1,323 research outputs found
The limitations of Slater's element-dependent exchange functional from analytic density functional theory
Our recent formulation of the analytic and variational Slater-Roothaan (SR)
method, which uses Gaussian basis sets to variationally express the molecular
orbitals, electron density and the one body effective potential of density
functional theory, is reviewed. Variational fitting can be extended to the
resolution of identity method,where variationality then refers to the error in
each two electron integral and not to the total energy. It is proposed that the
appropriate fitting functions be charge neutral and that all ab initio energies
be evaluated using two-center fits of the two-electron integrals. The SR method
has its root in the Slater's Xalpha method and permits an arbitrary scaling of
the Slater-Gaspar-Kohn-Sham exchange-correlation potential around each atom in
the system. Of several ways of choosing the scaling factors (Slater's exchange
parameters), two most obvious are the Hartree-Fock (HF), alpha_HF, values and
the exact atomic, alpha_EA, values. The performance of this simple analytic
model with both sets for atomization energies of G2 set of 148 molecules is
better than the local density approximation or the HF theory, although the
errors in atomization energy are larger than the target chemical accuracy.
To improve peformance for atomization energies, the SR method is
reparametrized to give atomization energies of 148 molecules to be comparbale
to those obtained by one of the most widely used generalized gradient
approximations. The mean absolute error in ionization potentials of 49 atoms
and molecules is about 0.5 eV and that in bond distances of 27 molecules is
about 0.02 Angstrom. The overall good performance of the computationally
efficient SR method using any reasonable set of alpha values makes it a
promising method for study of large systems.Comment: 33 pages, Uses RevTex, to appear in The Journal of Chemical Physic
Accurate molecular energies by extrapolation of atomic energies using an analytic quantum mechanical model
Using a new analytic quantum mechanical method based on Slater's Xalpha
method, we show that a fairly accurate estimate of the total energy of a
molecule can be obtained from the exact energies of its constituent atoms. The
mean absolute error in the total energies thus determined for the G2 set of 56
molecules is about 16 kcal/mol, comparable to or better than some popular pure
and hybrid density functional models.Comment: 5 pages, REVTE
Static dielectric response of icosahedral fullerenes from C60 to C2160 by an all electron density functional theory
The static dielectric response of C60, C180, C240, C540, C720, C960, C1500,
and C2160 fullerenes is characterized by an all-electron density-functional
method. First, the screened polarizabilities of C60, C180, C240, and C540, are
determined by the finite-field method using Gaussian basis set containing 35
basis functions per atom. In the second set of calculations, the unscreened
polarizabilities are calculated for fullerenes C60 through C2160 from the
self-consistent Kohn-Sham orbitals and eigen-values using the sum-over-states
method. The approximate screened polarizabilities, obtained by applying a
correction determined within linear response theory show excellent agreement
with the finite-field polarizabilities. The static dipole polarizability per
atom in C2160 is (4 Angstrom^3) three times larger than that in C60 (1.344
Angstrom^3). Our results reduce the uncertainty in various theoretical models
used previously to describe the dielectric response of fullerenes and show that
quantum size effects in polarizability are significantly smaller than
previously thought.Comment: RevTex, 3 figure
Recommended from our members
High Frequency (4th order) Sequence Stratigraphy of Early Miocene Deltaic Shorelines, Offshore Texas and Louisiana
DOE-NETL Award Numbers DE-FE0026083 and DEFE0029487Bureau of Economic Geolog
Effect of nonlinearity on the dynamics of a particle in dc field-induced systems
Dynamics of a particle in a perfect chain with one nonlinear impurity and in
a perfect nonlinear chain under the action of dc field is studied numerically.
The nonlinearity appears due to the coupling of the electronic motion to
optical oscillators which are treated in adiabatic approximation.
