Correlating axial and equatorial ligand field effects to the single-molecule magnet performances of a family of dysprosium bis-methanediide complexes

Treatment of the new methanediide–methanide complex [Dy(SCS)(SCSH)(THF)] (1Dy, SCS = {C(PPh₂S)₂}²⁻) with alkali metal alkyls and auxillary ethers produces the bis-methanediide complexes [Dy(SCS)₂][Dy(SCS)₂(K(DME)₂)₂] (2Dy), [Dy(SCS)₂][Na(DME)₃] (3Dy) and [Dy(SCS)₂][K(2,2,2-cryptand)] (4Dy). For further comparisons, the bis-methanediide complex [Dy(NCN)₂][K(DB18C6)(THF)(toluene)] (5Dy, NCN = {C(PPh₂NSiMe₃)₂}²⁻, DB18C6 = dibenzo-18-crown-6 ether) was prepared. Magnetic susceptibility experiments reveal slow relaxation of the magnetisation for 2Dy–5Dy, with open magnetic hysteresis up to 14, 12, 15, and 12 K, respectively (∼14 Oe s⁻¹). Fitting the alternating current magnetic susceptibility data for 2Dy–5Dy gives energy barriers to magnetic relaxation (U_eff) of 1069(129)/1160(21), 1015(32), 1109(70), and 757(39) K, respectively, thus 2Dy–4Dy join a privileged group of SMMs with U_eff values of ∼1000 K and greater with magnetic hysteresis at temperatures >10 K. These structurally similar Dy-components permit systematic correlation of the effects of axial and equatorial ligand fields on single-molecule magnet performance. For 2Dy–4Dy, the Dy-components can be grouped into 2Dy–cation/4Dy and 2Dy–anion/3Dy, where the former have almost linear C Dy C units with short average Dy C distances, and the latter have more bent C Dy C units with longer average Dy C bonds. Both U_eff and hysteresis temperature are superior for the former pair compared to the latter pair as predicted, supporting the hypothesis that a more linear axial ligand field with shorter M–L distances produces enhanced SMM properties. Comparison with 5Dy demonstrates unusually clear-cut examples of: (i) weakening the equatorial ligand field results in enhancement of the SMM performance of a monometallic system; (ii) a positive correlation between U_eff barrier and axial linearity in structurally comparable systems.

Studies on equatorial donor and C Dy C angle variation effects on energy barriers to the slow relaxation of magnetisation are reported.     

Magnitude Estimations for Line Bisection Under Lateral Visuo-Spatial Neglect

Human subjects can bisect a line, with error, even when they have neglect on one side. How this skill, even though inefficient, can be represented in nonlinear psychophysical theory is explored here. A problem for previous theoretical explanations of lateral neglect bisection, where the errors of bisection are reversed in sign for brain-damaged subjects, when very short lines are used as stimuli, is shown not in fact to be a problem for N(onlinear) P(sychophysical) D(ynamics) theory at all, but is exactly what is expected to arise when sensitivities are biassed on one side. It is suggested that an imbalance in channel inputs in a nonlinear system representation has results which do not follow from a more conventional connectionist approach.     

Confidence Judgments for Discriminations in Nonlinear Psychophysics

Psychophysical tasks requiring stimulus discrimination frequently report underconfidence; subjects think they are doing less accurately at discrimination or identification than is the case, measured in terms of probabilities of correct performance. An investigation to see if underconfidence is predictable from the intrinsic nonlinearities of the psychophysics, without assuming that confidence itself is a subjective analogue of a frequentist probability of correct identification, is explored using the algebra of cascaded nonlinear psychophysics previously developed.     

Herbart and “Psychological Research on the Strength of a Given Impression”

Herbart in 1812 published an analysis of sensory process formation, using differential equations, and attempted to relate within the same model considerations of upper and lower limits of sensory intensity, and the time course of process evolution within those limits. The analysis he proposed anticipates later psychophysics by at least half a century. It is perhaps the earliest example of a formal nonlinear dynamical treatment in theoretical psychology.     

Multistable switching series in chaotic nets

Examples of conscious and interpretable responses that have two or more forms alternating to the same stimuli have been known for centuries, and methods of describing how such situations arise have evolved in biological science. When switches between transient, perceptual or cognitive responses can occur and are mixed serially within time series exhibiting local terminal stability, then patterns arise where psychological data series are too brief to analyse empirically, and neurophysiological data and mathematical simulation are necessary. Modelling such conditions can be approached by using one modified Markov matrix, which we illustrate if we allow some singularities to exist in the dynamics. As soon as networks cease to be homogeneous and have a number of attractors present and operate with different local structures, then one or more response patterns may potentially exist at the same time. The patterns may be addressed within the behavioural dynamics by incorporating in turn very short transients that can be voluntary or involuntary, in sensory and cognitive data. Related software work for modelling, employing hierarchical Dirichlet structures projected into hidden Markov matrices is noted.     

Silyl‐Phosphino‐Carbene Complexes of Uranium(IV)

Unprecedented silyl‐phosphino‐carbene complexes of uranium(IV) are presented, where before all covalent actinide–carbon double bonds were stabilised by phosphorus(V) substituents or restricted to matrix isolation experiments. Conversion of [U(BIPM^TMS)(Cl)(μ‐Cl)₂Li(THF)₂] ( 1 , BIPM^TMS=C(PPh₂NSiMe₃)₂) into [U(BIPM^TMS)(Cl){CH(Ph)(SiMe₃)}] ( 2 ), and addition of [Li{CH(SiMe₃)(PPh₂)}(THF)]/Me₂NCH₂CH₂NMe₂ (TMEDA) gave [U{C(SiMe₃)(PPh₂)}(BIPM^TMS)(μ‐Cl)Li(TMEDA)(μ‐TMEDA)_0.5]₂ ( 3 ) by α‐hydrogen abstraction. Addition of 2,2,2‐cryptand or two equivalents of 4‐N,N‐dimethylaminopyridine (DMAP) to 3 gave [U{C(SiMe₃)(PPh₂)}(BIPM^TMS)(Cl)][Li(2,2,2‐cryptand)] ( 4 ) or [U{C(SiMe₃)(PPh₂)}(BIPM^TMS)(DMAP)₂] ( 5 ). The characterisation data for 3 – 5 suggest that whilst there is evidence for 3‐centre P?C?U π‐bonding character, the U=C double bond component is dominant in each case. These U=C bonds are the closest to a true uranium alkylidene yet outside of matrix isolation experiments.     

A direct complex stress function approach for modelling stiffened panels containing multiple site damage

The analysis of stiffened panel structures containing multiple site damage (MSD) is addressed through the complex variable method, in association with the requirement for displacement compatibility. The method is extended by replacing the usual single crack stress and displacement functions by those for a series of arbitrary straight collinear cracks which are used to model exactly the main and secondary crack damage in the sheet. It is shown that the problem can be reduced to a system of linear equations for the unknown forces at the attachment points between the sheet and the stiffener from which the stress intensity factor of the collinear cracks can be determined. The stress intensity factor and the attachment force distribution are determined for several configurations and compared with those from numerically based approaches.