Browsing by Author "Zhao, Jinmo"

Now showing 1 - 6 of 6
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    Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
    (American Physical Society, 2016) Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.
    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 wave function. 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 strengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
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    Projected coupled cluster theory
    (AIP Publishing, 2017) Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo; Scuseria, Gustavo E.
    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 wave functions. 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.
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    Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection
    (AIP Publishing, 2018) Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo; Scuseria, Gustavo E.
    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.
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    Ring-locking enables selective anhydrosugar synthesis from carbohydrate pyrolysis
    (Royal Society of Chemistry, 2016) Chen, Li; Zhao, Jinmo; Pradhan, Sivaram; Brinson, Bruce E.; Scuseria, Gustavo E.; Zhang, Z. Conrad; Wong, Michael S.
    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.
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    Symbolic solution for computational quantum many-body theory development
    (2018-03-02) Zhao, Jinmo; Scuseria, Gustavo E; Wolynes, Peter G; Várilly-Alvarado, Anthony
    Computational many-body theories in quantum chemistry, condensed matter, and nuclear physics aim to provide sufficiently accurate description of and insights into the motion of many interacting particles. Due to their intrinsic complexity, the development of such theories generally involves very complex, tedious, and error-prone symbolic manipulations. Here a complete solution to automate the symbolics in many-body theory development is attempted. General data structures based on an existing computer algebra system are designed to specifically address the symbolic problems for which there is currently no satisfactory handling. Based on the data structures, algorithms are given to accomplish common symbolic manipulations and simplifications. Noncommutative algebraic systems, tensors with symmetry, and symbolic summations can all enjoy deep simplifications efficient enough for theories of very complex form. After the symbolic derivation, novel algorithms for automatic optimization of tensor contractions and their sums are devised, which can be used together with automatic code generation tools. In this way, the burden of symbolic tasks in theory development can be vastly reduced, with the potential to spare scientists more time and energy for the actual art and science of many-body theories.
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    Tensor-structured coupled cluster theory
    (AIP Publishing, 2017) Schutski, Roman; Zhao, Jinmo; Henderson, Thomas M.; Scuseria, Gustavo E.
    We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on the 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(N6) with respect to the number of basis functions, we demonstrate numerically that we achieve sub-millihartree difference from the original theory with O(N4) 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.