The Self-assembly of Molecules: Molecular Quantum Mechanics

That molecules also self-assemble in the Universe is clear from observations of their presence in interstellar space. As a complete example of molecular self-assembly, we begin with the solution of the simplest molecule, the hydrogen molecular ion. The Born–Oppenheimer approximation is introduced in order to separate the nuclear and electronic wave functions. The matrix elements of the Hamiltonian are computed in order to find the energies of the gerade and ungerade states. The “overlap, Coulomb, and exchange integrals” are computed, leading to an understanding of the molecular binding potential energy as a function of the interproton distance and its relevance as a model for molecular self-assembly. Finally, the complete hydrogen molecule is solved in the molecular orbital approximation.