Locating multiple self-consistent field solutions: an approach inspired by metadynamics.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Electronic structure theory

Background:

• Locating all solutions to self-consistent field (SCF) equations is crucial for understanding molecular electronic structure.
• Traditional methods often struggle to find multiple, distinct solutions, particularly for complex systems.

Purpose of the Study:

• To develop and validate a novel computational method for efficiently locating multiple solutions to SCF equations.
• To demonstrate the method's capability in finding both known and previously unknown electronic states.

Main Methods:

• A metadynamics-based approach is employed, defining a distance metric between density matrices.
• A biasing potential is introduced during SCF calculations to prevent convergence to already found solutions.
• The method is applied to the H4 model and the nitrogen molecule.

Main Results:

• All known solutions for the H4 model were successfully located, along with one previously unknown solution.
• The method identified the complete set of restricted Hartree-Fock (RHF) solutions for the nitrogen molecule.
• A lower-energy broken-symmetry RHF solution was discovered for the nitrogen molecule, corresponding to doublet dissociation.

Conclusions:

• The proposed metadynamics-based method offers an effective strategy for exploring the solution landscape of SCF equations.
• This approach facilitates the discovery of diverse electronic states, including those with broken symmetry, relevant for chemical bonding and reactivity.
• The findings provide a more comprehensive understanding of the electronic structure of molecules like nitrogen.