Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Symmetry-Adapted Perturbation Theory (SAPT) is crucial for understanding intermolecular interactions.
• Calculating exchange energies in SAPT can be computationally intensive, especially for larger systems.
• Existing methods often rely on density-matrix formulations, which can be complex.

Purpose of the Study:

• To develop a general second-quantized form of the permutation operator for SAPT.
• To derive universal formulas for exchange energy approximations (S2n).
• To provide an alternative formalism to density-matrix methods for SAPT calculations.

Main Methods:

• Construction of a generalized second-quantized permutation operator by multiplying single-pair operators.
• Derivation of universal formulas for S2n approximations of exchange energies.
• Development of a method to sum overlap expansion series to infinity in second-quantization.

Main Results:

• The generalized permutation operator enables universal formulas for S2n exchange energy approximations.
• Expressions for S4 approximation corrections are presented and validated.
• A novel second-quantized approach to summing overlap expansions is outlined.

Conclusions:

• The new second-quantized formalism offers an efficient alternative for calculating exchange energies in SAPT.
• This approach facilitates advancements in SAPT, particularly for complex wavefunction theories.
• Integration with symbolic algebra programs can automate derivations and accelerate research.