ffsim.optimize_orbitals

ffsim.optimize_orbitals(rdm, hamiltonian, *, initial_orbital_rotation=None, real=None, method='L-BFGS-B', callback=None, options=None, return_optimize_result=False)[source]

Find orbitals that minimize the energy of a pair of one- and two-RDMs.

Uses scipy.optimize.minimize to find an orbital rotation that minimizes the energy of a pair of one- and two-RDMs with respect to a molecualar Hamiltonian.

The minimized energy can be computed from the returned orbital rotation as

rdm.rotated(orbital_rotation).expectation(mol_hamiltonian)

or

rdm.expectation(mol_hamiltonian.rotated(orbital_rotation.T.conj()))
Parameters:

  • rdm (ReducedDensityMatrix) – The reduced density matrices.

  • hamiltonian (MolecularHamiltonian) – The Hamiltonian.

  • initial_orbital_rotation (ndarray | None) – An initial guess for the orbital rotation. If not provided, the identity matrix will be used.

  • real (bool | None) – Whether to restrict the optimization to real-valued orbital rotations. The default behavior is to restrict to real-valued orbital rotations if the reduced density matrices, Hamiltonian, and initial orbital rotation (if one was given) are all real-valued, and to allow complex orbital rotations if any of these are complex-valued.

  • method (str) – The optimization method. See the documentation of scipy.optimize.minimize for possible values.

  • callback – Callback function for the optimization. See the documentation of scipy.optimize.minimize for usage.

  • options (dict | None) – Options for the optimization. See the documentation of scipy.optimize.minimize for usage.

  • return_optimize_result (bool) – Whether to also return the OptimizeResult returned by scipy.optimize.minimize.

Return type:

ndarray | tuple[ndarray, OptimizeResult]

Returns:

The orbital rotation, which, when applied to the reduced density matrix (or conjugated and applied to the Hamiltonian), minimizes its energy. If return_optimize_result is set to True, the OptimizeResult returned by scipy.optimize.minimize is also returned.