On the extension of quantum similarity to atomic nuclei: Nuclear quantum similarity

Quantum similarity is a useful tool to establish comparisons between elements of a quantum object set and, so far applied successfully to molecular physics, is applied here to atomic nuclei. Quantum Similarity Measures (QSM) and Indices (QSI) are introduced to study an arbitrary set of 20 nuclei. From this study, relationships between nuclear overlap‐like self‐similarities and size‐like properties are found. A bidimensional projection of the set is performed, and Mendeleev conjecture is invoked to predict qualitatively some nuclear ground‐state properties, such as total binding energy per nucleon, nuclear radius, nuclear volume, total and partial energies, etc. This revised version was published online in July 2006 with corrections to the Cover Date.     

Advection‐dispersion in symmetric field‐flow fractionation channels

We model the evolution of the concentration field of macromolecules in a symmetric field‐flow fractionation (FFF) channel by a one‐dimensional advection–diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously supported by centre manifold theory. Errors of the derived model are quantified for improved predictions if necessary. The advection–diffusion equation is used to find that the optimal condition in a symmetric FFF for the separation of two species of molecules with similar diffusivities involves a high rate of cross‐flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the role of reachability and observability in NMR experimentation

It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Wavelets for electronic structure calculations

Molecular electronic structure calculations have a multi‐scale character through the presence of a set of singularities corresponding to atomic nuclei, and thus there exists a potential to improve the efficiency of these calculations using fast wavelet transform techniques. We report on the development of a one dimensional prototype benchmark problem of sufficient complexity to capture the features of 3‐D problems that are being solved today in quantum electronics calculations. Theoretical estimates of decay across scales and spatial distribution of wavelet coefficients for the solutions of the 1‐D and 3‐D problems are derived and verified experimentally. Equivalence in a multi‐resolution context of the solutions of the 1‐D prototype and the 3‐D problem is established. This revised version was published online in July 2006 with corrections to the Cover Date.     

A general procedure for building the transmembrane domains of G‐protein coupled receptors

The only results available at present about the structural features of G‐protein coupled receptors are the low resolution electron projection maps obtained from microscopy studies carried out on two‐dimensional crystals of rhodopsin. These studies support previous suggestions that these integral proteins are constituted by seven transmembrane domains. The low resolution electron density map of rhodopsin can be used to extract information about helix relative positions and tilt. This information, together with a reliable procedure to assess the residues involved in each of the transmembrane regions, can be used to construct a model of rhodopsin at atomic resolution. We have developed an algorithm that can be used to generate such a model in a completely automated fashion. The steps involved are: (i) locate the centers of the helices according to the low resolution electron density map; (ii) compute the tilt of each helix based on the elliptical shape observed by each helix in the map; (iii) define a local coordinate system for each of the helices; (iv) bring them together in an antiparallel orientation; (v) rotate each helix through the helical axis in such a way that its hydrophobic moment points in the same direction as the bisector formed between three consecutive helices in the bundle; (vi) rotate each helix through an axis perpendicular to the helical one to assign a proper tilt; (vii) translate each of the helix to its center deduced from the projection map. A major advantage of the procedure presented is its generality and consequently can be used to obtain a model of any G‐protein coupled receptor with the only assumption that the shape of the bundle is the same as found in rhodopsin. This avoids uncertainties found in other procedures that construct models of G‐protein coupled receptors based on sequence homology using rhodopsin as template. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effective dynamic correlation in multiconfigurational wave-function calculations on atoms and molecules

An intuitive understanding of dynamic correlation in terms of a regularized electron repulsion expression is outlined. Expressions for cusp kinetic energy corrected regularized electron repulsion integrals are deduced and implemented in a multiconfigurational wave-function framework. A regularized complete active space self-consistent field (reg-CASSCF) technique is suggested and tested on atomic total energies, molecular structures and binding energies. Received: 26 November 1996 / Accepted: 21 April 1997     

Analysis of fourth-order Møller–Plesset limit energies: the importance of three-electron correlation effects

