Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) offers a reformulation of second-order ADC schemes for polarization propagators.
• Accelerating convergence and mitigating the sign problem are crucial for QMCADC calculations.

Purpose of the Study:

• To enhance the efficiency of QMCADC for large-scale molecular excited-state calculations.
• To integrate dense-sparse partitioning and importance ranking filtering into QMCADC.

Main Methods:

• Splitting configuration space into dense and sparse subsets.
• Decomposing the projection operator into four blocks: dense-to-dense, sparse-to-dense, dense-to-sparse, and sparse-to-sparse.
• Employing deterministic methods for dense-to-dense and sparse-to-dense blocks, and stochastic methods for dense-to-sparse and sparse-to-sparse blocks.
• Utilizing importance ranking filtering to reduce walker numbers and control bias in stochastic projections.

Main Results:

• Demonstrated significant efficiency enhancement of QMCADC through the integration of dense-sparse partitioning and importance ranking filtering.
• Enabled large-scale molecular excited-state calculations previously intractable.
• Maximized the utilization of the sparsity inherent in Algebraic Diagrammatic Construction (2) (ADC(2)) schemes.

Conclusions:

• The novel approach transforms QMCADC into a tailored framework specifically for ADC calculations.
• The integration of dense-sparse partitioning and importance ranking filtering represents a significant advancement in computational quantum chemistry.
• This methodology paves the way for more accurate and efficient studies of molecular excited states.