Perturbative Coordinate Descent Full Configuration Interaction

Area of Science:

• Quantum chemistry
• Computational chemistry
• Theoretical chemistry

Background:

• Accurate calculation of ground-state energies is crucial for understanding molecular systems.
• Full configuration interaction (FCI) methods provide high accuracy but are computationally expensive.
• Coordinate descent full configuration interaction (CDFCI) offers an efficient approach to FCI calculations.

Purpose of the Study:

• To introduce two novel perturbative extensions of the CDFCI method.
• To enhance the accuracy of ground-state energy calculations.
• To address limitations of existing perturbative approaches in computational chemistry.

Main Methods:

• Development of direct CDFCI + Perturbation Theory (PT).
• Introduction of iterative perturbative CDFCI (IP-CDFCI) to manage large perturbative spaces.
• Implementation of sparse vector storage (c, b, d) and Hamiltonian diagonal elements (h) for memory and time efficiency.
• Utilization of quadruple-precision floating-point numbers for improved numerical stability.

Main Results:

• The proposed methods, CDFCI + PT and IP-CDFCI, effectively correct variational energies.
• IP-CDFCI avoids large perturbative spaces and leverages variational stage information.
• Memory usage is optimized by utilizing redundant storage and a vector for Hamiltonian diagonals.
• Significant reduction in computational time is achieved through efficient memory management and calculation strategies.
• Demonstrated effectiveness on small molecular benchmarks and the challenging chromium dimer system.

Conclusions:

• The developed perturbative extensions of CDFCI significantly improve the accuracy and efficiency of ground-state energy calculations.
• IP-CDFCI offers a practical approach for handling complex molecular systems by optimizing computational resources.
• The use of quadruple precision enhances the reliability of perturbative energy computations.
• These advancements provide valuable tools for theoretical and computational chemists studying molecular systems.