改进的正则系综法对二阶Virial方程的推导

将正则配分函数中任一分子与其它所有 (N -1个 )分子间的相互作用能之和折算为其中任一对指定分子相互作用能的 N-1倍与一个校正系数 h之积 ,并假设这个积只与上述分子对的坐标相关。这样 ,配分函数即可化为分子对积分之积 ,其中积分常数由集团展开法求出。此法可比较合理地导出二阶维里方程 ,从而消除了经典正则系综方法中的数学困难

DERIVATION OF QUADRATIC VIRIAL EQUATION OF STATE BY MODIFIED CANONICAL ENSEMBLE METHOD

In the canonical ensemble distribution function Q , the total interactive energies between any selected molecule and all the other N-1 ones are converted to N-1 times of the interactive energies of an arbitrary pair of molecules among them multiplied by a rectification coefficient, and the product is regarded as a function only depending on the coordinates of the selected pair of molecules. Then, distribution function Q can be transformed into a product of integrals of N /2 pairs of molecules. The cluster integral expansion method is used to derive the integral constant, whose simplified form is substituted into Q . The former two terms in the logarithm expansion of Q are substituted into the definition expression of pressure in the canonical ensemble theory. In this way, quadratic virial equation of state can be derived reasonably, thus the mathematical difficulty in the classical canonical ensemble method is eliminated.