Contracted Schrodinger equation development

We have focused on the lower bound method, but density matrix research has moved forward on a much broader front than that. In particular, work on the contracted Schrodinger equation played an important role in developments. A more complete picture can be found in Coleman and Yukalov s book [23]. It has taken 55 years and work by many scientists to fulfill Coleman s 1951 claim at Chalk River that except for a few details which would be easily overcome in a couple of weeks—the A-body problem has been reduced to a 2.5-body problem ... 

Among the several 2-RDM-oriented methods that have been developed for the study of chemical systems, one of the most recent and promising techniques is based on the iterative solution of the second-order contracted Schrodinger equation (2-CSE) [1, 6, 15, 18, 36, 45-60, 62-65, 68, 70, 79-85, 103-111]. The 2-CSE was initially derived in 1976 in first quantization in the works of Cho [103], Cohen and Erishberg [104, 105], and Nakatsuji [106] and later on deduced in second quantization by Valdemoro [45] through the contraction of... 

From the begining of the development of the RDM theory the need to render N-and 5-representable a 2-RDM obtained by an approximative method was patent. The development first of the spin-adapted reduced Hamiltonian methodology and, more recently, that of the second-order contracted Schrodinger equation rendered the solution of this problem urgent. The purification strategies... 

C. Valdemoro, D. R. Alcoba, and L. M. Tel, Recent developments in the contracted Schrodinger equation method controlling the Ai-representabihty of the second-order reduced density matrix. hit. J. Quantum Chem. 93, 212 (2003). 

My second aim here is directly related with the research project which is being developed in our laboratory at present the iterative solution of the first and second order contracted Schrodinger equations, (1- and 2-CSE respectively). 

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