Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein–ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor $S(q,\omega )$, the static structure factor $S(q)$, and the interaction energy $v$. The ESA combines the recent neural-net representation by T. Dornheim et al., [ J. Chem. Phys. 151, 194104 (2019)] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function $g(0)$. It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [ Phys. Rev. Lett. 115, 115001 (2015)]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.