Necessary conditions for the N‐representability of pair distribution functions

A necessary condition for the N‐representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N‐representability conditions for the second‐order density matrix. The extension to spin‐resolved electron pair densities is considered, as is the extension to higher‐order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N‐representability constraints are considered. For reference, constraints for the N‐representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Effects of the cutoff center on the mean potential and pair distribution functions in liquid water

Molecular dynamics simulations of extended simple point charge (SPC/E) water have been performed to study the effects of the truncation of long-range interactions on some calculated bulk properties of the liquid. The mean potential calculated in liquid water is sensitive to the choice of the cutoff center in the water molecule. The pair distribution function is also dependent on this choice, although not as strongly as the mean potential. An analysis is carried out to understand the origin of these effects. A common cutoff center is at the oxygen atom in the water molecule, but our study shows that this choice does not yield a mean potential value consistent with a more accurate estimate when no cutoff is applied. © 1995 John Wiley & Sons, Inc.     

Phosphorus heterocycles: synthesis,spectroscopic study and X-ray crystallography of some new diazaphosphorinanes

New diazaphosphorinanes with formula R=C₆H₅O (2), 4-CH₃-C₆H₄NH (3), 4-NO₂-C₆H₄NH (4), R=Cl (5), 4-CH₃-C₆H₄O (6), and C₆H₅NH (7) were synthesized and characterized by ¹H, ¹³C, ³¹P NMR and IR spectroscopy and elemental analysis. The crystal structures of compounds 1 and (8) were determined using X-ray crystallography. In these structures, the P=O bond is placed in an equatorial position and the aliphatic six-membered rings show chair conformations. These compounds form two-dimensional polymeric chains via intermolecular P=O…H–N hydrogen bonds. ¹H NMR spectrum of compound 1 shows a ddd splitting pattern for the coupling of H_equatorial proton with phosphorus atom, H_axial atom, and NH proton with a high-value ³ J(PNCH) coupling constant = 26.1 Hz. But, H_axial indicates a dd splitting pattern because of the coupling with H_equatorial and NH protons. ¹³C NMR spectra of compounds 5–7, indicated high values for ³ J(P,C)_aromatic = 11.9, 11.3 and 10.2 Hz due to the coupling of the aromatic carbon atom of naphthalene moiety with the phosphorus atom. ³¹P NMR spectra indicate that the δ(³¹P) of compounds 1–4 and 8 containing NH groups connected to the aliphatic carbon atoms appear downfield relative to those of compounds 5–7 that containing NH groups connected to the aromatic naphthalene group.

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Graphical abstract

     

Comparative studies of the underlying local order corresponding to different radial distribution functions of disordered materials

We have investigated characteristics of the local symmetry, such as cosine distribution of bond angles and second-order invariants of spherical harmonics for simple disordered systems with systematically varied radial distributions. Two types of variation were used at three different packing fraction values. None of the perturbations affected the basic features, but the extent of local order changed considerably. The most significant alterations were found for the case with the lowest packing fraction. The results presented in this paper may be used as guidelines for assessing the quality of agreement between radial distribution functions from different sources, such as that of simulations and diffraction experiments.     

Improving the picture of atomic structure in nonoriented polymer domains using the pair distribution function: A study of polyamide 6

Investigations of the atomic structures within polyamides started over 80 years ago and continue today. These weakly ordered materials diffract X-rays poorly and typically require postprocessing to obtain idealized samples for structural studies. An important goal remains to develop techniques to study the local structure in its natural state, with atomic resolution, and with sensitivity to subtle changes due to synthesis conditions or other technologically relevant processing procedures. Here, we compare the structures of as-produced, nonoriented polyamide 6 ([C₆H₁₁NO] _n) from both hydrolytic and anionic processes. A total scattering pair distribution function approach is used to elucidate information about the atomic bonding, molecular conformation, chain packing, crystallite size, and ratio of ordered to disordered domain content. The results are compared with those from standard analytical methods.     

