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Dipole and quadrupole moment functions of the hydrogen halides HF, HCl, HBr, and HI: a Hirshfeld interpretation.

The dipole and quadrupole moment functions of the hydrogen halides are calculated using a large polarized basis and correlated wavefunctions and compared to experiment and previous calculations. These functions are analyzed in terms of local moments constructed using the Hirshfeld method. The dipole moment is the sum of the functions q(H)R+mu(H) and mu(X) with q(H) being the charge on the hydrogen atom, R the internuclear separation, mu(H) and mu(X) the atomic dipoles on the hydrogen and halogen atoms. We find that q(H)R+mu(H) is always positive and has a maximum at bond lengths larger than the equilibrium. In HF, mu(F) is slightly positive at the maximum in q(H)R+mu(H) and has little effect on the resultant maximum in the dipole moment function (DMF). mu(Cl), mu(Br), and mu(I), on the other hand, are increasingly more negative at the maximum of q(H)R+mu(H) and have a profound effect on the width of the maximum of the resulting DMF, successively broadening it and completely eliminating it at HI. The quadrupole moment function (QMF) (with the halogen as origin) is given by Theta(HX)=Theta(HX) (proto)+deltaTheta(X)+deltaTheta(H)+2mu(H)R+q(H)R(2), where Theta(HX) (proto) is the quadrupole moment of the separated atoms (the halogen in this instance) and deltaTheta(X)+deltaTheta(H) the change in the in situ quadrupole moments of the halogen and hydrogen atoms. The maximum in the QMF and its slope at equilibrium are determined essentially by 2mu(H)R+q(H)R(2), which is known once the DMF is known. deltaTheta(X)+deltaTheta(H) is always negative while Theta(HX) (proto) is positive, so one can approximate the molecular quadrupole moment to within 10% as Theta(HX)>Theta(HX) (proto)+2mu(H)R+q(H)R(2).