Multicomponent Cholesky Decomposition: Application to Nuclear-Electronic Orbital Theory.

The Cholesky decomposition technique is commonly used to reduce the memory requirement for storing two-particle repulsion integrals in quantum chemistry calculations that use atomic orbital bases. However, when quantum methods use multicomponent bases, such as nuclear-electronic orbitals, additional challenges are introduced due to asymmetric two-particle integrals. This work proposes several multicomponent Cholesky decomposition methods for calculations using nuclear-electronic orbital density functional theory. To analyze the errors in different Cholesky decomposition components, benchmark calculations using water clusters are carried out. The largest benchmark calculation is a water cluster (HO) where all 54 protons are treated quantum mechanically. This study provides energetic and complexity analyses to demonstrate the accuracy and performance of the proposed multicomponent Cholesky decomposition method.