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 <i>any</i> self-consistent field iterations at all. Our PIPS strategy exploits the fact that the eigenvectors of the Fock matrix <b>F</b> (or Kohn-Sham matrix <b>K</b>) are the same as the eigenvectors of a broad class of matrix functions, <i>f</i>(<b>F</b>). As a result, PIPS can be used to seek matrices <b>M</b> 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 C₁-C₄ hydrocarbons; further simulations of C₈-C₂₀ 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.