By David A. Mazziotti
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However, new ideas were needed. The ﬁnal breakthrough came with the advent of powerful computers, which enabled the algorithms of Hiroshi Nakatsuji, Carmela Valdemoro, and David Mazziotti to come to life. I feel very happy about the revival of the RDM approach to many-body problems. I apologize to all those RDM contributors whose worthy works I did not mention due to the limited space. References 1. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices, Coulson’s Challenge, Springer Verlag, New York, (2000).
NÞ, where the numbers represent the spatial and spin coordinates for each electron, is given by N Dð1; 2; . . ; N; 10 ; 20 ; . . ; N 0 Þ ¼ Éð1; 2; . . ; NÞÉÃ ð10 ; 20 ; . . ; N 0 Þ ð1Þ Integrating the N-electron density matrix over coordinates 3 to N generates the two-electron density matrix (2-RDM): 2 0 0 Dð1; 2; 1 ; 2 Þ ¼ Z Éð1; 2; . . ; NÞÉÃ ð10 ; 20 ; . . ; NÞd3 Á Á Á dN ð2Þ Because electrons are indistinguishable with only pairwise interactions, the energy of any atom or molecule may be expressed as a linear functional of the 2-RDM [3, 4].
Rosina and M. V. Mihailovic´, The determination of the particle hole excited states by using the variational approach to the ground state two body density matrix, in International Conference on Properties of Nuclear States, Montreal 1969, Les Presses de l’Universite´ de Montreal, 1969. 26. M. Bouten, P. Van Leuven, M. V. Mihailovic´, and M. Rosina, A new particle hole approach to collective states. Nucl. Phys. A202, 127 144 (1973). 27. M. Bouten, P. Van Leuven, M. V. Mihailovic´, and M. Rosina, Two exactly soluble models as a test of the Hermitian operator method.