This article examines the implications of phase space functions for psychological assessment. Behavior problems, causal variables, and causal relationships are dynamic and demonstrate complex nonlinear and discontinuous relationships. Measuring the temporal, dynamic, and nonlinear dimensions of variables can enhance the accuracy of predictions of the future time course of variables and of the strength of causal relationships for behavior problems. Cross-sectional, longitudinal, and time series research designs are prone to inferential errors because they often fail to consider the dynamic time course functions of variables. The value of a variable (its stale) coupled with the current direction and rate of change of the variable (its phase), at a single measurement point, is its phase state. Equal state values across persons on a variable dimension does not mean that those persons are in equal phases on that variable dimension.

Treatment of N(2),N(6)-bis(6-acrylamidopyridin-2-yl)pyridine-2,6-dicarboxamide with benzimidazole gives the acyclic aza-Michael addition product N(2),N(6)-bis(6-(3-(1H-benzo[d]imidazol-1-yl)propanamido)pyridin-2-yl)pyridine-2,6-dicarboxamide (2). The macrocycle N(1),N(7)-pyridine-2,6-dimethyl-N(2),N(6)-bis(6-(3-(1H-benzo[d]imidazol-1-yl)propanamido)pyridin-2-yl)pyridine-2,6-dicarboxamide dibromide ([H(2)L(2)]Br(2)) is formed through the double alkylation of 2 with 2,6-bis(bromomethyl)pyridine. The imidazole analogues of 2 and [H(2)L(2)]Br(2) (1 and [H(2)L(1)]Br(2), respectively) have also been prepared. Mercuration of the two benzimidazolium groups in [H(2)L(2)]Br(2) with mercury(II) acetate in the presence of [N(CH(3))(4)](2)[HgBr(4)] proceeds to give [HgL(2)][HgBr(4)] in good yield. The ability of [HgL(2)][HgBr(4)] to readily partake in transmetallation reactions is demonstrated by the reaction that occurs with PdCl(2)(COD) to form [PdClL(2)][PF(6)]. The structures of 2, [HgL(2)][HgBr(4)] and [PdClL(2)][PF(6)] have been determined.

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