Synthesis,X-ray crystallography,spectroscopy, electrochemistry,thermal and kinetic study of uranyl Schiff base complexes

Uranyl(VI) complexes [UO₂(L)(solvent)], where L denotes an asymmetric N₂O₂ Schiff base (salpyr, 3-MeOsalpyr, 4-MeOsalpyr, 5-MeOsalpyr, 5-Clsalpyr or 5-Brsalpyr; salpyr is N,N′-bis(salicyliden)-2,3-diaminopyridine), were synthesized and characterized in solution (UV–vis, ¹H NMR, cyclic voltammetry) and in the solid-state (X-ray crystallography, IR, TGA, C H N.). X-ray crystallography of UO₂(3-MeOsalpyr) revealed coordination of the uranyl by the tetradentate Schiff base and one disordered solvent, resulting in seven-coordinate uranium. Another disordered solvent was not coordinated. Cyclic voltammetry of [U^VIO₂(L)(solvent)] in acetonitrile was used to investigate the effect of the substituents of the Schiff base ligands on oxidation and reduction potential. The quasi-reversible redox reaction without any successive reactions was accelerated by groups with lesser electron withdrawing. We also investigated the kinetics and mechanism of the exchange reaction of the coordinated solvent with tributylphosphine using spectrophotometric method. The second-order rate constants at four temperatures and activation parameters showed an associative mechanism for all corresponding complexes with the following trend: UO₂(5-Clsalpyr)?>?UO₂(5-Brsalpyr)?>?UO₂(3-MeOsalpyr)?>?UO₂(4-MeOsalpyr)?>?UO₂(salpyr)?>?UO₂(5-MeOsalpyr). It was concluded that the steric and electronic properties of the complexes were important for the reaction rate.     

2- and 3-furancarboxylic acids: a comparative study using calorimetry, IR spectroscopy and X-ray crystallography

A thermophysical study by DSC for the 2- and 3-isomers of furancarboxylic acid, in the temperature intervals between T=268 K and their respective melting temperatures has been carried out, and an enhancement in the heat capacity curve of the 3-isomer was observed. The IR spectroscopy did not show significant changes either in the frequency band or in the relative band intensity in the temperature range where the small heat absorption occurs. The X-ray analysis reveals that the main differences in their supramolecular structure consist of the assembly of the carboxylic dimers into sheets.     

Interactions of Li, Ca, and Al with aromatic carbon materials: an ab initio study

The interactions of benzene (C6H6), naphthalene (C10H8), and perinaphthene (C13H9) with metal atoms (Li, Ca, and Al) were studied using second-order M?ller-Plesset perturbation theory. By analyzing the frontier molecular orbitals, geometric structures, binding energies, and charge transfers, it was found that these metal atoms can bond strongly with C13H9, but can only bond weakly with C6H6 and C10H8. The bonding nature between a metal atom and C13H9 at their ground state depends significantly on the valence orbital of the metal atom and the pi-bonding distribution of the aromatic hydrocarbons. The spindly shaped 3p valence orbital of an Al atom results in the deviation of the adsorption site to the edge of C13H9, whereas the ball-shaped 2s/4s valence orbitals of a Li and a Ca atom facilitate their overlap with the second lowest unoccupied molecular orbital of C13H9. Further, Hartree-Fock and density-functional theory methods were demonstrated generally to be unreliable in describing the interactions of metal atoms with these pi systems.     

Ligand migration in myoglobin: a combined study of computer simulation and x-ray crystallography

A ligand-migration mechanism of myoglobin was studied by a multidisciplinary approach that used x-ray crystallography and molecular dynamics simulation. The former revealed the structural changes of the protein along with the ligand migration, and the latter provided the statistical ensemble of protein conformations around the thermal average. We developed a novel computational method, homogeneous ensemble displacement, and generated the conformational ensemble of ligand-detached species from that of ligand-bound species. The thermally averaged ligand-protein interaction was illustrated in terms of the potential of mean force. Although the structural changes were small, the presence of the ligand molecule in the protein matrix significantly affected the 3D scalar field of the potential of mean force, in accordance with the self-opening model proposed in the previous x-ray study.     

