Dynamical monopoles and dipoles in a condensed molecular system: The case of liquid water

We propose a definition for the dipole of an individual molecule in a molecular solid or fluid. This problem is currently dealt with by partitioning-according to some prescription-the continuous electron density of the condensed phase. Instead, here we focus directly on the coupling of externally applied electric fields to the molecular motion. Our concept of dipole is therefore based on experimentally accessible quantities, such as the infrared spectra and, more generally, the low-frequency dielectric properties. For an isolated molecule, the coupling to an external field is trivially measured by its static dipole: we define the corresponding (less trivial) quantity in the condensed phase. Our theory can be regarded as a generalization of the one currently used for ionic and polar crystals, where the coupling between atomic displacements and electric fields is measured by the dynamical charge, also known as infrared charge. We show that, in a molecular system, the coupling of an electric field to librational modes is measured by a second-rank tensor; similarly, the coupling to translational modes is also measured by a second-rank tensor: we call them dynamical molecular dipole and dynamical molecular monopole, respectively. First-principles calculations provide us with explicit values for these two tensors in the case of liquid water. The monopole tensor is found to carry nonvanishing charge for specific directions, although it is overall traceless to ensure charge neutrality. This feature is at the root of the infrared translational band at similar to200 cm(-1). The dipole tensor is dominated by its antisymmetric part, equivalent to a vector of modulus 2.1 D. This value differs significantly from estimates for the static dipole in the liquid (2.5-3.1 D). We also briefly comment on the relevance of our findings to the construction of molecular force fields.