Method of the Green functions in the kinetics of adsorption from micellar surfactant solutions

The kinetics of adsorption from micellar surfactant solutions is considered theoretically from a uniform point of view. Three boundary value problems for the adsorption on flat and on spherical interface are solved analytically by means of the method of the Green functions. In this way the bulk concentration and the adsorption of surfactant monomers are expressed as functions of time. The contribution of the micelles (surfactant aggregates) to the diffusion of the monomers is accounted for as pseudo-first order reaction. The adsorption from surfactant solutions without micelles turns out to be the particular case of the problems considered here. Being general in form, the derived equations can be applied also to other practical problems in heterogeneous chemical kinetics, adsorption of gases, heat transfer, etc.     

Application of one-particle Green functions technique for calculation of vertical ionization potentials of closed-shell molecules described by CNDO/2 semiempirical Hamiltonian

A simple method of infinite summations of some dominant diagrams in the framework of the one-particle Green functions technique is suggested. This method for the calculation of the lowlying vertical ionization potentials of some simple closed-shell molecules described by CNDO/2 semiempirical Hamiltonian is applied. The obtained results are in quite-satisfactory agreement with the experimental values of the vertical ionization potentials measured by the photo-electron spectroscopy technique.     

Hypervirial theorems and restrictions on wave functions

The conditions that ensure that an optimal variational wave function ø under general restricting requirements satisfies the hypervirial theorem are analysed. Application is made to a system where thez -component of angular momentum is a constant of motion and results are discussed in connection with those obtained via symmetry considerations.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Green functions in the theory of semiconductor surfaces

Electronic properties of a few technologically important semiconductor surfaces, explored in surface Green function calculations, are presented and briefly discussed in comparison with experimental data from high-resolution surface spectroscopy. The emphasis is on results of first-principles calculations employing the local density approximation or the generalized gradient approximation of density functional theory. The systems addressed comprise of the prototype surfaces of the elemental semiconductors diamond and Si, as well as the group IV compound semiconductor SiC. The examples show that surface Green function calculations, as performed by Maria St licka and Sydney Davison in their early work on the surfaces of model systems, such as linear monoatomic chains or the Kronig–Penney model, can nowadays be applied to efficiently evaluate electronic properties of real surfaces. The results of such ab initio Green function calculations are found to be in very good agreement with experimental data.     

A point-charge representation of frost-model wave functions

A point-charge representation of Frost-model wave functions is derived from a symmetry-adapted perturbation theoretic expansion. The new point-charge model is simpler than those suggested previously yet gives good estimates of first-order molecular properties. The treatment can easily be extended to deal with second-order properties and, when this is done, formulae similar to those of the Drude theory are obtained. Using these formulae, theoretical expressions for the refractive indices of methane, ethane and water are computed and are in reasonable accord with experiment for the two hydrocarbons but less satisfactory for water.     

Systematic study of vibrational frequencies calculated with the self-consistent charge density functional tight-binding method

We present a detailed study of harmonic vibrational frequencies obtained with the self-consistent charge density functional tight-binding (SCC-DFTB) method. Our testing set comprises 66 molecules and 1304 distinct vibrational modes. Harmonic vibrational frequencies are computed using an efficient analytical algorithm developed and coded by the authors. The obtained results are compared to experiment and to other theoretical findings. Scaling factor for the SCC-DFTB method, determined by minimization of mean absolute deviation of scaled frequencies, is found to be 0.9933. The accuracy of the scaled SCC-DFTB frequencies is noticeably better than for other semiempirical methods (including standard DFTB method) and approximately twice worse than for other well established scaled ab initio quantum chemistry methods (e.g., HF, BLYP, B3LYP). Mean absolute deviation for the scaled SCC-DFTB frequencies is 56 cm(-1), while standard deviation is 82 cm(-1), and maximal absolute deviation is as large as 529 cm(-1). Using SCC-DFTB allows for substantial time savings; computational time is reduced from hours to seconds when compared to standard ab initio techniques.     

