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I have seen how sometimes people talk of orbitals obtained from a CAS or DMRG calculation. I haven't found any explanation of how this is possible. Given the many body wave function (obtained from exact diagonalization, Lanczos, DMRG, whatever), $\Psi(x_1,\ldots,x_n)$, how could one possible define a set of orbitals, which are one body functions? I think (not sure) that this is what computational chemists refer to as Natural Bond Orbitals, but I have only found conceptual explanations, not the mathematical details. Probably is related with diagonalizing the one-particle density matrix? Can someone provide mathematical details/references?

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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/9783540671480).

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