DFT$_{\mathrm{3}}$: An Efficient DFT Solver for Nanoscale Simulations and Beyond.

To date, there are two kinds of DFT algorithms: Kohn-Sham DFT (KS-DFT) and orbital-free DFT (OF-DFT). KS-DFT is most common, uses a prescription whereby the lowest $N$ eigenvalues (where $N$ is the number of electrons) of a one-particle Hamiltonian need to be computed. OF-DFT prescribes to compute just one state recovering the effect of the other states with pure density functionals. In this work, we propose a new DFT solver (DFT$_{\mathrm{3}})$. From KS-DFT we borrow the self-consistent field iteration, so that computationally expensive density functionals are evaluated seldom. From OF-DFT we borrow the reliance on kinetic energy functionals, thus removing the need to diagonalize bringing strong computational savings. DFT$_{\mathrm{3}}$ leverages recent advances in OF-DFT development to output a computationally cheap and accurate ab initio electronic structure method. The key aspect of DFT$_{\mathrm{3}}$ is its still make use of an eigenvalue-like problem targeting just one solution while retaining the ability to sample ensemble $N$-representable electron densities. We implemented this method in DFTpy software. In comparison to OF-DFT and KS-DFT, DFT$_{\mathrm{3}}$ cuts the timing down by orders of magnitude and maintains linear scalability with system size.