Reduced density matrix 2- RDM

Hamiltonians involving more than two electron interactions. I shall use this to illustrate the general case of arbitrary p. The second-order reduced density matrix (2-RDM) of a pure state ij/, a function of four particles, is defined as follows ... 

Then, in the Old Ages (1940 or 1951-1967) some ingenious people became aware that, in the case of two-body interactions, it is the two-particle reduced density matrix (2-RDM) that carries in a compact way all the relevant information about the system (energy, correlations, etc.). Early insight by Husimi (1940) and challenges by Charles Coulson were completed by a clear realization and formulation of the A-representability problem by John Coleman in 1951 (for the history, see his book [1] and Chapters 1 and 17 of the present book). Then a series of theorems on A-representability followed, by John Coleman and many... 

In 2001, Nakata and co-workers presented the results of realistic fermionic systems, like atoms and molecules, larger than previously reported for the variational calculation of the second-order reduced density matrix (2-RDM) [1]. 

Knowledge of the 2-particle reduced density matrix (2-RDM) allows one to calculate the energy and other observables for atomic and molecular systems with... 

In a famous after-dinner address at a 1959 conference in Boulder, Colorado, Charles Coulson [1] discussed both the promises and the challenges of using the two-electron reduced density matrix (2-RDM) rather than the many-electron wavefunction as the primary variable in quantum computations of atomic and molecular systems. Integrating the A-electron density matrix,... 

The authors are honored to dedicate this article in memory of Isaiah Shavitt whose remarkable contributions transformed electronic structure theory. Observables that depend on pairwise interactions can be directly computed with the two-electron reduced density matrix (2-RDM) without the A-electron wave function [10, 36]. Integration of the A-electron density matrix over all electrons save two yields the 2-RDM... 

In the last decade, a series of functionals has been developed [1, 2] using a reconstruction proposed by Piris [3] of the two-particle reduced density matrix (2-RDM) in terms of the one-particle RDM (1-RDM). In particular, the Piris natural orbital functional 5 (PNOF5) [4, 5] has proved to... 

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