Distributed multipole analysis

In computational chemistry, distributed multipole analysis (DMA) is a compact and accurate way of describing the spatial distribution of electric charge within a molecule. In computational chemistry, distributed multipole analysis (DMA) is a compact and accurate way of describing the spatial distribution of electric charge within a molecule. The DMA method was devised by Prof. Anthony Stone of Cambridge University to describe the charge distribution of a molecule in terms of a multipole expansion around a number of centers. The idea of using a multi-center multipole expansion was earlier proposed by Robert Rein. Typically, the centers correspond to the atoms constituting the molecule, though this is not a requirement. A multipole series, consisting of a charge, dipole, quadrupole and higher terms is located at each center. Importantly, the radius of convergence of this multipole series is sufficiently small that the relevant series will be convergent when describing two molecules in van der Waals contact. The DMA series are derived from ab initio or density functional theory calculations using Gaussian basis sets. If the molecular orbitals are written as linear combinations of atomic basis functions the electron density takes the form of a sum of products of the basis functions, called density matrix elements. Boys (1950) showed that the product of two spherical Gaussian functions, centered at different points, can be expressed as a single Gaussian at an intermediate point known as the overlap center. If a basis of Gaussian functions is used, the product of two s functions is spherically symmetric and can be represented completely just by a point charge at the ‘overlap center’ of the two Gaussian functions. The product of an s orbital and a p orbital has only charge and dipole components, and the product of two p functions has charge, dipole and quadrupole components.