Imposing bounds on the high-order reduced density matrices elements

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