Two-electron reduced density matrix 2-RDM

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... 

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 ... 

---