Electrostatically embedded grid-adapted many-body analysis (EE-GAMA): A charge embedded fragment-based quantum chemistry method for accurate modelling of neutral and charged molecular clusters

Accurate quantum mechanical modelling of large molecular systems remains a formidable challenge due to the steep computational scaling of conventional methods. Fragment-based quantum chemistry approaches offer a more efficient alternative, but their accuracy is often limited by the neglect of long-range inter-fragment electrostatic interactions. To overcome this, we introduce Electrostatically Embedded Grid-Adapted Many-Body Analysis (EE-GAMA), a fragment-based quantum chemistry method that combines systematic many-body energy decomposition with electrostatic embedding based on overlapping spatial grid-based fragments. In EE-GAMA, electrostatic charge embedding is implemented within the Many- Overlapping Body (MOB) expansion framework, an approach rarely explored in previous studies. Each fragment is embedded in the electrostatic field generated by background point charges derived from Mulliken, Hirshfeld, or CM5 charge models, and both Geometry Dependent (GD) and Geometry Independent (GI) embedding schemes are investigated. Our primary goal is to accurately reproduce full-system energies at the MP2/6-311G(d,p) level. Benchmark calculations on neutral water clusters and hydronium clusters show that EE-GAMA achieves near full-system MP2 accuracy and significantly outperforms the non-embedded GAMA method. In charged systems, EE-GAMA effectively captures long-range electrostatics and consistently demonstrates that GD embedding offers greater accuracy than GI, underscoring the importance of environment-specific charge representation in highly polarized systems. While GI embedding offers computational simplicity, GD embedding provides enhanced reliability in such contexts. Overall, EE-GAMA offers an excellent balance between computational efficiency and accuracy and lays a strong foundation for the future development of advanced embedding schemes incorporating polarization and charge-transfer effects in large-scale quantum calculations.