Some view the birth of quantum chemistry in the discovery of the Schrödinger equation and its application to the hydrogen atom in 1926.[cần dẫn nguồn] However, the 1927 article of Walter Heitler và Fritz London[31] is often recognised as the first milestone in the history of quantum chemistry.[32] This is the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. In the following years much progress was accomplished by Edward Teller, Robert S. Mulliken, Max Born, J. Robert Oppenheimer, Linus Pauling, Erich Hückel, Douglas Hartree, Vladimir Aleksandrovich Fock, to cite a few.[cần dẫn nguồn]

Still, skepticism remained as to the general power of quantum mechanics applied to complex chemical systems.[cần dẫn nguồn] The situation around 1930 is described by Paul Dirac:[33]

"The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation.

Hence the quantum mechanical methods developed in the 1930s and 1940s are often referred to as theoretical molecular or atomic physics to underline the fact that they were more the application of quantum mechanics to chemistry and spectroscopy than answers to chemically relevant questions."

In the 1940s many physicists turned from molecular or atomic physics to nuclear physics (like J. Robert Oppenheimer or Edward Teller). In 1951, a milestone article in quantum chemistry is the seminal paper of Clemens C. J. Roothaan on Roothaan equations.[34] It opened the avenue to the solution of the self-consistent field equations for small molecules like hydrogen or nitrogen. Those computations were performed with the help of tables of integrals which were computed on the most advanced computers of the time.[cần dẫn nguồn]