Symmetry-Adapted Relaxation Theory (SART): Variational Embedding for Convergent Infinite-Order Induction without Overpolarization.

The induction part of intermolecular interaction energy describes the effect of the mutual polarization of subsystems. Low-order induction effects can be reasonably described by symmetry-adapted perturbation theory (SAPT), but the capture of important higher-order polarization effects requires the use of an external correction from supermolecular Hartree-Fock (HF) theory, which is not free from artifacts. When one describes induction through a response to an embedding potential representing the other molecule(s) (which is the case in a number of existing approaches such as the electrostatic embedding, Hartree-Hartree-Fock, and explicit polarization methods), it is easy to succumb to overpolarization unless the embedding potential fully accounts for the exchange effects, enforcing the Pauli exclusion principle and preventing a variational collapse to a Pauli-forbidden state. Here, we propose a new embedding framework that accounts for both electrostatic polarization and exchange effects in many-body systems. As a proof of principle, we apply the novel embedding potentials in a variational approach called symmetry-adapted relaxation theory (SART) that succeeds in recovering infinite-order induction energy from the HF method without a need to compute the HF wave function or energy of the entire complex. SART is expected to be the foundation for a new class of intermolecular perturbation theories, while the newly proposed potentials can also be applied to incorporate complete exchange into various embedding algorithms.