We study for both the low and high values of field strength. Three different
range of nonlinearity is obtained where the dynamics is different. In low and
intermediate range of nonlinearity, it reduces the localization. In fact in the
intermediate range subdiffusive behavior in the perfect nonlinear chain is
obtained for a long time. In all the cases a critical value of nonlinear
strength exists where self-trapping transition takes place. This critical value
depends on the system and the field strength. Beyond the self-trapping
transition nonlinearity enhances the localization.Comment: 9 pages, Revtex, 6 ps figures include
Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder
Statistical and scaling properties of the Lyapunov exponent for a
tight-binding model with the diagonal disorder described by a dichotomic
process are considered near the band edge. The effect of correlations on
scaling properties is discussed. It is shown that correlations lead to an
additional parameter governing the validity of single parameter scaling.Comment: 5 pages, 3 figures, RevTe
Stationary Localized States Due to a Nonlinear Dimeric Impurity Embedded in a Perfect 1-D Chain
The formation of Stationary Localized states due to a nonlinear dimeric
impurity embedded in a perfect 1-d chain is studied here using the appropriate
Discrete Nonlinear Schrdinger Equation. Furthermore, the nonlinearity
has the form, where is the complex amplitude. A proper
ansatz for the Localized state is introduced in the appropriate Hamiltonian of
the system to obtain the reduced effective Hamiltonian. The Hamiltonian
contains a parameter, which is the ratio of stationary
amplitudes at impurity sites. Relevant equations for Localized states are
obtained from the fixed point of the reduced dynamical system. = 1 is
always a permissible solution. We also find solutions for which . Complete phase diagram in the plane comprising of both
cases is discussed. Several critical lines separating various regions are
found. Maximum number of Localized states is found to be six. Furthermore, the
phase diagram continuously extrapolates from one region to the other. The
importance of our results in relation to solitonic solutions in a fully
nonlinear system is discussed.Comment: Seven figures are available on reques
Topological Phases in Graphitic Cones
The electronic structure of graphitic cones exhibits distinctive topological
features associated with the apical disclinations. Aharonov-Bohm
magnetoconductance oscillations (period Phi_0) are completely absent in rings
fabricated from cones with a single pentagonal disclination. Close to the apex,
the local density of states changes qualitatively, either developing a cusp
which drops to zero at the Fermi energy, or forming a region of nonzero density
across the Fermi energy, a local metalization of graphene.Comment: 4 pages, RevTeX 4, 3 PostScript figure
Solution of the relativistic Dirac-Hulthen problem
The one-particle three-dimensional Dirac equation with spherical symmetry is
solved for the Hulthen potential. The s-wave relativistic energy spectrum and
two-component spinor wavefunctions are obtained analytically. Conforming to the
standard feature of the relativistic problem, the solution space splits into
two distinct subspaces depending on the sign of a fundamental parameter in the
problem. Unique and interesting properties of the energy spectrum are pointed
out and illustrated graphically for several values of the physical parameters.
The square integrable two-component wavefunctions are written in terms of the
Jacobi polynomials. The nonrelativistic limit reproduces the well-known
nonrelativistic energy spectrum and results in Schrodinger equation with a
"generalized" three-parameter Hulthen potential, which is the sum of the
original Hulthen potential and its square.Comment: 13 pages, 3 color figure
Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion
To study the shape formation process of carbon nanotubes, a string equation
describing the possible existing shapes of the axis-curve of multishell carbon
tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy,
that is the difference between the MCT energy and the energy of the
carbonaceous mesophase (CM). It is shown that there exists a threshold relation
of the outmost and inmost radii, that gives a parameter regime in which a
straight MCT will be bent or twisted. Among the deformed shapes, the regular
coiled MCTs are shown being one of the solutions of the string equation. In
particular,the optimal ratio of pitch and radius for such a coil is
found to be equal to , which is in good agreement with recent
observation of coil formation in MCTs by Zhang et al.Comment: RevTeX, no figure, 12 pages, to appear in Phys. Rev. Let
- …