Select-divide-and-conquer method for large-scale configuration interaction

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Configuration Interaction (CI) methods are crucial for accurate electronic structure calculations.
• Approximating the full CI space is necessary due to its exponential scaling with system size.
• Existing methods face challenges in handling large, complex molecular systems.

Purpose of the Study:

• To present a novel select-divide-and-conquer variational method for approximating CI.
• To develop a computationally efficient approach for large N-electron systems.
• To achieve high accuracy in determining energy eigenvalues for complex quantum systems.

Main Methods:

• A divide-and-conquer strategy is employed to split the N-electron space into manageable subspaces.
• Threshold-based selection (tao) is used to partition configurations based on their attributes.
• Davidson's eigensolver is iteratively applied to progressively larger subspaces.
• Subspace dimensions are managed to fit within Random Access Memory (RAM) constraints.

Main Results:

• The method achieves high accuracy, with energy eigenvalues consistently above exact eigenvalues.
• One microhartree accuracy was demonstrated for a problem with 24x10^6 dimensions and 1.2x10^12 non-zero matrix elements.
• Hamiltonian matrix-element evaluation becomes the rate-determining step in highly accurate calculations.

Conclusions:

• The select-divide-and-conquer variational method offers an efficient and accurate way to approximate CI.
• This approach effectively manages computational complexity for large quantum systems.
• The method provides a viable pathway for high-accuracy electronic structure calculations in computational chemistry.