Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

Complete Active Space Iterative Coupled Cluster Theory

In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected CC. This is accomplished by establishing a feedback loop between the CC and CAS parts of a calculation through a similarity transformation of the Hamiltonian with those CC amplitudes that are not encompassed by the active space. We denote this approach as the complete active space iterative coupled cluster (CASiCC) ansatz. We investigate its efficiency and accuracy in the singles and doubles approximation by studying the prototypical molecules H4, H8, H2O, and N2. Our results demonstrate that CASiCC systematically improves on the single-reference CCSD and the externally corrected CCSD methods across entire potential energy curves while retaining modest computational costs. However, the tailored coupled cluster method shows superior performance in the strong correlation regime, suggesting that its accuracy is based on error compensation. We find that the iterative versions of externally corrected and tailored coupled cluster methods converge to the same results.

The accuracies of effective interactions in downfolding coupled-cluster approaches for small-dimensionality active spaces

This paper evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories.

Quantum Flow Algorithms for Simulating Many-Body Systems on Quantum Computers

We conducted quantum simulations of strongly correlated systems using the quantum flow (QFlow) approach, which enables sampling large subspaces of the Hilbert space through coupled variational problems in reduced dimensionality active spaces. Our QFlow algorithms significantly reduce circuit complexity and pave the way for scalable and constant-circuit-depth quantum computing. Our simulations show that QFlow can optimize the collective number of wave function parameters without increasing the required qubits using active spaces having an order of magnitude fewer number of parameters.

Projection-Based Density Matrix Renormalization Group in Density Functional Theory Embedding

The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals

Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC_n method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, AC_n is more efficient than existing ab initio multireference dynamic correlation methods. AC_n affords excellent results for singlet-triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.

Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version

An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin-orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S₀ → S₁ vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. A UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.