稳定同位素分馏计算的一个普遍错误

A COMMON MISTAKE INVOLVED IN STABLE ISOTOPE FRACTIONATION CALCULATION

Urey模型(或称B igeleisen-Mayer公式)是稳定同位素分馏计算的理论基石,它需要使用不同同位素替代后的分子的振动频率来计算两个分子之间的同位素交换反应平衡常数。由于在Urey模型推导过程中使用了简谐振动和刚性转子近似,并利用了同样需要在简谐近似下才成立的Teller-Redlich乘积定则,导致当使用U-rey模型时,应该只能使用简谐振动频率。但是,从应用Urey模型进行分馏大小计算的几十年以来,无论Urey或B igeleisen本人,还是此后众多的研究者都忽略了这个要求。他们要么直接使用光谱数据(真实频率),也就是包含非谐(anharmonicity)贡献后的振动频率,要么使用量子化学方法计算出的简谐振动频率,用校正因子(scaling factor)向真实频率校正。这些做法,不仅不能提高Urey模型的计算精度,反而是造成误差的最主要的原因之一,这是一个历史性的错误。本文通过对Urey模型推导的某些关键步骤的解释,以及对比使用简谐振动频率和含非简谐校正频率的分馏计算结果之间的差别,说明了在Urey模型中必须使用简谐频率的重要性,尤其在量子化学计算已经广泛应用于同位素分馏计算的今天,纠正这种错误,会提高日益增多的这一类计算的精度。

The Urey model or the so-called Bigeleisen-Mayer equation has been the theoretical corner-stone of stable isotope geochemistry for decades. As for the use of this model, it needs vibrational frequency positions for different isotope-substituted molecules to calculate the equilibrium constant of the isotope exchange reaction. There are several approximations used in the Urey model, such as the harmonic oscillator and rigid rotator treatments. It also uses the Redlich-Teller product law to further simplify the formulation. These approximations require that only harmonic frequencies be used in the Urey model. However, since the publication of the Urey model, many researchers including Urey and Bigeleisen themselves have ignored this important requirement. They either directly use the spectroscopic data, which include anharmonic contributions, or use the quantum chemistry calculation to obtain the harmonic frequencies but with further scaling treatment to make the frequencies close to experimental data. Such scaling factors often are built in with the anharmonicity corrections which are not allowed for the Urey model. These wrong ways become one of the major error sources in the calculation of isotopic fractionation. It is therefore a common mistake. By reiterating the key steps of the deduction process of the Urey model, we showed how important it is to use the pure harmonic frequencies in the Urey model. Illustrations are also given to show differences between the spectroscopic frequencies and the pure harmonic ones in the Urey model. Due to the rapid increase of using quantum chemistry calculation to determine the isotopic fractionations, to correct this mistake is very important and will largely improve the accuracy of the calculations of this kind.