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

## TL;DR

This paper introduces a new method to automatically discover efficient algorithms for molecular electronic structure calculations without using traditional iterative methods.

## Contribution

The novel contribution is a physics-informed program synthesis approach that generates non-iterative algorithms matching the accuracy of HF and DFT.

## Key findings

- New algorithms reproduce HF or DFT energies to within 0.1 kcal/mol/atom.
- Algorithms require only a single matrix-diagonalization operation instead of iterative self-consistent field convergence.
- The approach shows transferability and efficiency for larger alkane species.

## Abstract

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 any self-consistent field iterations at all.
Our PIPS strategy exploits the fact that the eigenvectors of the Fock
matrix F (or Kohn–Sham matrix K)
are the same as the eigenvectors of a broad class of matrix functions, f(F). As a result, PIPS can be used to seek
matrices M 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.