Conformational energy contribution to the heat of solution in polymer–solvent systems. Part II. Experimental results

Heats of solution (ΔH_exp) in solvents of increasing thermodynamic power have been measured for four polymers: polystyrene (PS), poly(vinyl acetate) (PVAc), polyisobutylene (PIB) and polydimethylsiloxane (PDMS). After subtraction from ΔH_exp of an interaction term (calculated by the Hildebrand treatment based on solubility parameters) and the excess volume term, the quantity remaining is interpreted as the conformational energy contribution (ΔU_conf) to the heat of solution. ΔU_conf appears to correlate well with some basic conformational properties of the chain, such as the sign of the temperature coefficient of unperturbed dimensions derived from solution properties, and shows a monotonic behavior with α, the expansion coefficient of the polymer coil in the final solution. Numerical values of ΔU_conf, at least for those cases in which polymer solubility parameters are known with some certainty, are much larger than those evaluated from rubber elasticity experiments (through the experimentally accessible value of the energy component of the force of retraction im simple elongation).     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Experimental anomalies and the conformational theory of polymers

The influence of the size and shape of the torsional potential upon the theoretical temperature coefficient (T? ln 〈r₀²〉/?T) of a polymeric chain was studied. The uncorrelated end-to-end distance equations for isotactic, syndiotactic, and completely atactic chains were differentiated with respect to temperature and the integrals in the resulting equations were evaluated by the method of Gaussian quadrature. The calculated coefficients were found to be nonlinear functions of the energy ratio U_max/KT, where U_max is the maximum potential barrier and possess real roots which critically depend upon the size and shape of the potential. Qualitative anomalies between experiment and theory disappeared when the entire torsional potential was used in the conformational theory. It appears that quantitative agreement between theory and experiment can be established for polymeric materials if the entire potential is used, rotations within bulky side groups are included, and the potential is determined by the method of minimum conformational energy.     

Deformation mechanisms of constrained polymer chains. II. Deformation energetics of tie molecules

Energy-deformation characteristics for the primary T, S, and U conformational units of tie molecules were obtained from the analysis of data generated from a constrained minimization algorithm. Energy-deformation profiles (covering the range from compact equilibrium defect structures to the fully extended chain) are reported for the S₀ and S₁ members of the S_λ family and for the U₀₀ member of the U_mn family. Estimates of the energy content V⁰ and the elastic modulus E were obtained from the computed energy-deformation data in the vicinity of the equilibrium Structure—S₀ → {60°, 180°, ?60°}, V = 1.7 kcal/mole, E = 60 kcal/cm³ [250 × 10¹⁰ dyn/cm²];S₁ → {60°, 180°, 180°, 180°, ?60°}: V = 1.7 kcal/mole, E = 25 kcal/cm³ [100 × 10¹⁰ dyn/cm²]; and U₀₀ → {60°, 180°, 60°, 180°, 60°}: V = 2.7 kcal/mole, E = 80 kcal/cm³ [340 × 10¹⁰ dyn/cm²]. Although the elastic modulus of the U₀₀ unit is comparable to the elastic modulus of the fully extended chain, the highenergy content of this unit (V₀ = 2.7 Kcal/mole) prohibits a significant population and thereby mitigates an appreciable reinforcing effect from this rigid unit. A model for a surrogate force constant is introduced to generalize the results from this study to any member of the S_λ or U_mn family as well as any combination of S_λ and U_mn units. This generalization provides a basis for estimating the deformation characteristics of tie molecules comprised of various populations of these primary conformational building blocks.     

Molecular orbital calculations on the conformation of polypeptides and proteins

Quantum mechanical calculations using the PCILO method have been performed on the tripeptide model CH₃CO-X-Y-NHCH₃. Competition between C₅, C₇, C₁₀ rings and open structures has been investigated through mapping of the whole {φ, Ψ} conformational space and energy minimization. From these results, it appears that the C₁₀ ring simulating the folding named U-turn, involving a hydrogen bond between the i...i + 3 residues, is the most probable structure although not the most stable in energy. The results are used for predicting the frequency of U-turns in proteins, α-chymotrypsin is given as an example.     

Influence of variation of a side chain on the folding equilibrium of a β‐peptide: Limitations of one‐step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94 , 597), the one‐step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔG_F,U of six hepta‐β‐peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔG_F,U values obtained using one‐step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft‐core atoms in the side chain of the fifth residue showed an overall accuracy of about k_BT for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference‐state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ₁ and χ₂ torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔG_F,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one‐step perturbation technique to compute free enthalpies of folding are discussed. © 2013 Wiley Periodicals, Inc.     

