Low-Rank Algorithms for Ab Initio Valence Bond Approaches

Valence bond (VB) theory is an ab initio approach that provides intuitive pictures and insights into chemical bonds and reaction mechanisms. This work integrates low-rank algorithms, including the resolution of the identity and the chain of spheres for exchange, into VB methods. These algorithms significantly improve the efficiency of VB calculations by reducing the computational expense and storage requirement of Fock matrix construction and integral transformations while preserving chemical accuracy. Historically, VB methods were limited to small or model systems due to these computational challenges. The adoption of low-rank techniques now enables efficient optimization of the full set of orbitals in ab initio VB theory, extending its applicability to molecular systems exceeding 100 atoms. The low-rank algorithm expands the scope of VB theory, allowing the study of larger and more realistic molecular systems from a VB perspective.