Inversion-free formulation of the direct recursion (transfer matrix) method

The transfer matrix or direct recursion methods (DRM), the indirect (exact) perturbation methods (IPM) and the indirect recursion methods (IRM) — the latter two commonly called resolvent or Green function methods — are briefly discussed. Lee and Joannopoulos have shown the very computational advantages of a traditional DRM. For its further improvement, a new inversion-free DRM (IF DRM) is proposed which is based on the application of generalized eigenvalue equations. In the present formulation, the IF DRM is applicable to study surface electronic problems of bounded perfect crystals. The method of the framework translation is also described which avoids the Schmidt—Hori—Asahi-type transfer matrix trick. It is convenient to study layered structures. Finally, the advantages of a new IRM are stressed which also avoids the inversion difficulty.     

Self-consistent determination of surface and interface magnetism via the recursion method

We report our recent study of magnetic moments in metallic multilayer systems with the recursion method. We discuss the onset of live magnetic layers in vanadium and palladium slabs with different thicknesses and also for Pd layers epitaxially grown on Ag. Antiparall coupling at the interface between iron and chromium is always obtained.     

A method of calculation of the matrix elements between the spin-projected nonorthogonal Slater determinants

In the resonating Hartree–Fock calculation, we have to calculate the matrix element between spin-projected nonorthogonal Slater determinants (S dets). The matrix element between coherently spin-rotated S dets are given by a linear transformation of the spin-projected ones. Using the inverse transformation, we get the projected matrix elements from the coherently spin-rotated ones. By appropriately choosing the angles of the spin rotation, the required computational time is considerably reduced. © 1995 John Wiley & Sons, Inc.     

On the calculation of expectation values and transition matrix elements by coupled cluster method

Summary Finite order expressions are derived for expectation values and transition matrix elements within the framework of the coupled cluster method.     

Solution crystallisation via a submerged liquid-liquid phase boundary: oiling out

In many situations the process of crystallisation from solution is known to occur via metastable crystalline states (polymorphs or solvates). Here we present what we believe to be a novel example of small molecule crystallisation in which the initial separation of a solute rich liquid phase precedes the crystallisation event. We believe this occurs because a submerged liquid-liquid phase boundary is accessible within the metastable zone of the crystal nucleation process.     

A method for the rapid calculation of matrix elements with highly oscillatory JWKB radial wavefunctions

A method for the rapid computation of matrix elements with JWKB radial wavefunctions is discussed. The method consists of dividing the range of integration into segments determined by the nodes of the semiclassical wavefunction. The desired matrix elements are calculated by summing the contributions from each segment which are evaluated by integrating between nodes with a Gauss-Mehler quadrature formula. The results are compared with exact quantum mechanical calculations and were found to agree within 1–2%. The calculations with the present method were generally five to ten times faster than the quantum mechanical calculations.     

A simple method for controllable preparation of polymer nanotubes via a single capillary electrospinning

Polymer nanotubes have been successfully electrospun via a single capillary spinneret instead of coaxial electrospinning. By altering the volume of ethanol under a fixed amount of poly(vinyl pyrrolidone) (PVP) and tetraethyl orthosilicate (TEOS) in the precursor, the nanotubes could be controllably produced for a proper concentration of PVP solution. Further investigation showed that the diameters of nanotubes, the thicknesses of nanotube walls, and the ratios of the thickness of the nanotube wall to the nanotube diameter (RTNWND) could be controlled by altering the amount of TEOS in the precursor. With increasing the ratios of TEOS to PVP solution, the nanotube diameters were increased and the nanotube walls were decreased. Thus, the RTNWND were decreased. The applied voltages also have an effect on the nanotube diameter and the thickness of the nanotube wall, but little on the RTNWND. The effects of ethanol and TEOS on evaporation and phase separation processes were discussed.     

Isotropic periodic sum: a method for the calculation of long-range interactions

This work presents an accurate and efficient approach to the calculation of long-range interactions for molecular modeling and simulation. This method defines a local region for each particle and describes the remaining region as images of the local region statistically distributed in an isotropic and periodic way, which we call isotropic periodic images. Different from lattice sum methods that sum over discrete lattice images generated by periodic boundary conditions, this method sums over the isotropic periodic images to calculate long-range interactions, and is referred to as the isotropic periodic sum (IPS) method. The IPS method is not a lattice sum method and eliminates the need for a reciprocal space sum. Several analytic solutions of IPS for commonly used potentials are presented. It is demonstrated that the IPS method produces results very similar to that of Ewald summation, but with three major advantages, (1) it eliminates unwanted symmetry artifacts raised from periodic boundary conditions, (2) it can be applied to potentials of any functional form and to fully and partially homogenous systems as well as finite systems, and (3) it is more computationally efficient and can be easily parallelized for multiprocessor computers. Therefore, this method provides a general approach to an efficient calculation of long-range interactions for various kinds of molecular systems.     

