Using a fitted electronic density to improve the efficiency of a linear combination of Gaussian-type orbitals calculation

A moleculeʹs electronic density can be accurately fitted in a divide-and-conquer fashion. This fitting procedure scales linearly with system size and becomes more efficient than the conventional scheme for relatively small systems (/2~ 40 atoms for one-dimensional systems) and is only marginally more expensive for the smallest systems. A systemʹs electronic density is partitioned into a sum of subsystem contributions. This partitioning scheme is used to contructs an approximate density that can ease the burden associated with various calculations. Contributions arising from faraway subsystems are calculated using their fitted subsystem densities, while contributions arising from nearby subsystems are more accurately calculated using their exact subsystem densities. Its application to the calculation of the molecular electrostatic potential is shown. Though this scheme has been implemented and tested within a density functional program, the ideas presented may be used in any quantum mechanical program.