Fourth-order M?ller–Plesset (MP4) correlation energies are computed for 28 atoms and simple molecules employing Dunning's correlation-consistent polarized-valence m-zeta basis sets for m=2, 3, 4, and 5. Extrapolation formulas are used to predict MP4 energies for infinitely large basis sets. It is shown that both total and partial MP4 correlation energies can be extrapolated to limit values and that the sum of extrapolated partial MP4 energies equals the extrapolated total MP4 correlation energy within calculational accuracy. Therefore, partial MP4 correlation energies can be presented in the form of an MP4 spectrum reflecting the relative importance of different correlation effects. Typical trends in calculated correlation effects for a given class of electron systems are independent of the basis set used. As first found by Cremer and He [(1996) J Phys Chem 100:6173], one can use MP4 spectra to distinguish between electron systems with well-separated electron pairs and systems for which electrons cluster in a confined region of atomic or molecular space. MP4 spectra for increasing size of the basis set reveal that smaller basis set calculations underestimate the importance of three-electron correlation effects for both classes by overestimating the importance of pair correlation effects. The minimum size of a basis set required for reliable MP4 calculations is given by a valence triple-zeta polarized basis, which even in the case of anions performs better than a valence double-zeta basis augmented by diffuse functions. Received: 14 June 2000 / Accepted: 16 June 2000 / Published online: 24 October 2000     

Shape‐similarity relations based on topological resolution

Shape‐similarities of electron density clouds of molecules provide important clues concerning chemical and physical properties, including information about their reactivities in biochemical systems. The concept of topological resolution is used for quantifying molecular similarities: within a hierarchy of finer and cruder topologies, the crudest topology that already provides discrimination between two objects (such as two fuzzy electron density clouds) is used to define a measure of their similarities. The finer this topology, the more similar the two objects. This approach, the method of topological resolution‐based similarity measures (TRBSM), can be combined with a geometrically motivated resolution‐based similarity measure (RBSM) within a metric space. Some of the relations between these two approaches are discussed in this contribution, with special emphasis on applications to electron densities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quantum molecular similarity via momentum‐space indices

A method for assessing quantum molecular similarity has been developed based on the momentum‐space representation. The principles of the method are summarized and the results of two applications are presented. The approach emphasizes the variation of the outer valence electron density much more than the bonding topology, it avoids several problems associated with more conventional approaches based on the position‐space representation, and it can now be applied to extended series of large molecules. The first of the applications involves different sulfonylurea inhibitors of the enzyme acyl‐CoA : cholesterol acyltransferase (ACAT). The second is concerned with the relative toxicity of a number of anti‐HIV phospholipids. Further experimental work is suggested in both cases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two‐center p‐space integrals: diatomic molecular moments

Analytical expressions for the calculation of both orbital and total moments of diatomic molecules using Gaussian‐type orbitals are formulated. Moments with are computed for the ground state of 35 diatomic molecules at equilibrium bond length using 6‐311G(d,p) basis sets. In order to test our expressions, these expectation momentum values are compared with the values calculated using self‐consistent‐field wave functions of Hartree–Fock quality, which give Hartree–Fock limit energies. This revised version was published online in July 2006 with corrections to the Cover Date.     

On geminals and symplectic bases in quantum chemistry

The construction of a symplectic basis set with >N electrons is exhibited by means of three kinds of units, the first kind geminal, the second kind geminal and the one‐particle operators. The optimization procedure of the variation method is extended to the coefficients in the linear sum of the symplectic bases, the parameters in the geminals, and the orbitals. For practical use, these bases are expanded explicitly as a linear sum of the Slater determinants. For illustration, the LiH molecule, which is taken as an example, is calculated by using some symplectic bases. This revised version was published online in July 2006 with corrections to the Cover Date.     

