Arbitrarily Precise Quantum Alchemy

TL;DR

This paper demonstrates that quantum alchemy expansions can converge for small molecules, enabling efficient exploration of chemical space and geometry relaxation through high-precision derivatives, supported by an open-source code.

Contribution

It provides numerical evidence of convergence for quantum alchemy series, quantifies the convergence radius, and introduces a method for geometry relaxation using mixed derivatives.

Findings

Quantum alchemy series converges for small molecules.

Convergence applies to energy, density, and orbital properties.

Open-source code (APHF) supports arbitrary precision calculations.

Abstract

Doping compounds can be considered a perturbation to the nuclear charges in a molecular Hamiltonian. Expansions of this perturbation in a Taylor series, i.e. quantum alchemy, has been used in literature to assess millions of derivative compounds at once rather than enumerating them in costly quantum chemistry calculations. So far, it was unclear whether this series even converges for small molecules, whether it can be used for geometry relaxation and how strong this perturbation may be to still obtain convergent numbers. This work provides numerical evidence that this expansion converges and recovers the self-consistent energy of Hartree-Fock calculations. The convergence radius of this expansion is quantified for dimer examples and systematically evaluated for different basis sets, allowing for estimates of the chemical space that can be covered by perturbing one reference calculation alone. Besides electronic energy, convergence is shown for density matrix elements, molecular orbital energies, and density profiles, even for large changes in electronic structure, e.g. transforming He$_3$ into H$_6$. Subsequently, mixed alchemical and spatial derivatives are used to relax H$_2$ from the electronic structure of He alone, highlighting a path to spatially relaxed quantum alchemy. Finally, the underlying code (APHF) which allows for arbitrary precision evaluation of restricted Hartree-Fock energies and arbitrary-order derivatives is made available to support future method development.