Post-Density Matrix Renormalization Group Methods for Describing Dynamic Electron Correlation with Large Active Spaces

Abstract

The ab initio density matrix renormalization group (DMRG) method has been well-established and has become one of the most accurate numerical methods for the precise electronic structure solution of large active spaces. In the past few years, to capture the missing dynamic correlation, various post-DMRG approaches have been proposed through the combination of DMRG and multireference quantum chemical methods or density functional theory. With this in mind, this work provides a brief overview of ab initio DMRG principles and the new developments within post-DMRG methods. For clarity, post-DMRG methods are classified into two main categories depending on whether high-order n-electron reduced density matrices are used, and their merits and disadvantages are properly discussed. Finally, we conclude by discussing unsolved bottlenecks and giving development perspectives of post-DMRG approaches, which are expected to yield quantitative descriptions of complex electronic structures in large strongly correlated molecules and materials.

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals

“… 6 Although there exist many post-CAS methods aimed at including dynamic correlation (e.g. ref ( 7 )), none are satisfactory because of the limitations in both accuracy and efficiency. In particular, perturbation-theory-based approximations may suffer from the lack of size-consistency, intruder states, or the unbalanced treatment of closed- and open-shell systems, which must be cured by level-shifting.…”

“…The complete active space (CAS) method assumes the selection of a number of (active) electrons and orbitals crucial to the static correlation followed by exact diagonalization in the active orbital subspace. , The CAS model is a base of the CASSCF wave function and is also frequently employed in density matrix renormalization group (DMRG) calculations. The DMRG method is one of the most promising tools for strongly correlated molecules − because of its favorable scaling, which enables the handling of much more extensive active spaces than CASSCF allows. The reference energy, E ref in eq , for all CAS-based methods does not include a substantial portion of the electron correlation, called dynamic correlation, E corr in eq .…”

A Mixed-Precision Implementation of the Density Matrix Renormalization Group

“…Here we mainly focus on the algorithm and workflow, therefore, for detailed principles, we refer the interested readers to these nice review articles. [44][45][46][47][48][49] The DMRG method is based on a wave function ansatz that the full-CI wave function can be represented by a production of a series of tensors, which is called the matrix product state (MPS) ansatz (…”

Predicting the FCI energy of large systems to chemical accuracy from restricted active space density matrix renormalization group calculations

“…The observed very fast and robust convergence properties of the new method calls ultimately for a theoretical analysis in order to understand the underlying mechanisms and further improve the method. As has already been argued [27] and is elaborated below, the DMRG-RAS approach is a memory-efficient, Schmidt decomposition-based extension of the RAS scheme and it is an embedding method, in the sense that when orbitals are partitioned into two subspaces, CAS and EXT, the correlations between them are calculated self-consistently, in contrast to other post-DMRG approaches [37][38][39][40][41][42][43][44] which provide corrections on top of the DMRG wave function. In the DMRG-RAS procedure the excitation rank in the EXT subspace is truncated according to an a priori defined cutoff, inheriting the name RAS, while the eigenvalue equation for the many-body Hamiltonian defined on the tensor product space of the CAS and RAS is solved self-consistently by the usual DMRG procedure.…”

“…This is achieved by utilizing algorithmic progress developed in the past two decades based on concepts of quantum information theory [47]. Therefore, our novel approach presented below, relying on a rigorous error scaling, can be applied to general systems and has the potential to become a widely used tool to target strongly correlated systems, in particular multi-reference problems in quantum chemistry [44,[47][48][49][50][51], nuclear structure theory [52][53][54] and condensed matter theory [55][56][57].…”