Computation of determinant expansion coefficients within the graphically contracted function method.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Electronic Structure Theory

Background:

• Electronic structure methods commonly use Slater determinants or configuration state functions to represent wavefunctions.
• Traditional algorithms for computing expansion coefficients are computationally intensive and impractical for large systems.
• Existing methods face challenges with scalability due to exponential scaling with the number of electrons and orbitals.

Purpose of the Study:

• To develop an efficient algorithm for evaluating single determinant expansion coefficients.
• To enable accurate electronic structure calculations for very large molecular systems.
• To overcome the scalability limitations of traditional configuration interaction methods.

Main Methods:

• The study presents an algorithm for evaluating determinant coefficients using wavefunctions expanded as linear combinations of graphically contracted functions.
• Graphically contracted functions utilize variational parameters called arc factors, simplifying coefficient calculations.
• The algorithm employs a two-level recursive approach for efficient computation.

Main Results:

• The new algorithm computes determinant expansion coefficients recursively and more efficiently than traditional methods.
• The computational cost scales polynomially with system size, a significant improvement over exponential scaling.
• Successful application to systems with hundreds of electrons and orbitals demonstrates its effectiveness for large-scale problems.

Conclusions:

• The developed algorithm provides a computationally tractable approach for electronic structure calculations in large systems.
• This method significantly enhances the applicability of wavefunction-based methods to complex chemical and physical systems.
• The polynomial scaling allows for routine application to systems previously considered intractable.