Alchemical geometry relaxation

We propose the relaxation of geometries throughout chemical compound space using alchemical perturbation density functional theory (APDFT). APDFT refers to perturbation theory involving changes in nuclear charges within approximate solutions to Schrodinger's equation. We give an analytical formula to calculate the mixed second order energy derivatives with respect to both nuclear charges and nuclear positions (named alchemical force ) within the restricted Hartree-Fock case. We have implemented and studied the formula for its use in geometry relaxation of various reference and target molecules. We have also analyzed the convergence of the alchemical force perturbation series as well as basis set effects. Interpolating alchemically predicted energies, forces, and Hessian to a Morse potential yields more accurate geometries and equilibrium energies than when performing a standard Newton-Raphson step. Our numerical predictions for small molecules including BF, CO, N-2, CH4, NH3, H2O, and HF yield mean absolute errors of equilibrium energies and bond lengths smaller than 10 mHa and 0.01 bohr for fourth order APDFT predictions, respectively. Our alchemical geometry relaxation still preserves the combinatorial efficiency of APDFT: Based on a single coupled perturbed Hartree-Fock derivative for benzene, we provide numerical predictions of equilibrium energies and relaxed structures of all 17 iso-electronic charge-neutral BN-doped mutants with averaged absolute deviations of similar to 27 mHa and similar to 0.12 bohr, respectively.

Automated summary

In this study, we propose a method for relaxing geometries of chemical compounds using alchemical perturbation density functional theory. We provide an analytical formula for calculating mixed second order energy derivatives and implement it for relaxation of various reference and target molecules. The results show that our method yields more accurate geometries and equilibrium energies compared to standard methods.