Improved stochastic multireference perturbation theory for correlated systems with large active spaces

Abstract

We identify the dominant computational cost within the recently introduced stochastic and internally contracted FCIQMC-NEVPT2 method for large active space sizes. This arises from the contribution to the four-body intermediates arising from low-excitation level sampled determinant pairs. We develop an effective way to mitigate this cost via an additional stochastic step within the sampling of the required NEVPT2 intermediates. We find this systematically improvable additional sampling can reduce simulation time by 80% without introducing appreciable error. This saving is expected to increase for larger active spaces. We combine this enhanced sampling scheme with full stochastic orbital optimisation for the first time and apply it to find FCIQMC-NEVPT2 energies for spin states of an iron porphyrin system within (24,24) active spaces with relatively meagre computational resources. This active space size can now be considered as routine for NEVPT2 calculations of strongly correlated molecular systems within this improved stochastic methodology.

GRAPHICAL ABSTRACT

Keywords:

• Strong correlation
• complete active space
• quantum Monte Carlo
• full configuration interaction
• multireference Perturbation Theory

Acknowledgments

The authors dedicate this paper in honour of Professor Jürgen Gauss on the occasion of his 60th birthday. G.H.B. gratefully acknowledges support from the Royal Society via a University Research Fellowship, as well as funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 759063. We are also grateful to the UK Materials and Molecular Modelling Hub for computational resources, which is partially funded by EPSRC (EP/P020194/1).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In Figure 1, triple and quadruple excitations are sampled frequently relative to singles and doubles. These higher two excitation levels are sampled purely for the purposes of higher-body RDM sampling and do not affect the dynamics. Therefore, their relative ratio of sampling compared to single and double excitations is not a physical quantity, but rather a user-defined choice. This is controlled by a ‘granularity’ parameter (detailed in previous work [11]), which in this example was set to one, ensuring significant sampling of the higher-body excitations. In production simulations, we often choose to sample the higher-rank excitations less frequently. In this case, the promotion of the more expensive single and double excitations increasingly dominate the cost, and the issue of mitigating their undesirable scaling becomes even more important.

Additional information

Funding

G.H.B. gratefully acknowledges support from the Engineering and Physical Sciences Research Council, as well as funding from the H2020 European Research Council research and innovation programme [grant number 759063]. We are also grateful to the UK Materials and Molecular Modelling Hub for computational resources, which is partially funded by Royal Society [grant number EP/P020194/1].