The conformational dependence of vicinal 15N-C-C-H coupling constants in peptides

The conformational dependence of vicinal ¹⁵N-C-C-H coupling in N-methylacetamide as a model compound for coupling in the peptide backbone is investigated by means of the self-consistent perturbation formulation for coupling constants in the INDO approximation of self-consistent-field molecular orbital theory. Because the calculated coupling constants cover a range of at least 7 Hz, they should be useful in determining the ψ angles in peptides. The prediction of opposite signs for gauche and trans coupling indicates the need for sign determination. Non-negligible coupling constants of positive sign for the gauche arrangements are undoubtedly due to a substituent effect involving the lone pair electrons on the nitrogen and the π-electrons of the carbonyl group. Calculated results are compared with the available experimental data.     

Characterization of properly efficient solutions by generalized scalarization methods

A general class of scalarization methods for multiple-objective optimization is presented. It is then shown how the optimal solutions characterize the properly efficient points.     

Planck, the Quantum, and the Historians

In late 1900, the German theoretical physicist Max Planck derived an expression for the spectrum of black-body radiation. That derivation was the first step in the introduction of quantum concepts into physics. But how did Planck think about his result in the early years of the twentieth century? Did he assume that his derivation was consistent with the continuous energies inherent in Maxwellian electrodynamics and Newtonian mechanics? Or did he see the beginnings, however tentative and uncertain, of the quantum revolution to come? Historians of physics have debated this question for over twenty years. In this article, I review that debate and, at the same time, present Planck's achievement in its historical context.     

The geometry, vibrational frequencies, thermochemistry, quadrupole moments and electronic structure of C2Na2: Comparison with C2Li2, C2H2, C2F2 and C2Cl2

The electronic structure of Na₂C₂ is studied using ab initio electronic structure methods and is compared to the companion molecule Li₂C₂. Both the linear D_∞h and planar structures are minima on the ground state potential surface with the planar D_2h conformation being the lowest energy form, similar to Li₂C₂. At the CCSD(t) level the planar form is more stable that the linear by 11.2 kcal/mol as compared with 7.34 kcal/mol for Li₂C₂. Both molecules are significantly ionic. The vibrational frequencies, atomization energy at 0 K, D₀, and the standard enthalpy of formation, are calculated and compared to those of Li₂C₂ as well as HCCH, FCCF and ClCCCl. We find D₀ and to be 331.1 and 84.92 kcal/mol for Li₂C₂ and 298.3 and 93.25 kcal/mol for Na₂C₂. We calibrate these by calculating the same quantities for HCCH, FCCF and ClCCCl.     

The molecular structure of benzoylmethylidynetricobalt nonacarbonyl,C6H5C(O)CCo3(CO)9

The molecular structure of benzoylmethylidynetricobalt nonacarbonyl, C₆H₅C(O)CCo₃(CO)₉, has been determined by single crystal X-ray crystallography. The sample crystallized from heptane forms as monoclinic prisms of spae group P2₁/c, with a = 8.836(2), b = 14.097(10), c = 16.514(3), β = 103.37(6) and z = 2. The final R value was 0.053. The structure is regular and normal but does not aid in explaining the interesting properties of this cluster.     

The Franck-Hertz Experiments, 1911–1914 Experimentalists in Search of a Theory

In 1911, James Franck and Gustav Hertz began a collaboration to investigate the nature of collisions of slow electrons with gas molecules that led to a series of carefully planned and executed experiments, culminating in their discovery of inelastic collisions of electrons with mercury vapor atoms in 1914. This paper tells the story of their collaboration and the eventual reinterpretation of their results as a confirmation of Niels Bohr’s new atomic theory, largely as a result of experiments done in North America during the Great War.