4
The actual partition function is unimaginably formidable. For just $N$ point particles in a 3D box, it's already got $3N$ dimensions. If the box is length $L$, GROMACS would probably divide the box into a machine-precision grid and calculate the energy from $\sim L \times 10^{10}$ values in each dimension. The partition function would incorporate all of that ...
2
For any wave function, you can define the one particle density matrix $\int \psi(x_1, \dots, x_n)\psi^\ast(x_1^\prime, x_2, \dots, x_n) dx_2\cdots dx_n$. The eigenfunctions of this operator are single particle functions and are called natural orbitals. For a treatment of reduced density matrices see for instance [this book] (https://www.springer.com/gp/book/...
Only top voted, non community-wiki answers of a minimum length are eligible