Convergence acceleration for the multilevel Hartree–Fock model

Abstract

In the previously introduced multilevel Hartree–Fock (HF) model, the electronic density is optimised in a given region of the molecular system. The approach is based on generating an active occupied and active virtual space by decomposing a start guess density for the entire system. In this work, a diagonalisation based implementation for Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) and a quasi-Newton minimisation procedure using the augmented RH (ARH) approach are described for accelerating convergence for the multilevel HF model. The equations are derived to be consistent with convergence acceleration for traditional atomic orbital based HF calculations. The main idea is to formulate all quantities in the molecular orbital basis to exploit that the active molecular orbital basis is significantly smaller than the atomic orbital basis, and thus enable the application of wave function approaches that are well-studied for small molecular systems to large molecular systems. Thus, all equations are formulated such that no atomic orbital density or Fock matrices are needed for the DIIS and ARH algorithms. Results show that the acceleration schemes yield efficient optimisation of the multilevel HF wave function.

GRAPHICAL ABSTRACT

Keywords:

• Multilevel Hartree–Fock
• energy optimisation
• convergence acceleration
• embedding approaches

Acknowledgements

The author thanks Henrik Koch for discussions and Eirik Kjønstad for reading the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The author acknowledges computer time from NOTUR through project nn9409k and nn2962k, and financial support from the Norwegian Research Council (Norges Forskningsråd) through FRINATEK project no. 263110/F20 and ToppForsk project no. 275506.