A practical guide to density matrix embedding theory in quantum chemistry (1603.08443v2)

Abstract: Density matrix embedding theory (DMET) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code for the calculations in this work can be obtained from \url{https://github.com/sebwouters/qc-dmet}.

Overview of Density Matrix Embedding Theory in Quantum Chemistry

The paper "A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry" presents an in-depth discussion of density matrix embedding theory (DMET), focusing on its application to quantum chemistry problems. DMET is positioned as an invaluable framework that allows for the analysis of finite molecular or bulk fragments within their environments, even under significant correlation or entanglement scenarios.

DMET Conceptual Framework

The paper links DMET's conceptual roots to tensor network states (TNS) and dynamical mean-field theory (DMFT), combining advantages from both paradigms. TNS is proficient in characterizing quantum entanglement, whereas DMFT focuses on fluctuating environments through self-consistent Green's functions. DMET diverges by relying solely on the ground-state density matrix, thus bypassing the need for frequency-dependent formulations intrinsic to DMFT.

Numerical Implementation and Self-Consistency

In detailing DMET's numerical methodology, the authors emphasize the importance of self-consistent optimizations across different embedding strategies, tested on hydrogen and beryllium rings, as well as the S$_{\text{N}$2 reaction. The approach primarily employs Hartree-Fock (HF) theory for low-level descriptions paired with high-level treatments such as full configuration interaction (FCI) and coupled-cluster theory.

Practical Implications and Computational Considerations

The paper outlines the transformation and construction processes within DMET, beginning with bath orbital derivations from mean-field density matrices and transitioning into partitioned systems for practical analyses. Through insightful comparisons, the authors demonstrate DMET's proficiency in accurately calculating expectation values and determining the interplay between fragments and their broader system contexts.

Results and Future Directions

The results underscore DMET's accuracy in capturing correlation energies and determining bond orders. Notably, high numerical fidelity is achieved even with small impurity sizes, substantiating DMET's role in efficient computational resource usage. Looking ahead, the paper encourages the exploration of correlated low-level wavefunction strategies to refine bath orbital constructions further.

Conclusion

The guide effectively bridges theoretical formulations with pragmatic implementation strategies, asserting DMET's adaptability across diverse quantum systems. By fostering a deeper understanding of its multifaceted components, this work contributes significantly to the potential advancements in quantum chemistry computational techniques, promising more refined and comprehensive analytical capabilities.