While existing ion mobility calculators are capable of feats as impressive as calculating collision cross sections (CCS) within a few per cent and within a very reasonable time, the simplifications assumed in their estimations precludes them from being more precise, potentially overreaching with respect to the interpretation of existing calculations. With ion mobility instrumentation progressively reaching resolutions of several hundreds to thousands (accuracy in the range of ∼0.1%), a more accurate theoretical description of gas-phase ion mobility becomes necessary to correctly interpret experimental state-of-the-art separations. This manuscript entails an effort to consolidate the most relevant theoretical work pertaining to ion mobility within the ‘free molecular’ regime, describing in detail the rationale for approximations up to the two-temperature theory, using both a momentum transfer approach as well as the solution to the moments of the Boltzmann equation for the ion. With knowledge of the existing deficiencies in the numerical methods, the manuscript provides a series of necessary additions in order to better simulate some of the separations observed experimentally due to second-order effects, namely, high field effects, dipole alignment, angular velocities and moments of inertia, potential interactions and inelastic collisions among others.

中文翻译：

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自由分子体系中离子迁移率的基础。交错离子迁移率计算的过去、现在和未来

虽然现有的离子迁移率计算器能够在几个百分点和非常合理的时间内计算碰撞横截面 (CCS) 那样令人印象深刻，但其估计中假设的简化使它们无法更精确，可能会超出范围现有计算的解释。随着离子迁移率仪器逐渐达到数百到数千的分辨率（精度在 0.1% 范围内），需要对气相离子迁移率进行更准确的理论描述，以正确解释实验中的最新分离。这份手稿需要努力巩固与“自由分子”范围内的离子迁移率有关的最相关的理论工作，详细描述了接近双温度理论的基本原理，使用动量传递方法以及离子的玻尔兹曼方程的矩的解。了解数值方法中存在的缺陷后，手稿提供了一系列必要的补充，以便更好地模拟由于二阶效应（即高场效应、偶极对齐、角速度和力矩）而在实验中观察到的一些分离惯性、潜在相互作用和非弹性碰撞等。