The low-lying structures of [CH3NH3NO3]n protic ionic liquid clusters up to 20 ion-pairs have been explored by the combination of empirical OPLS-AA force field and high-level M06-2X functional.First,a series of independent molecular dynamics(MD)simulations with the empirical force field are carried out at different temperatures to produce at least 105 conformations for n > 6.Then,these MD conformations are optimized through a low-storage nonlinear optimization method to create a large database of local minima structures at the level of empirical force field.Next,single-point energy calculations at M06-2X/6-31G(d)are performed for the lowest 500 local minima.Finally,the lowest 10 structures obtained from the M06-2X/6-31G(d)energies are as starting points for full geometry optimizations at the same level.Our calculations demonstrate clearly that the low-lying structures of [CH3NH3NO3]n clusters begin to form the cubic cage structure at n = 4.As the cluster size increases up to n = 7,10,and 13,one-,two-,and three-centered cage structures can be formed with the interior anions(NO3-),respectively.Also,a four-centered cage structure embedded with one cation and three anions is found at n = 16 while three five-centered cage structures embedded with one cation and four anions are found at n ≥ 18.By analysis,we find that the anions prefer to locate in the inner region compared to the cations owing to the smaller size and lower surface energy of anions.Furthermore,these cage structures mainly consist of four-and six-membered rings through the hydrogen-bond(HB)network between cations and anions and few odd-membered rings can be found for all low-lying structures.In addition,the relevant HBs and relative stabilities of [CH3NH3NO3]n clusters are also discussed in detail.