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Quantum statistical mechanics of closed-ring molecular chains

机译：闭环分子链的量子统计力学

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A model for a closed-ring unhindered three-dimensional macromolecular chain. based on Quantum Mechanics, is presented. Upon starting from an extract non-relativistic Hamiltonian operator, we integrate out all electronic degrees of freedom, in the Born-Oppenheimer framework, giving rise to an effective vibro-rotational Hamiltonian for the chain. Then, assuming a harmonic oscillator-like vibrational potential between nearest-neighbour atoms, the integration of the atomic radial degrees of freedom is carried in the limit of high frequencies. Thus, all bond lengths become fixed, including the one which makes the chain to become a closed ring. This formulation leads to a specific Hamiltonian for the remaining angular variables of the closed-ring chain, and constitutes an alternative in comparison with standard Gaussian models, which do not, Use is made of a variational inequality by Peierls to find an approximate quantum partition function for the angular variables of the system. We then proceed to obtain approximately another representation for the angular partition function in the classical partition function are discussed. [References: 41]
机译：闭环无阻碍三维高分子链的模型。提出了基于量子力学的理论。从提取的非相对论哈密顿算子开始，我们在Born-Oppenheimer框架中整合了所有电子自由度，从而为链条产生了有效的振动旋转哈密顿量。然后，假设在最近的原子之间有类似谐波振荡器的振动势，则在高频的极限内进行原子径向自由度的积分。因此，所有的键长都是固定的，包括使链成为闭合环的键长。该公式可为闭环链的其余角度变量生成特定的哈密顿量，与标准高斯模型相比，它是一种替代方法，后者没有这样做。皮埃尔斯利用变分不等式来寻找近似的量子分配函数用于系统的角度变量。然后，我们将继续讨论经典分区函数中的角度分区函数，以获得近似的另一种表示形式。 [参考：41]

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