Limitations of the molecular multipole expansion treatment of electrostatic interactions for C-H...O and O-H...O hydrogen bonds and application of a general charge density approach

A molecular multipole expansion treatment (up to hexadecapole) is examined for its accuracy in describing hydrogen-bond electrostatic interactions, with particular reference to explaining the differences between blue-shifted C-H...O and red-shifted O-H...O bonds. In interactions of H2O and CH4 with point charges at hydrogen-bonding distances, we find that the molecular multipole treatment not only fails to reproduce ab initio energies but also forces on OH or CH bonds, and therefore cannot properly account for the electrostatic component of the interaction. A treatment based on a molecule's permanent charge density and its derivatives and the charge density and its derivatives induced by an external multipole distribution is in full accord with ab initio results, as shown by application to models of the H2O-H2O and CH4-FH systems. Such a charge density approach provides a fundamental basis for understanding the importance of interaction forces in initiating structural change and thereby altering molecular properties.