Unitary group approach to general system partitioning. I. Calculation of U(n = n1 + n2): U(n1) × u(n2) reduced matrix elements and reduced wigner coefficients

This paper is the first in a series of two directed toward a unitary calculus for group-function-type approaches to the many-electron correlation problem. In this paper we present a complete derivation of the matrix elements of the U(n = n₁ + n₂) generators, for the representations approapriate to many-electron systems, in a basis symmetry adapted to the subgroup U(n₁) × U(n₂). Explicit formulae for the fundamental U(n):U(n₁) × U(n₂) reduced Wigner coefficients, which are needed for the general multishell problem, are also obtained. The symmetry properties of the reduced Wigner coefficients and reduced matrix elements are investigated, and a suitable phase convention is given.     

Assignment of Vibrational Circular Dichroism Cross-Referenced Electronic Circular Dichroism Spectra of Flexible Foldamer Building Blocks: Towards Assigning Pure Chiroptical Properties of Foldamers

Assignment of the most established electronic circular dichroism (ECD) spectra of polypeptides and foldamers is either “evidence based” or relies on the 3D structures of longer oligomers of limited internal dynamics, which are derived from NMR spectroscopy (or X-ray) data. Critics warn that the use of NMR spectroscopy and ECD side by side has severe limitations for flexible molecules because explicit knowledge of conformational ensembles is a challenge. Herein, an old–new method of comparing ab initio computed and measured vibrational circular dichroism (VCD) data is presented to validate both the structures (conf(i)) and their relative weights (c(i)) that make up the conformational ensemble. Based on the array of {conf(i), c(i)}, the pure ECD spectra, g(i)^conf(i), can be ab initio calculated. The reconstructed spectrum Σc(i)g(i)^conf(i) can thus help to assign any experimental ECD counterparts. Herein, such a protocol is successfully applied to flexible foldamer building blocks of sugar β-amino acid diamides. The epimeric pair of the model system was selected because these molecules were conformationally tunable by simple chemical modification, and thus, the robustness of the current approach could be probed. The initial hydrogen bond (NH⋅⋅⋅O) eliminated by N-methylation reorients the amide plain, which influences the chiroptical properties of the foldamer building block; this structural change is successfully monitored by changes to the VCD and ECD transitions, which are now assigned to pure conformers. The current method seems to be general and effective without requiring extensive CPU and spectroscopic resources.     

Unitary group approach to the many-electron problem. III. Matrix elements of spin-dependent Hamiltonians

This is the final paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians. In this paper we derive the reduced matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables a direct evaluation of the matrix elements of spin-dependent Hamiltonians in the spin-orbit basis. An alternative (indirect) method, which employs the use of U(2n) ↓ U(n) × U(2) subduction coefficients, is also discussed.     

Oligonucleotide Analogues with Integrated Bases and Backbone. Part 16

The self‐complementary, ethylene‐linked U*[c_a]A⁽*⁾ dinucleotide analogues 8, 10, 12, 14, 16 , and 18 , and the sequence‐isomeric A*[c_a]U⁽*⁾ analogues 20, 22, 24, 26, 28 , and 30 were obtained by Pd/C‐catalyzed hydrogenation of the corresponding, known ethynylene‐linked dimers. The association of the ethylene‐linked dimers was investigated by NMR and CD spectroscopy. The U*[c_a]A⁽*⁾ dimers form linear duplexes and higher associates (K between 29 and 114M ^?1). The A*[c_a]U⁽*⁾ dimers, while associating more strongly (K between 88 and 345M ^?1), lead mostly to linear duplexes and higher associates; they form only minor amounts of cyclic duplexes. The enthalpy–entropy compensation characterizing the association of the U*[c_x]A⁽*⁾ and A*[c_x]U⁽*⁾ dimers (x=y, e, and a) is discussed.     

