Dividing a system into subsystems is a widely used approach that allows one to calculate the electronic structure of large and complex systems. Quite often, the first order reduced density matrix of the system is employed in this approach. Unfortunately, it turns out that the obtained values of the electronic populations of subsystems, which must correspond to the number of electrons in the subsystem, are fractional and they noticeably deviate from integers. In the present paper for a system in the state of a particular type it is shown that if the second order reduced density matrix is also taken into account in the subsystem generations, then the orthogonal one-electron basis can be found with which the calculated populations of subsystems will be practically equal to integer numbers. The said state of a particular type is the state whose wave function is a single determinant with doubly occupied orbitals. This is a reasonable approximation to the wave function for the singlet ground state of a standard atomic-molecular system.

将系统划分为子系统是一种广泛使用的方法，它允许人们计算大型和复杂系统的电子结构。这种方法经常采用系统的一阶降密度矩阵。不幸的是，事实证明，所获得的子系统电子种群的值必须与子系统中的电子数量相对应，是分数的，并且明显偏离整数。在本文中，对于处于特定类型状态的系统，表明如果子系统生成中也考虑了二阶降密度矩阵，则可以找到正交的单电子基，由此可以计算出总体子系统的个数实际上等于整数。所述特定类型的状态是其波函数是具有双重占据的轨道的单个行列式的状态。对于标准原子-分子系统的单重基态，这是对波函数的合理近似。