Importance of the hybrid orbital operator derivative term for the energy gradient in the fragment molecular orbital method

The hybrid orbital operator is crucial in the fragment molecular orbital (FMO) method for the fragmentation across covalent bonds, however, its gradients have not been properly derived. We show that these very substantial contributions are the cause of the major part of the gradient error in FMO, impeding geometry optimizations and molecular dynamics. Capped alanine decamer ( ALA ) 10 and chignolin (PDB: 1UAO) solvated by 157 water molecules are used to assess the accuracy of the energy gradients, and the errors are reduced by approximately one order of magnitude.