Density-matrix renormalization group algorithm with multi-level active space.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• The density-matrix renormalization group (DMRG) is a powerful method for handling large active spaces in electronic structure calculations.
• Traditional complete active space (CAS) methods can be computationally intensive for complex systems.
• DMRG offers an efficient alternative or complement to CAS-based approaches.

Purpose of the Study:

• To introduce a novel multi-level (ML) control strategy for the DMRG algorithm.
• To develop and present the ML-DMRG and its self-consistent field variant, ML-DMRG-SCF.
• To assess the computational efficiency gains of the ML-DMRG approach compared to standard DMRG.

Main Methods:

• Implementation of a multi-level (ML) active space control within the DMRG framework.
• Hierarchical orbital ordering based on chemical intuition to define active subspaces.
• Ground and excited state calculations for molecules (H2O, N2, indole) and a diatomic molecule (Cr2).

Main Results:

• ML-DMRG calculations demonstrated noticeable efficiency improvements over standard DMRG with a fixed number of kept states (M).
• The proposed orbital re-ordering strategy within hierarchical active subspaces reduced computational time.
• Efficiency gains were observed for both ML-DMRG and fixed-M DMRG calculations.

Conclusions:

• The multi-level (ML) control of the active space offers significant computational advantages for DMRG.
• Hierarchical orbital ordering is a beneficial strategy for optimizing DMRG calculations.
• ML-DMRG provides a more efficient computational tool for electronic structure studies involving large active spaces.