Improved Correlation Optimized Virtual Orbital Algorithm for Plane-Wave Full Configuration Interaction Calculations

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Full configuration interaction (FCI) calculations have historically faced significant challenges in dealing with periodic systems. The plane-wave basis sets are valued for their efficiency and broad applicability in various computational physics and chemistry simulations. Because of their natural periodicity, the plane-wave basis sets offer a potential solution to this problem. Moreover, FCI can address the limitations of widely used methods, such as density functional theory (DFT) with plane-wave basis sets, in accurately describing strongly correlated systems. However, the large basis set nature of the plane-wave makes them unsuitable for direct application in FCI calculations. To address this challenge, we propose an improved algorithm based on the correlation-optimized virtual orbital (COVOS) framework. By incorporating rotational matrices to enhance the active space dimension and optimizing orbitals through iterative coupled processes, we successfully compress the extensive plane-wave basis set into a manageable number of virtual orbitals suitable for FCI calculations while retaining most of the original basis set characteristics. We apply this method to supercell calculations and potential energy curves of periodic metallic systems. To further validate our approach, we test it on nonperiodic small molecular systems and compare the results with those obtained from DFT, second-order Møller-Plesset perturbation theory (MP2), random phase approximation (RPA), FCI calculations using the 6-31G or cc-pVDZ basis sets, and the original COVOS algorithm. The improved COVOS framework demonstrates significant advantages in convergence and correlation description over the original method. Furthermore, we observe metal divergence issues in MP2 calculations for certain metallic systems and note that RPA may overestimate the correlation energy of such systems. These findings underscore the importance of achieving FCI calculations with plane-wave basis sets.