Why Is Quantum Chemistry So Complicated?

The myriad tools of quantum chemistry are now widely used by a diverse community of chemists, biologists, physicists, and material scientists. The large number of methods (e.g., Hartree-Fock, density functional theory, configuration interaction, perturbation theory, coupled-clusters, equations of motion, Green's functions, and more) and the multitude of atomic orbital basis sets often give rise to consternation and confusion. In this Perspective, I explain why quantum chemistry has so many different methods and why researchers should understand their relative strengths and weaknesses. I explain how chemistry's use of orbitals and the need for wave functions to be antisymmetric causes computational-effort scaling proportional to the cube or higher power of the number of orbitals. I also illustrate how the fact that the Schro''dinger equation's energies are extensive makes it difficult to extract intensive properties such as bond and excitation energies, ionization potentials, and electron affinities.

Automated summary

The diverse community of chemists, biologists, physicists, and material scientists now widely use the myriad tools of quantum chemistry. However, the large number of methods and atomic orbital basis sets often lead to confusion. This Perspective explains the reasons for the existence of numerous methods in quantum chemistry and emphasizes the importance of understanding their relative strengths and weaknesses.