We present new insight into the nature of aromaticity in metal clusters. We give computational arguments in favor of using the ring-current model over local indices, such as nucleus independent chemical shifts, for the determination of the magnetic aromaticity. Two approaches for estimating magnetically induced ring currents are employed for this purpose, one based on the quantum theory of atoms in molecules (QTAIM) and the other where magnetically induced current densities (MICD) are explicitly calculated. We show that the two-zone aromaticity/antiaromaticity of a number of 3d metallic clusters (Sc3(-), Cu3(+), and Cu4(2-)) can be explained using the QTAIM-based magnetizabilities. The reliability of the calculated atomic and bond magnetizabilities of the metallic clusters are verified by comparison with MICD computed at the multiconfiguration self-consistent field (MCSCF) and density functional levels of theory. Integrated MCSCF current strength susceptibilities as well as a visual analysis of the calculated current densities confirm the interpretations based on the QTAIM magnetizabilities. In view of the new findings, we suggest a simple explanation based on classical electromagnetic theory to explain the anomalous magnetic shielding in different transition metal clusters. Our results suggest that the nature of magnetic aromaticity/antiaromaticity in transition-metal clusters should be assessed more carefully based on global indices.
Nondynamical electron correlation based on a genuine multiconfigurational theory is of considerable importance for a balanced ab initio calculation of aromatic and antiaromatic molecules either with open-shell character or quasi-degeneracy in the electronic states. Among the various aromaticity indices, the calculation of magnetically induced ring current densities (MICD) has emerged as a strong contender, providing both a qualitative and a quantitative description of the effect. We report here the first implementation of MICD at the multiconfigurational self-consistent field (MCSCF) level of theory together with example calculations. This extension makes the method applicable to systems that cannot be appropriately handled with earlier implementations based on a single-reference starting function. We present the formulation of the MCSCF MICD theory along with applications to a prototypical antiaromatic (cyclobutadiene) and an aromatic (benzyne) system, both systems that require a multiconfigurational description. We compare the MCSCF results to those obtained using Hartree-Fock and Kohn-Sham density functional theory and discuss the effects of static correlation on the aromaticity.
Complete Active Space SCF (CASSCF) theory may provide poor 0th order descriptions due to the lack of dynamic correlation. The most popular post-CASSCF approaches for recovering dynamic correlation are methods which keep the configuration interaction coefficients fixed at the CASSCF level and use internal contraction. This may result in severe inaccuracies where the wavefunction changes considerably under the influence of dynamic correlation. In this paper, we propose and compare several variants of a straightforward method of the "perturb-then-diagonalize" type that is aimed at keeping this balance while remaining computationally tractable and numerically stable. The method is loosely based on the theory of intermediate Hamiltonians and has been given the acronym "dynamic correlation dressed CAS" (DCD-CAS), with the second-order treatment, DCD-CAS(2), being the most practically useful member of the family. The dynamic correlation energy is treated to second order with a 0th order Hamiltonian based on Dyall's Hamiltonian. The method is orbitally invariant with respect to unitary transformations in the occupied, active, and virtual subspaces. It yields the ground- and low-lying excited states at the same time. Detailed numerical evaluations show that DCD-CAS(2) is superior to NEVPT2 for the difficult situations mentioned above while being very close to it when CASSCF provides a good 0th order description.
Hemilabile ligands, which have one donor that can reversibly bind to a metal, are widely used in transition-metal catalysts to create open coordination sites. This change in coordination at the metal can also cause spin-state changes. Here, we explore a cobalt(I) system that is poised on the brink of hemilability and of a spin-state change and can rapidly interconvert between different spin states with different structures ("spin isomers"). The new cobalt(I) monocarbonyl complex L(tBu)Co(CO) (2) is a singlet ((1)2) in the solid state, with an unprecedented diketiminate binding mode where one of the C═C double bonds of an aromatic ring completes a pseudo-square-planar coordination. Dissolving the compound gives a substantial population of the triplet ((3)2), which has exceptionally large uniaxial zero-field splitting due to strong spin-orbit coupling with a low-lying excited state. The interconversion of the two spin isomers is rapid, even at low temperature, and temperature-dependent NMR and electronic absorption spectroscopy studies show the energy differences quantitatively. Spectroscopically validated computations corroborate the presence of a low minimum-energy crossing point (MECP) between the two potential energy surfaces and elucidate the detailed pathway through which the β-diketiminate ligand "slips" between bidentate and arene-bound forms: rather than dissociation, the cobalt slides along the aromatic system in a pathway that balances strain energy and cobalt-ligand bonding. These results show that multiple spin states are easily accessible in this hemilabile system and map the thermodynamics and mechanism of the transition.
One generic difficulty of most state-specific many-body formalisms using the Jeziorski-Monkhorst ansatz: ψ = Σ(μ)exp(T(μ))|φ(μ)>c(μ) for the wave-operators is the large number of redundant cluster amplitudes. The number of cluster amplitudes up to a given rank is many more in number compared to the dimension of the Hilbert Space spanned by the virtual functions of up to the same rank of excitations. At the same time, all inactive excitations--though linearly independent--are far too numerous. It is well known from the success of the contracted multi-reference configuration interaction (MRCI(SD)) that, at least for the inactive double excitations, their model space dependence (μ-dependence) is weak. Considerable simplifications can thus be obtained by using a partially internally contracted description, which uses the physically appealing approximation of taking the inactive excitations T(i) to be independent of the model space labels (μ-independent). We propose and implement in this paper such a formalism with internal contractions for inactive excitations (ICI) within Mukherjee's state-specific multi-reference coupled cluster theory (SS-MRCC) framework (referred to from now on as the ICI-SS-MRCC). To the extent the μ-independence of T(i) is valid, we expect the ICI-SS-MRCC to retain the conceptual advantages of size-extensivity yet using a drastically reduced number of cluster amplitudes without sacrificing accuracy. Moreover, greater coupling is achieved between the virtual functions reached by inactive excitations as a result of the internal contraction while retaining the original coupling term for the μ-dependent excitations akin to the parent theory. Another major advantage of the ICI-SS-MRCC, unlike the other analogous internally contracted theories, such as IC-MRCISD, CASPT2, or MRMP2, is that it can use relaxed coefficients for the model functions. However, at the same time it employs projection manifolds for the virtuals obtained from inactive n hole-n particle (nh-np) excitations on the entire reference function containing relaxed model space coefficients. The performance of the method has been assessed by applying it to compute the potential energy surfaces of the prototypical H(4); to the torsional potential energy barrier for the cis-trans isomerism in C(2)H(4) as well as that of N(2)H(2), automerization of cyclobutadiene, single point energy calculation of CH(2), SiH(2), and comparing them against the SS-MRCC results, benchmark full CI results, wherever available and those from the allied MR formalisms. Our findings are very much reminiscent of the experience gained from the IC-MRCISD method.
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