Seniority Number in Valence Bond Theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Valence Bond (VB) theory is a fundamental approach in quantum chemistry for describing chemical bonding.
• Accurate calculation of potential energy curves (PECs) is crucial for understanding molecular behavior and reactions.
• Traditional methods can face challenges in computational cost and accuracy for complex electronic structures.

Purpose of the Study:

• To propose and apply a novel hierarchy of valence bond (VB) methods.
• To utilize the concept of seniority number for truncating the VB expansion.
• To investigate the accuracy and efficiency of seniority-based VB methods for calculating PECs.

Main Methods:

• Development of a seniority number-based hierarchy within Valence Bond (VB) theory.
• Application of these methods to calculate the PECs of H8, N2, and C2 molecules.
• Comparison with full configuration interaction (FCI) and complete active space self-consistent field (CASSCF) limits, as well as molecular orbital (MO) theory.

Main Results:

• The seniority-based VB expansion demonstrates rapid convergence towards FCI/CASSCF limits.
• Seniority-based VB methods yield more accurate PECs with reduced nonparallelity errors compared to MO analogues.
• Nonorthogonal orbital-based VB theory efficiently truncates the active Hilbert space using seniority numbers.

Conclusions:

• Seniority number is an effective criterion for truncating VB wavefunctions.
• The proposed VB hierarchy offers a more efficient and accurate approach for calculating molecular PECs.
• This method provides a valuable alternative for studying strongly correlated systems in computational chemistry.