Distance Dependence and Spatial Distribution of the Molecular Quadrupole Moments of H₂, N₂, O₂, and F₂

We have estimated the complete basis set limits for the Hartree−Fock, MP2, CASSCF, and CASSCF+1+2 wave functions for the titled molecules and calculated the molecular quadrupole moment as a function of bond length. Our recommended values for ϑ ( v =0, J =0) compare favorably to the current experimental values and previous high-level calculations. To aid in the analysis of the relationship between the molecule's electronic structure and quadrupole moment, we introduce the concept of a quadrupole moment density that permits one to write the molecular quadrupole moment as a sum of the separated atoms quadrupole moments and a purely molecular contribution. The quadrupole density provides a (reference state dependent) means of determining the contribution to ϑ from various regions in the molecule and gives considerable insight into the relationship between the electron density and the magnitude and sign of ϑ, and it allows a detailed assessment of the contribution of electron correlation to ϑ.