Floating origin constraints

In polar space groups, which have a floating origin (e.g. PI where the origin is entirely arbitrary, or P2i where the origin can be anywhere on the b axis), a shift of the entire atomic model along a polar axis does not violate the space group symmetry. In the presence of a heavy atom in the stmcture, this atom s coordinates can be constrained to certain values (e.g. (0,0,0) for PI or (x, 0, z) for P2i). Alternatively, the sum of the coordinates of all atoms in the stmcture can be constrained to remain constant, which removes one parameter per polar axis. 

SHELXL uses a mathematically different and somewhat more stable approach, restraining the weighted sum over all coordinates to remain constant as introduced by Flack and Schwarzenbach (1988). A relatively high weight for this floating origin restraint makes it almost equivalent to a constraint. 

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The general influence of temperature on chromatographic retention can be explained as follows. In order to be retained on the stationary phase, molecules need to transform from a state of very little order while floating in the mobile phase to a much more ordered immobilized state in the stationary phase. This is a process that implies a reduction in entropy. In order to make retention still an energetically favorable process, thermodynamics defines that it must release heat. Thus, retention in chromatography is typically an exothermic process. If the temperature is increased, exothermic processes escape from this constraint by shifting the equilibrium to the original side. This implies that temperature increase is accompanied by a shift to the desorbed state of the molecules and thus a lower retention. There are some rare exemptions to this rule (as always), but those are based on secondary equilibria that overrule the effect described earlier. 

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