Molecular shape,shape of the geometrically active atomic states,and hybridization

In a recent publication [C. A. Nicolaides and Y. Komninos, Int. J. Quant. Chem. 67 , 321 (1998)], we proposed that in certain classes of molecules the fundamental reason for the formation of covalent polyatomic molecules in their normal shape is to be found in the existence of a geometrically active atomic state (GAAS) of the central atom, whose shape, together with its maximum spin‐and‐space coupling to the ligands, predetermines the normal molecular shape (NMS). The shape of any atomic state was defined as that which is deduced from the maxima of the probability distribution ϱ(cos θ₁₂) of the angle formed by the position vectors of two electrons of an N‐electron atom. Because the shape of the GAAS determines the NMS and because the NMS allows the construction of corresponding hybrid orbitals, we examined and discovered the connection between the GAAS shape and Pauling's function for the strength of two equivalent orthogonal orbitals at angle θ₁₂ with one another. It is shown that the computed ϱ(cos θ₁₂) of the GAAS can be cast in a form which allows the deduction of the composition of the hybrid orbitals of maximum spin states with configurations sp³, sp³d⁵, sp³d⁵f⁷, slⁿ, s²lⁿ and the demonstration of the central atom's tendency to form bonds in directions which coincide with the nodal cones of the hybrid bond orbitals. These results not only reinforce the validity of the theory as to the fundamental “mechanism” for the formation in the normal shape of coordination compounds and covalently bonded polyatomic molecules, but also provide the justification for the relevance and importance of the hybridization model. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 25–34, 1999     

Adaptive hybrid (prismatic–tetrahedral) grids for incompressible flows

Hybrid grids consisting of prisms and tetrahedra are employed for the solution of the 3-D Navier–Stokes equations of incompressible flow. A pressure correction scheme is employed with a finite volume–finite element spatial discretization. The traditional staggered grid formulation has been substituted with a collocated mesh approach which uses fourth-order artificial dissipation. The hybrid grid is refined adaptively in local regions of appreciable flow variations. The scheme operations are performed on an edge-wise basis which unifies treatment of both types of grid elements. The adaptive method is employed for incompressible flows in both single and multiply-connected domains. © 1998 John Wiley & Sons, Ltd.     

Geometrically active atomic states and the formation of molecules in their normal shapes

We present a theory of molecular formation according to which the shape of polyhedral or coordination compounds is fixed to a very good approximation by the shape of a particular state (or states) of the central atom, which is activated by spin and spacial coupling of optimal strength between this state, called the geometrically active atomic state (GAAS) and the state of the ligands. For a molecule with a central atom, spacial coupling of optimal strength, means that the shape of the GAAS fixes the position of the ligands according to the maximum overlap principle of the Heitler–London, Slater, and Pauling theory of covalent bonding, whereby much of the energy lowering from the free atom limit is obtained by the maximization of the contribution of the exchange integrals. Hence, a direct causal relationship between the shape of the GAAS and the shape of the molecular state at equilibrium seems to exist. This relationship implies a picture of diabatic connection between the geometrically asymptotic region and the equilibrium region, which is driven by the coupled GAAS and provides the “why” of molecular shape. Since the latter is fixed by the shape of the GAAS (in cases of electronic complexity or of molecular instability it is possible that more than one GAAS contribute simultaneously), prediction of the shape of certain large systems can be made based on the a priori recognition of the corresponding GAAS. The concept of the shape of atomic states defined and computed quantum mechanically from the probability distribution ϱ(cos θ₁₂) of the angle θ₁₂ that the position vectors of two electrons form in the given atomic state. Specifically, it is deduced from the distribution's maxima which provide the most probable values of θ₁₂. As shown previously [Y. Komninos and C. A. Nicolaides, Phys. Rev. A 50 , 3782 (1994)], ϱ(cos θ₁₂) is obtainable directly from the state-specific expression for the Coulomb interaction, where the R^k integrals are replaced by Legendre polynomials P_k, multiplied by normalization constants and radial overlaps. The theory is demonstrated by explaining the shape of BeH₂, BH₂, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, SF₆, and TiH₄ in terms of the shapes of the following GAAS. Be: 2s2p ³P⁰, B: 2s2p^{2 4}P, C: 2s2p^{3 5}S⁰, Si: 3s3p^{3 5}S⁰, O: 2s2p^{5 3}P⁰, S: 3s²3p³3d ³P⁰, N: 2s2p^{4 4}P, P: 3s3p³3d ⁴P⁰, S: 3s3p³3d^{2 7}F⁰, and Ti: 3d²4s4p ⁵G⁰. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 321–328, 1998     

CO2 laser excitation of triethylsilane: Time resolved luminescence of diethylsilyl radical

The infrared multiphoton excitation of triethylsilane in the gas phase, with a pulsed CO₂ laser at high intensities (I > 700 MW/cm²), produced an intense luminescence. The spectrum and time profile of this luminescence was studied as a function of pressure, and laser frequency. The radiative lifetime of this emission was 357 ± 10 ns, and the quenching rates by Cl₂ and NO were determined from lifetime measurements. A reasonable mechanism for the interpretation of this luminescence involves the initial infrared multiphoton decomposition of triethylsilane, followed by the secondary infrared multiphoton excitation of the primary photofragment diethylsilyl radical, which subsequently undergoes relaxation to an excited electronic state. The addition of O₂ resulted in a new chemiluminescence at shorter wavelengths, which corresponds to the SiO* chromophore group. © 1994 John Wiley & Sons, Inc.     

