1,581 research outputs found
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
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
Deciphering the Curly Arrow Representation and Electron Flow for the 1,3-Dipolar Rearrangement between Acetonitrile Oxide and (1S,2R,4S)â2-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 CâC bond takes place via a usual sharing
model before the OâC 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 NâC
triple bond and creation of the V(N) and V(C) monosynaptic basins, depopulation of the
former CâC double bond with the creation of V(C,C) basins, and final formation of the V(O,C) basin associated with the OâC
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
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
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.
Bayesian inference of biochemical kinetic parameters using the linear noise approximation
Background
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.
Results
We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.
Conclusion
The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods
Proposal of an extended t-J Hamiltonian for high-Tc cuprates from ab initio calculations on embedded clusters
A series of accurate ab initio calculations on Cu_pO-q finite clusters,
properly embedded on the Madelung potential of the infinite lattice, have been
performed in order to determine the local effective interactions in the CuO_2
planes of La_{2-x}Sr_xCuO_4 compounds. The values of the first-neighbor
interactions, magnetic coupling (J_{NN}=125 meV) and hopping integral
(t_{NN}=-555 meV), have been confirmed. Important additional effects are
evidenced, concerning essentially the second-neighbor hopping integral
t_{NNN}=+110meV, the displacement of a singlet toward an adjacent colinear
hole, h_{SD}^{abc}=-80 meV, a non-negligible hole-hole repulsion
V_{NN}-V_{NNN}=0.8 eV and a strong anisotropic effect of the presence of an
adjacent hole on the values of the first-neighbor interactions. The dependence
of J_{NN} and t_{NN} on the position of neighbor hole(s) has been rationalized
from the two-band model and checked from a series of additional ab initio
calculations. An extended t-J model Hamiltonian has been proposed on the basis
of these results. It is argued that the here-proposed three-body effects may
play a role in the charge/spin separation observed in these compounds, that is,
in the formation and dynamic of stripes.Comment: 24 pages, 4 figures, submitted to Phys. Rev.
Graphite and Hexagonal Boron-Nitride Possess the Same Interlayer Distance. Why?
Graphite and hexagonal boron nitride (h-BN) are two prominent members of the
family of layered materials possessing a hexagonal lattice. While graphite has
non-polar homo-nuclear C-C intra-layer bonds, h-BN presents highly polar B-N
bonds resulting in different optimal stacking modes of the two materials in
bulk form. Furthermore, the static polarizabilities of the constituent atoms
considerably differ from each other suggesting large differences in the
dispersive component of the interlayer bonding. Despite these major differences
both materials present practically identical interlayer distances. To
understand this finding, a comparative study of the nature of the interlayer
bonding in both materials is presented. A full lattice sum of the interactions
between the partially charged atomic centers in h-BN results in vanishingly
small monopolar electrostatic contributions to the interlayer binding energy.
Higher order electrostatic multipoles, exchange, and short-range correlation
contributions are found to be very similar in both materials and to almost
completely cancel out by the Pauli repulsions at physically relevant interlayer
distances resulting in a marginal effective contribution to the interlayer
binding. Further analysis of the dispersive energy term reveals that despite
the large differences in the individual atomic polarizabilities the
hetero-atomic B-N C6 coefficient is very similar to the homo-atomic C-C
coefficient in the hexagonal bulk form resulting in very similar dispersive
contribution to the interlayer binding. The overall binding energy curves of
both materials are thus very similar predicting practically the same interlayer
distance and very similar binding energies.Comment: 18 pages, 5 figures, 2 table
Three-body non-additive forces between spin-polarized alkali atoms
Three-body non-additive forces in systems of three spin-polarized alkali
atoms (Li, Na, K, Rb and Cs) are investigated using high-level ab initio
calculations. The non-additive forces are found to be large, especially near
the equilateral equilibrium geometries. For Li, they increase the three-atom
potential well depth by a factor of 4 and reduce the equilibrium interatomic
distance by 0.9 A. The non-additive forces originate principally from chemical
bonding arising from sp mixing effects.Comment: 4 pages, 3 figures (in 5 files
Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
Precise variational solutions are given for problems involving diverse
fermionic and bosonic -body systems. The trial wave functions are chosen
to be combinations of correlated Gaussians, which are constructed from products
of the single-particle Gaussian wave packets through an integral
transformation, thereby facilitating fully analytical calculations of the
matrix elements. The nonlinear parameters of the trial function are chosen by a
stochastic technique. The method has proved very efficient, virtually exact,
and it seems feasible for any few-body bound-state problems emerging in nuclear
or atomic physics.Comment: 39 pages (revtex) + 3 figures (appended as compressed uuencoded .ps
files
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