A rigorous generation of spin-adapted (spin-free) substitution operators for high spin (S = Sz) references of an arbitrary substitution order and spin quantum number S is presented. The generated operators lead to linearly independent but non-orthogonal configuration state functions (CSFs) when applied to the reference and span the complete spin space. To incorporate spin completeness, spectating substitutions (e.g., Êivva) are introduced. The presented procedure utilizes Löwdin’s projection operator method of spin eigenfunction generation to ensure spin completeness. The generated operators are explicitly checked for (i) their linear independence and (ii) their spin completeness for up to tenfold substitutions and up to a multiplicity of 2S + 1 = 11. A proof of concept implementation utilizing the generated operators in a coupled cluster (CC) calculation was successfully applied to the high spin states of the boron atom. The results show pure spin states and small effects on the correlation energy compared to spin orbital CC. A comparison to spin-adapted but spin-incomplete CC shows a significant spin-incompleteness error.

Reactions involved in the autoxidation of ascorbate have been investigated with quantum chemical first-principles and ab initio methods. Reaction energies and Gibbs energies of the reactions were calculated at the density functional theory level applying the gradient-corrected BP86 and the hybrid B3LYP functionals together with def2-TZVP basis sets. Results of single-point CC2, CCSD, and CCSD(T) calculations were used for calibration of the density functional theory data and show excellent agreement with the B3LYP values. Based on the Gibbs energy ascorbic acid AscH2 is found to be the energetically lowest species in aqueous solution, whereas the monoanion ascorbate AscH - is the most abundant one near pH = 7. Asc 2- was found to be the preferred reducing agent for autoxidation and oxidation processes. The results also support a metal-catalyzed synthesis of the reactive oxygen species H2 O2 according to a redox cycling mechanism proposed in literature. © 2016 Wiley Periodicals, Inc.

In this paper, we report on a correctly scaling novel coupled cluster singles and doubles (CCSD) implementation for arbitrary high-spin open-shell states. The chosen cluster operator is completely spin-free, i.e., employs spatial substitutions only. It is composed of our recently developed Löwdin-type operators [N. Herrmann and M. Hanrath, J. Chem. Phys. 153, 164114 (2020)], which ensure (1) spin completeness and (2) spin adaption, i.e., spin purity of the CC wave function. In contrast to the proof-of-concept matrix-representation-based implementation presented there, the present implementation relies on second quantization and factorized tensor contractions. The generated singles and doubles operators are embedded in an equation generation engine. In the latter, Wick’s theorem is used to derive prefactors arising from spin integration directly from the spin-free full contraction patterns. The obtained Wick terms composed of products of Kronecker deltas are represented by special non-antisymmetrized Goldstone diagrams. Identical (redundant) diagrams are identified by solving the underlying graph isomorphism problem. All non-redundant graphs are then automatically translated to locally—one term at a time—factorized tensor contractions. Finally, the spin-adapted and spin-complete (SASC) CCS and CCSD variants are applied to a set of small molecular test systems. Both correlation energies and amplitude norms hint toward a reasonable convergence of the SASC-CCSD method for a Baker–Campbell–Hausdorff series truncation of order four. In comparison to spin orbital CCSD, SASC-CCSD leads to slightly improved correlation energies with differences of up to 1.292mEH (1.10% with respect to full configuration identification) for quintet CH2 in the cc-pVDZ basis set.

Volatile influences from global markets force manufacturing companies to be more flexible, innovative and efficient. Implementing these attributes in products, processes and production resources, requires a high rate of change in development periods of decreasing lengths. The increasing level of perceived complexity is a critical result of these changes. Manifold approaches were developed and studies were conducted to derive measures for complex issues. But in the industrial field, the usability of such measures poses a major challenge. In this paper, we bridge the gap between the scientific and the practical perspective on complexity and extract three basic complexity cases. On this basis, our procedure supports the systematic analysis, classification and quantification of complex issues in automotive production. The approach has been successfully applied in an industrial use case of an automotive assembly line.