1,270 research outputs found
ROHF Theory Made Simple
Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected
self-consistent unrestricted HF (UHF) model by mathematically constraining spin
density eigenvalues. The resulting constrained UHF (CUHF) wave function is
identical to that obtained from Roothaan's effective Fock operator. Our
and CUHF Fock operators are parameter-free and have canonical
orbitals and orbital energies that are physically meaningful as in UHF, except
for eliminating spin contamination. The present approach removes ambiguities in
ROHF orbital energies and the non-uniqueness of methods that build upon them.
We present benchmarks to demonstrate CUHF physical correctness and good
agreement with experimental results
Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations
The past several years have seen renewed interest in the use of
symmetry-projected Hartree-Fock for the description of strong correlations.
Unfortunately, these symmetry-projected mean-field methods do not adequately
account for dynamic correlation. Presumably, this shortcoming could be
addressed if one could combine symmetry-projected Hartree-Fock with a many-body
method such as coupled cluster theory, but this is by no means straightforward
because the two techniques are formulated in very different ways. However, we
have recently shown that the singlet -projected unrestricted Hartree-Fock
wave function can in fact be written in a coupled cluster-like wave function:
that is, the spin-projected unrestricted Hartree-Fock wave function can be
written as a polynomial of a double-excitation operator acting on some
closed-shell reference determinant. Here, we extend this result and show that
the spin-projected generalized Hartree-Fock wave function (which has both
and projection) is likewise a polynomial of low-order excitation
operators acting on a closed-shell determinant, and provide a closed-form
expression for the resulting polynomial coefficients. We include a few
preliminary applications of the combination of this spin-projected Hartree-Fock
and coupled cluster theory to the Hubbard Hamiltonian, and comment on
generalizations of the methodology. Results here are not for production level,
but a similarity transformed theory that combines the two offers the promise of
being accurate for both weak and strong correlation, and particularly may offer
significant improvements in the intermediate correlation regime where neither
projected Hartree-Fock nor coupled cluster is particularly accurate.Comment: accepted by Phys. Rev.
On the equivalence of LIST and DIIS methods for convergence acceleration
Self-consistent field extrapolation methods play a pivotal role in quantum
chemistry and electronic structure theory. We here demonstrate the mathematical
equivalence between the recently proposed family of LIST methods [J. Chem.
Phys. 134, 241103 (2011); J. Chem. Theory Comput. 7, 3045 (2011)] with Pulay's
DIIS [Chem. Phys. Lett. 73, 393 (1980)]. Our results also explain the
differences in performance among the various LIST methods
On the difference between variational and unitary coupled cluster theories
There have been assertions in the literature that the variational and unitary
forms of coupled cluster theory lead to the same energy functional. Numerical
evidence from previous authors was inconsistent with this claim, yet the small
energy differences found between the two methods and the relatively large
number of variational parameters precluded an unequivocal conclusion. Using the
Lipkin Hamiltonian, we here present conclusive numerical evidence that the two
theories yield different energies. The ambiguities arising from the size of the
cluster parameter space are absent in the Lipkin model, particularly when
truncating to double excitations. We show that in the symmetry adapted basis
under strong correlation the differences between the variational and unitary
models are large, whereas they yield quite similar energies in the weakly
correlated regime previously explored. We also provide a qualitative argument
rationalizing why these two models cannot be the same. Additionally, we study a
generalized non-unitary and non-hermitian variant that contains excitation,
de-excitation and mixed operators with different amplitudes and show that it
works best when compared to the traditional, variational, unitary, and extended
forms of coupled cluster doubles theories
A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
We introduce a mean-field and perturbative approach, based on clusters, to
describe the ground state of fermionic strongly-correlated systems. In cluster
mean-field, the ground state wavefunction is written as a simple tensor product
over optimized cluster states. The optimization of the single-particle basis
where the cluster mean-field is expressed is crucial in order to obtain
high-quality results. The mean-field nature of the ansatz allows us to
formulate a perturbative approach to account for inter-cluster correlations;
other traditional many-body strategies can be easily devised in terms of the
cluster states. We present benchmark calculations on the half-filled 1D and
(square) 2D Hubbard model, as well as the lightly-doped regime in 2D, using
cluster mean-field and second-order perturbation theory. Our results indicate
that, with sufficiently large clusters or to second-order in perturbation
theory, a cluster-based approach can provide an accurate description of the
Hubbard model in the considered regimes. Several avenues to improve upon the
results presented in this work are discussed.Comment: 22 pages, 21 figure
Edge Effects in Finite Elongated Graphene Nanoribbons
We analyze the relevance of finite-size effects to the electronic structure
of long graphene nanoribbons using a divide and conquer density functional
approach. We find that for hydrogen terminated graphene nanoribbons most of the
physical features appearing in the density of states of an infinite graphene
nanoribbon are recovered at a length of 40 nm. Nevertheless, even for the
longest systems considered (72 nm long) pronounced edge effects appear in the
vicinity of the Fermi energy. The weight of these edge states scales inversely
with the length of the ribbon and they are expected to become negligible only
at ribbons lengths of the order of micrometers. Our results indicate that
careful consideration of finite-size and edge effects should be applied when
designing new nanoelectronic devices based on graphene nanoribbons. These
conclusions are expected to hold for other one-dimensional systems such as
carbon nanotubes, conducting polymers, and DNA molecules.Comment: 4 pages, 4 figure
Composite Boson Mapping for Lattice Boson Systems
We present a canonical mapping transforming physical boson operators into
quadratic products of cluster composite bosons that preserves matrix elements
of operators when a physical constraint is enforced. We map the 2D lattice
Bose-Hubbard Hamiltonian into composite bosons and solve it at mean
field. The resulting Mott insulator-superfluid phase diagram reproduces well
Quantum Monte Carlo results. The Higgs boson behavior along the particle-hole
symmetry line is unraveled and in remarkable agreement with experiment. Results
for the properties of the ground and excited states are competitive with other
state-of-the-art approaches, but at a fraction of their computational cost. The
composite boson mapping here introduced can be readily applied to frustrated
many-body systems where most methodologies face significant hurdles.Comment: 8 pages, 4 figure
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