In Quantummechanics you can treat a positronium in the same way as a hydrogenatom. Basically, you first transform into the center of mass system and then solve the schrödinger-equation for the electron with a so called reduced mass to get its wavefunction. This wavefunction is equal to the hydrogen-electron-wavefunction except for the mass-factor. So the physical and chemical behaviour of Ps is similar to that of a hydrogenatom, so as long as the positron doesn't annihilate with another electron. Due to the different masses however ionisation energies and other things are different. This justifies calling Ps an atom and covalent binding of two Ps a molecule (of course again with lower reduced mass causing for example differences in rotation-excitation-states).
In this way, the name molecule does fit very well,sorry.
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It doesnt't matter where the center of mass is, the resulting wavefunction depends only on the distance between the two constituents.
You don't. Their wavefunctions are overlapping and it is only a matter of time before they transform into photons. Thus the short lifetime.
In Quantummechanics you can treat a positronium in the same way as a hydrogenatom. Basically, you first transform into the center of mass system and then solve the schrödinger-equation for the electron with a so called reduced mass to get its wavefunction. This wavefunction is equal to the hydrogen-electron-wavefunction except for the mass-factor. So the physical and chemical behaviour of Ps is similar to that of a hydrogenatom, so as long as the positron doesn't annihilate with another electron. Due to the different masses however ionisation energies and other things are different. This justifies calling Ps an atom and covalent binding of two Ps a molecule (of course again with lower reduced mass causing for example differences in rotation-excitation-states). In this way, the name molecule does fit very well,sorry.