A multipolar approach to the interatomic covalent interaction energy.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Interatomic exchange-correlation energies are crucial for understanding covalent contributions to chemical bonds.
• Current methods for calculating these energies are computationally intensive, limiting their widespread application.
• The multipolar (mp) expansion is a common technique for approximating classical Coulomb interactions in biomolecular modeling.

Purpose of the Study:

• To investigate the applicability of the multipolar (mp) expansion for approximating interatomic exchange-correlation (xc) energies within the Interacting Quantum Atoms (IQA) method.
• To assess the accuracy and convergence of the mp approximation for xc energies in various chemical systems.

Main Methods:

• Application of the multipolar (mp) expansion to approximate interatomic exchange-correlation (xc) energies.
• Numerical analysis of the convergence properties of the xc mp series.
• Validation of the approximation across diverse molecular systems, including hydrogen-bonded dimers, covalent, and aromatic molecules.

Main Results:

• The full xc mp series exhibits divergence for directly bonded atoms (1-2 pairs) but is generally effective for non-bonded interactions (1-n, n>2).
• The xc mp series demonstrates asymptotic convergence, similar to conventional perturbation theory.
• A truncated xc mp approximation including terms up to l1+l2=2 yields accurate results, even for directly bonded atoms in many cases.
• An exact algebraic relationship was established between the monopole-monopole xc mp term and the inter-atomic bond order (delocalization index).

Conclusions:

• The truncated multipolar expansion offers a computationally feasible and accurate approach for approximating interatomic exchange-correlation energies.
• This method provides valuable insights into covalent interactions and bond orders, extending the applicability of IQA calculations.
• The findings facilitate more efficient and widespread analysis of chemical bonding in complex molecular systems.