11 research outputs found
Projected Coupled Cluster Theory
Coupled cluster theory is the method of choice for weakly correlated systems.
But in the strongly correlated regime, it faces a symmetry dilemma, where it
either completely fails to describe the system, or has to artificially break
certain symmetries. On the other hand, projected Hartree-Fock theory captures
the essential physics of many kinds of strong correlations via symmetry
breaking and restoration. In this work, we combine and try to retain the merits
of these two methods by applying symmetry projection to broken symmetry coupled
cluster wavefunctions. The non-orthogonal nature of states resulting from the
application of symmetry projection operators furnishes particle-hole
excitations to all orders, thus creating an obstacle for the exact evaluation
of overlaps. Here we provide a solution via a disentanglement framework theory
that can be approximated rigorously and systematically. Results of projected
coupled cluster theory are presented for molecules and the Hubbard model,
showing that spin projection significantly improves unrestricted coupled
cluster theory while restoring good quantum numbers. The energy of projected
coupled cluster theory reduces to the unprojected one in the thermodynamic
limit, albeit at a much slower rate than projected Hartree-Fock.Comment: Submitted to JCP. Extra figures appear in the ancillary fil
Tensor-Structured Coupled Cluster Theory
We derive and implement a new way of solving coupled cluster equations with
lower computational scaling. Our method is based on decomposition of both
amplitudes and two electron integrals, using a combination of tensor
hypercontraction and canonical polyadic decomposition. While the original
theory scales as with respect to the number of basis functions, we
demonstrate numerically that we achieve sub-millihartree difference from the
original theory with scaling. This is accomplished by solving directly
for the factors that decompose the cluster operator. The proposed scheme is
quite general and can be easily extended to other many-body methods
Projected Coupled Cluster Theory: Optimization of cluster amplitudes in the presence of symmetry projection
Methods which aim at universal applicability must be able to describe both
weak and strong electronic correlation with equal facility. Such methods are in
short supply. The combination of symmetry projection for strong correlation and
coupled cluster theory for weak correlation offers tantalizing promise to
account for both on an equal footing. In order to do so, however, the coupled
cluster portion of the wave function must be optimized in the presence of the
symmetry projection. This paper discusses how this may be accomplished, and
shows the importance of doing so for both the Hubbard model Hamiltonian and the
molecular Hamiltonian, all with a computational scaling comparable to that of
traditional coupled cluster theory.Comment: revised versio
Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
We present a similarity transformation theory based on a polynomial form of a
particle-hole pair excitation operator. In the weakly correlated limit, this
polynomial becomes an exponential, leading to coupled cluster doubles. In the
opposite strongly correlated limit, the polynomial becomes an extended Bessel
expansion and yields the projected BCS wavefunction. In between, we interpolate
using a single parameter. The effective Hamiltonian is non-hermitian and this
Polynomial Similarity Transformation Theory follows the philosophy of
traditional coupled cluster, left projecting the transformed Hamiltonian onto
subspaces of the Hilbert space in which the wave function variance is forced to
be zero. Similarly, the interpolation parameter is obtained through minimizing
the next residual in the projective hierarchy. We rationalize and demonstrate
how and why coupled cluster doubles is ill suited to the strongly correlated
limit whereas the Bessel expansion remains well behaved. The model provides
accurate wave functions with energy errors that in its best variant are smaller
than 1\% across all interaction stengths. The numerical cost is polynomial in
system size and the theory can be straightforwardly applied to any realistic
Hamiltonian
Composite fermion-boson mapping for fermionic lattice models
We present a mapping of elementary fermion operators onto a quadratic form of
composite fermionic and bosonic operators. The mapping is an exact isomorphism
as long as the physical constraint of one composite particle per cluster is
satisfied. This condition is treated on average in a composite particle
mean-field approach, which consists of an ansatz that decouples the composite
fermionic and bosonic sectors. The theory is tested on the one- and
two-dimensional Hubbard models. Using a Bogoliubov determinant for the
composite fermions and either a coherent or Bogoliubov state for the bosons, we
obtain a simple and accurate procedure for treating the Mott insulating phase
of the Hubbard model with mean-field computational cost
Ring-locking enables selective anhydrosugar synthesis from carbohydrate pyrolysis
NEWS COVERAGE: A news release based on this journal publication is available online: http://news.rice.edu/2016/08/08/another-brick-in-the-molecule/The selective production of platform chemicals from thermal conversion of biomass-derived carbohydrates is challenging. As precursors to natural products and drug molecules, anhydrosugars are difficult to synthesize from simple carbohydrates in large quantities without side products, due to various competing pathways during pyrolysis. Here we demonstrate that the nonselective chemistry of carbohydrate pyrolysis is substantially improved by alkoxy or phenoxy substitution at the anomeric carbon of glucose prior to thermal treatment. Through this ring-locking step, we found that the selectivity to 1,6-anhydro-β-D-glucopyranose (levoglucosan, LGA) increased from 2% to greater than 90% after fast pyrolysis of the resulting sugar at 600 °C. DFT analysis indicated that LGA formation becomes the dominant reaction pathway when the substituent group inhibits the pyranose ring from opening and fragmenting into non-anhydrosugar products. LGA forms selectively when the activation barrier for ring-opening is significantly increased over that for 1,6-elimination, with both barriers affected by the substituent type and anomeric position. These findings introduce the ring-locking concept to sugar pyrolysis chemistry and suggest a chemical-thermal treatment approach for upgrading simple and complex carbohydrates