# How do temporary dipole-dipole interactions work in quantum mechanics?

The standard presentation of temporary dipole-dipole interactions (in high school at least) is classical: the electrons in an atom/molecule 'orbit' around its nucleus/nuclei. As a direct result of this orbital motion, at any particular time there will be a higher charge density in one region of the atom/molecule than in another. This creates a temporary dipole in the atom/molecule and can lead to interactions with other atoms/molecules.

However when we model atoms using quantum mechanics the electrons no longer have classical 'orbits'. How then do these interactions arise?

Consider two atoms at some distance $R$ from each other. The Hamiltonian of this system is then the sum of the Hamiltonians of the two atoms plus interaction terms involving the electrostatic interaction between the electrons of one atom with the electron and nucleus of the other atom. You can then calculate what the shift in the ground state energy of the system is due to the interaction term.
So, the total energy of atoms placed a distance $R$ from each other can be interpreted as an effective potential energy, the effective force is then minus the derivative of the effective potential energy.