A non-iterative approximation to the effects of triple and quadruple excitations in the framework of the multireference configuration interaction method, including single and double excitations (MRCISD), for molecular electronic structure is suggested. The approximation is derived from perturbative expansions of lower and upper bounds of a self-consistent, second-order approximation to the MRCISDTQ energy. Numerical studies on a number of well studied model systems support the hypothesis that the suggested method, which can be referred to as MRCISD(TQ), is a new, viable, ultrahigh accuracy method. (C) 2003 Elsevier Science B.V. All rights reserved.