Automated Selection of Active Orbital Spaces (1602.03835v1)

Abstract: One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations on the applicability of this most general class of ab initio methods. A poor choice of the active orbital space may yield even qualitatively wrong results. This is obviously a severe problem, especially for wave function methods that are designed to be systematically improvable. Here, we show how the iterative nature of the density matrix renormalization group combined with its capability to include up to about one hundred orbitals in the active space can be exploited for a systematic assessment and selection of active orbitals. These benefits allow us to implement an automated approach for active orbital space selection, which can turn multi-configuration models into black box approaches.

• The paper's main contribution is an automated DMRG-based method that uses entanglement measures like von Neumann entropy and mutual information to identify key orbitals.
• It leverages iterative DMRG computations over large orbital spaces to systematically determine an optimal active space for complex quantum chemical systems.
• Validation on chromium complexes, oxo-Mn(salen), and Cu2O2 isomerization demonstrates the method's reliability and potential to streamline black-box quantum chemical simulations.

Overview of Automated Selection of Active Orbital Spaces

The paper "Automated Selection of Active Orbital Spaces" by Christopher J. Stein and Markus Reiher addresses a significant challenge in quantum chemistry, particularly in multi-configuration methods which necessitate the manual selection of orbitals to define the active space. Improper selection of the active orbital space can lead to erroneous results, which is a hindrance to the systematic improvement of wave function methods.

Key Findings and Methodology

The authors propose an automated approach leveraging the Density Matrix Renormalization Group (DMRG), which can handle active spaces containing up to 100 orbitals, making it a potential black-box method for orbital selection. This approach overcomes the traditional complete active space (CAS) technique that suffers from the exponential scaling of configurations which limited the CAS to about 18 electrons in 18 orbitals.

The main aspects of this paper include:

1. DMRG Flexibility: By utilizing the iterative nature of DMRG, qualitative convergence of the wave function is possible after just a few iterations, which crucially supports automatic orbital selection.
2. Initial Exploration: The paper discusses initial DMRG computations over a large orbital space to identify high-entanglement orbitals. These are then selected for the subsequent accuracy-improved DMRG calculations.
3. Selection Protocols: The orbital selection relies on observable entanglement measures and scoring functions, such as the von Neumann entropy and mutual information. These measures are used to evaluate the degree of electron correlation among orbitals.

Results

Several molecules were studied to validate this automated selection process:

• Chromium Complexes (CrF$_6$ / CrF$_6^{3-}$): The method correctly distinguishes the effective CAS size based on the covalency of metal-ligand bonds.
• Oxo-Mn(salen) Spin States: The approach selects a unified active space adaptable for various spin states without manual biases, crucial for computing accurate relative energies.
• Cu$_2$O$_2^{2+}$ Isomerization: Demonstrates consistent and automated selection of active spaces along a reaction path, corroborated by comparison with high-quality ab initio methods.

Implications and Future Work

The paper heralds a significant step toward black-box quantum chemical computations, reducing the need for expert intuition in choosing the active space for calculations. The method could greatly simplify computations in complex systems, increasing confidence in the results while saving computational resources.

Future developments could involve integrating this automated orbital selection into broader quantum chemical modeling platforms, allowing for further automation and enhancement of computational efficiency. These advancements could potentially broaden the scope of systems explored and refined using multi-reference methods.

Overall, this work represents a notable advancement in the methodology for quantum chemistry, providing a systematic and automated framework for selecting the active orbital space, thus ensuring the reliability and efficiency of quantum chemical simulations.