Multi-temperature models are often used as a simplified way to describe nonequilibrium gases. These models assume Boltzmann distributions within each energy mode, which is useful for reducing the number of parameters in computations. This assumption requires that the energy modes are properly separated (which is valid, for instance, for vibration and rotation in low-lying rovibrational levels of diatomic molecules). For polyatomic molecules, several limitations arise. First, certain energy modes are often grouped together to further reduce the number of parameters, which requires additional hypotheses, and sometimes arbitrary grouping schemes. Moreover, the rovibrational levels of polyatomic molecules are often strongly coupled, and the assignment of the coupling terms to one or another energy mode is arbitrary. In this work, we present a method to quantify the influence of assignment or grouping schemes on nonequilibrium spectral models by comparing their impact on nonequilibrium partition functions, and we apply it to the CO₂ molecule. We show that significant differences arise when reducing the nonequilibrium model to two temperatures only, as often done in CFD or spectroscopy applications. In particular, one should carefully justify whether the vibrational bending mode is in equilibrium with the rotational mode or with the other vibrational modes. We then determine the nonequilibrium range where a simple Uncoupled Vibrating Rotor model is sufficient, where the coupling term assignment scheme becomes important, and where the uncertainty induced by the assignment of the coupling terms can no longer be neglected. This approach can be extended to other molecules.

多温度模型通常用作描述非平衡气体的简化方法。这些模型假设每个能量模式内的玻尔兹曼分布，这对于减少计算中的参数数量很有用。这个假设要求能量模式被适当地分离（例如，对于双原子分子的低振动水平中的振动和旋转是有效的）。对于多原子分子，会出现一些限制。首先，某些能量模式经常被组合在一起以进一步减少参数的数量，这需要额外的假设，有时还需要任意的分组方案。此外，多原子分子的振动能级通常是强耦合的，将耦合项分配给一种或另一种能量模式是任意的。在这项工作中，₂分子。我们表明，当将非平衡模型减少到两个温度时，会出现显着差异，这在 CFD 或光谱应用中经常这样做。特别是，应该仔细证明振动弯曲模式是否与旋转模式或其他振动模式平衡。然后，我们确定了非平衡范围，其中简单的非耦合振动转子模型就足够了，耦合项分配方案变得重要，并且由耦合项分配引起的不确定性不能再被忽略。这种方法可以扩展到其他分子。