Screened Coulomb interaction in the maximally localized Wannier basis

We discuss a maximally localized Wannier function approach for constructing lattice models from first-principles electronic structure calculations, where the effective Coulomb interactions are calculated in the constrained random-phase-approximation. The method is applied to the 3d transition metals and a perovskite (SrVO_3). We also optimize the Wannier functions by unitary transformation so that U is maximized. Such Wannier functions unexpectedly turned out to be very close to the maximally localized ones.Comment: 22 pages, 6 figure

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

Molecular-orbital theory for the stopping power of atoms in the low velocity regime:the case of helium in alkali metals

A free-parameter linear-combination-of-atomic-orbitals approach is presented for analyzing the stopping power of slow ions moving in a metal. The method is applied to the case of He moving in alkali metals. Mean stopping powers for He present a good agreement with local-density-approximation calculations. Our results show important variations in the stopping power of channeled atoms with respect to their mean values.Comment: LATEX, 3 PostScript Figures attached. Total size 0.54

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

Astronomical identification of CN-, the smallest observed molecular anion

We present the first astronomical detection of a diatomic negative ion, the cyanide anion CN-, as well as quantum mechanical calculations of the excitation of this anion through collisions with para-H2. CN- is identified through the observation of the J = 2-1 and J = 3-2 rotational transitions in the C-star envelope IRC +10216 with the IRAM 30-m telescope. The U-shaped line profiles indicate that CN-, like the large anion C6H-, is formed in the outer regions of the envelope. Chemical and excitation model calculations suggest that this species forms from the reaction of large carbon anions with N atoms, rather than from the radiative attachment of an electron to CN, as is the case for large molecular anions. The unexpectedly large abundance derived for CN-, 0.25 % relative to CN, makes likely its detection in other astronomical sources. A parallel search for the small anion C2H- remains so far unconclusive, despite the previous tentative identification of the J = 1-0 rotational transition. The abundance of C2H- in IRC +10216 is found to be vanishingly small, < 0.0014 % relative to C2H.Comment: 5 pages, 4 figures; accepted for publication in A&A Letter

Second bound state of the positronium molecule and biexcitons

A new, hitherto unknown bound state of the positronium molecule, with orbital angular momentum L=1 and negative parity is reported. This state is stable against autodissociation even if the masses of the positive and negative charges are not equal. The existence of a similar state in two-dimension has also been investigated. The fact that the biexcitons have a second bound state may help the better understanding of their binding mechanism.Comment: Latex, 8 pages, 2 Postscript figure