Two-electron reduced density matrix

VARIATIONAL TWO-ELECTRON REDUCED-DENSITY-MATRIX THEORY... 

G. Gidofalvi and D. A. Mazziotti, Spin and symmetry adaptation of the variational two-electron reduced-density-matrix method. Phys. Rev. A 72, 052505 (2005). 

So it is the probability that orbital i is empty and orbitals j and k are filled or that orbital i is filled and orbitals j and k are empty. It is interesting that these particular three-electron correlations can be evaluated using the two-electron reduced density matrix. 

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 two-electron reduced density matrix is a considerably simpler quantity than the N-electron wavefunction and again, if the A -representability problem could be solved in a simple and systematic manner the two-matrix would offer possibilities for accurate treatment of very large systems. The natural expansion may be compared in form to the expansion of the electron density in terms of Kohn-Sham spin orbitals and it raises the question of the connection between the spin orbital space and the -electron space when working with reduced quantities, such as density matrices and the electron density. 

The two-electron reduced density matrix of the AGP can be brought to an interesting form, called, Box and Tail ... 

Back in the 1960s, hopes for future progress in electronic structure theory were associated with correlated wave function techniques and the tantalizing possibility of variational calculations based on the two-electron reduced density matrix [294]. DFT was not on the quantum chemistry agenda at that time. The progress of wave function techniques has been remarkable, as documented elsewhere in this volume. In contrast, the density matrix approach has not yet materialized into a competitive computational method, despite many persistent efforts [295]. Meanwhile, approximate DFT has become the most widely used method of quantum chemistry, offering an unprecedented accuracy-to-cost ratio. 

Sand, A. M., Schwerdtfeger, C. A., Mazziotti, D. A. (2012). Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene. The Journal of Chemical Physics, 136, 034112. 

Keyvrords Two-electron reduced density matrix N-representability conditions Strong electron correlation Hubbard models... 

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... 

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