Ignorable coordinates

A cylindrical frame of reference (r, cp,z) is introduced where cp is an ignorable coordinate. In this frame the velocity vector is now assumed to have the form... 

Since Hamilton s equations imply that pk = 0 if = 0, pk is a constant of motion if qt is such an ignorable coordinate. An ingenious choice of generalized coordinates can produce such constants and simplify the numerical or analytic task of integrating the equations of motion. 

The essential step in the construction[of the molecular Hamiltonian]is the removal of the ignorable coordinates corresponding to the overall translation and overall rotation of the molecule. 

Because water has a concentration of approximately 55 M, it varies by only trivial amounts for reactions of dilute species. As a result, it is convenient, and traditional, to leave out the solvent term and usually also to ignore coordinated water molecules. We shall adopt this representation henceforth - but do not assume we are dealing with bare metal ions This reduces Equation (5.1) to Equation (5.4) ... 

Figure Al.4.7. A cross-section of the potential energy surface of PH obtained by ignoring the version b (see figure Al.4.6). The coordinate p is defined in figure Al.4.5.

Coordin ates of atom s can he set by n orm al translation orrotation of HyperCh cm molecules, fo set initial velocities, however, it is necessary to edit th e H l. file explicitly. The tin it o f velocity in the HIN file is. An gstrom s/picosecon d.. Areact.hin file and a script react.scr are in eluded with HyperChem to illustrate one simple reacting trajectory. In order to have these initial velocities used in a trajectory the Restart check box of the Molecular Dynamics Option s dialog box must he checked. If it is n ot, the in itial velocities in the HIN file will be ignored and a re-equilibration to the tern peratiire f of th e Molecular Dyn am ics Option s dialog box will occur. This destroys any imposed initial conditions on the molecular dynamics trajectory. 

I le u. . erlap between the 2pK and 2p orbitals in this new coordinate system is j(2p — 2p ). If tile zei o differential overlap approximation were applied, then different results would be oliLiined for the two coordinate systems unless the overlap in the new, transformed svntem was also ignored. 

Sketch the molecules on graph paper to help in determining the atomic coordinates. This is the first use of molecular geometry, a property that will become increasingly important as we go on. At this stage, the geometries are approximate the difference, for example, between cis and trans isomer s is ignored. 

For the shear buckling mode in Figure 3-55, the fiber displacements are equal and in phase with one another. The matrix material is alternately sheared in one direction and then the other as the x-direction is traversed. However, changes in deformation in the y-direction are ignored. Thus, the shear strains are presumed to be a function of the fiber-direction coordinate alone. The matrix is sheared according to... 

Here is a graph showing the positions of the carbon and chlorine atoms in the XY-plane, ignoring their common Z-coordinate ... 

Nevertheless, crystal fields cannot be completely ignored. The intensities of a number of bands ( hypersensitive bands) show a distinct dependence on the actual ligands which are coordinated. Also, in the same way that crystal fields lift some of the orbital degeneracy (2L -)- 1) of the terms of d" ions, so they lift some of the 2J -)- 1 degeneracy of the sates of P ions, though in this case only by the order of 100cm This produces fine structure in some bands of Ln spectra. 

Taylor s series in terms of the normal coordinate Qi (Appendix). If the displacement is small we may ignore higher order terms in the expansion. 

The activated character of the dependence tj(T) shown in (1.123) is often considered as a feature suggesting a quasicrystal model of the liquid. Data taken from liquid-vapour co-existence curves are frequently analysed in coordinates In tj from 1/T in order to determine t/o- The point that tj(n, T) is a function not only of the temperature T, but also of the density n is ignored. The density along the co-existence curve is... 

It is very common for inorganic chemists to neglect or ignore the presence of solvent molecules coordinated to a metal centre. In some cases, this is just carelessness, or laziness, as in the description of an aqueous solution of cobalt(ii) nitrate as containing Co ions. Except in very concentrated solutions, the actual solution species is [Co(H20)6] . In other cases, it is not always certain exactly what ligands remain coordinated to the metal ion in solution, or how many solvent molecules become coordinated. Solutions of iron(iii) chloride in water contain a mixture of complex ions containing a variety of chloride, water, hydroxide and oxide ligands. 

While often somewhat ignored by coordination chemists, the interaction of Group I ions has recently received increased attention, particularly with regard to duplex DNA. To a large extent these ions are involved in charge neutralization of the anionic backbone of (deoxy)-ribonucleotide polymers. However, more specific effects have been... 

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