Automated Discovery of Algorithms for Molecular Electronic Structure Calculations Using Physics-Informed Program Synthesis.

We demonstrate a physics-informed program synthesis (PIPS) approach that can be used to identify entirely new algorithms that approximate the results of single-reference electronic structure approaches like Hartree-Fock (HF) and density-functional theory (DFT)─but without self-consistent field iterations at all. Our PIPS strategy exploits the fact that the eigenvectors of the Fock matrix (or Kohn-Sham matrix ) are the same as the eigenvectors of a broad class of matrix functions, (). As a result, PIPS can be used to seek matrices that yield the same molecular orbital coefficients as converged HF or DFT calculations. We demonstrate this approach by generating new algorithms that accurately predict total energies for a series of heterodiatomic molecules (LiCl, LiF, NaCl, NaF) and C-C hydrocarbons; further simulations of C-C alkane species demonstrate further transferability and efficiency of the resulting algorithms. We obtain novel algorithms that can reproduce HF or DFT energies to within 0.1 kcal/mol/atom while requiring only a single matrix-diagonalization operation, rather than an iterative self-consistent field convergence. The approach demonstrated here could be similarly applied to more complex wave function ansatze, opening an interesting optimization-based pathway to identifying accurate yet efficient algorithms for molecular quantum chemistry.