Ghost molecule

Table 5. The Basis Set Superposition Error (BSSE) for CH5(H2). The Monomers in Parentheses are Ghost Molecules. " AE Indicates the Difference between the Energy of the Monomer within the Monomer vs. the Dimer Basis...

However, once one is aware of the problem the basis set superposition error can easily be checked by a ghost molecule treatment Proceeding in this manner... 

The excess chemiccil potential is thus determined from the average of exp[—lT (r )/fe In ensembles other than the canonical ensemble the expressions for the excess chem potential are slightly different. The ghost particle does not remain in the system and the system is unaffected by the procedure. To achieve statistically significant results m Widom insertion moves may be required. However, practical difficulties are encounte when applying the Widom insertion method to dense fluids and/or to systems contain molecules, because the proportion of insertions that give rise to low values of y f, dramatically. This is because it is difficult to find a hole of the appropriate size and sha... 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

One usually distinguishes two types of lattice models. The first type may be called lattice-gas models. In this case, the number of molecules in the system is less than the number of available sites. In other words, there are vacant sites. The second type of lattice models may be called lattice fluids. In this case, all lattice sites are filled exactly by the molecular components in the system the system is considered to be incompressible. It is easily shown that a two-component incompressible lattice fluid model can be mapped on a one-component lattice gas one. In other words, it is possible to interpret vacant sites to be occupied by a ghost ... 

Chemistry is a physical science that studies the structure and properties of elementary matter. Matter interacts with other substances. Matter can be defined as something that occupies space, has mass, and cannot be created or destroyed, but can be changed from one form to another. Matter is stuff that can be perceived by one or more of our senses, as opposed to something intangible such as an idea, the mind, or spirits (ghosts and angels). We usually think of matter as the chemical elements composed of atoms and the compounds composed of molecules, which are combinations of atoms. Chemistry is the science of how and what... 

MD simulations, complete with ghost particle insertions (160, 161), may be used to obtain static and dynamic information. (These particle insertions were performed after the MD runs and do not affect the calculations they merely probe the insertion of particles into the system.) The MD simulations performed by Snurr et al. (155) were slightly more expensive than the GC-MC calculations, but they produced similar isotherms and also yielded important information about the structure of the adsorbed fluid. The methane molecules appeared to behave like an ordered fluid at all concentrations, although the structure does change. This change reflects the changing importance of sorbate-sorbate and zeolite-sorbate interactions as a function of loading. 

Fig. 12.5 Illustration of the orientation angles used in the Stockmayer intermolecular potential. Molecule j consists of atoms A and B, and molecule i consists of atoms C and D. The vector ry runs from the center of mass of molecule i to the center of mass of molecule j. The vector JTJ gives the orientation and magnitude of the dipole moment of molecule i, with a similar definition for JTj. A ghost copy of molecule j is shifted to left to more easily visualize the orientation angle ifr. See Eqs. 12.11 to 12.13 and accompanying text for definition and description of these angles.

Occasionally, a laboratory will need an in-line detector of radio-labeled molecules. These detectors take the flow from the column or from an initial detector, mix it with fluorescing compound, and measure the fluorescence due to radioactive breakdown. A different system uses beads in the flow cell with an immobilized fluorescing compound, but these systems suffer from ghosting and cannot be used with very hot labeled compounds because of secondary radiation problems. These systems are very useful with tritiated samples and less so with carbon14 labeled compounds. Some success has been reported with sulfur32 label detection. 

A ghost orbital pt is imagined as being attached to each atom of the metal. This orbital represents that part of the wave function of the atom which is antisymmetric with respect to the plane of the ethylene molecule. It is supposed also that each atom contributes one electron. 

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