Generalized electron number distribution functions: real space versus orbital space descriptions

The algebraic expressions previously derived to compute the electron number distribution functions (EDF) for exhaustive partitions of the physical space into sharp-boundary atoms are generalized to allow for the use of fuzzy atoms and orbital-based partitions. In some of the latter, the atomic overlap matrix required to obtain the EDF is analytical. This makes them attractive alternatives to other definitions, as the one based on the atomic basins of the quantum theory of atoms in molecules (QTAIM), which are more physically sound but also much more demanding computationally. We will compute the EDF for a series of test molecules using different fuzzy and orbital-based partitions and compare them to QTAIM EDF. The effects of electron correlation and the use of the core approximation on the EDF will also be explored.     

An electron number distribution view of chemical bonds in real space

Several key concepts of chemical bonding theory, such as electron pair sharing, polarity, charge transfer, multiple bonding, etc., are shown to be recovered from the statistical properties of multivariate electron number distribution functions. The latter are constructed from the real-space atomic partition provided by the quantum theory of atoms in molecules. We present the basic formalism and several exemplifying calculations.     

Spin resolved electron number distribution functions: how spins couple in real space

The probabilities of finding arbitrary partitions of the N(alpha)m(s)=12 and N(beta)m(s)=-12 electrons of a molecule into m arbitrary regions that exhaust the physical space are developed and computed, both for atomic and electron localization function basins, in a number of test systems. These spin resolved electron number distribution functions provide access to the coarse-grained distribution of spins in space even for singlet states, a nontrivial result. It is found that atoms within molecules partially retain their in vacuo preferences for certain spin configurations. This may lead to long range spin coupling among basins. An aufbaulike rule favoring spin coupling, particularly for Hartree-Fock wave functions, has also been found.     

Electron number probability distributions for correlated wave functions

Efficient formulas for computing the probability of finding exactly an integer number of electrons in an arbitrarily chosen volume are only known for single-determinant wave functions [E. Cances et al., Theor. Chem. Acc. 111, 373 (2004)]. In this article, an algebraic method is presented that extends these formulas to the case of multideterminant wave functions and any number of disjoint volumes. The derived expressions are applied to compute the probabilities within the atomic domains derived from the space partitioning based on the quantum theory of atoms in molecules. Results for a series of test molecules are presented, paying particular attention to the effects of electron correlation and of some numerical approximations on the computed probabilities.     

Vibronic effects on resonant electron conduction through single molecule junctions

The influence of vibrational motion on electron conduction through single molecules bound to metal electrodes is investigated employing first-principles electronic-structure calculations and projection-operator Green’s function methods. Considering molecular junctions where a central phenyl ring is coupled via (alkane)thiol-bridges to gold electrodes, it is shown that – depending on the distance between the electronic π-system and the metal – electronic–vibrational coupling may result in pronounced vibrational substructures in the transmittance, a significantly reduced current as well as a quenching of negative differential resistance effects.     

Direct determination of hydrogen-bonded structures in resonant and tautomeric reactions using ultrafast electron diffraction

We elucidate the keto-enol tautomeric equilibrium in acetylacetone, the structure of both keto and enol forms, and the nature of the intramolecular O-H...O HB in enolic acetylacetone using our ultrafast electron diffraction apparatus, thereby shedding new light on the nature of the hydrogen bond in resonant tautomeric structures. The enolic structure exhibits some pi-resonance delocalization; however, this delocalization is not strong enough to give a symmetric skeletal geometry. The long O...O distance in the refined structure renders the homonuclear O-H...O hydrogen bond in acetylacetone localized and asymmetric.     

Collective motions of rigid fragments in protein structures from smoothed electron density distributions

In this work, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) approaches are applied to describe the dynamics of protein structure graphs built from calculated promolecular electron density (ED) distribution functions. A first set of analyses is carried out on results obtained from ED maxima calculated at various smoothing levels. A second set is achieved for ED networks whose edges are weighted by ED overlap integral values. Results are compared with those obtained through the classical GNM and ANM approaches applied to networks of C(alpha) atoms. It is shown how the network model and the consideration of crystal packing as well as of the side chains may lead to various improvements dependent upon the structure under study. The selected protein structures are Crambin and Pancreatic Trypsin Inhibitor because of their small size and numerous dynamical data obtained by other authors.     

Ultrafast electron diffraction: oriented molecular structures in space and time.

