On the empirical validity of koopmans’ theorem

The application of Koopmans' theorem is investigated within the context of the LCAO interpretation of a general SCF formalism. An empirical criterion for the validity of the assumption of identity of corresponding orbitals in the ion and parent system is discussed. Calculations on He, Li, Be and pyridine are reported.

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Zusammenfassung Die Gültigkeit von Koopmans' Theorem läßt sich mittels eines verallgemeinerten SCF-Formalismus prüfen. Ein Kriterium für das Zutreffen der Annahme, einander entsprechende Einteilchenzustände in Atom und Tochter-Ion seien identisch, wird in diesem Zusammenhang diskutiert. Die Rechnungen sind am Helium, Lithium, Beryllium und Pyridin durchgeführt worden.

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Résumé La validité du théorème de Koopmans dans un formalisme SCF général est étudiée au cadre d'une interprétation LCAO. Un critère empirique pour l'identité des orbitales de l'ion et du système père correspondant est discuté. Nous rapportons des calculs sur He, Li, Be et pyridine.

     

Electronic structure and bonding of the pentasulfur hexanitride (S5N6) molecule

An ab initio version of the Hartree–Fock–Slater method is applied to obtain molecular orbitals and eigenvalues for S₅N₆. The electronic structure, bonding, stability, and electronic spectrum are discussed.     

Hartree Fock instabilities of sulfur-nitrogen ring systems: S2N2

The Hartree-Fock instablities of S₂N₂ are reported and compared with those of S₃N and S₄N. These unsaturated sulfur nitrogen planar rings are π electron rich and although the symmetry adapted HF solutions are singlet stable at the experimental bond lengths they become unstable with only a very modest increase in bond length. The broken symmetry solutions for S₂N₃, S₃N, and S₄N are of planar C_2v type with one of the nitrogens stripped of its π electrons, producing a π hole.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

Fluid percolation in bond-site size-correlated three-dimensional networks

A treatment of sites appropriate to fluid percolation in bond controlled processes results in sensitivity of breakup of the defender to the degree of size-correlation for three-dimensional networks. In strongly correlated lattices network control of invasion yields to a statistical treatment as a result of improved accessibility.     

Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Gaussian Property of the Rings R(X) and R〈X〉

The content of a polynomial f over a commutative ring R is the ideal c(f) of R generated by the coefficients of f. A commutative ring R is said to be Gaussian if c(fg) = c(f)c(g) for every polynomials f and g in R[X]. A number of authors have formulated necessary and sufficient conditions for R(X) (respectively, R?X?) to be semihereditary, have weak global dimension at most one, be arithmetical, or be Prüfer. An open question raised by Glaz is to formulate necessary and sufficient conditions that R(X) (respectively, R?X?) have the Gaussian property. We give a necessary and sufficient condition for the rings R(X) and R?X? in terms of the ring R in case the square of the nilradical of R is zero.     

An N‐Heterocyclic Carbene with a Saturated Backbone and Spatially‐Defined Steric Impact

The synthesis and coordination chemistry of a saturated analogue of a “bulky‐yet‐flexible” N‐heterocyclic carbene (NHC) ligand are described. “SIPaul” is a 4,5‐dihydroimidazol‐2‐ylidene ligand with unsymmetrical aryl N‐substituents, and is one of the growing class of “bulky‐yet‐flexible” NHCs that are sufficiently bulky to stabilize catalytic intermediates, but sufficiently flexible that they do not inhibit productive chemistry at the central metal atom. Here, the synthesis of SIPaul.HCl and its complexes with copper, silver, iridium, palladium, and nickel, and its selenourea, are reported. The steric impact of the ligand is quantified using percent buried volume (% V_bur), whereas the electronic properties are probed and quantified using the Tolman Electronic Parameter (TEP) and δ_Se of the corresponding selenourea. This work shows that despite the often very different performance of saturated versus unsaturated carbenes in catalysis, the effect of backbone saturation on measurable properties is very small.     

Cyanide (13)C NMR hyperfine shifts in paramagnetic cyanide-bridged mixed-valence complexes

Paramagnetic (hyperfine) NMR shifts in the (13)C cyanide bridge and (31)P resonances in a set of mixed valence complexes [(eta(5)-C(5)R(5))Ru(PPh(3))L((13)CN)Ru(NH(3))(5)](n+) (R = H; L = PPh(3), CO, NO(+); R = Me; L = PPh(3)) are sensitive to the extent of intermetallic charge-transfer, and are strongly solvent dependent.