This paper presents a simple one-electron expression for electron rotational factors (ERFs) in the context of surface hopping (FSSH) dynamics. The goal is to construct one-electron operators that account for electronic motion and ensure conservation of linear and angular momentum during nonadiabatic transitions. The authors address the challenge of removing the angular component of derivative couplings between electronic states, which is essential for accurate FSSH simulations. The paper begins by discussing the limitations of existing approaches to momentum conservation in FSSH, where linear momentum is not conserved due to the rescaling of nuclear momentum along the derivative coupling direction. Angular momentum conservation is also problematic, though less well understood. The authors propose a semi-local approach to construct ERFs, which are one-electron operators that can be expressed in terms of atomic orbitals. The key result is the derivation of a compact, semi-local expression for ERFs that satisfy both the constraints of linear and angular momentum conservation. These ERFs are constructed using a weighting factor that ensures locality, allowing for size-consistent results. The authors also show that these ERFs can be derived from a constrained minimization approach, demonstrating their physical relevance. The paper further discusses the rotational and translational invariance of the derived ERFs, showing that they are invariant under both translations and rotations of the molecular frame. This is crucial for ensuring that the rescaling direction of momentum remains consistent regardless of the molecule's orientation or position. The authors also provide numerical results for two systems, [5]helicene and methanol, demonstrating the effectiveness of their approach. They show that the choice of a parameter controlling the locality of the ERFs (w) must be carefully balanced to ensure both numerical stability and physical consistency. In conclusion, the paper presents a new and efficient method for constructing one-electron ERFs that can be used in FSSH simulations to ensure proper conservation of momentum. These ERFs are not only physically meaningful but also computationally efficient, making them a valuable tool for future surface hopping algorithms and other quantum-classical simulations.This paper presents a simple one-electron expression for electron rotational factors (ERFs) in the context of surface hopping (FSSH) dynamics. The goal is to construct one-electron operators that account for electronic motion and ensure conservation of linear and angular momentum during nonadiabatic transitions. The authors address the challenge of removing the angular component of derivative couplings between electronic states, which is essential for accurate FSSH simulations. The paper begins by discussing the limitations of existing approaches to momentum conservation in FSSH, where linear momentum is not conserved due to the rescaling of nuclear momentum along the derivative coupling direction. Angular momentum conservation is also problematic, though less well understood. The authors propose a semi-local approach to construct ERFs, which are one-electron operators that can be expressed in terms of atomic orbitals. The key result is the derivation of a compact, semi-local expression for ERFs that satisfy both the constraints of linear and angular momentum conservation. These ERFs are constructed using a weighting factor that ensures locality, allowing for size-consistent results. The authors also show that these ERFs can be derived from a constrained minimization approach, demonstrating their physical relevance. The paper further discusses the rotational and translational invariance of the derived ERFs, showing that they are invariant under both translations and rotations of the molecular frame. This is crucial for ensuring that the rescaling direction of momentum remains consistent regardless of the molecule's orientation or position. The authors also provide numerical results for two systems, [5]helicene and methanol, demonstrating the effectiveness of their approach. They show that the choice of a parameter controlling the locality of the ERFs (w) must be carefully balanced to ensure both numerical stability and physical consistency. In conclusion, the paper presents a new and efficient method for constructing one-electron ERFs that can be used in FSSH simulations to ensure proper conservation of momentum. These ERFs are not only physically meaningful but also computationally efficient, making them a valuable tool for future surface hopping algorithms and other quantum-classical simulations.