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 $O(N^6)$ with respect to the number of basis functions, we demonstrate numerically that we achieve sub-millihartree difference from the original theory with $O(N^4)$ 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

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