We use four different methods to calculate an anharmonic correction factor f_vib to the conventional RRHO partition functions for H₂O, HO₂, ³CH₂, H₂O₂, and CH₄ over a temperature range up to 3000 K. The exact quantum mechanical method benchmarks the other three approximate methods that are based on classical Monte Carlo phase space integrals, on vibrational perturbation theory, and on conventional harmonic partition functions evaluated with fundamental, rather than harmonic, frequencies. The last two of these methods converge on the exact partition function below temperatures that vary from 1500 K for the least anharmonic system (H₂O) to 250 K for the most anharmonic system (H₂O₂). For ³CH₂ and H₂O₂, both these methods are qualitatively incorrect because they are insensitive to a low energy barrier for internal motion. The classical method qualitatively overestimates quantum mechanical results at low temperatures because of the exclusion of zero point energy. However, here anharmonic corrections are small. At high temperatures, our anharmonic corrections can be large (up to 40% for CH₄ at 3000 K) and at high enough temperatures the classical and exact quantum results will converge. Comparing perturbation theory and the classical method, the classical method becomes the approximate method of choice above ∼750 K for H₂O₂ and CH₄, ∼2100 K for ³CH₂, ∼2700 K for HO₂, and > 3000 K for H₂O.

我们使用四种不同的方法来计算的非调谐校正因子˚F _VIB为小时常规RRHO分函数₂ O，HO ₂，³ CH ₂，H ₂ ö ₂，和CH ₄在高达3000 K的温度范围内。精确的量子力学方法对其他三种近似方法进行了基准测试，这些方法基于经典的蒙特卡洛相空间积分，振动摄动理论以及使用基波而不是谐波进行评估的常规谐波分配函数，频率。这些方法中的最后两种收敛于温度低于最小非谐系统（H ₂ O）的1500 K到最大非谐系统（H ₂ O ₂）的250 K的温度下的精确分配函数。对于³ CH ₂和H ₂ O ₂，这两种方法在质量上都是不正确的，因为它们对内部运动的低能垒不敏感。由于排除了零点能量，因此经典方法定性地高估了低温下的量子力学结果。但是，这里的非谐波校正很小。在高温下，我们的非谐校正可能很大（在3000 K下，CH _4的校正高达40％），而在足够高的温度下，经典精确的量子结果将收敛。比较摄动理论和经典方法，经典方法成为H ₂ O ₂和CH ₄约750 K以上，³ CH ₂约2100 K，HO ₂约2700 K以上的近似选择方法。，对于H ₂ O > 3000K 。