Arbitrarily Precise Quantum Alchemy

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.

References in corpus (8)

• Phonons and related properties of extended systems from density-functional perturbation theory
• Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
• Automatic differentiation in quantum chemistry with an application to fully variational Hartree-Fock
• Exploring water adsorption on isoelectronically doped graphene using alchemical derivatives
• Atoms in molecules from alchemical perturbation density functional theory
• Rapid and accurate molecular deprotonation energies from quantum alchemy
• Effects of perturbation order and basis set on alchemical predictions
• Arbitrarily Precise Quantum Alchemy

Cited by in corpus (4)

• Arbitrarily Precise Quantum Alchemy
• Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation
• Alchemical geometry relaxation
• Antisymmetry rules of response properties in certain chemical spaces