Final answer:
The electron configuration consists of doubly occupied first and second orbitals, and singly occupied third and fourth orbitals, facilitating the exchange interactions specified. Full energy includes one-electron, Coulomb, and exchange integrals for electron-electron interactions.
Step-by-step explanation:
The student's question relates to constructing an electron configuration in molecular orbitals and writing out the full energy expression based on one-electron, Coulomb, and exchange integral contributions. A single determinant with energy terms -2K12, -K13, -K23, -K14, -K24 implies that there are double occupations in the first and second orbitals, and single occupations in the third and fourth orbitals. This configuration facilitates the necessary exchange interactions. The full energy expression should consider one-electron integrals (hii terms for each electron), Coulomb integrals (Jij terms for repulsion between electrons in different orbitals), and exchange integrals (Kij terms due to the antisymmetry requirement of the wave function).
To express the full energy for this determinant, we would begin by adding up the hii terms for each occupied orbital, then include the Coulomb (Jij) and exchange (Kij) terms. Thus, the energy expression includes terms h11, h22, h33, and h44, corresponding to the one-electron energies, alongside the Coulomb and exchange integrals derived from considering electron-electron interactions between different orbitals. The Coulomb terms account for the repulsive energy between electrons in different orbitals, while the exchange terms account for the quantum mechanical exchange energy between electrons of parallel spin in these configurations.