Vibrational relaxation of highly excited molecules: VV transfer from SF6 to N2O

Vibrational energy transfer from SF₆ to N₂O was studied as a function of SF₆ vibrational energy. The intensity, rise time and decay time of N₂O fluorescence increased monotonically with the level of donor excitation. The observations are consistent with a mechanism that is not mode specific, with donor VT relaxation faster than intermolecular VV transfer.     

Independent highly sensitive characterization of asparagine deamidation and aspartic acid isomerization by sheathless CZE‐ESI‐MS/MS

Amino acids residues are commonly submitted to various physicochemical modifications occurring at physiological pH and temperature. Post‐translational modifications (PTMs) require comprehensive characterization because of their major influence on protein structure and involvement in numerous in vivo process or signaling. Mass spectrometry (MS) has gradually become an analytical tool of choice to characterize PTMs; however, some modifications are still challenging because of sample faint modification levels or difficulty to separate an intact peptide from modified counterparts before their transfer to the ionization source. Here, we report the implementation of capillary zone electrophoresis coupled to electrospray ionization tandem mass spectrometry (CZE‐ESI‐MS/MS) by the intermediate of a sheathless interfacing for independent and highly sensitive characterization of asparagine deamidation (deaN) and aspartic acid isomerization (isoD). CZE selectivity regarding deaN and isoD was studied extensively using different sets of synthetic peptides based on actual tryptic peptides. Results demonstrated CZE ability to separate the unmodified peptide from modified homologous exhibiting deaN, isoD or both independently with a resolution systematically superior to 1.29. Developed CZE‐ESI‐MS/MS method was applied for the characterization of monoclonal antibodies and complex protein mixture. Conserved CZE selectivity could be demonstrated even for complex samples, and foremost results obtained showed that CZE selectivity is similar regardless of the composition of the peptide. Separation of modified peptides prior to the MS analysis allowed to characterize and estimate modification levels of the sample independently for deaN and isoD even for peptides affected by both modifications and, as a consequence, enables to distinguish the formation of l ‐aspartic acid or d ‐aspartic acid generated from deaN. Separation based on peptide modification allowed, as supported by the ESI efficiency provided by CZE‐ESI‐MS/MS properties, and enabled to characterize and estimate studied PTMs with an unprecedented sensitivity and proved the relevance of implementing an electrophoretic driven separation for MS‐based peptide analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

On a new edge function on complete weighted graphs and its application for locating Hamiltonian cycles of small weight

In this paper, we define a new combinatorial function on the edges of complete weighted graphs. This function assigns to each edge of the graph the sum of the weights of all Hamiltonian cycles that contain the edge. Since this function involves the factorial function, whose exact calculation is intractable due to its superexponential asymptotic rate of increase, we also introduce a normalized version of the function that is efficiently computable. From this version, we derive an upper bound to the weight of the minimum weight Hamiltonian cycle of the graph based on the weights of the graph edges. Then we investigate the possible algorithmic applications of this normalized function using the Nearest Neighbor Heuristic and a smallest edge first heuristic. As evidence for its applicability, we show that the use of this function as a criterion for the selection of the next edge, improves the performance of both heuristics for approximating the minimum weight Hamiltonian cycles in Euclidean plane graphs. Moreover, our experimental results show that the use of the function is more suitable with the structure of the smallest edge first heuristic since it provides a solution closer to the best known solution of known hard TSP instances but in \(O(n^3)\) time.     

Probing the Mechanism of Allylic Substitution of Morita–Baylis–Hillman Acetates (MBHAs) by using the Silyl Phosphonite Paradigm: Scope and Applications of a Versatile Transformation

A P?C bond‐forming reaction between silyl phosphonites and Morita–Baylis–Hillman acetates (MBHAs) is explored as a general alternative towards medicinally relevant β‐carboxyphosphinic structural motifs. Conversion rates of diversely substituted MBHAs to phosphinic acids 9 or 14 that were recorded by using ³¹P NMR spectroscopy revealed unexpected reactivity differences between ester and nitrile derivatives. These kinetic profiles and DFT calculations support a mechanistic scenario in which observed differences can be explained from the “lateness” of transition states. In addition, we provide experimental evidence suggesting that enolates due to initial P‐Michael addition are not formed. Based on the proposed mechanistic scenario in conjunction with DFT calculations, an interpretation of the E/Z stereoselectivity differences between ester and nitriles is proposed. Synthetic opportunities stemming from this transformation are presented, which deal with the preparation of several synthetically capricious phosphinic building blocks, whose access through the classical P‐Michael synthetic route is not straightforward.