Among the three methods, the AEX method yields the most accurate density calculations for all molecular systems, with a calculated MAD value of 57.7 kg/m³ , which is smaller than the MAD values of EX1 (excluding BUT) and EX2 by 25.2 kg/m³ and 106.7 kg/m³ , respectively. The AEX method combines the advantages of both the EX1 and EX2 methods, causing errors to offset each other, hence producing more accurate results. In subsequent discussions, our primary analysis focuses on simulation outcomes derived from the AEX method.