Imposing bounds on the high-order reduced density matrices elements

A family of N-representability conditions are imposed on the third- and fou rth-order reduced density matrix elements in order to ascertain that they a re within bounds. These bounds are needed in the construction of high-order reduced density matrices as well as in the correction of the matrices whic h result from the iterative solution of the standard and of the modified co ntracted Schrodinger equations. The results obtained for the fourth-order r educed density matrix are strikingly good in two nontrivial cases. A new an d more economical method for constructing the fourth-order reduced density matrix in terms of the lower order ones is also reported here. (C) 2001 Joh n Wiley & Sons, Inc.