The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

A new look at the reduced-gradient-following path

 The mathematical structure of the reduced-gradient-following (RGF) path introduced by Quapp et al. (1988 J. Comput. Chem. 19:1087) is reviewed and analyzed. We report two new algorithms to evaluate the RGF path. The RGF path is also compared mathematically and computationally with the gradient extremals path. An example of the evaluation of the RGF path is also reported. Received: 21 May 2001 / Accepted: 27 September 2001 / Published online: 9 January 2002     

Solid-Solute Phase Equilibria in Aqueous Solutions XIV [1]. Thermodynamic Analysisof the Solubility of Hellyerite in Water

Summary.  The solubility of hellyerite, NiCO₃ · 6H₂O, in water was studied at different temperatures. From the experimental data obtained, a preliminary set of the thermodynamic quantities Δ_f G ^⊖, Δ_f H ^⊖, and S ^⊖ for hellyerite was derived using the ChemSage optimizer routine. Received January 16, 2001. Accepted January 18, 2001     

Comparison of extraction techniques for gas chromatographic determination of volatile carbonyl compounds in alcohols

Two extraction procedures, i.e. conventional liquid-liquid extraction (LLE) and liquid solid-phase microextraction (SPME) for extraction of the oximes formed after derivatization of carbonyl compounds with o-(2,3, 4,5,6-pentafluorobenzyl) hydroxylamine (PFBHA) in alcoholic solutions have been compared. The limit of detection for LLE followed by GC-ECD determination of C₁–C₆ was in the range of 0.23–3.3 μg/L, whereas for liquid SPME 0.005–0.33 μg/L. Both methods elaborated can be applied to the determination of carbonyl compounds present in spirits and alcoholic beverages. Received: 26 September 2000 / Revised: 14 January 2001 / Accepted: 16 January 2001     

Relativistic virial theorem for atoms

A relativistic virial theorem is derived for atoms in a general manner. The virial ratio consists of the usual V/T term and a correction term W/T, where T, V, and W are the kinetic energy, the potential energy, and correction terms, respectively. Explicit forms of W are presented for four specific nuclear potential models. Numerical calculations for a uniform nuclear charge model show that the magnitude of the correction term W/T increases with increasing atomic numbers and that it modifies the ratio V/T considerably for atoms with large atomic numbers in particular. Received: 21 November 2000 / Accepted: 8 January 2001 / Published online: 3 April 2001     

How autoverification through the expert system VALAB can make your laboratory more efficient

For over 10 years now various expert systems have been on the market, but very few have reached the level of performance of Validation Assistée pour les Laboratoires d’Analyses Biologiques (VALAB). Over 25,000 rules are combined through an inference engine to reproduce human reasoning in the complex ”biological validation” process. After a review of the product concept and its development program, we will see how this ”intelligent” tool can bring quality to clinical laboratories, from a production as well as legislation point of view. With more than 140 laboratories using VALAB in Europe in daily routines, our designer and vendor experience in installation, maintenance, upgrading, reliability, efficiency, and liability is excellent. Received: 9 October 2001 Accepted: 22 July 2002 Presented at the European Conference on Quality in the Spotlight in Medical Laboratories, 7–9 October 2001, Antwerp, Belgium Correspondence to E. Rogari     

Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Theoretical study of group 11 metal–silonyl complexes: M–SiO and M–(SiO)2 (M = Cu, Ag, or Au)

 The spectroscopic properties of M–SiO and M–(SiO)₂ (1–1 and 1–2 complexes with M = Cu, Ag, or Au) have been theoretically studied. It has been shown that both M–SiO and M–(SiO)₂ compounds in their ground state are bent with a metal–Si bonded structure. The calculated M(ns) spin density agrees well with the electron spin resonance experimental data. From a topological analysis, it has been shown that a rather large charge transfer occurs from the metal towards the SiO moiety, and that the M–Si bond energy correlates with the electron density located at the M–Si bond path (bond critical point). Received: 6 July 2000 / Accepted: 11 October 2000 / Published online: 19 January 2001     

Gradient of the ZAPT2 energy

 An explicit expression for the analytical first derivative of the Z-averaged perturbation theory taken to second order energy, due to Lee and Jayatilaka, is presented for application to high-spin systems described by a restricted open-shell Hartree–Fock wavefunction. The use of frozen core orbitals is incorporated into the derivation. Received: 23 April 2001 / Accepted: 31 August 2001 / Published online: 9 January 2002     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Intercomparison of suspended particles sampling methodologies

Sampling and sample preparation/processing are known to carry large, but typically unknown uncertainty contribution to the final analytical data and there is a lack of qualitative and quantitative data on the comparability of results achieved by the different sampling methods. To this end, an intercomparison programme was founded by the European Commission, in which different institutions participated using their own ”in-situ” methods (”ANPA”, ”EDF” and ”MIDIYA”) for collection of water and suspended material in freshwater bodies. The main criterion for this intercomparison was the agreement among the ¹³⁷Cs activity concentrations in the dissolved phase (Bq l^–1), those associated with the suspended particles (Bq g^–1) and the concentrations of total suspended material (TSM) in the water body (mg l^–1). The results show that the sampling systems provide TSM concentration results with low accuracy; on the contrary, they are recommended for the determination of ¹³⁷Cs activity concentration in the dissolved phase. Concerning the determination of radiocaesium activity concentration in the suspended particles, the ”EDF” system provides the more reliable results. Received: 10 December 2001 Accepted: 4 March 2002     