An approximate method of self-consistent electronic structure calculations of a crystal surface. The Ir(111) surface

The Slater approximation for atomic electron energies is employed to calculate the electronic structure of the Ir(111) surface. The results are used to estimate the shift of the 4f_7/2 level on the surface relative to its position in the volume. The electron state densities in the neighborhood of the center of the surface Brillouin zone (SBZ) are compared with photoelectronic spectra for emission normal to the Ir(111) surface. On this basis, the accuracy of this approximation is estimated. Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 1, pp. 17–24, January–February, 1994. Translated by O. Kharlamova     

Determination of plutonium isotope ratios at very low levels by ICP-MS using on-line electrochemically modulated separations

Electrochemically modulated separations (EMS) are shown to be a rapid and selective means of extracting and concentrating Pu from complex solutions prior to isotopic analysis by inductively coupled plasma mass spectrometry (ICP‐MS). This separation is performed in a flow injection mode, on‐line with the ICP‐MS. A three‐electrode, flow‐by electrochemical cell is used to accumulate Pu at an anodized glassy carbon electrode by redox conversion of Pu(III) to Pu (IV&VI). The entire process takes place in 2% (v/v) (0.46 M) HNO₃. No redox chemicals or acid concentration changes are required. Plutonium accumulation and release is redox dependent and controlled by the applied cell potential. Large transient volumetric concentration enhancements can be achieved. Based on more negative U(IV) potentials relative to Pu(IV), separation of Pu from uranium is efficient, thereby eliminating uranium hydride interferences. EMS‐ICP‐MS isotope ratio measurement performance will be presented for femtogram to attogram level plutonium isotope injections.     

Structure of X-ray photoelectron, emission, and conversion spectra and molecular orbitals of uranium compounds

The fine structure of X-ray photoelectron spectra of uranium compounds in the range of electron binding energies from 0 to ∼50 eV is largely determined by the electrons of the outer and inner valence molecular orbitals arising from the valence atomic shells, including the U6p and Lns low-energy occupied atomic shells. This result is in agreement with the data of the electronic structure calculations of these compounds and confirmed by the nuclear electron (conversion) and X-ray emission spectroscopic investigations. It is shown that the fine structure of X-ray photoelectron spectra associated with the electrons of inner valence molecular orbitals makes it possible to judge the participation of the electrons of the occupied atomic shells in chemical bonding, the structure of the nearest environments of the atom, and the bond lengths in the compounds. The overall contribution of the electrons of these molecular orbitals to the absolute value of binding energy may prove to be comparable to the contribution of the electrons of the outer valence molecular orbitals to atomic bonding. This is a new and important fact in chemistry. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 6, pp. 1037–1046, November–December, 1998.     

Relativistic theory of an inhomogeneous electron liquid in relation to atomic binding energies

Experimentally determined ionization potentials in the literature are used to plot the binding energies for neutral atoms as a function of atomic number Z for Z?=?2–30, 32, 36, 42. From this pretty smooth plot we have subtracted non-relativistic Hartree–Fock binding energies, using both available numerical values and the almost analytical result, based on the non-relativistic Thomas–Fermi statistical theory valid for large Z. The difference is still relatively smooth. For Mo, with Z?=?42, the difference is about 70 atomic units. This difference is then analyzed using first relativistic theory of an inhomogeneous electron liquid and then the Local Density Approximation (LDA), and for Mo their results yield approximately 88 and 67 atomic units respectively. We infer that a highly accurate relativistic many-electron theory will therefore be needed before reliable electron correlation energies can be extracted from the experimental binding energies for atoms heavier than Argon. This fact has prompted us to use available LDA calculations to confront three theoretical predictions of the Z dependence of non-relativistic electron correlation energies at large Z.     

Hartree-Fock energy partitioning in terms of Hirshfeld atoms.

