Elsevier

Chemical Physics Letters

Volume 428, Issues 4–6, 20 September 2006, Pages 277-282
Chemical Physics Letters

High-level ab initio calculations on the NiO2 system

https://doi.org/10.1016/j.cplett.2006.07.075Get rights and content

Abstract

Several high-level ab initio methods were employed in studies of the narrow singlet-triplet separation of the cyclic form of nickel dioxide (NiO2). It is shown that the complete versions of the locally renormalized coupled cluster method with singles, doubles, and noniterative triples (LR-CCSD(T)) approach, in contrast to the standard CCSD(T) method, provides results in concert with predictions of the density functional theory (DFT) and internally contracted multi-reference configuration interaction method (IC-MRCI), which favor the triplet state to be the lowest one. Relevant discussion of several aspects related to the underlying CCSD calculations, indicate that the dominant role of singly excited amplitudes violates the paradigm about the leading role of two-body effects in the description of the correlation energy. We also show that the multireference perturbation theory, exemplified here by the Generalized Van Vleck Perturbation Theory, requires the use of very large model space in order to properly describe the non-dynamical correlation effects.

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.

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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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