A solver-independent constrained orbital optimization framework on the Stiefel manifold using RDMs, shown to lower energies and improve convergence for MP2, CASCI, and DMRG on LiF, H2O, and pyrazine.
The Geometry of Algorithms with Orthogonality Constraints
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abstract
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.
fields
physics.chem-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Constrained Optimization Algorithms for Orbital Optimization in Quantum Chemistry
A solver-independent constrained orbital optimization framework on the Stiefel manifold using RDMs, shown to lower energies and improve convergence for MP2, CASCI, and DMRG on LiF, H2O, and pyrazine.