Gravity rules

Figure 2.9. Illustration of relative gravity rules influencing cells A and B...

It is observed that the CA dynamics, with these rules, results in a pattern in which clusters of X are scattered among clusters of Y. This is not what is seen in the laboratory. In reality, two immiscible liquids will separate into two layers, each responding to a different influence from gravity. What the CA model shows is the separation experienced in the weightlessness of space. A gravity rule must be added. 

The gravity rules were described in Chapter 2. They are selected to impart a different orientation among molecules X and Y. If the gravity rule, Gr(XY) favors X over Y, then X molecules will tend to be the upper layer. The relationship of up and down for relative gravity now requires a reference in the grid construction for these gravity rules to be operative. There must be an upper and a lower boundary on the grid. Therefore, the X and Y molecules cannot pass... 

In the crystal field model, the split 3d orbital energy levels are assumed to obey a centre of gravity rule. As a result, the three t2g orbitals are lowered by 0.4Ao below, and the two eg orbitals raised by 0.6Ao above, the baricentre. This follows from a simple algebraic argument that the energy of six electrons in the three t2g orbitals is compensated by the energy of four electrons in the two eg... 

The cellular automata models described here contained some novel techniques for this paradigm. The use of a gravity rule to set the stage for the... 

To form Pj" s P, for example, we need only nse the valne of z at each vertex to obtain P Hiickel approximation (see Hiickel Theory), but this is simply to provide an idea of the bonding/antibonding character, and some more accurate calculations will be discussed below. (Note that the splitting obeys another center-of-gravity rule.) The normalization is simply 1 /s/l, as overlap between the two a orbitals has been neglected. ... 

Note that a baricentre rule holds for the Ds terms, but not for the Dt terms. Thus the splitting of the cubic e and <2 orbitals on applying a tetragonal distortion does not obey a centre of gravity rule, although many authors have assumed that it does in discussions of tetragonal distortions in copper(II) complexes ). 

The center of gravity rule can be useful for obtaining parameter estimates, locating extra lines, and detecting the presence of an unsuspected second per-turber. When main and extra lines are observed for more than two J-values at... 

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