a.) Write down for yourself the secular determinant for the hypothetical molecule linear H3 making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α=-2.00 eV and β= -3 eV, what is the total electronic energy in eV? b.) Write down the secular determinant for the hypothetical molecule cyclic H3 making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α=-2.00 eV and β= -2 eV, what is the total electronic energy in eV?

1 a) Build the LCAO-MO (eigenfunctions of Ŝ2) Slater determinants for the electronic ground state of B2 and C2. b) Build the Valence-bond treatment Slater determinants for the electronic ground state of B2 and C2. c) What is the bond order of the two molecules in the LCAO-MO (from (a))? Does valence-bond treatment predict a bond? Compare the two approaches generally.

In the context of the Born-Oppenheimer approximation, write the Hamiltonian for the molecular cation H₂⁺.

The particle in a box (PiB) model can be applied to electrons which move freely in a molecule such as π electrons. 1,3-butadiene CH2=CH-CH=CH2 has an absorption peak in the UV-Vis spectrum at 290 nm. This peaks is assigned to the π → π* transition of the lowest energy. This transition is also called the HOMO → LUMO transition. As a simple approximation, let’s consider molecule of butadiene as being potential 1D box of length 3 * 1.4 Å = 4.2 Å, when counting three carbon-carbon bonds each 1.4 Å long. Also let’s consider the four π electrons occupy molecular orbitals MOs and energy of MOs is calculated according to the PiB model. a) Sketch the scheme of MOs of butadiene molecule and populate them with electrons. b) Calculate the wavelength of light λcalc which corresponds to absorption of light and excitation of π electron from the HOMO to the LUMO in the molecule of butadiene. c) Compare this calculated λcalc with experimental value of λexp = 290 nm provided above, and explain the…