Definitive Assessment of the Accuracy, Variationality, and Convergence of Relativistic Coupled Cluster and Density Matrix Renormalization Group in 100-Orbital Space

TL;DR

This paper benchmarks relativistic coupled cluster and density matrix renormalization group methods against numerically exact CI calculations in large 100-orbital spaces, using the STP-CI framework for accuracy.

Contribution

It introduces the use of the STP-CI framework for large-scale exact CI calculations to benchmark advanced relativistic electronic structure methods.

Findings

Provides definitive accuracy benchmarks for relativistic coupled cluster and DMRG methods.

Demonstrates the effectiveness of the gap theorem in establishing error bounds.

Extends the feasible size of exact CI calculations to 100-orbital spaces.

Abstract

Accuracy, variationality, and convergence underpin the reliability of modern electronic structure methods, yet definitive benchmarks in the relativistic regime remain elusive due to the absence of numerically exact full configuration interaction (CI) references. Recent algorithmic advances in the CI framework, enabled by the small-tensor-product (STP) decomposition approach, have dramatically extended the tractable size of the configuration space, making numerically exact CI calculations feasible in large active spaces previously beyond reach. In this work, we employ the recently developed STP-CI framework to perform large-scale numerically exact CI calculations and directly benchmark relativistic coupled cluster and density matrix renormalization group methods. Definitive benchmarking of approximate relativistic electronic structure methods is ensured through the application of the gap theorem, which provides rigorous error bounds on the CI reference and establishes a controlled standard for assessing accuracy, variationality, and convergence.