Abstract: A computer-implemented method for solving low energy excitation spectrum and their corresponding eigenstates is provided. The eigenstates solved include ground state and single-fermion excited states. The method includes: calculating ground state and single-fermion excited states of a system and/or a sub-system of particles in isolation; calculating a coupling between fermions using a quantum mechanical hopping matrix elements between hybridized fermions and long range Coulomb and exchange interactions for a given charge and spin density; calculating a system free energy as a function of structural properties of molecules based on an energy spectrum that depends on positions of the particles and orientations of the particles, the positions being the center of charge for each of the particles; and simulating the systems of particles by integrating a time evolution of the structural properties using full quantum mechanical time evolution of a quantum state given the initial state.