The technique of ultrafast electron diffraction allows direct measurement of changes which occur in the molecular structures of isolated molecules upon excitation by femtosecond laser pulses. The vectorial nature of the molecule-radiation interaction also ensures that the orientation of the transient populations created by the laser excitation is not isotropic. Here, we examine the influence on electron diffraction measurements--on the femtosecond and picosecond timescales--of this induced initial anisotropy and subsequent inertial (collision-free) molecular reorientation, accounting for the geometry and dynamics of a laser-induced reaction (dissociation). The orientations of both the residual ground-state population and the excited- or product-state populations evolve in time, with different characteristic rotational dephasing and recurrence times due to differing moments of inertia. This purely orientational evolution imposes a corresponding evolution on the electron scattering pattern, which we show may be similar to evolution due to intrinsic structural changes in the molecule, and thus potentially subject to misinterpretation. The contribution of each internuclear separation is shown to depend on its orientation in the molecular frame relative to the transition dipole for the photoexcitation; thus not only bond lengths, but also bond angles leave a characteristic imprint on the diffraction. Of particular note is the fact that the influence of anisotropy persists at all times, producing distinct differences between the asymptotic "static" diffraction image and the predictions of isotropic diffraction theory.     

Crystalline polymers in real space

Recent work has resolved uncertainties as to how polymers develop their melt-crystallized textures and brought a unified context to the subject. Spherulites form because of the long molecular length not because of its polydispersity. When a molecule is only partly attached to a growing lamella the unattached portions will occupy adjacent space and exert a short-range repulsive pressure on any neighbouring lamella at a branch point. This is confirmed by monodisperse long n-alkanes forming spherulites only with chainfolded lamellae not when crystallizing as extended chains. An additional textural element, cellulation, is superposed on regular spherulitic growth beyond a certain radius (in linear-low-density polyethylenes) when there is sufficient fractional crystallization of segregated species which lower the local equilibrium melting temperature and thence the isothermal supercooling and growth rate, the last declining continuously to an asymptotic limit. First results show that both the radius to cellulation and the cell width are effectively independent of growth velocity; neither scales with the diffusion length. A possible explanation is proposed for this novel situation which has no precedent in either polymeric or non-polymeric systems.     

Spatial distributions of metastable argon,temperature and electron number density in an inductively coupled argon plasma

Spatially resolved radial distributions of excitation temperature and electron number density in an argon ICP were obtained. The argon excitation temperature and electron number density near the plasma center were found to 7000 K and 5 × 10¹⁵ cm^?3, respectively, at an RF power of 1.5 kW and a carrier argon flow rate 0.65 1 min^?1.Various distributions of the absorbance at the Ar I 811.5 nm line, which has one of the metastable levels as the lower level, were obtained with and without carrier argon flow, where an MIP was used as a light source. Introduction of a large amount of potassium did not influence the distribution of the absorbance. The emission intensities at Ar I 811.5 nm were also measured for comparison.     

Why define atoms in real space?

The physics of a system is determined by a variation of the action integral, i.e., by a variation of the space–time volume integral of the Lagrange function. If one demands that the properties of an atom in a molecule be derived from physics, the atom must generate its own space–time volume, requiring that its boundaries be defined in real space. The variations in the action are related to the actions of generators of infinitesimal unitary transformations. In the general case, the action integral is altered by generators acting in both the spacelike and timelike surface bounding the space–time volume, whereas for a total isolated system, the physics is totally determined by their action in just the spacelike surfaces at the two time endpoints. It is shown and illustrated for a one-dimensional system that the definition of an atom corresponds to the possibility of choosing a subsystem in such a way that the contributions to the change in action resulting from the evolution in time of its spatial boundaries vanishes identically. The properties of these subsystems and of the total system of which they are a part are, therefore, determined by one and the same action principle. This choice of subsystem corresponds to the possibility of augmenting the Lagrange function by the divergence of the gradient of the electron density a step that, while leaving the equations of motion unchanged, modifies the generating operators in the required manner. © 1994 John Wiley & Sons, Inc.     

Electronic structures and long‐range electron transfer through DNA molecules

Quantum chemical calculation on an entire molecule of segments of native DNA was performed in an ab initio scheme with a simulated aqueous solution environment by overlapping dimer approximation and negative factor counting method. The hopping conductivity was worked out by random walk theory and compared with recent experiment. We conclude that electronic transport in native DNA molecules should be caused by hopping among different bases as well as phosphates and sugar rings. Bloch type transport through the delocalized molecular orbitals on the whole molecular system also takes part in the electronic transport, but should be much weaker than hopping. The complementary strand of the double helix could raise the hopping conductivity for more than 2 orders of magnitudes, while the phosphate and sugar ring backbone could increase the hopping conductivity through the base stacks for about 1 order of magnitude. DNA could transport electrons easily through the base stacks of its double helix but not its single strand. Therefore, the dominate factor that influences the electronic transfer through DNA molecules is the π stack itself instead of the backbone. The final conclusion is that DNA can function as a molecular wire in its double helix form with the conditions that it should be doped, the transfer should be a multistep hopping process, and the time period of the transfer should be comparable with that of an elementary chemical reaction. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 112–130, 2000     

