Interpolating Hamiltonians in chemical compound space

Abstract

We analyze the Hamiltonian-interpolating schemes in chemical compound space. We show that if one allows for system-dependent information there are trivial solutions to this problem that allow to linearly interpolate between any two given iso-electronic Hamiltonians. If, on the other hand, one do not use any information about the system's Hamiltonians, we prove that there are no system-independent multiplicative interpolating procedures that linearize the energy. K E Y W O R D S alchemical changes, chemical compound space, conceptual density functional theory, interpolating Hamiltonians Int J Quantum Chem. 2017;117:e25384.

Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists

“…Thus, there has been an effort to linearize properties, such as energy, with respect to the coupling parameter λ for isoelectronic transformations . The linearization enables the use of first-order alchemical derivatives to compute exact energies, though no general method for linearizing energy in λ exists without relying on specific system information . However, as shown previously, accurate results can be obtained using the first-order derivative for certain systems.…”

“…38 The linearization enables the use of first-order alchemical derivatives to compute exact energies, though no general method for linearizing energy in λ exists without relying on specific system information. 90 However, as shown previously, accurate results can be obtained using the first-order derivative for certain systems. Improvements in numerical methods for determining paths in λ for which the first-order perturbation is valid, combined with guidelines when the approximation fails, could lead to the rapid identification of improved catalysts at minimal computational cost.…”