Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of Non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian
nature of the forms of
the coupled-cluster
(CC) theory widely used in quantum chemistry has usually been viewed
as a negative, but the present paper shows how this can be used to
an advantage. Specifically, the non-symmetric nature of the reduced
one-particle density matrix (in the molecular orbital basis) is advocated
as a diagnostic indicator of computational quality. In the limit of
the full coupled-cluster theory [which is equivalent to full configuration
interaction (FCI)], the electronic wave function and correlation energy
are exact within a given one-particle basis set, and the symmetric
character of the exact density matrix is recovered. The extent of
the density matrix asymmetry is shown to provide a measure of “how
difficult the problem is” (like the well-known T1 diagnostic), but its variation with the level of theory
also gives information about “how well this particular method
works”, irrespective of the difficulty of the problem at hand.
The proposed diagnostic is described and applied to a select group
of small molecules, and an example of its overall utility for the
practicing quantum chemist is illustrated through its application
to the beryllium dimer (Be2). Future application of this
idea to excited states, open-shell systems, and symmetry-breaking
problems and an extension of the method to the two-particle density
are then proposed.