Generalized nonorthogonal matrix elements. II: Extension to arbitrary excitations.

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Electronic structure methods often rely on orthogonal orbitals.
• Nonorthogonal Slater determinants present computational challenges in calculating matrix elements.
• Previous work extended Wick's theorem for one- and two-body matrix elements.

Purpose of the Study:

• To extend the generalized nonorthogonal Wick's theorem to higher-order excitations.
• To develop efficient computational methods for nonorthogonal matrix elements.
• To facilitate advancements in nonorthogonal electronic structure theory.

Main Methods:

• Generalized extension of nonorthogonal Wick's theorem.
• Computation of matrix elements between higher-order excited configurations.
• Pre-computation and storage of intermediate values.
• Development of the LIBGNME computational library.

Main Results:

• Explicit expressions for generalized nonorthogonal matrix elements between higher-order excitations.
• Achieved O(1) scaling for one- and two-body matrix element evaluation.
• LIBGNME library enables practical implementation of efficient calculations.
• Demonstrated that nonorthogonal matrix element evaluation is nearly as facile as orthogonal counterparts.

Conclusions:

• The extended framework significantly simplifies the computation of nonorthogonal matrix elements.
• LIBGNME provides a practical tool for implementing these efficient calculations.
• These developments pave the way for broader adoption and advancement of nonorthogonal electronic structure methods.