Towards a multiconfigurational method of increments

ABSTRACT

The method of increments (MoI) allows one to successfully calculate cohesive energies of bulk materials with high accuracy, but it encounters difficulties when calculating dissociation curves. The reason is that its standard formalism is based on a single Hartree–Fock (HF) configuration whose orbitals are localised and used for the many-body expansion. In situations where HF does not allow a size-consistent description of the dissociation, the MoI cannot be guaranteed to yield proper results either. Herein, we address the problem by employing a size-consistent multiconfigurational reference for the MoI formalism. This leads to a matrix equation where a coupling derived by the reference itself is employed. In principle, such an approach allows one to evaluate approximate values for the ground as well as excited states energies. While the latter are accurate close to the avoided crossing only, the ground state results are very promising for the whole dissociation curve, as shown by the comparison with density matrix renormalisation group benchmarks. We tested this two-state constant-coupling MoI on beryllium rings of different sizes and studied the error introduced by the constant coupling.

KEYWORDS:

• Method of increments
• multiconfigurational
• size-consistency
• strong correlation
• DMRG

Acknowledgments

This research was supported by the German Research Foundation (DFG) and the Agence Nationale de la Recherche (ANR) via the project ‘Quantum-chemical investigation of the metal-insulator transition in realistic low-dimensional systems’ (action ANR-11-INTB-1009 MITLOW PA1360/6-1), as well as by the National Research, Development and Innovation Office (NKFIH) through Grant Nos. K120569, NN110360 and within the Quantum Technology National Excellence Program (Project No. 2017-1.2.1-NKP-2017-00001). The support of the Zentraleinrichtung für Datenverarbeitung (ZEDAT) at the Freie Universität Berlin is gratefully acknowledged. E. Fertitta thanks the support by the Max Planck Society via the International Max Planck Research School. At last, D. Koch and E. Fertitta would like to thank PD Dr Dirk Andrae and Dr Carsten Müller for the many fruitful discussions and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors..

Additional information

Funding

Agence Nationale de la Recherche and Deutsche Forschungsgemeinschaft [ANR-11-INTB-1009 MITLOW PA1360/6-1]; National Research, Development and Innovation Office (NKFIH) [grant number K120569], [grant number NN110360]; Quantum Technology National Excellence Program [project number 2017-1.2.1-NKP-2017-00001].