Graphical Approach to Interpreting and Efficiently Evaluating Geminal Wavefunctions.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Antisymmetrized products of geminals (APG) offer a simple extension of Slater determinants for wavefunctions.
• High computational cost limits the extensive use of APG wavefunctions due to complex orbital pair combinations.

Purpose of the Study:

• To reduce the computational cost associated with evaluating the overlap of APG wavefunctions with Slater determinants.
• To develop a more efficient method for calculating electronic wavefunctions in quantum chemistry.

Main Methods:

• Graphical interpretation of Slater determinants.
• Application of the maximum weighted matching algorithm to identify significant orbital pair combinations.
• Reducing the cost of partitioning occupied orbitals in wavefunction overlap calculations.

Main Results:

• Computational cost reduced from O(N^4) to O(N^3).
• Identified that many orbital pair combinations are unnecessary for accurate wavefunction solutions.
• Demonstrated the efficiency of the maximum weighted matching algorithm in this context.

Conclusions:

• The developed method significantly reduces the computational expense of APG wavefunctions.
• This approach enhances the tractability of complex wavefunctions, applicable to various geminal ansätze and potentially generalized quasiparticle wavefunctions.
• Opens avenues for more efficient quantum mechanical calculations involving multi-electron components.