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Annual reports in computational chemistry

Regularized and Renormalized Many-Body Techniques for Describing Correlated Molecular Systems: A Coupled-Cluster Perspective

Karol Kowalski, Jiří Brabec, Bo Peng

Published Jan 1, 2018• 7 citations
Publisher
DOI
10.1016/bs.arcc.2018.06.001

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We discuss reduced-scaling strategies employing the recently introduced subsystem embedding subalgebra (SES) coupled-cluster (CC) formalism to describe quantum many-body systems. These strategies utilize properties of the SES CC formulations where the equations describing certain classes of subsystems can be integrated into computational flows composed of coupled eigenvalue problems of reduced dimensionality. Additionally, these flows can be determined at the level of the CC ansatz by the inclusion of selected classes of cluster amplitudes, which define the wave-function ``memory'' of possible partitioning of the many-body system into constituent subsystems. One of the possible ways of solving these coupled problems is through implementing procedures where the information is passed between the subsystems in a self-consistent manner. As a special case we consider local flow formulations where the local character of correlation effects can be closely related to the properties of subsystem embedding subalgebras employing a localized molecular basis. We also generalize flow equations to the time domain and to downfolding methods utilizing a double-exponential unitary CC ansatz, where the reduced dimensionality of constituent subproblems offers a possibility of efficient utilization of limited quantum resources in modeling realistic systems.
Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious fermionic modes. Our method shows reduced theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear $\ce{H10}$-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wavefunction methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.
This study integrates a Hermitian coupled-cluster downfolding technique with the Density Matrix Renormalization Group (DMRG) method to accurately treat both static and dynamic correlations in complex electronic systems. By calculating ground-state energies of active-space Hamiltonians via DMRG, we achieve efficient and accurate simulations of strongly correlated systems, demonstrated on molecular benchmarks including N 2, benzene, porphyrin, and tetramethyleneethane. This combined approach offers a promising advancement in computational chemistry for complex chemical processes.