Heats of Formation for CrO, CrO2, and CrO3: An Extreme Challenge for Black-Box Composite Procedures

In the present study, we use composite methods, denoted CM(5)Λ and CM5, with post-CCSD(T) terms up to CCSDTQ(5)Λ and CCSDTQ5, respectively, to evaluate the atomization energies for CrO, CrO2, and CrO3. The heats of formation (ΔHf,298) based on our best estimated atomization energies are 198.3 ± 5 kJ mol(-1) (CrO), -81.3 ± 5 kJ mol(-1) (CrO2), and -286.8 ± 20 kJ mol(-1) (CrO3). Standard G4-type composite methods yield atomization energies that are adequate for CrO, less good for CrO2, and least good for CrO3. CrO3 is highly multireference in character, and therefore, a "black box" approach of using a single-reference RHF wave function is inadequate, even for "high-level" G4-type methods. We find that, for CrO3, there is a very large difference in the G4 atomization energies depending on whether an RHF or a UHF reference is used, which is mainly associated with large differences in the MP4 components. In general, we propose that a large R-versus-U difference is likely to be an indication of potential problems in the theoretical treatment. Going beyond G4 to a more rigorous UCCSD(T)-based composite scheme [termed U-CM(3:[DZ,TZ]) in the present study], we again find a large difference (but significantly smaller than that for G4) between the CrO3 atomization energies based on RHF or UHF references. Intriguingly, the use of Brueckner orbitals as reference orbitals in all components, as in the corresponding Brueckner Doubles (BD) procedure [B-CM(3:[DZ,TZ])], produces results for CrO3 that are independent of whether RHF or UHF orbitals are used as the starting point.