The divide expand consolidate scheme for unrestricted second order Møller–Plesset perturbation theory ground state energies

Abstract

The linear scaling divide–expand–consolidate (DEC) framework is expanded to include unrestricted Hartree–Fock references. By partitioning the orbital space and employing local molecular orbitals, the full molecular calculation can be performed as independent calculations on individual fragments, making the method well-suited for massively parallel implementations. This approach also incorporates error control through the fragment optimization threshold (FOT), which maintains precision and consistency throughout the calculations. A benchmark was conducted for correlation energies of open-shell systems and the relative energies of both open- and closed-shell molecules at the MP2 level of theory. The full calculation result is achieved as the FOT approaches zero. For correlation energies, an FOT of 10−3 is sufficient to recover over 98% of the full result in all cases. However, for relative energies and the electronic energy component of oxidation potentials, a tighter FOT of 10−4 is required to keep the DEC error within 10% for both open- and closed-shell molecules. This is likely due to a lack of systematic error cancellation for the molecules with vastly different chemical natures. Therefore, for accurate relative energies, the FOT should be an order of magnitude lower, and additional caution is needed, particularly for large systems. The DEC method extension to unrestricted references maintains favorable features of linear scaling and can be implemented in a massively parallel algorithm to calculate correlation energies for large open-shell systems.