1,879 research outputs found

### 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

### Deciphering the Curly Arrow Representation and Electron Flow for the 1,3-Dipolar Rearrangement between Acetonitrile Oxide and (1S,2R,4S)â€‘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 Câˆ’C bond takes place via a usual sharing
model before the Oâˆ’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 Nâˆ’C
triple bond and creation of the V(N) and V(C) monosynaptic basins, depopulation of the
former Câˆ’C double bond with the creation of V(C,C) basins, and final formation of the V(O,C) basin associated with the Oâˆ’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

### 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.

### Direct generation of local orbitals for multireference treatment and subsequent uses for the calculation of the correlation energy

We present a method that uses the one-particle density matrix to generate directly localized orbitals
dedicated to multireference wave functions. On one hand, it is shown that the definition of local
orbitals making possible physically justified truncations of the CAS ~complete active space! is
particularly adequate for the treatment of multireference problems. On the other hand, as it will be
shown in the case of bond breaking, the control of the spatial location of the active orbitals may
permit description of the desired physics with a smaller number of active orbitals than when starting
from canonical molecular orbitals. The subsequent calculation of the dynamical correlation energy
can be achieved with a lower computational effort either due to this reduction of the active space,
or by truncation of the CAS to a shorter set of references. The ground- and excited-state energies are
very close to the current complete active space self-consistent field ones and several examples of
multireference singles and doubles calculations illustrate the interest of the procedur

### 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

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