631 research outputs found
Hybrid functional calculations of the Al impurity in silica: Hole localization and electron paramagnetic resonance parameters
We performed first-principle calculations based on the supercell and cluster
approaches to investigate the neutral Al impurity in smoky quartz. Electron
paramagnetic resonance measurements suggest that the oxygens around the Al
center undergo a polaronic distortion which localizes the hole being on one of
the four oxygen atoms. We find that the screened exchange hybrid functional
successfully describes this localization and improves on standard local density
approaches or on hybrid functionals that do not include enough exact exchange
such as B3LYP. We find a defect level at about 2.5 eV above the valence band
maximum, corresponding to a localized hole in a O 2p orbital. The calculated
values of the g tensor and the hyperfine splittings are in excellent agreement
with experiment.Comment: 5 pages, 2 figures, 1 tabl
The mystery of relationship of mechanics and field in the many-body quantum world
We have revealed three fatal errors incurred from a blind transferring of
quantum field methods into the quantum mechanics. This had tragic consequences
because it produced crippled model Hamiltonians, unfortunately considered
sufficient for a description of solids including superconductors. From there,
of course, Fr\"ohlich derived wrong effective Hamiltonian, from which incorrect
BCS theory arose.
1) Mechanical and field patterns cannot be mixed. Instead of field methods
applied to the mechanical Born-Oppenheimer approximation we have entirely to
avoid it and construct an independent and standalone field pattern. This leads
to a new form of the Bohr's complementarity on the level of composite systems.
2) We have correctly to deal with the center of gravity, which is under the
field pattern "materialized" in the form of new quasipartiles - rotons and
translons. This leads to a new type of relativity of internal and external
degrees of freedom and one-particle way of bypassing degeneracies (gap
formation).
3) The possible symmetry cannot be apriori loaded but has to be aposteriori
obtained as a solution of field equations, formulated in a general form without
translational or any other symmetry. This leads to an utterly revised view of
symmetry breaking in non-adiabatic systems, namely Jahn-Teller effect and
superconductivity. These two phenomena are synonyms and share a unique symmetry
breaking.Comment: 24 pages, 9 sections; remake of abstract, introduction and
conclusion; more physics, less philosoph
Dual kinetic balance approach to basis set expansions for the Dirac equation
A new approach to finite basis sets for the Dirac equation is developed. It
solves the problem of spurious states and, as a result, improves the
convergence properties of basis set calculations. The efficiency of the method
is demonstrated for finite basis sets constructed from B splines by calculating
the one-loop self-energy correction for a hydrogenlike ion.Comment: 14 pages, 1 tabl
Relativistic J-matrix method
The relativistic version of the J-matrix method for a scattering problem on
the potential vanishing faster than the Coulomb one is formulated. As in the
non-relativistic case it leads to a finite algebraic eigenvalue problem. The
derived expression for the tangent of phase shift is simply related to the
non-relativistic case formula and gives the latter as a limit case. It is due
to the fact that the used basis set satisfies the ``kinetic balance
condition''.Comment: 21 pages, RevTeX, accepted for publication in Phys. Rev.
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
Correct quantum chemistry in a minimal basis from effective Hamiltonians
We describe how to create ab-initio effective Hamiltonians that qualitatively
describe correct chemistry even when used with a minimal basis. The
Hamiltonians are obtained by folding correlation down from a large parent basis
into a small, or minimal, target basis, using the machinery of canonical
transformations. We demonstrate the quality of these effective Hamiltonians to
correctly capture a wide range of excited states in water, nitrogen, and
ethylene, and to describe ground and excited state bond-breaking in nitrogen
and the chromium dimer, all in small or minimal basis sets
Centre-of-mass separation in quantum mechanics: Implications for the many-body treatment in quantum chemistry and solid state physics
We address the question to what extent the centre-of-mass (COM) separation
can change our view of the many-body problem in quantum chemistry and solid
state physics. It was shown that the many-body treatment based on the
electron-vibrational Hamiltonian is fundamentally inconsistent with the
Born-Handy ansatz so that such a treatment can never respect the COM problem.
Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case
where the degrees of freedom can be treated in a classical way. Beyond the B-O
approximation they are inseparable in principle. The unique covariant
description of all equations with respect to individual degrees of freedom
leads to new types of interaction: besides the known vibronic (electron-phonon)
one the rotonic (electron-roton) and translonic (electron-translon)
interactions arise. We have proved that due to the COM problem only the
hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true
physical meaning in molecules and crystals; nevertheless, the use of pure
vibrations (phonons) is justified only in the adiabatic systems. This fact
calls for the total revision of our contemporary knowledge of all non-adiabatic
effects, especially the Jahn-Teller effect and superconductivity. The vibronic
coupling is responsible only for removing of electron (quasi)degeneracies but
for the explanation of symmetry breaking and forming of structure the rotonic
and translonic coupling is necessary.Comment: 39 pages, 11 sections, 3 appendice
Review of biorthogonal coupled cluster representations for electronic excitation
Single reference coupled-cluster (CC) methods for electronic excitation are
based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in
terms of excited CC states, also referred to as correlated excited (CE) states,
and an associated set of states biorthogonal to the CE states, the latter being
essentially configuration interaction (CI) configurations. The bCC
representation generates a non-hermitian secular matrix, the eigenvalues
representing excitation energies, while the corresponding spectral intensities
are to be derived from both the left and right eigenvectors. Using the
perspective of the bCC representation, a systematic and comprehensive analysis
of the excited-state CC methods is given, extending and generalizing previous
such studies. Here, the essential topics are the truncation error
characteristics and the separability properties, the latter being crucial for
designing size-consistent approximation schemes. Based on the general order
relations for the bCC secular matrix and the (left and right) eigenvector
matrices, formulas for the perturbation-theoretical (PT) order of the
truncation errors (TEO) are derived for energies, transition moments, and
property matrix elements of arbitrary excitation classes and truncation levels.
In the analysis of the separability properties of the transition moments, the
decisive role of the so-called dual ground state is revealed. Due to the use of
CE states the bCC approach can be compared to so-called intermediate state
representation (ISR) methods based exclusively on suitably orthonormalized CE
states. As the present analysis shows, the bCC approach has decisive advantages
over the conventional CI treatment, but also distinctly weaker TEO and
separability properties in comparison with a full (and hermitian) ISR method
Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
We have applied the momentum space version of the Density Matrix
Renormalization Group method (-DMRG) in quantum chemistry in order to study
the accuracy of the algorithm in the new context. We have shown numerically
that it is possible to determine the desired accuracy of the method in advance
of the calculations by dynamically controlling the truncation error and the
number of block states using a novel protocol which we dubbed Dynamical Block
State Selection (DBSS). The relationship between the real error and truncation
error has been studied as a function of the number of orbitals and the fraction
of filled orbitals. We have calculated the ground state of the molecules
CH, HO, and F as well as the first excited state of CH. Our
largest calculations were carried out with 57 orbitals, the largest number of
block states was 1500--2000, and the largest dimensions of the Hilbert space of
the superblock configuration was 800.000--1.200.000.Comment: 12 page
State-of-the-Art Quantum Chemistry Meets Variable Reaction Coordinate Transition State Theory to Solve the Puzzling Case of the H2S + Cl System
The atmospheric reaction of HS with Cl has been reinvestigated to check
if, as previously suggested, only explicit dynamical computations can lead to
an accurate evaluation of the reaction rate because of strong recrossing
effects and the breakdown of the variational extension of transition state
theory. For this reason, the corresponding potential energy surface has been
thoroughly investigated, thus leading to an accurate characterization of all
stationary points, whose energetics has been computed at the state of the art.
To this end, coupled-cluster theory including up to quadruple excitations has
been employed, together with the extrapolation to the complete basis set limit
and also incorporating core-valence correlation, spin-orbit, and scalar
relativistic effects as well as diagonal Born-Oppenheimer corrections. This
highly accurate composite scheme has also been paralleled by less expensive yet
promising computational approaches. Moving to kinetics, variational transition
state theory and its variable reaction coordinate extension for barrierless
steps have been exploited, thus obtaining a reaction rate constant (8.16 x
10 cm molecule s at 300 K and 1 atm) in remarkable
agreement with the experimental counterpart. Therefore, contrary to previous
claims, there is no need to invoke any failure of the transition state theory,
provided that sufficiently accurate quantum-chemical computations are
performed. The investigation of the puzzling case of the HS + Cl system
allowed us to present a robust approach for disclosing the thermochemistry and
kinetics of reactions of atmospheric and astrophysical interest.Comment: 49 pages, 7 figures, published online in JCT
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