强关联分子体系电子结构方法研究进展

Abstract

In recent years, numerous novel materials have emerged in fields such as high-temperature superconductivity and quantum communication, including unconventional superconductors, topological insulators, and spin liquids. These materials exhibit significant quantum phenomena such as quantum interference, tunneling, fluctuations, and entanglement, often arising from strong correlation effects among electrons within molecules. In the community of quantum chemistry, strong correlation effects are typically classified into dynamic electron correlation and static electron correlation. Dynamic electron correlation, caused by the instantaneous movement of electrons leading to charge density fluctuations, presents computational challenges due to the necessity of introducing a multi-particle form of the wave function. This departure from the mean-field single-particle perspective results in a substantial increase in the computational cost for calculating electron correlation levels. On the other hand, static electron correlation arises from the near-degeneracy of numerous frontier molecular orbitals, resulting in a quantum superposition of electron configurations. It requires the use of multi-configuration methods and faces the well-known “exponential wall” challenge, where computational complexity exponentially grows with the system size. Therefore, due to the involvement of both dynamic and static electron correlations in strongly correlated systems, achieving precise electronic structure calculations is exceptionally difficult, representing a significant challenge in theoretical chemistry and computational physics. Traditionally, to describe the static correlation, quantum chemists often define crucial correlated orbitals and their electrons within the complete active space (CAS). Full configuration interaction (FCI) calculations are performed within the CAS, while the region outside the CAS is described by mean-field methods. While these multi-configuration methods allow for arbitrary electron arrangement within the CAS, effectively capturing the static correlation of the system, they struggle to handle the dynamic correlations beyond the CAS. Therefore, combining them with multi-reference configuration interaction (MRCI), multi-reference perturbation theory (MRPT), multi-reference coupled cluster theory (MRCC), and other multi-reference methods becomes essential to accurately handle strong correlation systems. Constructing multi-configuration wave functions to obtain static correlation by multi-configuration methods, and then generating excitation configurations based on these multi-configuration wave functions to obtain dynamic correlation has become the mainstream of the development of current wave function methods. Challenges in this direction include the exponential growth in computational complexity with an increase in CAS size and the precision of multi-reference methods affecting the accuracy of capturing dynamic correlations beyond the active space. Over the last decade, various multi-configuration methods, such as selected configuration interaction (sCI), Density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and neural-network quantum states (NQS), have successfully expanded the computable active space by explicitly or implicitly extracting and compressing complete configuration space information. Furthermore, combining these multi-configuration methods with traditional multi-reference approaches, such as MRCI, MRPT and MRCC, enables capturing dynamic correlations caused by electronic instantaneous interactions beyond the active space. This achieves higher precision and quantitative descriptions for mid-sized strongly correlated molecular systems (around 50 active orbitals). Additionally, novel methods like Block-Correlated Coupled Cluster Theory (BCCC) have made progress in attempting to discuss static and dynamic correlations within a unified framework. This article primarily introduces the advancements in wave function theory electronic structure methods for strongly correlated molecular systems in recent years. The first section details multi-configuration methods that have expanded the CAS size, including sCI, DMRG, FCIQMC, NQS, and outlines their developmental trajectories. The second section delves into the combination of these multi-configuration methods with traditional multi-reference approaches, leveraging larger active spaces to address dynamic correlations and achieve higher precision results. Finally, the article discusses the prospects of these methods in three directions: Handling static and dynamic correlations within a unified framework, integrating with relativistic effects, and combining with machine learning.