Diagrammatic Multiplet-Sum Method (MSM) Density-Functional Theory (DFT): Investigation of the Transferability of Integrals in "Simple" DFT-Based Approaches to Multi-Determinantal Problems

Static correlation is a difficult problem for density-functional theory (DFT) as it arises in cases of degenerate or quasi-degenerate states where a multideterminantal wave function provides the simplest reasonable first approximation to the true interacting wave function. This is also where Kohn-Sham DFT may also fail to be noninteracting v-representible (NVR). In contrast, Kohn-Sham DFT typically works well for describing the missing dynamic correlation when a single-determinantal reference wave function provides a good first approximation to the true interacting wave function. Multiplet sum method (MSM) DFT [Theor. Chim. Acta 4, 877 (1977)] provides one of the earliest and simplest ways to include static correlation in DFT. MSM-DFT assumes that DFT provides a good description of single-determant energies and uses symmetry and simple ansatzes to include the effects of static correlation. This is equivalent to determining the off-diagonal matrix elements in a small configuration interaction (CI) eigenvalue problem. We have developed a diagrammatic approach to MS-DFT facilitates comparison with wave function CI and so allows educated guesses of off-diagonal CI matrix elements even in the absence of symmetry. In every case, an additional exchange-only ansatz (EXAN) allows the MSM-DFT formulae to be transformed into wave function formulae. This EXAN also works for transforming time-dependent DFT into time-dependent Hartree-Fock. Although not enough to uniquely guess DFT formulae from wave function formulae, the diagrammatic approach and the EXAN provide important constraints on any guesses that might be used. Some alternative guesses are tried out for problems concerning the ground and excited states of H2 , LiH, and O2 in order to assess how much difference might be involved for different DFT guesses for off-diagonal matrix elements

Versatile Barium and Calcium Imidazolium-Dicarboxylate Heterogeneous Catalysts in Quinoline Synthesis

This article details the development of heterogeneous catalysts based on calcium and barium in combination with the organic linker 1,3-bis(carboxymethyl)imidazolium (bcmim). The linker and the materials from alkaline earth metals are easily prepared under very smooth conditions. The use of linkers with different counterions (Cl or Br) provided different materials. Calcium- and barium-based catalysts were successfully employed in the preparation of quinoline derivatives from ketones and 2-aminoarylaldehydes or 2-aminoarylketones. In general, barium-based catalysts provided better results than calcium, although the latter are an excellent complement for certain substrates. Thus, a notable feature of such catalysts is the possibility of accessing a variety of complementary heterogeneous catalytic systems, rendering the catalysis adaptive to the reactant.The Ministerio de Economía y Competitividad, CTQ2015-66624-P) and the University of Alicante (VIGROB-285) are gratefully acknowledged for financial support. M. A. S. thanks the Ministerio de Educación, Cultura y Deporte, FPU15/06040) for a predoctoral fellowship