Conventional and unconventional techniques in quantum chemistry

The computational cost of ab initio molecular electronic structure calculations is dominated by the generation of electron–electron repulsion integrals, of which there are O ( N 4 ), where N is the dimension of the basis set. Even if allowance is made for integral economization schemes, the rapidity with which the computational cost grows as N increases is a problem for all ab initio calculations, particularly the intrinsically more laborious relativistic approaches. There is therefore a strong motive to search for accurate but inexpensive algorithms without having to simplify the equations. We report a preliminary assessment of a promising new scheme that scales much more slowly with N . The key idea is the equivalence of the conventional expression for the energy of an atom or molecule with the integral of the energy density of the related electromagnetic fields over all space. The electrostatic energy density can be constructed cheaply as the sum of scalar products of O ( N 2 ) pairs of electric fields E ij ( r ) generated by the overlap charge densities ρ ij ( r ). The integration of the total energy density over the whole molecule can be done by adapting a numerical integration scheme used in contemporary density functional (DFT) algorithms requiring only a relatively small number of cubature points. We explore the implications of this approach for calculations in quantum chemistry. In relativistic quantum theory the total energy can be expressed as the sum of scalar products of both electric E ij ( r ) fields and magnetic B ij ( r ) fields generated by the overlap charge and current densities. In the long‐wavelength approximation, in which retardation is neglected, this leads to a new interpretation of the Breit interaction energy as the energy of the associated magnetic fields. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004