On the convergence improvement in the metadynamics simulations: a Wang-Landau recursion approach

As a popular tool in exploring free energy landscapes, the metadynamics method has been widely applied to elucidate various chemical or biochemical processes. As deeply discussed by Laio et al. [J. Phys. Chem. B 109, 6714 (2005)], the size of the updating Gaussian function is pivotal to the free energy convergence toward the target free energy surface. For instance, a greater Gaussian height can facilitate the quick visit of a conformation region of interest; however, it may lead to a larger error of the calculated free energy surface. In contrast, a lower Gaussian height can guarantee a better resolution of the calculated free energy surface; however, it will take longer time for such a simulation to navigate through the defined conformational region. In order to reconcile such confliction, the authors present a method by implementing the Wang-Landau recursion scheme in the metadynamics simulations to adaptively update the height of the unit Gaussian function. As demonstrated in their model studies on both a toy system, and a realistic molecular system treated with the hybrid quantum mechanical and molecular mechanical (QMMM) potential, the present approach can quickly result in more decently converged free energy surfaces, compared with the classical metadynamics simulations employing the fixed Gaussian heights.     

A fast algorithm for calculation of the distance matrix of a molecule

A rapid method is described for calculating the number of bonds on the shortest path between each two pairs of atoms of a molecule.     

The first observation in an organic medium and DFT calculation of the TMM radical anion generated via a single electron reduction of a methylenecyclopropane

γ-Irradiation of 2,2-diphenyl-1-methylenecyclopropane (3) in a degassed 2-methyltetrahydrofuran glassy matrix at 77 K gave an intense UV/vis absorption band with λ_ab at 496 nm. This result and calculations based on density functional theory for its radical anion 3⁻ and the corresponding trimethylenemethane radical anion (2⁻) strongly suggest that single electron reduction of 3 followed by ready ring opening affords 2⁻, whose molecular geometry is largely twisted (θ = 45.5°), and the negative charge and spin are localized mainly in the diphenyl methyl and allyl moieties, respectively.     

Classical S matrix: Application of the Bessel uniform approximation to a chemical reaction

The Bessel uniform approximation developed by Stine and Marcus is applied to the collinear H + H₂ reaction on Diestler's potential energy surface no. 3 to which we have previously applied other orders of approximation of classical S matrix theory. It appears that an accurate treatment of this system by classical S matrix theory requires interference of real and complex trajectories. Calculations were also performed on two other potential energy surfaces in order to more clearly understand the interrelationships of previous semiclassical and quasiclassical studies of this reaction.     

Full variational molecular orbital method: Application to the positron-molecule complexes

Optimal Gaussian-type orbital (GTO) basis sets of positron and electron in positron-molecule complexes are proposed by using the full variational treatment of molecular orbital (FVMO) method. The analytical expression for the energy gradient with respect to parameters of positronic and electronic GTO such as the orbital exponents, the orbital centers, and the linear combination of atomic orbital (LCAO) coefficients, is derived. Wave functions obtained by the FVMO method include the effect of electronic or positronic orbital relaxation explicitly and satisfy the virial and Hellmann–Feynman theorems completely. We have demonstrated the optimization of each orbital exponent in various positron-atomic and anion systems, and estimated the positron affinity (PA) as the difference between their energies. Our PA obtained with small basis set is in good agreement with the numerical Hartree–Fock result. We have calculated the OH⁻ and [OH⁻; e⁺] species as the positron-molecular system by the FVMO method. This result shows that the positronic basis set not only becomes more diffuse but also moves toward the oxygen atom. Moreover, we have applied this method to determine both the nuclear and electronic wave functions of LiH and LiD molecules simultaneously, and obtained the isotopic effect directly. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 491–501, 1998     

Measuring metal homogeneity in a matrix via the measurement of the ratio metal to matrix oxide using ICP-MS

A simple method has been developed that allows a fast determination of the homogeneity of an element M in an alloy, even for minor components. This is done by measuring a ratio of ion currents I, I ^M/I ^M’O, whereby M’ is the matrix element, by inductively coupled plasma mass spectrometry (ICP-MS). The method can be used to determine the homogeneity of one component in a binary alloy and allows to estimate the sample size necessary to minimise uncertainty contributions due to inhomogeneity in the analysis of such an alloy. In this work the homogeneity of a niobium/0.1% zirconium alloy was determined on 1 mg samples. Accurate weighings of these small samples are not required, as the method is based on the measurement of the niobium/zirconium amount ratio in the dissolved samples. As this ratio is fairly large, the Zr/NbO amount ratio was measured instead to decrease the magnitude of the measured ratio. This ratio was found to be sufficiently stable over time for homogeneity testing. In this particular case the Zr/NbO ratio in the samples was found to vary by 0.049 relative for a 1 mg samples size.