High-level ab initio calculations on the NiO2 system
Graphical abstract
Several high-level ab initio methods were employed in studies of the narrow singlet-triplet separation of the cyclic form of nickel dioxide. The results obtained with the LR-CCSD(T) approach are in agreement with those produced by the MRCISD and DFT methods.
Introduction
In recent years, transition metal dioxides have been a subject of intensive studies of several research groups [1], [2], [3], [4], [5], [6]. Because of the inherent quasidegeneracy of the transition metal atoms, systems of this type set the bar very high especially for the high level single reference coupled cluster (SR-CC) methods. These problems can be well exemplified by the cyclic form of nickel dioxide (NiO2), which is characterized by a very small energy difference between optimized singlet and triplet states. In contrast to various DFT, MRCI, and CASSCF approaches the CCSD(T) predicts the singlet state to be the lowest one [6]. For example, the internally contracted MRCI method [8], [9] using a multi-reference analogue of the Davidson correction yields a 12.78 kcal/mol separation ΔE = E(1A1) − E(3B1), defined as the difference of optimized energies of 1A1 and 3B1 states. Quantitatively similar results of 8.25 kcal/mol and 12.31 kcal/mol were obtained with CASSCF and internally contracted averaged coupled pair functional (IC-ACPF) [7] methods, respectively [6].
Probably, as stated in Ref. [6], the main reason for the above uncertainty lies in the treatment of electron correlation for 3d systems. Ideally, one should resort to rather elaborate multireference CC theories that for a well defined model space, properly address both the non-dynamical as well as dynamical correlation effects. However, in this Letter we would like to explore to what extent the single-reference noniterative CC approaches can be applied in this demanding situation. In our calculations we use a number of GGA, hybrid and meta-GGA DFT methods (PBE, H407, PBE0, and TPSSh, methods [10]) and locally renormalized CCSD(T) (LR-CCSD(T)) approaches recently implemented in NWChem package [11]. Also, the multireference perturbation theory approach based on the second order of the generalized Van Vleck perturbation (GVVPT2) approach was used in our studies.
Section snippets
Methods
Arguably, the SR-CC methodology [12], [13], [14] should be viewed as a one of the most accurate and theoretically justified approaches to the electron correlation problem. The mathematically rigorous representation of the CC wavefunction through the exponential Ansatz provides an excellent basis for stepwise inclusion of higher-order components of the cluster operator that eventually leads to a chain of approximate approaches converging to the exact, full configuration interaction (FCI) limit.
Computational details
As reported in Ref. [6] the relativistic effects and the size of the basis set have only a minor effect on the singlet-triplet splitting. Therefore we decided to employ medium size basis sets composed of the aug-cc-pVTZ basis set [31], [32] on the oxygens and the NASA Ames ANO basis set [33], [34] localized on the nickel atom. In all CC calculations core orbitals were kept frozen.
We have employed several variants of the LR-CCSD(T) method, including the LR-CCSD(T), IB, LR-CCSD(T), IIB, and
Results and discussion
We commence our discussion by noticing that the use of the RHF reference resulted in a large values of the T1 amplitudes obtained in the CCSD calculations. For example, the largest T1 amplitude obtained for the CCSD(T)-optimized 1A1 state is as big as 0.292 (for comparison, the largest T2 amplitude equals −0.142 and is smaller than the second largest T1 amplitude, which is on the order of −0.170).
For the CCSD(T)-optimized equilibrium geometry of the 3B1 state the situation is only slightly
Acknowledgements
This work has been performed using the Environmental Molecular Sciences Laboratory (EMSL) at the Pacific Northwest National Laboratory. The William R. Wiley Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory is funded by the Office of Biological and Environmental Research in the U.S. Department of Energy. The Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by the Battelle Memorial Institute under Contract
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