Effects of noncrystallographic symmetry on the epsilon 1 relationship. I. Bicentric arrangements in P1.
An exact Fourier representation of the probability for the epsilon 1 relationship is derived, which takes into account the presence of noncrystallographic centrosymmetry in the asymmetic unit of the space group P1. Illustrative examples show that the main effect of noncrystallographic symmetry is to decrease the probability that E2h is positive, as compared to the corresponding probability in the absence of such symmetry. The effect appears to be more pronounced in the equal-atom case than it is for a structure having a heterogeneous atomic composition.
Shmueli
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Physical Sciences Laboratory, Division of Computer Research and Technology, National Institutes of Heath, Bethesda, Maryland 20892.
Weiss
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D002627:Chemistry, Physical / Q000379:methods*; D003461:Crystallography / Q000379:methods*; D005583:Fourier Analysis; D015394:Molecular Structure; D011336:Probability