Molecule dynamics (MD) simulation has been developed to investigate molecular properties in many systems such as living bodies and polymer materials. In MD, atoms are typically modelled as points, and interactions between atoms are described by energy potentials. Such simple modelling of molecules made it possible to treat spatially very complex structures such 1 as protein and DNA. Remarkably, the recent development of computational resources has achieved systems composed of extraordinary number of atoms like a virus. As a result, molecular dynamic simulations have gained more and more attention despite the long history of development. On the other hand, such molecular dynamic simulations are based on Newton's equation mdv/dt = F to calculate the movement of atoms. This typically limits time steps allowed in simulation to femtosecond (fs) scales. In other words, a tremendous simulation loop is needed to treat longer time scale phenomena. As a result, how to expand the time scale of MD has been one of the central interests in many scientific areas. For example, coarse-grain modelling of atoms and accelerated methods have been proposed. Phase-field simulation, which is based on diffusive equations, has been widely used to investigate materials properties in nano to microseconds scales. For example, crystal growth is modelled as the movement of the interface between 0 (not crystalized) and 1 (crystalized) distributions. Other than crystal growth, phase-field simulations have successfully reproduced many materials properties such as dislocations, ferroelectricity, and their couplings. A recent remarkable advance is that phase-field simulation has been expanded to atomic-scale regions. In this atomistic phase-field simulation, atoms are modelled not as points but as densities like electron densities in quantum simulation. This treatment of atoms has made it possible to depart from Newton's equations, clarifying the dynamics of atoms in a diffusive time scale. Therefore, phase-field simulation will be a powerful strategy to clarify atomistic phenomena at a longer time scale. However, molecules, in which atoms complexly connect with each other by chemical bonds, cannot be treated by such phase-field modelling. This is because they have been mainly developed in materials science and assume the periodicity of atoms in a solid-state. Thus, another strategy is needed to treat molecules in phase-field simulations.