Non-eigenstate Ab Initio Density Matrix Downfolding to produce 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) [J. Chem. Phys. 2015, 143 (10), 102814] allows the derivation of model Hamiltonians, of any form, in a systematically improvable fashion, by matching the energy spectrum of ab initio 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 practical performance are well understood. In this work we evaluated the performance of DMD, based on non-eigenstates of ab initio 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 understanding 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.