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? Would this result have been anticipated by examining the shape and nodal structure of the HOMO?
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 singlet 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 , , , , . 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?
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