Representations of Atomic Environments and effects on Body-Ordering and Electrostatics on Machine-Learning Potentials

Machine learning interatomic potentials (MLIPs) achieve DFT-level accuracy by replacing rigid functional forms with neural network architectures that allow for much more effective regression at the cost of less intuitive representations. This thesis explores how representations of atomic environments used by MLIPs behave in two regimes: at short range in how body-ordered expansions converge with respect to their basis functions, and at long range, in improving modeling the electronic response of systems sensitive to electrostatic interactions. We determined that Atomic Cluster Expansions (ACE) are only able to recover the DFT dimer curve if the self-interactions inherent in their efficient tensor product construction are filtered with a purification operator. Moreover, we highlight that the canonical many-body expansion has a non-monotonic and non-convergent scaling with higher body orders in trimers and systems with symmetric interactions. We also studied the ad hoc modeling of long range electrostatics through physically-motivated charge flow models, namely charge equilibration (QEq). We diagnosed how QEq-based treatments that parameterize through local atomic descriptors fail to accurately capture the correct dielectric response as diagnosed by the bare susceptibility $\bm{\chi}_0$, and extended the capabilities of our in-house code PANNA to include the split charge equilibration (SQE) model. Phonon dispersions from trained SQE models show signatures of finite longitudinal optical-transverse optical splitting in MgO where short range and charge equilibration counterparts fail to manifest, suggesting that the SQE model has the necessary ingredients to capture finite screening in ionic crystals. Both results show that physically-grounded constraints on MLIP representations recover behavior that unconstrained flexibility misses: recovering the canonical expansion through the purification methods as well as imposing restraints in charge flow through the bond topology in SQE.