High resolution heat flow DSC: Application to study of phase transitions,and pore size distribution in saturated porous materials

Suitable container design permits very high temperature and differential temperature resolution in DSC even when relatively large (? 0.14 cm³) samples are used; and thus energy signals associated with phase change occurring over large temperature intervals may be analysed in differential elements. An original and powerful high resolution low temperature DSC technique (the authorsψ plot”) for studying and comparing pore size distributions (PSD) in water saturated samples (for pores having Kelvin radii between 1,2 and about 500 nm) is given, together with an application which shows that the PSD in a water saturated organic ion exchanger could be obtained from analysis of three Gaussian distributions which precisely generate a curve which is an excellent empirical fit to the recorded low temperature exotherm obtained by freezing pure water within the sample.     

Short- and long-range order in the positive electrode material, Li(NiMn)0.5O2: a joint X-ray and neutron diffraction, pair distribution function analysis and NMR study

The local environments and short-range ordering of LiNi(0.5)Mn(0.5)O(2), a potential Li-ion battery positive electrode material, were investigated by using a combination of X-ray and neutron diffraction and isotopic substitution (NDIS) techniques, (6)Li Magic Angle Spinning (MAS) NMR spectroscopy, and for the first time, X-ray and neutron Pair Distribution Function (PDF) analysis, associated with Reverse Monte Carlo (RMC) calculations. Three samples were studied: (6)Li(NiMn)(0.5)O(2), (7)Li(NiMn)(0.5)O(2), and (7)Li(NiMn)(0.5)O(2) enriched with (62)Ni (denoted as (7)Li(ZERO)Ni(0.5)Mn(0.5)O(2)), so that the resulting scattering length of Ni atoms is null. LiNi(0.5)Mn(0.5)O(2) adopts the LiCoO(2) structure (space group Rm) and comprises separate lithium layers, transition metal layers (Ni, Mn), and oxygen layers. NMR experiments and Rietveld refinements show that there is approximately 10% of Ni/Li site exchange between the Li and transition metal layers. PDF analysis of the neutron data revealed considerable local distortions in the layers that were not captured in the Rietveld refinements performed using the Bragg diffraction data and the LiCoO(2) structure, resulting in different M-O bond lengths of 1.93 and 2.07 Angstroms for Mn-O and Ni/Li-O, respectively. Large clusters of 2400-3456 atoms were built to investigate cation ordering. The RMC method was then used to improve the fit between the calculated model and experimental PDF data. Both NMR and RMC results were consistent with a nonrandom distribution of Ni, Mn, and Li cations in the transition metal layers; both the Ni and Li atoms are, on average, close to more Mn ions than predicted based on a random distribution of these ions in the transition metal layers. Constraints from both experimental methods showed the presence of short-range order in the transition metal layers comprising LiMn(6) and LiMn(5)Ni clusters combined with Ni and Mn contacts resembling those found in the so-called "flower structure" or structures derived from ordered honeycomb arrays.     

A consideration of orientational correlation functions,time-dependent distribution functions and pictorial representations of the orientational motions of molecules.

The relationships between experimental quantities which arise due to the dynamics of molecules and the underlying time-correlation functions and time-dependent distribution functions are considered, with special emphasis being given to reorientational motions as detected by dielectric and closely related techniques. It is shown that pictorial representations of angular motion (small-step diffusion, free rotation, collision-interrupted rotation) may be given in terms of three and two dimensional diagrams of the time-dependent orientation distribution functions and that these afford a physical insight and appreciation of the averaged motions of ensembles of molecules.     

Theoretical study on the structure, stability, and electronic properties of the guanine-Zn-cytosine base pair in M-DNA