A Hirshfeld decomposition scheme of the Hartree-Fock total molecular energy into atomic energies is presented. The calculations are performed by direct numerical integration and the results are compared for a set of 28 molecules containing different kinds of atoms. The calculated atomic energies show a strong dependency on changes of atomic electron population and hybridization. Linear correlations are found between the energy and the population for H, these being related to the electronegativity of this atom and to the external potential created by the remaining atoms. The proposed energy partitioning scheme appears to be useful for studies such as proton acidity, the anomeric effect and group transferability, and allows atomic virial ratios to be obtained. Finally, the atomic potential energies are found to mimic trends based on exact expressions as well as trends displayed by molecular quantities, thus lending credibility to the partitioning scheme used.     

Pascal’s triangle, non‐adjacent numbers, and D-dimensional atomic orbitals

The topics in chemico‐physical poblems which are related to Pascal’s triangle and asymmetrical Pascal’s triangle are collected and their mathematical relations are discussed. The selected topics are: ESR hyperfine splitting, spin–spin coupling of NMR, topological indices of linear and cyclic hydrocarbons, and the number of degeneracy of the atomic orbitals of D-dimensional hydrogen atom. The relation between the Pascal’s and asymmetrical Pascal’s triangles is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

The convergence of energy expansions for molecules in electrostatic fields: A linear‐response coupled‐cluster study

The radii of convergence of power series expansions describing energy of a molecule in external electrostatic field are investigated usingD’Alembert ratio test, standard and generalized Cauchy–Hadamardcriteria, and Padé approximants. The corresponding coefficients at various field and field‐gradient components, representing multipole moments and (hyper)polarizabilities and including terms of tenth or even twentieth order, are determined using an ab initio linear responsecoupled‐cluster theory. Most calculations are performed for the HF molecule described by the basis set of double zeta quality, while the role of basis set is discussed by comparing the results with estimates of the radii of convergence obtained with the basis set of [5s3p2d/3s2p] quality. Emphasis is placed on the dependence of the interval of convergence of power series expansion describing energy of a molecule in applied electrostatic field on the nuclear geometry. The results might have important implications for various numerical methods used to calculate electrostatic molecular properties as functions of the internuclear geometry, including the finite‐field andfixed‐point‐charge approaches. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theoretical analysis of the internal rotation in aminoborane and borylphosphine

Using a recently proposed orbital deletion procedure and the block-localized wavefunction method, the rotational barriers in H₂BNH₂ and H₂BPH₂ are analyzed in terms of conjugation, hyperconjugation, steric effect and pyramidalization. With the zero-point energy corrections, the π-binding strengths in the planar H₂BNH₂ and H₂BPH₂ are both around 20 kcal/mol at the HF level using the 6-311+G** basis set. With the deactivation of the π atomic orbitals on the boron atom and the evolution from a planar structure to a 90°-twisted structure, the steric repulsion between the B‐H and the N‐H or P‐H is relieved and moreover, the negative hyperconjugation from the lone electron pair or pairs on the nitrogen or phosphorus atoms to the antibonding orbital ^χ* _B H ₂ of the BH₂ group stabilizes the twisted structure by 7.4(8.8) or 4.0(5.0) kcal/mol at the HF/6-31G*(6-311+G**) level. However, the repulsive interaction between the lone pair(s) and the two BH σ bonds is so prominent that the overall steric effect contributes 20.3(22.9) and 19.3(19.8) kcal/mol to the rotational barriers in H₂BNH₂ and H₂BPH₂ with the 6-31G*(6-311+G**) basis set. The present techniques and analyses may also give some clues to justify the parameterization in the empirical molecular mechanics methods. Received: 17 April 1998 / Accepted: 17 September 1998 / Published online: 1 February 1999     

Mass transfer to tubular electrodes. Part 2: CE process

The kinetic equations for an electrochemical process consisting of a homogeneous first‐order chemical reaction followed by electron transfer at the electrode surface are solved numerically, for linear sweep voltammetry under hydrodynamical conditions in a tubular electrode. Models for both the cases involving reversible as well as irreversible electrode charge transfer reaction are investigated. The influence on current–potential voltammograms of the experimentally measurable parameters like the potential scan rate, axial flow rate and chemical equilibrium parameter is examined and depicted graphically. This revised version was published online in July 2006 with corrections to the Cover Date.