High-Entropy Lithium Argyrodite Solid Electrolytes Enabling Stable All-Solid-State Batteries

Superionic solid electrolytes (SEs) are essential for bulk-type solid-state battery (SSB) applications. Multicomponent SEs are recently attracting attention for their favorable charge-transport properties, however a thorough understanding of how configurational entropy (ΔS_conf) affects ionic conductivity is lacking. Here, we successfully synthesized a series of halogen-rich lithium argyrodites with the general formula Li_5.5PS_4.5Cl_xBr_1.5-x (0≤x≤1.5). Using neutron powder diffraction and ³¹P magic-angle spinning nuclear magnetic resonance spectroscopy, the S²⁻/Cl⁻/Br⁻ occupancy on the anion sublattice was quantitatively analyzed. We show that disorder positively affects Li-ion dynamics, leading to a room-temperature ionic conductivity of 22.7 mS cm⁻¹ (9.6 mS cm⁻¹ in cold-pressed state) for Li_5.5PS_4.5Cl_0.8Br_0.7 (ΔS_conf=1.98R). To the best of our knowledge, this is the first experimental evidence that configurational entropy of the anion sublattice correlates with ion mobility. Our results indicate the possibility of improving ionic conductivity in ceramic ion conductors by tailoring the degree of compositional complexity. Moreover, the Li_5.5PS_4.5Cl_0.8Br_0.7 SE allowed for stable cycling of single-crystal LiNi_0.9Co_0.06Mn_0.04O₂ (s-NCM90) composite cathodes in SSB cells, emphasizing that dual-substituted lithium argyrodites hold great promise in enabling high-performance electrochemical energy storage.     

Solid state interaction between V2O5 and MoO3: specific features related to minor vanadia transfer

Vanadia transport, which is a minor reaction flux in the solid state reaction between V₂O₅ and MoO₃, was studied using chemical and neutron activation analyses and electron spectroscopy for chemical analysis. It was found that negligible quantities of vanadia were transferred in a molybdena briquette during the reaction. Vanadia was presumably localized in thin external layers of molybdena grains. The reaction potential difference U _r across a Pt|MoO₃|V₂O₅|Pt cell was studied. It was shown that in this cell U _r was produced at the molybdena briquette and was due to vanadia transport. The U _r value changed with time in two stages. The reaction potential difference U _r was constant (or diminished slightly) at the first stage and dropped abruptly at the second stage. The duration of the first stage depended on the initial thickness of the MoO₃ briquette: the thicker the briquette, the longer the U _r value was nearly constant. Causes and probable mechanisms of U _r generation are discussed in different terms: chemical reaction, variation of a _{O 2} at the boundary between the reaction product and initialoxides, or surface spreading of the minor (V₂O₅ or V₉Mo₆O₄₀) diffusant. The last mechanism, which received the least study in the general case, was shown to be the most probable one for the reaction at hand. Electronic Publication     

Spatial structures of natural sesquiterpenes of the humulene type

The spatial structures of the natural sesquiterpenes -,-, and -humulenes have been studied by the method of molecular mechanics (MM). The conformational states of the 11-membered macrocycle in the humulenes have been analyzed on the basis of calculated figures and x-ray structural results. It has been shown that four conformational states, differing by the mutual positions of the C14 and C15 methyl groups and the C7 and C8 atoms relative to the plane of the macrocycle are characteristic for all humulenes. These conformational states are denoted as₁₄U⁸ ₇,¹⁴U⁸ ₇,₁₄U⁷ ₈, and¹⁴U⁷ ₈. The conformational flexibility of the 11-membered ring in the humulenes has been evaluated.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 40 64 75. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 287–296, May–June, 1997.     

High-order anharmonicity parameters in various representations of the diatomic potential function and exact relations between spectroscopic constants. application to the co molecule

Closed formulae for Born—Oppenheimer anharmonicity parameters a_n in terms of isotopically invariant constants U_mj are derived for Dunham, Simons—Parr—Finlan, Ogilvie—Tipping and Thakkar representations and are applied to the CO molecule. Models for a fit of vibration—rotation and pure rotational transitions based on the exact relations U_mj = f(U_k,o, U_k-1.1) and U_mj = α(U_k,1, U_k,2) are discussed.     

The true diatomic potential as a perturbed Morse function

The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U^t by an analytical function U^a is discussed. The perturbed Morse function is in the form U^a = U^M + ∑b_nyⁿ, where the Morse potential is U^M = Dy², y = 1 ?exp(?;a(r ? r_e)). The problem is reduced to determination of the coefficients b_n so U^a(r) = U^t(r). A standard least-squares method is used, where the number N of b_n is given and the average discrepancy ΔU = |(U^t ? U^a)/U^t| is observed over the useful range of r. N is varied until ΔU is stable. A numerical application to the carbon monoxide X¹∑ state is presented and compared to the results of Huffaker¹ using the same function with N = 9. The comparison shows that the accuracy obtained by Huffaker is reached in one model with N = 5 only and that the best ΔU is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E_v and the rotational constant B_v, for both potentials, shows that the present method gives values of ΔE and ΔB that are smaller than those found by Huffaker. The dissociation energy obtained here is 2.3% from the experimental value, which is an improvement over Huffaker's results. Applications to other molecules and other states show similar results. © 1995 by John Wiley & Sons, Inc.     

