Incremental Treatments of the Full Configuration Interaction Problem
Janus J. Eriksen, J\"urgen Gauss

TL;DR
The paper reviews the MBE-FCI method for electronic structure calculations, discussing its advantages, drawbacks, algorithmic details, recent applications, and future research directions within near-exact wave function methods.
Contribution
It provides a comprehensive review and critical assessment of the MBE-FCI method, including algorithmic improvements and application examples.
Findings
Highlights the strengths and limitations of MBE-FCI
Showcases recent successful applications of MBE-FCI
Outlines future research directions for the method
Abstract
The recent many-body expanded full configuration interaction (MBE-FCI) method is reviewed by critically assessing its advantages and drawbacks in the context of contemporary near-exact electronic structure theory. Besides providing a succinct summary of the history of MBE-FCI to date within a generalized and unified theoretical setting, its finer algorithmic details are discussed alongside our optimized computational implementation of the theory. A selected few of the most recent applications of MBE-FCI are revisited, before we close by outlining its future research directions as well as its place among modern near-exact wave function-based methods.
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