First-order symmetry-adapted perturbation theory for multiplet splittings

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Existing Symmetry-Adapted Perturbation Theory (SAPT) formalisms are primarily limited to high-spin states of interacting systems.
• Accurate calculation of spin state splittings in low-spin complexes formed from high-spin open-shell molecules is challenging.
• Understanding spin interactions is crucial for predicting molecular complex properties.

Purpose of the Study:

• To develop and implement a novel SAPT approach for calculating interactions between high-spin open-shell molecules that yield low-spin states.
• To provide the first SAPT-based method for estimating spin state splittings in such complexes.
• To derive and implement the first-order exchange energy term responsible for spin state splittings.

Main Methods:

• Development of a symmetry-adapted perturbation theory (SAPT) formalism for high-spin open-shell molecules interacting to form low-spin states.
• Derivation and implementation of the first-order exchange energy within the S² approximation.
• Formulation of the approach using both molecular-orbital and atomic-orbital expressions, enabling density-fitted implementation.

Main Results:

• The new SAPT approach successfully estimates spin state splittings, going beyond previous high-spin limitations.
• First-order exchange energies are shown to be linear combinations of diagonal and spin-flip terms, determined by Clebsch-Gordan coefficients.
• The S² approximation leads to a Heisenberg Hamiltonian picture with a single coupling parameter for all splittings.

Conclusions:

• The developed SAPT formalism provides a robust method for calculating spin state splittings in low-spin complexes of open-shell molecules.
• The approach offers a significant advancement for theoretical studies of magnetic interactions in molecular systems.
• Tested on various systems, including diatomic molecules and the phenalenyl dimer, demonstrating its broad applicability.