M-DNA is a type of metalated DNA that forms at high pH and in the presence of Zn, Ni, and Co, with the metals placed in between each base pair, as in G-Zn-C. Experiments have found that M-DNA could be a promising candidate for a variety of nanotechnological applications, as it is speculated that the metal d-states enhance the conductivity, but controversy still clouds these findings. In this paper, we carry out a comprehensive ab initio study of eight G-Zn-C models in the gas phase to help discern the structure and electronic properties of Zn-DNA. Specifically, we study whether a model prefers to be planar and has electronic properties that correlate with Zn-DNA having a metallic-like conductivity. Out of all the studied models, there is only one which preserves its planarity upon full geometry optimization. Nevertheless, starting from this model, one can deduce a parallel Zn-DNA architecture only. This duplex would contain the imino proton, in contrast to what has been proposed experimentally. Among the nonplanar models, there is one that requires less than 8 kcal/mol to flatten (both in gas and solvent conditions), and we propose that it is a plausible model for building an antiparallel duplex. In this duplex, the imino proton would be replaced by Zn, in accordance with experimental models. Neither planar nor nonplanar models have electronic properties that correlate with Zn-DNA having a metallic-like conductivity due to Zn d-states. To understand whether density functional theory (DFT) can describe appropriately the electronic properties of M-DNAs, we have investigated the electronic properties of G-Co-C base pairs. We have found that when self-interaction corrections (SIC) are not included the HOMO state contains Co d-levels, whereas these levels are moved below the HOMO state when SIC are considered. This result indicates that caution should be exercised when studying the electronic properties of M-DNAs with functionals that do not account for strong electronic correlations.     

Acyclic N‐halamine‐based fibrous materials: Preparation,characterization, and biocidal functions

Methacrylamide (MAA) was grafted onto cotton cellulose. The influence of the reaction conditions on the grafting was studied in detail. Upon a chlorine bleach treatment, some of the amide groups in the grafted MAA side chains were transformed into stable acyclic N‐halamines; Hoffman‐type degradation was not observed. The resultant cotton celluloses provided a total kill of 10⁸–10⁹ CFU/mL for Escherichia coli (Gram‐negative bacteria), Staphylococcus aureus (Gram‐positive bacteria), and Candida tropicalis (fungi) in 3 min, 10⁶–10⁷ PFU/mL for the MS2 virus in 5 min, and 10⁶–10⁷ spores/mL for Bacillus subtilis in 4 h. The antibacterial, antifungal, antiviral, and antispore activities were both durable and rechargeable. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3588–3600, 2006     

The study of electron energy distribution functions, Swarm parameters, and transition rates in N2+O2 plasma

Using the Boltzman equation electron energy distribution functions, swarm parameters (mean energy, characteristic energy, drift velocity and diffusion coefficient), and transition rates (one for vibrational and one for electronical excitation for each of the gases) for N₂+O₂ (80%+20%) mixture plasma have been calculated. The influence of the applied reduced electric field and the vibrational temperatures on these quantities is studied.     

Monte Carlo investigations of dense copolymer systems, 1. Pivot algorithm and pair distribution function

ABA triblock copolymers (the solvent being a θ-solvent for B and an athermal one for A) as well as their constituent homopolymers were investigated by means of Monte Carlo simulations in a 5-choice cubic lattice. The polymer concentration (represented by the fraction ϕ of sites occupied by the polymer) varied from 0 (isolated chain) to 0.80. An investigation of the usefulness of the pivot algorithm in dense systems resulted in reasonable acceptance fractions up to a volume fraction of 0.12 (athermal chain and ABA copolymer) and 0.05 (θ-chain). For larger volume fractions only the chain-ends remain mobile. The overlap concentration of the polymers defined by several quantities was approximately 0.07 (athermal chain), 0.12 (θ-chain) and 0.09 (ABA copolymer). At a polymer fraction of 0.32, the chains had the same number of inter- and intramolecular contacts on average. At higher concentrations, the behaviour of the chains was primarily determined by intermolecular interactions. Contrary to isolated pairs, the pair distribution function g(r) of two athermal chains in a (cubic) box exceeded unity at intermediate distances because of the influence of the finite size of the box. The larger the size of the box, the smaller the (positive) deviation was. In the limit of r → 0 the pair distribution function g(r) – being smaller than unity – increased with increasing concentration while the maximum at intermediate distances simultaneously decreased. Ultimately, at the highest concentration, the pair distribution function resembled that of isolated θ-chains. The concentration dependence of the θ-pair distribution function itself, however, is negligible. At low concentrations the pair distribution function of the ABA triblock copolymer behaved like that of an athermal chain (up to ϕ ≈ 0.40) where characteristic oscillations around 1 developed. This might be taken as indicative of the formation of a lamellar phase.