Electron density in Mo/ller–Plesset theory

The Mo/ller–Plesset theorem states that for the electronic Hamiltonian in the form H = 𝒥pFp+V, where the eigenfunctions of Fp are the Hartree–Fock molecular spin orbitals and the eigenvalues are the one-electron energies, by treating V as a perturbation the first order term in the expansion of the electron density vanishes. In spite of this, some one-electron properties are not given at the H–F level. This Note presents the expression for the second order correction to the electron density.