Prediction of DNA far-IR absorption spectra based on normal mode analysis

 We present a computational method which couples normal mode analysis in internal coordinates of a molecule with very far IR spectroscopy. The analytical expression for the dependence of IR absorption on frequency incorporates frequencies and optical activities of each normal mode. In order to predict far-IR spectra of a molecule we evaluate the optical activity of each normal mode. This optical activity is determined by the vibration amplitude of the dipole moment produced by a normal mode. We calculated normal modes of DNA double-helical fragments (dA)₁₂ · (dT)₁₂ and (dA-dT)₆ · (dA-dT)₆ and evaluated their optical activities. These were found to be very sensitive to the DNA base-pair sequence. The positions of the resonance peaks in the calculated absorption spectrum of (dA)₁₂ · (dT)₁₂ are in a good agreement with those obtained by Fourier transform IR spectroscopy (Powell JW et al. 1987 Phys Rev A 35: 3929–3939). Received: 20 June 2000 / Accepted: 5 January 2001/ Published online: 3 May 2001     

Energy decomposition in the topological theory of atoms in molecules and in the linear combination of atomic orbitals formalism: a note

 It is shown that the molecular energy calculated at the self-consistent-field level can be strictly expressed as a sum of one- and two-atom energy components in the framework of Bader's topological theory of atoms in molecules (AIM). The expressions of our recent “chemical energy component analysis” can be obtained from the AIM ones as some linear combination of atomic orbitals mappings of the integrations over the atomic basins. Received: 15 June 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Hybrid materials based on vanadium pentoxide intercalation complexes

Neutral macrocyclic compounds (crown ethers and cryptands) and charged molecular species (alkylammonium iodides) were intercalated into vanadium oxide xerogel (V₂O₅ · nH₂O) to study their influence on the electrical behaviour of this inorganic 2D host lattice. Treatment with alkyl or arylammonium iodide solutions produced the intercalation of organic cations accompanied by the reduction of a fraction of V (V) to V (IV). Characterisation by different techniques allowed the postulation of the interlayer arrangement of the guest species. The study of electrical behaviour at different temperatures indicated that the properties of the hybrid materials can be mainly related to the nature of guest species, the degree of host lattice reduction, the interlayer water content, and the␣presence of metal ions deliberately introduced in the system. Received: 23 January 2001 Accepted: 5 April 2001     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

A theoretical study on the ionization of OCS with an analysis of vibrational structures of the photoelectron spectrum

 Ab initio calculations have been performed to study the molecular structures and vibrational levels of the four low-lying ionic states (1, 2²Π, and 1, 2²Σ⁺) of carbonyl sulfide. The global regions of the potential-energy surfaces have been obtained by multireference single and double excitation configuration interaction calculations. Vibrational calculations using explicit vibrational Hamiltonians have been used for vibrational analysis. The equilibrium molecular structures and a vibrational analysis of the four ionic states are presented. The theoretical ionization intensity curves including the vibrational structures of the ionic states are also presented and are compared with the photoelectron spectrum. Received: 20 January 2001 / Accepted: 22 August 2001 / Published online: 30 October 2001     

Distances and volumina for graphs

It has long been realized that connected graphs have some sort of geometric structure, in that there is a natural distance function (or metric), namely, the shortest-path distance function. In fact, there are several other natural yet intrinsic distance functions, including: the resistance distance, correspondent “square-rooted” distance functions, and a so‐called “quasi‐Euclidean” distance function. Some of these distance functions are introduced here, and some are noted not only to satisfy the usual triangle inequality but also other relations such as the “tetrahedron inequality”. Granted some (intrinsic) distance function, there are different consequent graph-invariants. Here attention is directed to a sequence of graph invariants which may be interpreted as: the sum of a power of the distances between pairs of vertices of G, the sum of a power of the “areas” between triples of vertices of G, the sum of a power of the “volumes” between quartets of vertices of G, etc. The Cayley–Menger formula for n-volumes in Euclidean space is taken as the defining relation for so-called “n-volumina” in terms of graph distances, and several theorems are here established for the volumina-sum invariants (when the mentioned power is 2). This revised version was published online in July 2006 with corrections to the Cover Date.     

Linearly polarized white fluorescence from shish-kebab type liquid crystalline poly(P-phenylenevinvlene)s with (P-phenylene)s as kebab

Liquid crystalline(LC) polymers with a shish-kebab-type moiety on their cross-conjugated(p-phenylene)s-poly(p-phenylenevinylene) s main chains were synthesized through Gilch polymerization in order to develop a kind of polymers available for linearly polarized white-light-emitting from single chain.In this system,the 2,5-bis(4’-alkoxyphenyl)benzene as the "kebabs" connects with poly(p-phenylenevinylene)(PPV) main chain backbone using its molecular gravity center and the PPV as the "shish" or "skewer"(the "shish-kebab").The polymers possess desirable properties such as excellent solubility and liquid crystalline properties.To drop the "kebabs" of the 2,5-bis(4’-alkoxyphenyl)benzene into the orientation microgroove of aligned polyimide film,not only the "shish" of polymer main chain can be aligned by the virtue of orientation of "kebabs" but also the uniform cross-conjugated structure between the "kebabs" and "shish" can be broken. Then,the alignment of the polymer main chain showed yellow light emission and was also accompanied by orientation of the LC side chains showing blue light emission,this gave rise to a notable linearly polarized white fluorescence.