Atoms in Molecules From Alchemical Perturbation Density Functional Theory.
Based on thermodynamic integration we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas (jellium) as reference, and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this universal choice affords unambiguous and exact definitions of energies and electron densities of AIMs. Numerical results are presented for neutral small molecules (CO, N2, BF, CO2), various small molecules with different electronic hybridisation states of carbon (CH4, C2H6, C2H4, C2H2, HCN), and for all the possible BN doped mutants connecting benzene to borazine (C2nB3-nN3-nH6, 0 ≦ n≦ 3). Our results, as well as comparison to atomic energy estimates resulting from DFT trained neural network models and atomic basis set overlap within CCSD, suggest that APDFT based AIMs enable meaningful, interesting, and counter-intuitive interpretations of chemical bonding and electron densities.