Moderately concentrated solutions of polystyrene. II. Integrated-intensity light scattering as a function of concentration,temperature, and molecular weight

Integrated-intensity light scattering data are reported for moderately concentrated solutions of polystyrene in benzene and in cyclopentane. The benzene system is one for which the second virial coefficient A₂ is large; data obtained over the range 0.5 < A₂Mc < 30, with c the polymer concentration, are analyzed in terms of the (extrapolated) intensity at zero angle and the angular dependence of the intensity. The former is discussed in terms of power law representations based on scaling relations, which are found to represent the data. The latter is discussed in terms of the dependence of the chain dimensions on concentration. With cyclopentane, the behavior is similar for temperatures for which A₂ is near its maximum, but for T near either Θ_U or Θ_L, for which A₂ is zero or small, the angular dependence of the scattering is distinctly different, with the intensity exhibiting a maximum as a function of scattering angle.     

Influence of Electrochemical Parameters on the Etching of Macropores in Silicon

The process of formation of macropores in silicon with stationary irradiation and a constant current density during the electrochemical process in dependence on the initial bias on the silicon anode, U ₀, has been studied. Stable formation of macropores began when the bias reached U _c, corresponding to a critical concentration of holes p _c at the silicon–electrolyte interface. The process of macropore formation is unstable with U ₀ > U _c.     

Ex‐Situ Kinetic Investigations of the Formation of the Poly‐Oxo Cluster U38

The ex‐situ qualitative study of the kinetic formation of the poly‐oxo cluster U₃₈, has been investigated after the solvothermal reaction. The resulting products have been characterized by means of powder XRD and scanning electron microscopy (SEM) for the solid phase and UV/Vis, X‐ray absorption near edge structure (XANES), extended X‐ray absorption fine structure (EXAFS), and NMR spectroscopies for the supernatant liquid phase. The analysis of the different synthesis batches, stopped at different reaction times, revealed the formation of spherical crystallites of UO₂ from t=3 h, after the formation of unknown solid phases at an early stage. The crystallization of U₃₈ occurred from t=4 h at the expense of UO₂, and is completed after t=8 h. Starting from pure uranium(IV) species in solution (t=0–1 h), oxidation reactions are observed with a U^IV/U^VI ratio of 70:30 for t=1–3 h. Then, the ratio is inversed with a U^IV/U^VI ratio of 25/75, when the precipitation of UO₂ occurs. Thorough SEM observations of the U₃₈ crystallites showed that the UO₂ aggregates are embedded within. This may indicate that UO₂ acts as reservoir of uranium(IV), for the formation of U₃₈, stabilized by benzoate and THF ligands. During the early stages of the U₃₈ crystallization, a transient crystallized phase appeared at t=4 h. Its crystal structure revealed a new dodecanuclear moiety (U₁₂), based on the inner hexanuclear core of {U₆O₈} type, decorated by three additional pairs of dinuclear U₂ units. The U₁₂ motif is stabilized by benzoate, oxalates, and glycolate ligands.     

Thermal Responsive Ion Selectivity of Uranyl Peroxide Nanocages: An Inorganic Mimic of K+ Ion Channels

An actinyl peroxide cage cluster, Li_48+mK₁₂(OH)_m[UO₂(O₂)(OH)]₆₀ (H₂O)_n (m≈20 and n≈310; U₆₀), discriminates precisely between Na⁺ and K⁺ ions when heated to certain temperatures, a most essential feature for K⁺ selective filters. The U₆₀ clusters demonstrate several other features in common with K⁺ ion channels, including passive transport of K⁺ ions, a high flux rate, and the dehydration of U₆₀ and K⁺ ions. These qualities make U₆₀ (a pure inorganic cluster) a promising ion channel mimic in an aqueous environment. Laser light scattering (LLS) and isothermal titration calorimetry (ITC) studies revealed that the tailorable ion selectivity of U₆₀ clusters is a result of the thermal responsiveness of the U₆₀ hydration shells.