Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI...

Area of Science:

• Quantum chemistry
• Computational physics

Background:

• Selected configuration interaction (CI) methods are advancing rapidly.
• These methods are becoming competitive with highly accurate techniques for quantum Hamiltonian solutions.

Purpose of the Study:

• To develop efficient selected CI/exact diagonalization algorithms.
• To enhance the adaptive sampling configuration interaction (ASCI) algorithm.

Main Methods:

• Algorithms driven by fast sorting, inspired by matrix-vector multiplication.
• New ASCI search modes (integral-driven and coefficient-driven).
• Dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays.

Main Results:

• Developed fast and scalable algorithms for selected CI.
• Demonstrated efficiency superior to other considered approaches due to sorting-based design.
• Applied ASCI to large systems (e.g., Si2H6 with 34 electrons) and basis sets, achieving full-CI level accuracy.
• Presented benchmark data for G1 data set (double- and triple-ζ).

Conclusions:

• The new ASCI-based algorithms provide a powerful and efficient tool for solving quantum Hamiltonians.
• These methods enable practical, high-accuracy simulations of large quantum systems with modern hardware.
• Preliminary results show potential for fast deterministic perturbation theory using hash functions for large basis sets.