中文摘要：

综述了稳定同位素平衡和动力学分馏的一些主要的理论方法。首先介绍了平衡分馏的理论方法，从平衡分馏的核心理论--Bigeleisen-Mayer公式（或称Urey模型）以及对它的一些高级能量校正开始，介绍了基于路径积分的分子动力学方法和蒙特卡罗方法对同位素非谐效应的处理，介绍了压力效应的理论计算方法，最后介绍了核体积效应及其理论计算方法，并强调核体积效应是未来重金属同位素研究的重要部分。另外，综述了同位素动力学分馏的主要理论和计算方法，首先介绍了在稳态下因温度梯度引发的同位素分馏，着重介绍了基于局部热力学平衡理论的计算方法和最新结果；然后从如何使用过渡态理论计算化学反应导致的同位素动力学分馏出发，深入介绍了磁同位素效应和由于核体积效应引发的异常同位素动力学分馏；然后对低温下矿物生长的同住素动力学理论模型进行了介绍，尤其是仔细介绍了其中DePaolo的表面动力学模型，并对由吸附和共沉降过程产生的动力学分馏也进行了介绍。最后详细介绍了在气化过程、固体中、高温硅酸洋熔体中由于扩散引起的同位素动力学分馏，以及如何对这些过程进行理论处理，强调了开展固体矿物扩散理论计算的重要性。

英文摘要：

Important theoretical treatments on equilibrium or kinetic stable isotope fractionation calculation have been reviewed. First, for equilibrium isotope effects, the so-called core theory of equilibrium isotope fractionation-the Bigeleisen-Mayer equation （or the Urey model） has been introduced and also its higher-order corrections. Then, the path-integral molecular dynamics and path-integral Monte Carlo methods have been introduced with emphasis on their treatments of anharmonic corrections of isotope fractionation. Furthermore, the pressure effect of isotope {ractionation has been introduced in details. In the last, the nuclear volume effect, which is one of the most important parts of future heavy metal isotope investigations, has been reviewed. For kinetic isotope effects （KIE）, several important theoretical methods on KIE calculation have been reviewed. First, the theoretical models of isotope fractionation under temperature gradient have been introduced in detail. Then, from the introduction of transition-state theory, the KIE associated with uni- direction chemical reactions is introduced, including magnetic isotope effect and strange KIE results caused by nuclear volume effects. There are several theoretical models on kinetic isotope effects during mineral precipitation. The surface kinetic model of DePaolo （2011） is introduced in detail. Besides, the KIEs from adsorption and co-precipitation processes have been also introduced. Finally, the KIEs from diffusion processes, such as in vaporization process, in solids and in silicate melts, have been introduced, with the emphasis on the importance of diffusional isotope fractionation in solids.