Generalization of the New Resonance Theory: Second Quantization Operator, Localization Scheme, and Basis Set

Area of Science:

• Quantum chemistry
• Computational chemistry
• Theoretical chemistry

Background:

• Evaluating resonance structures is crucial for understanding chemical bonding.
• Previous methods relied on specific population analysis and localization schemes.
• The singlet-coupling scheme of an electron pair offers a novel approach.

Purpose of the Study:

• To generalize a previously developed method for calculating resonance structure weights.
• To remove restrictions related to Mulliken population (MP) and Boys-Foster (BF) localization.
• To assess the method's independence from population analysis and localization schemes.

Main Methods:

• Utilizing second quantization and biorthogonal operators.
• Employing Löwdin population (LP) and various localization schemes.
• Analyzing the invariance of resonance weights across different computational parameters.

Main Results:

• Resonance weights were found to be invariant to the choice of population analysis (MP, LP) and localization schemes (BF, etc.).
• The computed resonance weights showed independence from the chosen basis set.
• The generalized method provides reliable resonance weights consistent with chemical intuition.

Conclusions:

• The resonance weight calculation method is robust and broadly applicable.
• The invariant nature of resonance weights suggests a fundamental property.
• This approach shows promise for advanced molecular orbital analysis and understanding chemical bonding.