Performance Tests of the Second-Order Approximate Internally Contracted Multireference Coupled-Cluster Singles and Doubles Method icMRCC2.

Benchmark results are presented for the second-order approximation of the internally contracted multireference coupled-cluster method with single and double excitations, icMRCC2 [Köhn, Bargholz, J. Chem. Phys. 2019, 151, 041106], which was designed as a multireference analogue of the single-reference second-order approximate coupled-cluster method CC2 [Christiansen, Koch, Jørgensen, Chem. Phys. Lett. 1995, 243, 409-418]. Vertical excitation energies of various small to medium-sized organic molecules are investigated based on established test sets from the literature. Additionally, the spectroscopic constants of ground and excited states of diatomics and the geometric parameters of excited triatomic molecules were determined and compared to the experimental data. The results show that the method clearly extends the applicability of single-reference CC2, including doubly excited states, and also artifacts of CC2 like too low Rydberg excitations and too weak multiple bonds are eliminated. The method is computationally more demanding than standard multireference second-order perturbation theories but improves significantly in accuracy, as shown by the benchmark results. In addition, it is demonstrated that small active spaces are often sufficient to obtain accurate energies with icMRCC2. Example applications like the automerization of cyclobutadiene, the deactivation pathway of ethylene, and the excited states of an iron complex with a noninnocent nitrosyl ligand demonstrate the potential of icMRCC2 in cases with strong multireference character.

Probing Exfoliated Graphene Layers and Their Lithiation with Microfocused X-rays.

X-ray diffraction is measured on individual bilayer and multilayer graphene single-crystals and combined with electrochemically induced lithium intercalation. In-plane Bragg peaks are observed by grazing incidence diffraction. Focusing the incident beam down to an area of about 10 µm × 10 µm, individual flakes are probed by specular X-ray reflectivity. By deploying a recursive Parratt algorithm to model the experimental data, we gain access to characteristic crystallographic parameters of the samples. Notably, it is possible to directly extract the bi/multilayer graphene c-axis lattice parameter. The latter is found to increase upon lithiation, which we control using an on-chip peripheral electrochemical cell layout. These experiments demonstrate the feasibility of in situ X-ray diffraction on individual, micron-sized single crystallites of few- and bilayer two-dimensional materials.