Magnitude and Significance of the Higher-Order Reduced Density Matrix Cumulants

Using full configuration interaction wave functions for Be and LiH, in both minimal and extended basis sets, we examine the absolute magnitude and energetic significance of various contributions to the three-electron reduced density matrix (3-RDM) and its connected (size-consistent) component, the 3-RDM cumulant (3-RDMC). Minimal basis sets are shown to suppress the magnitude of the 3-RDMC in an artificial manner, whereas in extended basis sets, 3-RDMC matrix elements are often comparable in magnitude to the corresponding 3-RDM elements, even in cases where this result is not required by spin angular momentum coupling. Formal considerations suggest that these observations should generalize to higher-order p-RDMs and p-RDMCs (p 3). This result is discussed within the context of electronic structure methods based on the contracted Schrödinger equation (CSE), as solution of the CSE relies on 3and 4-RDM “reconstruction functionals” that neglect the 3-RDMC, the 4-RDMC, or both. Although the 3-RDMC is responsible for at most 0.2% of the total electronic energy in Be and LiH, it accounts for up to 70% of the correlation energy, raising questions regarding whether (and how) the CSE can offer a useful computational methodology. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 107: 703–711, 2007