Noneigenstate <i>Ab Initio</i> Density Matrix Downfolding for Constructing Model Hamiltonians in Quantum Chemistry

Model Hamiltonians represent a convenient way of reducing complex problems of many-electron quantum mechanics to much simpler problems: they can fully reproduce the core behaviors of a system of interest by encoding only the dominant physical interactions and using only a small number of associated parameters. Model Hamiltonians have been successfully applied to describe many chemical and physical phenomena. Density matrix downfolding (DMD) [ <i>J. Chem. Phys.</i> 2015, 143 (10), 102814] allows the derivation of model Hamiltonians of any form in a systematically improvable fashion by matching the energy spectrum of <i>ab initio</i> Hamiltonians with those of the model Hamiltonians. This method allows not only the improvement of existing models but also the construction of accurate and efficient physical models for various systems. While DMD looks like a promising approach, it has rarely been applied within chemistry, and neither its limits nor its practical performance is well-understood. In this work, we evaluated the performance of DMD, based on noneigenstates of <i>ab initio</i> Hamiltonians, for several realistic chemical systems: benzene, naphthalene, FeSe, and a prototypical Fe(IV)═O complex found in the active sites of 2-oxoglutarate-dependent oxygenases. Our results show that DMD is a reliable and computationally efficient tool for obtaining optimized model Hamiltonians in quantum chemistry. This not only opens the door to studying complex systems at reduced computational cost but also to isolating and <i>understanding</i> the physical core principles that dominate their behavior─this might offer new insights for tuning or even designing chemical systems for applications ranging from biochemistry to catalysis.