Distance dependence and spatial distribution of the molecular quadrupole moments of H-2, N-2, O-2, and F-2

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 Theta (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 Theta from various regions in the molecule and gives considerable insight into the relationship between the electron density and the magnitude and sign of Theta, and it allows a detailed assessment of the contribution of electron correlation to Theta.