AbstractThis article deals with two topics: bounds on electrostatic interactions and new approaches to the expansion of electron densities in ab initio calculations on large systems. Schwartz inequalities derived from positive definite self‐energy integrals are reviewed and new bounds on electrostatic interactions consisting only of kinetic energy and overlap integrals are derived. Several applications are discussed. In the expansion of electron densities occurring in the treatment of large systems, numerous densities that are relatively small in magnitude are expanded whenever possible in terms of large densities already present in the calculation. Rigorous error bounds are used to judge the acceptability of the expansion. Proceeding in this way allows a simplifying reorganization of the information that must be stored for use in many‐electron configuration interaction calculations, thereby enabling the application of this method to larger systems. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002