The Spirit Is Willing: Nonlinearity, Bifurcations, and Mental Control

In recent years there has been considerable interest in the construction of nonlinear models of the dynamics of human behavior. In this exploratory article we argue that attempts at controlling problematic thoughts, emotions, or behaviors can lead to nonlinearity in mental/behavioral dynamics. We illustrate our model by fitting threshold autoregression models to self-recorded time series of the daily highs in intensity of anxiety and obsessive ruminations, kept by an individual in therapy for this problem. In our discussion, we raise the possibility that bifurcations that occur in this nonlinear model may offer insight into mental control paradoxes.     

Peak area measurements of cross-polarization magic-angle-spinning 13C-NMR spectra of crosslinked polystyrenes

Cross-polarization magic-angle-spinning ¹³C-NMR spectra of polystyrenes crosslinked with 1–20% of methine vinyl carbon ¹³C-labeled p-divinylbenzene and of Friedel–Crafts crosslinked poly(chloromethylstyrene)s have been obtained with both glossy solid and CDCl₃-swollen gel samples. The spectra of natural abundance, uncrosslinked, glassy polystyrene, and the spectra of the solid labeled networks give aliphatic and aromatic peak areas only 0.7 times as large per ¹³C atom as that of poly(oxymethylene). Similarly the crosslinked poly(chloromethylstyrene) gave peak areas about 0.6 times that of internal poly(oxymethylene). The labeled gels give peak areas 0.2–0.6 times as large per ¹³C atom as glassy polystyrene, and the peak areas in spectra of gels increase with the divinylbenzene content     

Kinetics of the thermal unimolecular decomposition of hex-1-ene-3-yne. Heat of formation and resonance stabilization energy of the 3-ethenylpropargyl radical

The thermal unimolecular decomposition of hex-1-ene-3-yne (HEY) has been investigated over the temperature range 949–1230 K using the technique of very low-pressure pyrolysis (VLPP). One reaction pathway is the expected C₅? C₆ bond fission to form the resonance-stabilized 3-ethenylpropargyl radical. There is a concurrent process producing molecular hydrogen which probably occurs via the intermediate formation of hexatrienes and cyclohexa-1,3-diene. RRKM calculations yield the extrapolated high-pressure rate parameters at 1100 K given by the expressions 10^16.0±0.3 exp(?300.4 ± 12.6 kJ mol^?1/RT) s^?1 for bond fission and 10^13.2+0.4 exp(?247.7 ± 8.4 kJ mol^?1/RT) for the overall formation of hydrogen. The A factors were assigned from the results of previous studies of related alkynes, alkenes, and alkadienes. The activation energy for the bond fission reaction leads to ΔH [H₂CCHCC?H₂] = 391.9, DH [H₂CCHCCCH₂? H] = 363.3, and a resonance stabilization energy of 56.9 ± 14.0 kJ mol^?1 for the 3-ethenylpropargyl radical, based on a value of 420.2 kJ mol^?1 for the primary C? H bond dissociation energy in alkanes. Comparison with the revised value of 46.6 kJ mol^?1 for the resonance energy of the unsubstituted propargyl radical indicates that the ethenyl substituent (CH₂?CH) on the terminal carbon atom has only a small effect on the propargyl resonance energy. © John Wiley & Sons, Inc.     

Molecular orbital theory of the properties of inorganic and organometallic compounds. 3. STO-3G basis sets for first- and second-row transition metals

STO -3G minimal basis sets for first- and second-row transition metals have been formulated and applied to the calculation of equilibrium geometries for a variety of inorganic systems, metal carbonyls, and organometallic compounds. While the overall level of agreement with experiment is not as good as that previously noted for main-group compounds, most trends and many subtle features in geometries are reproduced.     

ALKALINE QUENCHING OF BACTERIORHODOPSIN TRYPTOPHANYL FLUORESCENCE: EVIDENCE FOR AQUEOUS ACCESSIBILITY OR A HYDROGEN-BONDED CHAIN

Abstract— Comparison between Trp fluorescence yields of membrane-bound bacteriorhodopsin (BR) and retinylidene-free bacterioopsin (BO) is consistent with a model in which all eight Trp residues are active fiuorophores in the latter, while the emission of all but two residues in the former is lost by energy transfer to retinal. The visible chromophore of BR is progressively bleached with increasing pH. Up to pH 12 this bleaching is reversed on reneutralization; but above this the change is irreversible with the appearance of a new absorption band characteristic of free retinal. Emission yields for both proteins decrease with increasingly alkaline pH in a manner typical of energy transfer to weakly-fluorescent tyrosinate. The limiting yields, reached at a pH corresponding to that producing irreversible bleaching of the visible chromophore, agree with an integral value of one remaining active Trp fluorophore in BR and between one and two in BO and show that the bulk of Trp are within the 11 Å Förster energy-transfer distance of Tyr accessible to OH⁻. Current models of the native protein structure of BR arrange the polypeptide chain primarily in a bundle of seven helical segments with axes perpendicular to the lipid bilayer plane and with buried polar residues, including Trp and Tyr, located at intrahelical surfaces. An interpretation of the observed accessibility of buried Tyr to OH⁻ is that an aqueous region exists within the protein structure. Moreover, this putative aqueous region must be close to the retinylidene chromophore and thus may be associated with the light-driven ion transport system. The results are also compatible with energy transfer to internal Tyr residues which are connected via a chain of phenolate hydrogen bonds to a surface Tyr.     

Dye laser excitation of the fluorosulfate radical. Totally symmetric upper state fundamentals

Upper state vibronic levels associated with totally symmetric fundamentals of the fluorosulfate radical were populated by means of dye laser excitation. The analysis of the resulting fluorescence confirmed the assignment of these levels. Theoretical intensities using the Green's function approach to vibronic coupling were calculated and compared to the experimental values.     

The magnetic susceptibilities of cobaltocene and chromocene

The magnetic susceptibilities of cobaltocene and chromocene have been measured between 83 and 293 K; for cobaltocene the results suggest an appreciable orthorhombic splitting of the ²∏(σ²πδ⁴ ground state, whilst for chromocene the data provide further support for the ³Δ(σδ³) ground state previously deduced.     

Stereochemically controlled synthesis of unsaturated acids via diphenylphosphinoyl (Ph2PO) -ketoacids

Acylation of phosphine oxide anions with derivatives of cyclic anhydrides or oxidative cleavage of cyclic allyl phosphine oxides gives Ph₂PO-ketoacids: reduction, separation of diastereoisomers, and completion of the Horner-Wittig reaction gives single isomers ($\text{E}$) or ($\text{Z}$) of unsaturated acids.