the LUMO).

b. Optimize the geometries of (singlet) BH^•₂ and CH₂ using the HF/6-31G* model. Are the results of the quantum chemical calculations in line with your qualitative arguments?

c. Perform a series of geometry optimizations on singlet CH₂ with the bond angle constrained to 90°, 100°, 110°, . . . , 180°. Plot the total energy as a function of the angle as well as the HOMO and LUMO energies. Display the LUMO for some intermediate structure. Does the plot of HOMO energy versus angle in CH₂ mirror the plot of LUMO energy versus angle in BeH₂? Rationalize your answer. Does the energy of the LUMO in CH₂ increase, decrease, or remain constant with increase in bond angle (or is it at a minimum or maximum somewhere between)? Is the change in LUMO energy smaller, larger, or about the same as the change in the energy of the HOMO over the same range of bond angles? Rationalize these two observations by reference to the shape and nodal structure of the LUMO. What do you anticipate would happen to the geometry of CH₂ as electrons are added to the LUMO? Take a guess at the structure of NH^•₂ (one electron added to the LUMO) and H₂O (two electrons added to the LUMO).

d. Optimize the geometries of NH^•₂ and H₂O using the HF/6-31G* model. Are the results of the quantum chemical calculations in line with your qualitative arguments?