Electronic anisotropy between open shell atoms in first and second order perturbation theory

Area of Science:

• Atomic and Molecular Physics
• Quantum Chemistry
• Intermolecular Forces

Background:

• Atomic interactions with nonzero electronic orbital angular momenta exhibit anisotropy.
• Spherical tensor expansion is a method to represent these anisotropic interactions.
• Understanding these interactions is crucial for molecular structure and dynamics.

Purpose of the Study:

• To derive expressions for anisotropic interaction coefficients (first and second order).
• To investigate the role of dynamic polarizabilities, including odd-rank ones, in describing second-order interactions.
• To connect tensorial expansion coefficients to adiabatic Born-Oppenheimer potentials and van der Waals coefficients.

Main Methods:

• Spherical tensor expansion of atomic interactions.
• Derivation of interaction coefficients using multipole moments and dynamic polarizabilities.
• Relating tensorial coefficients to adiabatic Born-Oppenheimer potentials.

Main Results:

• Expressions for first-order (electrostatic) and second-order (dispersion, induction) anisotropic interaction coefficients were derived.
• A complete description of second-order interactions necessitates odd-rank dynamic polarizabilities.
• Linear and nonlinear constraints were found between tensorial expansion coefficients and van der Waals coefficients of molecular potentials.

Conclusions:

• The study provides a detailed theoretical framework for anisotropic atomic interactions.
• Odd-rank polarizabilities are essential for accurately modeling second-order intermolecular forces.
• The findings establish relationships between atomic interaction coefficients and the macroscopic properties of molecules.