(a) (i) For a two-electron system, prove that a Hartree product of spin orbitals does not obey the Pauli principle. (6 marks) (ii) Give the general mathematical expression for a Gaussian primitive basis function and discuss the parameters that characterise it. (4 marks) (b) Write the electronic Hamiltonian operator, , in atomic units for each of the Se atom, H, H2+ and CH3+. (10 marks) (c) What is the main difference between Hartree and Hartree-Fock theory and why does this difference matter? (5 marks) (a) (i) For a two-electron system, prove that a Hartree product of spin orbitals does not obey the Pauli principle. (6 marks) (ii) Give the general mathematical expression for a Gaussian primitive basis function and discuss the parameters that characterise it. (4 marks) (b) Write the electronic Hamiltonian operator, , in atomic units for each of the Se atom, H, H2+ and CH3+. (10 marks) (c) What is the main difference between Hartree and Hartree-Fock theory and why does this difference matter