Libwa analysis with STATE_ANALYSIS true

In more recent versions of QChem (5.4 ->) I find that running EOM_CCSD calculation with
generates a libwa OPDM analysis of the “difference density matrix” in the Excited state properties output pass, before a second libwa OPDM analysis of the (A->B) “transition density matrix” under the transition properties output. In Q-Chem v5.0 I only ever saw the latter (expected) transition analysis.

What is the “difference density matrix”? I can find no mention of this, but the results for a given excited state look very different from the subsequent transition density matrix result, and I am unclear how, or which of these to interpret now that this alternative appears.

The distinction is probably whether you are analyzing DeltaP = P(exc) - P(gnd), or the transition density matrix, which are not the same in methods that go beyond single excitations. (Also not the same in CIS/TDDFT if the Z-vector component is included in DeltaP.) The difference is orbital relaxation. See here:

Thank you. A local colleague pointed me towards a more current version of the Q-Chem manual which states, as you do, that the difference density and transition density are not the same. In practise I was finding that the differences between eg the |<re - rh>| that libwfa reports for these two different density matrices were surprisingly large, but I’ll now use your reference to try to better understand this.

Especially for CT states the orbital relaxation effects can be very large, which would be reflected in the difference between those two forms of analysis. I discussed this in the context of TDDFT in Section 2.3 of this review: