FCIQMC-Tailored Distinguishable Cluster Approach

Striking the right balance of encoding electron correlation in the Hamiltonian and the wavefunction ansatz

Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell molecules and chemical reactions. Multi-configurational models are therefore essential to establish universally applicable, predictive ab initio methods for chemistry. Here, we present a discussion of explicit correlation approaches which address the nagging problem of dealing with static and dynamic electron correlation in multi-configurational active-space approaches. We review the latest developments and then point to their key obstacles. Our discussion is supported by new data obtained with tensor network methods. We argue in favor of simple electron-only correlator expressions that may allow one to define transcorrelated models in which the correlator does not bear a dependence on molecular structure.

Orbital optimisation in xTC transcorrelated methods

We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Additionally, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.

Permutation symmetry in spin-adapted many-body wave functions

In the domain of exchange-coupled polynuclear transition-metal (PNTM) clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the configuration interaction (CI) eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, . Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the number of distinct site permutations.

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.

Renormalized Internally Contracted Multireference Coupled Cluster with Perturbative Triples

In this work, we combine the many-body formulation of the internally contracted multireference coupled cluster (ic-MRCC) method with Evangelista's multireference formulation of the driven similarity renormalization group (DSRG). The DSRG method can be viewed as a unitary multireference coupled cluster theory, which renormalizes the amplitudes based on a flow equation approach to eliminate numerical instabilities. We extend this approach by demonstrating that the unitary flow equation approach can be adapted for nonunitary transformations, rationalizing the renormalization of ic-MRCC amplitudes. We denote the new approach, the renormalized ic-MRCC (ric-MRCC) method. To achieve high accuracy with a reasonable computational cost, we introduce a new approximation to the Baker-Campbell-Hausdorff expansion. We fully consider the linear commutator while approximating the quadratic commutator, for which we neglect specific contractions involving amplitudes with active indices. Moreover, we introduce approximate perturbative triples to obtain the ric-MRCCSD[T] method. We demonstrate the accuracy of our approaches in comparison to advanced multireference methods for the potential energy curves of H8, F2, H2O, N2, and Cr2. Additionally, we show that ric-MRCCSD and ric-MRCSSD[T] match the accuracy of CCSD(T) for evaluating spectroscopic constants and of full configuration interaction energies for a set of small molecules.

Quantum Information Orbitals (QIO): Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality

The simultaneous treatment of static and dynamic correlations in strongly correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wave function is a formidable and longstanding problem. As a contribution toward its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wave function, once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more nontrivial information on the many-body wave function, indicated by the improved wave function and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C2 and Cr2 molecule.

A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems

The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multiconfigurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference-coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper, we explore the potential of incorporating ideas from conventional MRCC-namely, the treatment of the strongly correlated space in a configuration interaction formalism-to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.

Performance of a one-parameter correlation factor for transcorrelation: Study on a series of second row atomic and molecular systems

In this work, we investigate the performance of a recently proposed transcorrelated (TC) approach based on a single-parameter correlation factor [E. Giner, J. Chem. Phys. 154, 084119 (2021)] for systems involving more than two electrons. The benefit of such an approach relies on its simplicity as efficient numerical-analytical schemes can be set up to compute the two- and three-body integrals occurring in the effective TC Hamiltonian. To obtain accurate ground state energies within a given basis set, the present TC scheme is coupled to the recently proposed TC-full configuration interaction quantum Monte Carlo method [Cohen et al., J. Chem. Phys. 151, 061101 (2019)]. We report ground state total energies on the Li-Ne series, together with their first cations, computed with increasingly large basis sets and compare to more elaborate correlation factors involving electron-electron-nucleus coordinates. Numerical results on the Li-Ne ionization potentials show that the use of the single-parameter correlation factor brings on average only a slightly lower accuracy (1.2 mH) in a triple-zeta quality basis set with respect to a more sophisticated correlation factor. However, already using a quadruple-zeta quality basis set yields results within chemical accuracy to complete basis set limit results when using this novel single-parameter correlation factor. Calculations on the H₂O, CH₂, and FH molecules show that a similar precision can be obtained within a triple-zeta quality basis set for the atomization energies of molecular systems.

