Quasi-complete model space

Kutzelnigg et. al795/ have discussed in detail the Fock—space classification of operators for quasi— complete model space. They also introduced a new type od IMS, called the isolated incomplete model space(IIMS). In IIMS, products of q—open operators are all q-open, never closed. As a result O. = 1., just as in a CMS. THe resulting CC equations for IIMS have thus exacly the same structure as in the CMS. 

The above formulation is quite general and applies equally well to quasi-complete model spaces having m holes and n partic 1es.When there are several p-h valence ranks in the parent model space, the situation is fairly complicated. The subduced model spaces in this case may belong to the parent model space itself. The valence-universality of ft in such a situation implies that ft is the wave—operator for all the subduced model spaces, in addition to those which have same number of electrons as in the parent model space. It appears that a more convenient route to solve this problem is to redefine the core in such a way that holes for the problem become particles and treat it as an IMS involving valence particles only. 

In our formalism, we choose in every all open and quasi-open operators. For an arbitrary IMS, a given quasi-open operator, acting on a given model function, may lead to excitation to some specific model function, but there would be at least one model function which, when acted upon by this quasi-open operator, would lead to excitations out of the IMS. A closed operator, by contrast, cannot lead to excitations out of the IMS by its action on any function in the IMS. Clearly, any pair of model functions and (f> can be reached with respect to each other by either a quasi-open or a closed operator, but not both. This follows from the definition of these operators. For an arbitrary IMS, it is possible to remain within the IMS if a quasi-open operator acts on a specific model function. On another model function, it may lead to excitation out of the IMS. The QCMS (Quasi-Complete Model Space) is a special class of IMS, where we group orbitals into various subsets, labeled A, B, etc. and form a model space spanned by model functions... 

Initially, the void space between the particles is completely filled with liquid ( = 0 for all voxels). Evaporation from the liquid-gas interface and liquid relaxation into capillary equilibrium are then computed in an alternating sequence. For this simulation we assume a scale separation in time, i.e., that the evaporation occurs on a much slower time scale than the liquid motion. We resolve only the evaporation time scale, which yields a quasi-static approach in each evaporation step, liquid is removed according to the local evaporation rates computed from the solution of the vapor diffusion problem in the gas phase. Then the liquid is relaxed to the capillary equilibrium by volume-preserving mean curvature flow. This quasi-static approach is in contrast to a fully dynamic simulation (via computational fluid dynamics), but may come with considerably lower computational cost. Evaporation is modeled by vapor diffusion in the gas phase, with a no-flux condition at solid-gas interfaces and equilibrium vapor pressure imposed on liquid-gas interfaces (for more details, see [15]). The equilibrium liquid disttibution... 

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