Assessment and formation mechanism of laser-induced periodic surface structures on polymer spin-coated films in real and reciprocal space

In this work we evaluate the potential of grazing incidence X-ray scattering techniques in the investigation of laser-induced periodic surface structures (LIPSSs) in a series of strongly absorbing model spin-coated polymer films which are amorphous, such as poly(ethylene terephthalate), poly(trimethylene terephthalate), and poly(carbonate bisphenol A), and in a weaker absorbing polymer, such as semicrystalline poly(vinylidene fluoride), over a narrow range of fluences. Irradiation was performed with pulses of 6 ns at 266 nm, and LIPSSs with period lengths similar to the laser wavelength and parallel to the laser polarization direction are formed by devitrification of the film surface at temperatures above the characteristic glass transition temperature of the polymers. No crystallization of the surface is induced by laser irradiation, and crystallinity of the material prevents LIPSS formation. The structural information obtained by both atomic force microscopy and grazing incidence small-angle X-ray scattering (GISAXS) correlates satisfactorily. Comparison of experimental and simulated GISAXS patterns suggests that LIPSSs can be well described considering a quasi-one-dimensional paracrystalline lattice and that irradiation parameters have an influence on the order of such a lattice.     

Making "real" molecules in virtual space

Predicting "realistic" compounds of given chemical reactions with virtual synthesis tools usually requires the manual intervention of experienced chemists in the enumeration phase for the selection of appropriate reactants, assignment of the corresponding reaction sites, and removal of the unlikely products. To automate the virtual synthesis process, we have moved the expertise intensive parts from the compound library design phase to the reaction library design phase. ChemAxon is building an in silico reaction library containing important preparative transformations, where each reaction definition contains a generic transformation scheme and additional rules to handle the various starting compounds according to the corresponding chemo-, regio-, and stereoselectivity issues. Having well designed reaction definitions in hand, our software tool is able to generate synthetically feasible compound libraries with minimal effort in the enumeration phase.     

Particle number density and velocity distributions in laser plumes

A time-of-flight mass spectrometer with electron impact ionization facility was used in investigations of the laser plume structure. Densities and velocity distributions of positively charged and neutral species were measured 12 cm downstream of the target. Velocities of particles in a plume were measured by the retarding potential method. The combination of a skimmer and declining electric field was used to suppress the influence of charged particles during the measurement of the neutral component parameters. In the case of YBaCuO ceramic laser ablation, a strong variation of the laser-induced plume composition was observed from its head to its tail. It seems to be accounted for by the difference of the starting (phase transition) temperatures of various layers of a plume. Ions detected mainly in the head of a plume were followed by atoms, molecules and clusters in inverse succession to their appearance in the plume under the light intensity increase. The characteristic of the number density dependence upon the laser spot diameter make it clear that most of the molecules BaO and YO are the direct product of ablation. In contrast, the detected clusters with masses up to 2000 amu are the product of condensation in the expanding plume under the conditions of the experiments.     

Dark channels in resonant tunneling transport through artificial atoms

We investigate sequential tunneling through a multilevel quantum dot confining multiple electrons in the regime where several channels are available for transport within the bias window. By analyzing solutions to the master equations of the reduced density matrix, we give general conditions on when the presence of a second transport channel in the bias window quenches transport through the quantum dot. These conditions are in terms of distinct tunneling anisotropies which may aid in explaining the occurrence of negative differential conductance in quantum dots in the nonlinear regime.     

Effects of Lagrangian multipliers on SWCNT in real space

Electronic properties, band‐width, band gap, and van Hove singularities of (3,0), (4,0), and (9,0) zigzag nanotubes are investigated comparatively in the Harigaya model and a toy model, including the contributions of bonds of different types to the SSH Hamiltonian differently. Optical transition frequencies are calculated. In this way, an experimental correlation between the two models is achieved. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Influence of the vibrational quantum number of the resonant state in resonant multiphoton ionization/dissociation of hydrogen molecules

We have studied the resonant multiphoton ionization of hydrogen in a three-photon excitation, one-photon ionization scheme. Superimposed on the ionization process we find a dissociation mechanism which manifests itself in a strong H⁺ signal. The ratio of H⁺ to H⁺₂ signals depends on the vibrational quantum number v' of the intermediate state and on the laser intensity. We present a simple model which qualitatively reflects this dependence.