Explicitly Correlated Electronic Structure Calculations with Transcorrelated Matrix Product Operators

In this work, we present the first implementation of the transcorrelated electronic Hamiltonian in an optimization procedure for matrix product states by the density matrix renormalization group (DMRG) algorithm. In the transcorrelation ansatz, the electronic Hamiltonian is similarity-transformed with a Jastrow factor to describe the cusp in the wave function at electron-electron coalescence. As a result, the wave function is easier to approximate accurately with the conventional expansion in terms of one-particle basis functions and Slater determinants. The transcorrelated Hamiltonian in first quantization comprises up to three-body interactions, which we deal with in the standard way by applying robust density fitting to two- and three-body integrals entering the second-quantized representation of this Hamiltonian. The lack of hermiticity of the transcorrelated Hamiltonian is taken care of along the lines of the first work on transcorrelated DMRG [ J. Chem. Phys. 2020, 153, 164115] by encoding it as a matrix product operator and optimizing the corresponding ground state wave function with imaginary-time time-dependent DMRG. We demonstrate our quantum chemical transcorrelated DMRG approach at the example of several atoms and first-row diatomic molecules. We show that transcorrelation improves the convergence rate to the complete basis set limit in comparison to conventional DMRG. Moreover, we study extensions of our approach that aim at reducing the cost of handling the matrix product operator representation of the transcorrelated Hamiltonian.

FCIQMC-Tailored Distinguishable Cluster Approach: Open-Shell Systems

A recently proposed tailored approach based on the distinguishable cluster method and the stochastic FCI solver, FCIQMC [J. Chem. Theory Comput. 2020, 16, 5621], is extended to open-shell molecular systems. The method is employed to calculate spin gaps of various Fe(II) complexes, including a Fe(II) porphyrin model system. Both distinguishable cluster and fully relaxed CASSCF natural orbitals were used in this work as reference for the subsequent tailored distinguishable cluster calculations. The distinguishable cluster natural orbitals occupation numbers were also used as an aid to the selection of the active space. The effect of the active space sizes and of the explicit correlation correction (F12) onto the predicted spin gaps is investigated. The tailored distinguishable cluster with singles and doubles yields consistently more accurate results compared to the tailored coupled cluster with singles and doubles.

Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach

In this article, we demonstrate that a first-order spin penalty scheme can be efficiently applied to the Slater determinant based Full-CI Quantum Monte Carlo (FCIQMC) algorithm, as a practical route toward spin purification. Two crucial applications are presented to demonstrate the validity and robustness of this scheme: the ¹Δ_g ← ³Σ_g vertical excitation in O₂ and key spin gaps in a [Mn₃^(IV)O₄] cluster. In the absence of a robust spin adaptation/purification technique, both applications would be unattainable by Slater determinant based ground state methods, with any starting wave function collapsing into the higher-spin ground state during the optimization. This strategy can be coupled to other algorithms that use the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver, including the Stochastic Generalized Active Space, the similarity-transformed FCIQMC, the tailored-CC, and second-order perturbation theory approaches. Moreover, in contrast to the GUGA-FCIQMC technique, this strategy features both spin projection and total spin adaptation, making it appealing when solving anisotropic Hamiltonians. It also provides spin-resolved reduced density matrices, important for the investigation of spin-dependent properties in polynuclear transition metal clusters, such as the hyperfine-coupling constants.

Full Configuration Interaction Quantum Monte Carlo treatment of fragments embedded in a periodic mean field

We present an embedded fragment approach for high-level quantum chemical calculations on local features in periodic systems. The fragment is defined as a set of localized orbitals (occupied and virtual) corresponding to a converged periodic Hartree-Fock solution. These orbitals serve as the basis for the in-fragment post-Hartree Fock treatment. The embedding field for the fragment, consisting of the Coulomb and exchange potential from the rest of the crystal, is included in the fragment's one-electron Hamiltonian. As an application of the embedded fragment approach we investigate the performanceof full configuration interaction quantum Monte Carlo (FCIQMC) with the adaptive shift. As the orbital choice we use the natural orbitals from the distinguishable cluster method with singles and doubles. FCIQMC is a stochastic approximation to the full CI method and can be routinely applied to much larger active spaces than the latter. This makes this method especially attractive in the context of open shell defects in crystals, where fragments of adequate size can be ratherlarge. As a test case we consider dissociation of a fluorine atom from a fluorographane surface. This process poses a challenge for high-level electronic structure models as both the static and dynamic correlations are essential here. Furthermore the active space for an adequate fragment (32 electrons in 173 orbitals) is already quite large even for FCIQMC. Despite this, FCIQMC delivers accurate dissociation and total energies.

Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various small- and medium-sized molecules containing diatomics (N₂, F₂, C₂, CN⁺, CO, BN, BO⁺, and Cr₂) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Stochastic Generalized Active Space Self-Consistent Field: Theory and Application

An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overhead of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF [5·(6, 6)] optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS toward fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the ³E_g over the ⁵A_1g spin state; (c) the study of an Fe₄S₄ cluster's spin-ladder energetics via highly truncated stochastic-GAS [4·(5, 5)] wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.

The Sign Problem in Density Matrix Quantum Monte Carlo

Density matrix quantum Monte Carlo (DMQMC) is a recently developed method for stochastically sampling the N-particle thermal density matrix to obtain exact-on-average energies for model and ab initio systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants. In principle, this means that DMQMC needs to sample a space that scales in the system size, N, as O[(exp(N))²]. In practice, removing the sign problem requires a total walker population that exceeds a system-dependent critical walker population (N_c), imposing limitations on both storage and compute time. We establish that N_c for DMQMC is the square of N_c for FCIQMC. By contrast, the minimum N_c in the interaction picture modification of DMQMC (IP-DMQMC) is only linearly related to the N_c for FCIQMC. We find that this difference originates from the difference in propagation of IP-DMQMC versus canonical DMQMC: the former is asymmetric, whereas the latter is symmetric. When an asymmetric mode of propagation is used in DMQMC, there is a much greater stochastic error and is thus prohibitively expensive for DMQMC without the interaction picture adaptation. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger systems with large basis sets. This suggests that IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.

Accuracy of the distinguishable cluster approximation for triple excitations for open-shell molecules and excited states

The distinguishable cluster approximation for triple excitations has been applied to calculate thermochemical properties and excited states involving closed-shell and open-shell species, such as small molecules, 3d transition metal atoms, ozone, and an iron-porphyrin model. Excitation energies have been computed using the ΔCC approach by directly optimizing the excited states. A fixed-reference technique has been introduced to target selected spin-states for open-shell molecular systems. The distinguishable cluster approximation consistently improves coupled cluster with singles doubles and triples results for absolute and relative energies. For excited states dominated by a single configuration state function, the fixed-reference approach combined with high-level coupled-cluster methods has a comparable accuracy to the corresponding equation-of-motion coupled-cluster methods with a negligible amount of spin contamination.

Taming the Sign Problem in Auxiliary-Field Quantum Monte Carlo Using Accurate Wave Functions

We explore different ways of incorporating accurate trial wave functions into free projection auxiliary-field quantum Monte Carlo (fp-AFQMC). States employed include coupled-cluster singles and doubles, multi-Slater, and symmetry-projected mean-field wave functions. We adapt a recently proposed fast multi-Slater local energy evaluation algorithm for fp-AFQMC, making the use of long expansions from selected configuration interaction methods feasible. We demonstrate how these wave functions serve to mitigate the sign problem and accelerate convergence in quantum chemical problems, allowing the application of fp-AFQMC to systems of substantial sizes. Our calculations on the widely studied model Cu₂O₂²⁺ system show that many previously reported isomerization energies differ substantially from the near-exact fp-AFQMC value.

Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD(T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources

We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We use the density matrix renormalization group (DMRG) and heat-bath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H₂O, N₂, and F₂. We find that the triples correction significantly improves upon ecCCSD, and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes against the accuracy of the subsequent CC calculation. In this context, we find that very approximate wave functions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the ecCCSD and renormalized triples combination studied in this work via a well-known wave function diagnostic.

