Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems

Symmetry-projected cluster mean-field theory applied to spin systems

We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

A power series approximation in symmetry projected coupled cluster theory

Projected Hartree–Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. On the other hand, single-reference methods, such as configuration interaction or coupled cluster theory, can handle weakly correlated problems but cannot properly account for strong correlations. Ideally, we would like to combine these techniques in a symmetry-projected coupled cluster approach, but this is far from straightforward. In this work, we provide an alternative formulation to identify the so-called disentangled cluster operators, which arise when we combine these two methodological strands. Our formulation shows promising results for model systems and small molecules.

Improved Description and Efficient Implementation of Spin-Projected Perturbation Theory for Practical Applications

In this study, we continue to develop the recently proposed second-order perturbation theory for the spin-projected Hartree-Fock method [Tsuchimochi, T.; Ten-no, S. L. J. Chem. Theory Comput. 2019, 15, 6688] in various aspects. A new, stable imaginary level-shift scheme is derived to obtain a well-conditioned equation, enabling a significantly faster convergence. To achieve a further speed-up, we propose a preconditioning scheme considering the pair character on a spin-projected basis. We also eliminate the computational memory bottleneck in solving the linear equation for large systems using a distributed memory parallel implementation. Finally, for the description of open-shell molecules, several modified zeroth-order Hamiltonians are introduced and tested using the Mn₂O₂(NHCHCO₂)₄ complex. These developments enable practical calculations of a second-order perturbation theory with improved accuracy at a reduced computational cost.

Coupled-Cluster Calculations of Neutrinoless Double-β Decay in ^{48}Ca

We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-β decay of ^{48}Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For ^{48}Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-β decay of ^{48}Ca with a quenching factor deduced from two-body currents in recent ab initio calculation of the Ikeda sum rule in ^{48}Ca [Gysbers et al., Nat. Phys. 15, 428 (2019)NPAHAX1745-247310.1038/s41567-019-0450-7].

A multireference coupled-electron pair approximation combined with complete-active space perturbation theory in local pair-natural orbital framework

The Complete-Active Space Second-order Perturbation Theory (CASPT2) has been one of the most widely-used methods for reliably calculating electronic structures of multireference systems. Because of its lowest level treatment of dynamic correlation, it has a high computational feasibility; however, its accuracy in some cases falls short of needs. Here, as a simple yet higher-order alternative, we introduce a hybrid theory of the CASPT2 and a multireference variant of the Coupled-Electron Pair Approximation (CEPA), which is a class of high level correlation theory. A central feature of our theory (CEPT2) is to use the two underlying theories for describing different divisions of correlation components based on the full internal contraction framework. The external components, which usually give a major contribution to the dynamic correlation, are intensively described using the CEPA Ansatz, while the rests are treated at the CASPT2 level. Furthermore, to drastically reduce the computational demands, we have incorporated the pair-natural orbital (PNO) method into our multireference implementations. This development, thus, requires highly complex derivations and coding, while it has been largely facilitated with an automatic expression and code generation technique. To highlight the accuracy of the CEPT2 approach and to assess the errors caused by the PNO truncation, benchmark calculations are shown on small- to medium-size molecules, illustrating the high accuracy of the present CEPT2 model. By tightening the truncation thresholds, the PNO-CEPT2 energy converges toward the canonical counterpart and is more accurate than that of PNO-CASPT2 as long as the same truncation thresholds are used.

Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations

Our goal is to remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. Previous work along these lines has taken us from a diagram-level analysis of the coupled-cluster equations to an understanding of the collective modes which can occur in various channels of the coupled-cluster equations to the exploration of non-exponential wavefunctions in efforts to combine coupled-cluster theory with symmetry projection. In this manuscript, we extend these efforts by introducing a new, polynomial product wavefunction ansatz that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods. We describe the new approach in detail within the context of our previous efforts, explore some illustrative calculations, and consider one route for reducing the computational cost of the new method.

Extending spin-symmetry projected coupled-cluster to large model spaces using an iterative null-space projection technique

Recently, we introduced an orbital-invariant approximate coupled-cluster (CC) method in the spin-projection manifold. The multi-determinantal property of spin-projection means that the parametrization in the spin-extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi-reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin-projected Hartree-Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null-space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F₂ and transition metal complexes such as NiO, Mn₂ , and [Cu₂ O₂ ]²⁺ , which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin-projected Hartree-Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.