Tuning the electrical conductivity of nanotube-encapsulated metallocene wires

We analyze a new family of carbon nanotube-based molecular wires, formed by encapsulating metallocene molecules inside the nanotubes. Our simulations, that are based on a combination of non-equilibrium Green function techniques and density functional theory, indicate that these wires can be engineered to exhibit desirable magnetotransport effects for use in spintronics devices. The proposed structures should also be resilient to room-temperature fluctuations, and are expected to have a high yield.Comment: 4 pages, 6 figures. Accepted in Physical Review Letter

Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

A priori Wannier functions from modified Hartree-Fock and Kohn-Sham equations

The Hartree-Fock equations are modified to directly yield Wannier functions following a proposal of Shukla et al. [Chem. Phys. Lett. 262, 213-218 (1996)]. This approach circumvents the a posteriori application of the Wannier transformation to Bloch functions. I give a novel and rigorous derivation of the relevant equations by introducing an orthogonalizing potential to ensure the orthogonality among the resulting functions. The properties of these, so-called a priori Wannier functions, are analyzed and the relation of the modified Hartree-Fock equations to the conventional, Bloch-function-based equations is elucidated. It is pointed out that the modified equations offer a different route to maximally localized Wannier functions. Their computational solution is found to involve an effort that is comparable to the effort for the solution of the conventional equations. Above all, I show how a priori Wannier functions can be obtained by a modification of the Kohn-Sham equations of density-functional theory.Comment: 7 pages, RevTeX4, revise

New representation of orbital motion with arbitrary angular momenta

A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total angular momentum $L$, and thereby needs no explicit coupling of partial waves between particles. A simple generating function for the correlated Gaussian is exploited to derive the matrix elements. The formulation is applied to various Coulomb three-body systems such as $e^-e^-e^+, tt\mu, td\mu$, and $\alpha e^-e^-$ up to $L=4$ in order to show its usefulness and versatility. A stochastic selection of the basis functions gives good results for various angular momentum states.Comment: Revte

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters

We report a first-principles theoretical study of hyperfine interactions, zero-point effects and defect energetics of muonium and hydrogen impurities in silicon and germanium. The spin-polarized density functional method is used, with the crystalline orbitals expanded in all-electron Gaussian basis sets. The behaviour of hydrogen and muonium impurities at both the tetrahedral and bond-centred sites is investigated within a supercell approximation. To describe the zero-point motion of the impurities, a double adiabatic approximation is employed in which the electron, muon/proton and host lattice degrees of freedom are decoupled. Within this approximation the relaxation of the atoms of the host lattice may differ for the muon and proton, although in practice the difference is found to be slight. With the inclusion of zero-point motion the tetrahedral site is energetically preferred over the bond-centred site in both silicon and germanium. The hyperfine and superhyperfine parameters, calculated as averages over the motion of the muon, agree reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.

Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

Deciphering the Curly Arrow Representation and Electron Flow for the 1,3-Dipolar Rearrangement between Acetonitrile Oxide and (1S,2R,4S)‑2-Cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl Acetate Derivatives

This study is focused on describing the molecular mechanism beyond the molecular picture provided by the evolution of molecular orbitals, valence bond structures along the reaction progress, or conceptual density functional theory. Using bonding evolution theory (BET) analysis, we have deciphered the mechanism of the 1,3-dipolar rearrangement between acetonitrile oxide and (1S,2R,4S)-2-cyano-7-oxabicyclo[2.2.1]hept-5-en-2-yl acetate derivatives. The BET study revealed that the formation of the C−C bond takes place via a usual sharing model before the O−C one that is also formed in the halogenated species through a not very usual sharing model. The mechanism includes depopulation of the electron density at the N−C triple bond and creation of the V(N) and V(C) monosynaptic basins, depopulation of the former C−C double bond with the creation of V(C,C) basins, and final formation of the V(O,C) basin associated with the O−C bond. The topological changes along the reaction pathway take place in a highly synchronous way. BET provides a convenient quantitative method for deriving curly arrows and electron flow representation to unravel molecular mechanisms