Atomic coordinates subset function

For KHCO3, the wave function in the ground state should be antisym-metrical with respect to proton permutation and invariant for permutation of carbon and oxygen atoms (bosons). Therefore, the set of atomic coordinates split into strictly independent subsets, composed of indistinguishable fermions, ctis, aia, on the one hand, and bosons, [AJS, Aja, on the other. Then, the antisymmetrized wave function Ho analogous to (13) can be factored into wave functions (I>(7 and (I>(7/, for fermions and bosons, respectively,... 

One of the first approaches introduced and used in condensed phases, also in the sense of the historical development, was a biasing technique known as the Blue Moon [55]. This approach was better refined over the years [56] to become more user-friendly and easily implementable in a computer code. For all the details, we refer the reader to the cited original publications. Just to summarize the essential points, let us recall that in the case of first principles dynamical simulation, the method relies on the identification of a reaction coordinate, or order parameter, = (R/) of a given subset of atomic coordinates (Lagrangean variables) R/ able to track the activated process or chemical reaction on which one wants to focus. The simplest example is represented by the distance = R/—Ry between two atoms that are expected to form or break a chemical bond. This analytical function is added to, e.g., a Car-Parrinello Lagrangean as a holonomic constraint. 

The coordination behavior of molybdenum(VI) with D-mannaric acid 64 is similar to that with galactaric acid two molybdenum atoms are bonded either by the two a-alkoxidocarboxylato moieties of fourfoldly deprotonated D-mannaric acid or by the aikoxido functions of the C1-C3 subset and the C4—C6 subset, respectively, of entirely deprotonated D-mannaric acid. Due to the f/ireo-conflguration of the central diol residue, a threo complex is established in neutral solutions with a molar ratio of Mo ligand of 4 1 instead of an erythro complex which was observed with galactaric acid (compare structure 20 and 14 (O Fig. 2), respectively) [75]. The latter threo complex as well as a complex with the a-alkoxidocarboxylato moieties as chelation sites is also formed by tungsten(VI) [76]. 

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