Quantum Chemistry: solving the Schrödinger equation with Julia

The computational evaluation of the electronic properties of atoms and moleculesentails the use of quantum mechanics. The computational cost of some routines, in most cases, does not scale linearly and becomes very dependent on the size of the system. Thus, over time, the development of effective tools to accelerate such computations can benefit of new programming languages, like Julia, focused on numerical, scientific and faster programming.

In this piece of research, the central aim is to joint both approaches to present a new Julia library capable to calculate the molecular integrals proposed by Taketa, Huzinaga, and O-ohata in 1966. The performance associated with Julia codes will allow us to calculate electron repulsion integrals, ERIs, without taking too much time when compared with Python, for example. As the system gets larger, the computation of ERIs, becomes more expansive, since it is one of the most time-consuming steps in the whole calculation These results were compared with those obtained by the ORCA software, and by implementing the same integrals in Python. The results shown a good agreement of the energy values obtained by Julia implementation and ORCA software (a very well stablished software in the computational chemistry field) calculations, and Julia is also the faster implementation analyzed, being a promise for new electronic structure calculations codes. The library developed for the calculation of molecular integrals in question (S: over- lap integrals matrix; T : kinetic integrals matrix; V : electron-nuclear attraction integrals matrix; G: electron-electron repulsion integrals tensor) was named QuantumFoca.jl and is available on GitHub as a free and open source code.