Tensorial green‐function theory of atomic‐wire T‐junction transmission

A tensorial Green‐function treatment of the electronic transmission properties of an atomic wire T‐junction is presented within the framework of the tight‐binding approximation. The adoption of the tensorial formalism enables overlap effects to be included in a straightforward manner, without the need to resort to a change in the Hilbert space. The T‐junction structure and the presence of overlap effects both give rise to antiresonances. Although those due to the former are located inside the energy band, the latter appear at the band edges. The transmission is seen to depend in different ways on the bond energy and the overlap between the attached atom and the wire. © 2012 Wiley Periodicals, Inc.     

Hydrogen surface passivation of Si and Ge nanowires: A semiempirical approach

A semiempirical nearest‐neighbor tight‐binding approach, that reproduces the indirect band gaps of elemental semiconductors, has been applied to study the electronic and optical properties of Si and Ge nanowires (NWs). The calculations show that Si‐NWs keep the indirect bandgap whereas Ge‐NWs changes into the direct bandgap when the wire cross section becomes smaller. Also, the band gap enhancement of Si‐NWs showing to quantum confinement effects is generally larger than that of similar‐sized Ge‐NWs, confirming the larger quantum confinement effects in Si than in Ge when they are confined in two dimensions. Finally, the dependence of the imaginary part of the dielectric function on the quantum confinement within two different schemes: intra‐atomic and interatomic optical matrix elements are applied. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2448–2454, 2010     

Electric and magnetic dipole shielding constants for the ground state of the relativistic hydrogen‐like atom: Application of the Sturmian expansion of the generalized Dirac‐Coulomb Green function

The Sturmian expansion of the generalized Dirac‐Coulomb Green function (Szmytkowski, J Phys B, 1997, 30, 825; erratum 1997, 30, 2747) is exploited to derive closed‐form expressions for electric $(\sigma_{E})$ and magnetic $(\sigma_{M})$ dipole shielding constants for the ground state of the relativistic hydrogen‐like atom with a point‐like and spinless nucleus of charge Ze. It is found that $\sigma_{E}=Z^{-1}$ (as it should be) and where $\gamma_{1}=\sqrt{1-(Z\alpha)^{2}}$ (α is the fine‐structure constant). This expression for $\sigma_{M}$ agrees with earlier findings of several other authors, obtained with the use of other analytical techniques, and is elementary compared to an alternative one presented recently by Cheng et al. (J Chem Phys 2009, 130, 144102), which involves an infinite series of ratios of the Euler's gamma functions. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Radial distribution functions of atoms and voids in large computer models of water

The molecular dynamics method is employed to construct models of 5832 water molecules at temperatures from 330 K to 250 K. The radial distributions of atoms and interstitial voids, as well as the corresponding structural factors, have been calculated. The first maximum of the structural factor of voids coincides in its position with the first maximum of the structural factor of oxygen atoms. Thus the first diffraction peak of water located at much smaller angles than for normal liquids (so-called prepeak) is caused by correlations in the arrangement of voids. The tetrahedricity of the hydrogen bond net of water described in different ways becomes more pronounced after overcooling of water.     

Performance of density‐functional tight‐binding models in describing hydrogen‐bonded anionic‐water clusters

Density‐functional tight‐binding (DFTB) models are computationally efficient approximations to density‐functional theory that have been shown to predict reliable structural and energetic properties for various systems. In this work, the reliability and accuracy of the self‐consistent‐charge DFTB model and its recent extension(s) in predicting the structures, binding energies, charge distributions, and vibrational frequencies of small water clusters containing polyatomic anions of the Hofmeister series (carbonate, sulfate, hydrogen phosphate, acetate, nitrate, perchlorate, and thiocyanate) have been carefully and systematically evaluated on the basis of high‐level ab initio quantum‐chemistry [MP2/aug‐cc‐pVTZ and CCSD(T)/aug‐cc‐pVQZ] reference data. Comparison with available experimental data has also been made for further validation. The self‐consistent‐charge DFTB model, and even more so its recent extensions, are shown to properly account for the structural properties, energetics, intermolecular polarization, and spectral signature of hydrogen‐bonding in anionic water clusters at a fraction of the computational cost of ab initio quantum‐chemistry methods. This makes DFTB models candidates of choice for investigating much larger systems such as seeded water droplets, their structural properties, formation thermodynamics, and infrared spectra. © 2014 Wiley Periodicals, Inc.     

