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In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born-Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace (complete active space (CAS)) of the considered Hubert space that covers the static correlation. A one-particle spectral gap assumption is introduced, separating the CAS from the remaining Hubert space. This replaces the nonexisting or nearly nonexisting gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital usually encountered in standard single-reference quantum chemistry. The analysis covers, in particular, CC methods tailored by tensor-network states (TNS-TCC methods). The problem is formulated in a nonlinear functional analysis framework, and, under certain conditions such as the aforementioned gap, local uniqueness and existence are proved using Zarantonello's lemma. From the Aubin-Nitscheduality method, a quadratic error bound valid for TNS-TCC methods is derived, e.g., for lineartensor-network TCC schemes using the density matrix renormalization group method.

The mathematical foundation of the so-called extended coupled-cluster method for the solution of the many-fermion Schrödinger equation is here developed. We prove an existence and uniqueness result, both in the full infinite-dimensional amplitude space as well as for discretized versions of it. The extended coupled-cluster method is formulated as a critical point of an energy function using a generalization of the Rayleigh-Ritz principle: the bivariational principle. This gives a quadratic bound for the energy error in the discretized case. The existence and uniqueness results are proved using a type of monotonicity property for the flipped gradient of the energy function. A comparison to the analysis of the standard coupled-cluster method is made, and it is argued that the bivariational principle is a useful tool, both for studying coupled-cluster type methods and for developing new computational schemes in general.

The method of moments of coupled-cluster equations (MMCC), which provides a systematic way of improving the results of the standard coupled-cluster (CC) and equation-of-motion CC (EOMCC) calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The MMCC theory and its generalized MMCC (GMMCC) extension that enables one to use the cluster operators resulting from the standard as well as nonstandard CC calculations, including those obtained with the extended CC (ECC) approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction (CI) and CC or EOMCC energies. These relationships can be used to design the noniterative corrections to the CC/EOMCC energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference CC/EOMCC methods fail. Several MMCC and GMMCC approximations are discussed, including the renormalized and completely renormalized CC/EOMCC methods for closed- and open-shell states, the quadratic MMCC approaches, the CI-corrected MMCC methods, and the GMMCC approaches for multiple bond breaking based on the ECC cluster amplitudes.

Barium monofluoride (BaF) is a polar molecule of interest in measurements of the electron electric dipole moment. For this purpose, efforts are underway to investigate this molecule embedded within cryogenic matrices, e.g., in solid Ne. For a theoretical understanding of the electronic structure of such an embedded molecule, the need arises for efficient methods which are accurate but also able to handle a number of atoms which surround the molecule. The calculation for gas-phase BaF can be reduced to involve only outer electrons by representing the inner core of Ba with a pseudopotential, while carrying out a non-relativistic calculation with an appropriate basis set. Thus, the method is effectively at a scalar-relativistic level. In this work, we demonstrate to which extent this can be achieved using coupled-cluster methods to deal with electron correlation. As a test case, the SrF(X2Σ+→B2Σ+) transition is investigated, and excellent accuracy is obtained with the EOM-CC3 method. For the BaF(X2Σ+→A′2Δ, X2Σ+→A2Π, X2Σ+→B2Σ+) transitions, various coupled-cluster approaches are compared with very good agreement for EOM-CC3 with experimentally derived spectroscopic parameters, at the level of tens of cm−1. An exception is the excitation to the A′2Δ state, for which the energy is overestimated by 230cm−1. The poor convergence behavior for this particular state is demonstrated by providing results from calculations with basis sets of n = 3, 4, 5)-zeta quality. The calculated excitation energy for the B2Σ+ state agrees better with a deperturbation analysis than with the effective spectroscopic value, with a difference of 120cm−1.

