  Quantum computers offer a promising approach to simulate the ground state of
molecules, which is crucial for understanding molecular properties and chemical
reactions. However, the limited number of available qubits on current devices
poses a challenge for simulation. This paper investigates the feasibility of
reducing the qubit usage of molecular simulation by examining specific
fermionic states according to Hund's rule.
  We introduced a new framework based on qubit efficiency encoding. Based on
this framework, the Hamiltonian is restricted to the Hund subspace. Compared to
only concerned particle conservation, the proposed method can reduce $N$ qubit
usage for an $M$ orbitals and $N$ electrons molecule when $M\gg N$.
Additionally, when using the STO-3G basis sets, the simulations of the $15$
molecules with given molecular geometry by the proposed method are close to the
full configuration interaction. The absolute difference is at most $0.121\%$.
Meanwhile, predictions from potential energy surfaces using the proposed method
have an absolute difference at most $4.1\%$.
