Machine Learning of Two-Electron Reduced Density Matrices for Many-Body Problems

Area of Science:

• Quantum Chemistry
• Computational Physics
• Machine Learning

Background:

• The many-electron problem in quantum chemistry is computationally intensive.
• Existing methods often face steep scaling issues or rely on functional approximations.
• Accurate prediction of electronic energies is crucial for understanding molecular behavior.

Purpose of the Study:

• To develop a novel machine learning algorithm for solving the many-electron problem.
• To predict electronic energies using two-electron reduced density matrices (2-RDMs).
• To achieve high accuracy without steep scaling or functional approximations.

Main Methods:

• Developed a machine learning algorithm predicting a convex combination of 2-RDMs.
• Utilized upper- and lower-bound energy calculations for 2-RDMs.
• Incorporated information about RDMs and their violation of N-representability conditions.

Main Results:

• The algorithm predicts electronic energies with high accuracy, capturing dynamic and static correlation.
• Demonstrated accuracy comparable to exact diagonalization for BH and N2 potential energy curves.
• Achieved results within a few millihartrees of exact diagonalization.

Conclusions:

• The 2-RDM machine learning approach provides a general framework for improving electronic structure calculations.
• This method offers a scalable alternative to traditional quantum chemistry methods.
• Potential for wide-ranging applications in moderately and strongly correlated molecular systems.