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Arbitrarily accurate quantum alchemy.

Guido Falk von Rudorff1

  • 1Faculty of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria.

The Journal of Chemical Physics
|December 16, 2021
PubMed
Summary
This summary is machine-generated.

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Quantum alchemy, a Taylor series expansion for molecular simulations, is shown to converge for calculating energies and properties. This method enables efficient exploration of chemical space and geometry relaxation for derivative compounds.

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Doping compounds perturb molecular Hamiltonians, traditionally requiring costly quantum chemistry calculations.
  • Quantum alchemy uses Taylor series expansions to approximate properties of derivative compounds, but its convergence and applicability were unclear.

Purpose of the Study:

  • To provide numerical evidence for the convergence of quantum alchemy expansions for molecular systems.
  • To assess the convergence radius and applicability of quantum alchemy for geometry relaxation and large electronic structure changes.
  • To develop and release code for evaluating restricted Hartree-Fock energies and derivatives.

Main Methods:

  • Taylor series expansion of nuclear charge perturbations (quantum alchemy).

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  • Hartree-Fock (HF) calculations to obtain self-consistent energies and properties.
  • Evaluation of convergence for electronic energy, density matrix elements, molecular orbital energies, and density profiles.
  • Application of mixed alchemical and spatial derivatives for geometry relaxation.

    • Main Results:

    • Numerical evidence confirms the convergence of the quantum alchemy expansion, recovering HF self-consistent energies.
    • The convergence radius was quantified for dimers across various basis sets, defining the accessible chemical space.
    • Convergence was demonstrated for electronic energy, density matrix, MO energies, and density profiles, even for significant electronic structure transformations (e.g., He3 to H6).
    • Geometry relaxation of H2 was achieved using mixed alchemical and spatial derivatives.

    Conclusions:

    • Quantum alchemy is a convergent method for calculating molecular properties and enabling geometry relaxation.
    • The study quantifies the convergence radius, providing insights into the chemical space accessible via this approach.
    • The released code facilitates further development and application of quantum alchemy.