Advances in Chemical Physics, Special by David A. Mazziotti

By David A. Mazziotti

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0 nq ð61Þ or in terms of the 1- and the 2-RDMs nq 2 i;j nd i;j Qk;l ¼ 2 Ik;l À N 1 Dik ^ 1 Ilj þ 2 Di;j k;l 2 2 ð62Þ and the elements of the two-particle G-matrix are given by 2 Gi;k l; j ¼ 1 hÉjayi ak ayj al jÉi ! 0 ng ð63Þ or in terms of the 1- and the 2-RDMs j 1 i 2 i;j ng 2 Gi;k l; j ¼ Ndk Dl þ nd Dk;l ð64Þ The factors nd , nq , and ng , which normalize the D-, the Q- and the G-matrices to unity, are given by NðN À 1Þ, ðr À NÞðr À N À 1Þ, and Nðr À N þ 1Þ, respectively. Because the D-, the Q-, and the G-matrices are expressible as metric (or overlap) matrices M, ^ j y jÉi !

Coorganizers: A. J. Coleman and R. M. Erdahl. Proceedings: A. J. Coleman and R. M. Erdahl, editors, Report of the Density Matrix Seminar, Queen’s Press (1969), 151 pp. Some previous and some new participants continued to explore the characterization of RDMs, related conceptual problems, as well as practical problems to incorporate correlations. 4. Reduced Density Operators Conference, Kingston, June 20 22, 1974. Sponsored by: National Research Council of Canada; Queen’s University. Organizer: R.

Then a series of theorems on N-representability followed, by John Coleman and many Reduced Density Matrix Mechanics: With Application to Many Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134, edited by David A. Mazziotti. Series editor Stuart A. Rice. Copyright # 2007 John Wiley & Sons, Inc. , Fukashi Sasaki’s upper bound on eigenvalues of 2-RDM [2]). Claude Garrod and Jerome Percus [3] formally wrote the necessary and sufficient N-representability conditions.

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