The self‐consistent charge density functional tight‐binding theory study of carbon adatoms using tuned Hubbard U parameters

The self‐consistent charge density functional tight‐binding (DFTB) theory is a useful tool for realizing the electronic structures of large molecular complex systems. In this study, the electronic structure of C₆₁ formed by fullerene C₆₀ with a carbon adatom is analyzed, using the fully localized limit and pseudo self‐interaction correction methods of DFTB to adjust the Hubbard U parameter (DFTB + U). The results show that both the methods used to adjust U can significantly reduce the molecular orbital energy of occupied states localized on the defect carbon atom and improve the gap between highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) of C₆₁. This work will provide a methodological reference point for future DFTB calculations of the electronic structures of carbon materials.     

Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding

The Shift‐and‐invert parallel spectral transformations (SIPs), a computational approach to solve sparse eigenvalue problems, is developed for massively parallel architectures with exceptional parallel scalability and robustness. The capabilities of SIPs are demonstrated by diagonalization of density‐functional based tight‐binding (DFTB) Hamiltonian and overlap matrices for single‐wall metallic carbon nanotubes, diamond nanowires, and bulk diamond crystals. The largest (smallest) example studied is a 128,000 (2000) atom nanotube for which ～330,000 (～5600) eigenvalues and eigenfunctions are obtained in ～190 (～5) seconds when parallelized over 266,144 (16,384) Blue Gene/Q cores. Weak scaling and strong scaling of SIPs are analyzed and the performance of SIPs is compared with other novel methods. Different matrix ordering methods are investigated to reduce the cost of the factorization step, which dominates the time‐to‐solution at the strong scaling limit. A parallel implementation of assembling the density matrix from the distributed eigenvectors is demonstrated. © 2015 Wiley Periodicals, Inc.     

Green approach using monolithic column for simultaneous determination of coformulated drugs

Green chemistry and sustainability is now entirely encompassed across the majority of pharmaceutical companies and research labs. Researchers’ attention is careworn toward implementing the green analytical chemistry principles for more eco‐friendly analytical methodologies. Solvents play a dominant role in determining the greenness of the analytical procedure. Using safer solvents, the greenness profile of the methodology could be increased remarkably. In this context, a green chromatographic method has been developed and validated for the simultaneous determination of phenylephrine, paracetamol, and guaifenesin in their ternary pharmaceutical mixture. The chromatographic separation was carried out using monolithic column and green solvents as mobile phase. The use of monolithic column allows efficient separation protocols at higher flow rates, which results in short time of analysis. Two‐factor three‐level experimental design was used to optimize the chromatographic conditions. The greenness profile of the proposed methodology was assessed using eco‐scale as a green metrics and was found to be an excellent green method with regard to the usage and production of hazardous chemicals and solvents, energy consumption, and amount of produced waste. The proposed method improved the environmental impact without compromising the analytical performance criteria and could be used as a safer alternate for the routine analysis of the studied drugs.     

A theoretical study on cyclacenes: Analytical tight‐binding approach

We present a theoretical study of cyclacene molecules performed at tight‐binding level. The orbital energies and eigenvectors have been analytically computed, and exact expressions for the axial component of the total position spread and polarizability tensors have been obtained. In absence of dimerization, the system has a D_nh symmetry, where n is the number of hexagonal units. The energy bands present no gap at the Fermi level, and to this fact it corresponds a diverging (per‐electron) polarizability for in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the σ_h symmetry plane, conversely, remain finite for . The total position spread tensor presents a qualitatively different behavior, since all the three components of the position spread per electron remain finite for . The results are analyzed and discussed for both axial and planar components separately as these are affected differently with respect to the increasing system size. Both dipole polarizability and total position spread have been computed using an ab initio approach for the smallest systems, to compare the analytical tight‐binding expressions with a higher‐level theory.