Spin-Conserved and Spin-Flip Optical Excitations from the Bethe-Salpeter Equation Formalism

Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe–Salpeter equation (BSE) formalism of many-body perturbation theory, in its static approximation, is “blind” to double (and higher) excitations, which are ubiquitous, for example, in conjugated molecules like polyenes. Here, we apply the spin-flip ansatz (which considers the lowest triplet state as the reference configuration instead of the singlet ground state) to the BSE formalism in order to access, in particular, double excitations. The present scheme is based on a spin-unrestricted version of the GW approximation employed to compute the charged excitations and screened Coulomb potential required for the BSE calculations. Dynamical corrections to the static BSE optical excitations are taken into account via an unrestricted generalization of our recently developed (renormalized) perturbative treatment. The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries.

A full configuration interaction quantum Monte Carlo study of ScO, TiO, and VO molecules

Accurate ab initio calculations of 3d transition metal monoxide molecules have attracted extensive attention because of their relevance in physical and chemical science as well as theoretical challenges in treating strong electron correlation. Meanwhile, recent years have witnessed the rapid development of the full configuration interaction quantum Monte Carlo (FCIQMC) method to tackle electron correlation. In this study, we carry out FCIQMC simulations to ScO, TiO, and VO molecules and obtain accurate descriptions of 13 low-lying electronic states (ScO ²Σ⁺, ²Δ, ²Π; TiO ³Δ, ¹Δ, ¹Σ⁺, ³Π, ³Φ; VO ⁴Σ^-, ⁴Φ, ⁴Π, ²Γ, ²Δ), including states that have significant multi-configurational character. The FCIQMC results are used to assess the performance of several other wave function theory and density functional theory methods. Our study highlights the challenging nature of the electronic structure of transition metal oxides and demonstrates FCIQMC as a promising technique going forward to treat more complex transition metal oxide molecules and materials.

High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F-F bond breaking in F₂, the automerization of cyclobutadiene, and the double dissociation of the water molecule.

A new form of transcorrelated Hamiltonian inspired by range-separated DFT

The present work introduces a new form of explicitly correlated factor in the context of the transcorrelated methods. The new correlation factor is obtained from the r₁₂ ≈ 0 mathematical analysis of the transcorrelated Hamiltonian, and its analytical form is obtained such that the leading order in 1/r₁₂ of the scalar part of the effective two-electron potential reproduces the long-range interaction of the range-separated density functional theory. The resulting correlation factor exactly imposes the cusp and is tuned by a unique parameter μ, which controls both the depth of the coulomb hole and its typical range in r₁₂. The transcorrelated Hamiltonian obtained with such a new correlation factor has a straightforward analytical expression depending on the same parameter μ, and its physical contents continuously change by varying μ: One can change from a non-divergent repulsive Hamiltonian at large μ to a purely attractive one at small μ. We investigate the convergence of the ground state eigenvalues and right eigenvectors of such a new transcorrelated Hamiltonian as a function of the basis set and as a function of μ on a series of two-electron systems. We found that the convergence toward the complete basis set is much faster for quite a wide range of values of μ. We also propose a specific value of μ, which essentially reproduces the results obtained with the frozen Gaussian geminal introduced by Ten-no [Chem. Phys. Lett. 330, 169 (2000)].

The Shape of Full Configuration Interaction to Come

We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.

Tailored coupled cluster theory in varying correlation regimes

The tailored coupled cluster (TCC) approach is a promising ansatz that preserves the simplicity of single-reference coupled cluster theory while incorporating a multi-reference wave function through amplitudes obtained from a preceding multi-configurational calculation. Here, we present a detailed analysis of the TCC wave function based on model systems, which require an accurate description of both static and dynamic correlation. We investigate the reliability of the TCC approach with respect to the exact wave function. In addition to the error in the electronic energy and standard coupled cluster diagnostics, we exploit the overlap of TCC and full configuration interaction wave functions as a quality measure. We critically review issues, such as the required size of the active space, size-consistency, symmetry breaking in the wave function, and the dependence of TCC on the reference wave function. We observe that possible errors caused by symmetry breaking can be mitigated by employing the determinant with the largest weight in the active space as reference for the TCC calculation. We find the TCC model to be promising in calculations with active orbital spaces which include all orbitals with a large single-orbital entropy, even if the active spaces become very large and then may require modern active-space approaches that are not restricted to comparatively small numbers of orbitals. Furthermore, utilizing large active spaces can improve on the TCC wave function approximation and reduce the size-consistency error because the presence of highly excited determinants affects the accuracy of the coefficients of low-excited determinants in the active space.