Assessment of density functionals for the high-spin/low-spin energy difference in the low-spin iron(II) tris(2,2'-bipyridine) complex.

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.     

Single-atom test of all-atom empirical potentials: Fe in myoglobin

The measured Fe vibrational density of states in deoxy-myoglobin, obtained from nuclear resonance vibrational spectroscopy, is compared to results from a normal-mode analysis using an all-atom empirical potential. Substantial disagreement reveals that for this one atom, the empirical potential does not accurately describe the actual forces. A Green function technique is developed to calculate the iron vibrational spectrum of deoxy-myoglobin by coupling the independently calculated heme and globin normal modes; nonbonded interactions between the heme molecule and the protein are essential for a good fit to the measurements. A projection of the eigenvectors from this potential onto the displacements induced by binding of CO demonstrates that normal modes over a broad range centered around 50-150 cm(-1) may drive the ligand-induced structural changes.     

An analysis of Markovian model microfield methods for stark broadening

Stark broadening theories which concentrate on the statistics of the plasma electric microfield rather than the dynamics of collisions have come to be known as Model Microfield Methods. In the present paper we present an analysis of Stark broadening problems based on Markovian model microfield statistics. Our derivation permits an easy comparison with traditional Stark broadening theories such as the impact and unified theories; this comparison is used to clarify the physical nature of the approximations employed by Markovian models. The strengths and weaknesses of various models are discussed, emphasizing the kangaroo process of Brissaud and Frisch, and methods are suggested for improving the current model microfield approach.     

Intersections among Steiner systems

A Steiner system S(l, m, n) is a system of subsets of size m (called blocks) from an n-set S, such that each d-subset from S is contained in precisely one block. Two Steiner systems have intersection k if they share exactly k blocks. The possible intersections among S(5, 6, 12)'s, among S(4, 5, 11)'s, among S(3, 4, 10)'s, and among S(2, 3, 9)'s are determined, together with associated orbits under the action of the automorphism group of an initial Steiner system. The following are results: (i) the maximal number of mutually disjoint S(5, 6, 12)'s is two and any two such pairs are isomorphic; (ii) the maximal number of mutually disjoint S(4, 5, 11)'s is two and any two such pairs are isomorphic; (iii) the maximal number of mutually disjoint S(3, 4, 10)'s is five and any two such sets of five are isomorphic; (iv) a result due to Bays in 1917 that there are exactly two non-isomorphic ways to partition all 3-subsets of a 9-set into seven mutually disjoint S(2, 3, 9)'s.     

Group contribution method for the swelling behavior of thermo‐responsive hydrogels

A group contribution method is introduced to describe the swelling behavior of thermo‐sensitive hydrogel systems. The accuracy of group contribution calculations is strongly dependent on the choice of thermodynamic model. Therefore, we revise the modified double lattice (MDL) model and develop a new expression for the interaction energy parameter using the association theory of Sanchez to take into account complex polymer/solvent mixing. The net Helmholtz energy for a hydrogel is established by combining the revised MDL model and modified Flory–Rehner elastic model. Group parameters are generated by fitting to experimental swelling data from both homopolymer and copolymer gel systems. The effect of salt on the volume phase transition is modeled by introducing an additional salt‐specific parameter to investigate various stimuli‐response swelling behavior. Calculated swelling equilibria using the new group contribution method shows excellent agreement with experimental data and various stimuli‐response volume phase transitions. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 455–463     

Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback

The paper presents analytical and numerical studies of the primary resonance and the 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay. By using the method of multiple scales, the first order approximations of the resonances are derived and the effect of time delay on the resonances is analyzed. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. In order to numerically solve the problem of history dependence prior to the start of excitation, the concepts of the Poincaré section and fixed points are generalized. Then, a modified shooting scheme associated with the path following technique is proposed to locate the periodic motion of the delayed system. The numerical results show the efficacy of the first order approximations of the resonances.     

Some new transition probabilities for mercury I

Detailed studies of a pure mercury positive column have allowed us to determine the densities and effective temperatures which characterize the discharge. From this knowledge of the discharge conditions, a series of transition probabilities is derived for 70 lines in the neutral mercury spectrum in the wavelength range 238–1530 nm, including many lines for which transition probabilities have not previously been published.     

A thermochemical investigation of the binding of 12-phosphotungstic acid and chloride ion to bovine serum albumin

The reaction of bovine serum albumin (BSA) and several other proteins with 12-phosphotungstic acid (12-PTA) has been investigated by the method of thermometric enthalpy titration. For all proteins tested the enthalpograms indicate that the reaction proceeds in two stages. The reaction of BSA with 12-PTA has been studied as a function of pH From 1 to 5, of ionic strength from 0.10 to 1.0 M in sodium chloride—hydrochloric acid mixtures and as a function of BSA concentration from 0.50 to 20 g I^?1. The studies indicate that some chloride (or other anion) binds to or condenses on the surface of the positively charged protein. Other chloride ions are present near the protein only as counter ions in order to satisfy electroneutrality considerations. When I 2-PTA is added slowly and continuously to a protein it first reacts with the available positive sites to which no anion is strongly bound thus:

In the second reaction stage the chloride ion is displaced from the protein precipitate by additional 12-PTA.