The performance of the recently proposed version of the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (SD), which employs a modest-size configuration interaction wave function as an external source for a small subset of approximate connected three- and four-body cluster amplitudes that are primarily responsible for the nondynamic correlation effects, and which has been perturbatively corrected for the remaining triples along the same line as in the standard CCSD(T) method (Li X., Paldus J.: J. Chem. Phys. 2006 , 124 , 174101), referred to by the acronym RMR CCSD(T), is being tested by evaluating equilibrium spectroscopic constants for a demanding system of the beryllium dimer, as well as by computing atomization energies for several di- and triatomics. The focus is on the equilibrium properties, since it has been demonstrated earlier that the RMR CCSD method corrects well for the nondynamic correlation in bond-breaking situations. We find that in all the cases we have examined, the RMR CCSD(T) method does in fact improve the performance of CCSD(T) even in the vicinity of the equilibrium geometry. For states possessing a moderate multireference character, the improvement in computed thermochemical properties relative to CCSD(T) amounts to a few kJ/mol, a meaningful amount when striving for chemical accuracy.

Quantum computing leverages the principles of quantum mechanics in novel ways to tackle complex chemistry problems that cannot be accurately addressed using traditional quantum chemistry methods. However, the high computational cost and available number of physical qubits with high fidelity limit its application to small chemical systems. This work employed a quantum-classical framework which features a quantum active space-embedding approach to perform simulations of chemical reactions that require up to 14 qubits. This framework was applied to prototypical example metal hydrogenation reactions: the coupling between hydrogen and Li2, Li3, and Li4 clusters. Particular attention was paid to the computation of barriers and reaction energies. The predicted reaction profiles compare well with advanced classical quantum chemistry methods, demonstrating the potential of the quantum embedding algorithm to map out reaction profiles of realistic gas-phase chemical reactions to ascertain qualitative energetic trends. Additionally, the predicted potential energy curves provide a benchmark to compare against both current and future quantum embedding approaches.

Accurate potential energy curves (PECs) are determined for the twenty-two electronic states of LiRb. In contrast to previous studies, the applied approach relies on the first principle calculations involving correlation among all electrons. The current methodology is founded on the multireference coupled cluster (CC) scheme constructed within the Fock space (FS) formalism, specifically for the (2,0) sector. The FS methodology is established within the framework of the intermediate Hamiltonian formalism and offers an intruder-free, efficient computational scheme. This method has a distinctive feature that, when applied to the doubly ionized system, provides the characteristics of the neutral case. This proves especially beneficial when investigating PECs in situations where a closed-shell molecule dissociates into open-shell fragments, yet its double positive ion forms closed-shell species. In every instance, we successfully computed continuous PECs spanning the entire range of interatomic distances, from the equilibrium to the dissociation limit. Moreover, the spectroscopic characteristic of various electronic states is presented, including relativistic effects. Relativistic corrections included at the third-order Douglas-Kroll level have a non-negligible effect on the accuracy of the determined spectroscopic constants.

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.

The potential energy curves (PECs) and spectroscopic constants of the ground and excited states of a LiMg+ molecular cation were investigated. We obtained accurate results for the fifteen lowest-lying states of the LiMg+ cation using the Intermediate Hamiltonian Fock Space Multireference Coupled Cluster (IH-FS-CC) method applied to the (2,0) sector. Relativistic corrections were accounted for using the third-order Douglas–Kroll method. In each instance, smooth PECs were successfully computed across the entire range of interatomic distances from equilibrium to the dissociation limit. The results are in good accordance with previous studies of this molecular cation. Notably, this study marks the first application of IH-FS-CC in investigating a mixed alkali and alkaline earth molecular cation, proving its usability in determining accurate PECs of such diatomics and their spectroscopic constants.

Reliable information on transition matrix elements of various property operators between molecular electronic states is of crucial importance for predicting spectroscopic, electric, magnetic and radiative properties of molecules. The finite-field technique is a simple and rather accurate tool for evaluating transition matrix elements of first-order properties in the frames of the Fock space relativistic coupled cluster approach. We formulate and discuss the extension of this technique to the case of transitions between the electronic states associated with different sectors of the Fock space. Pilot applications to the evaluation of transition dipole moments between the closed-shell-like states (vacuum sector) and those dominated by single excitations of the Fermi vacuum (the 1h1p sector) in heavy atoms (Xe and Hg) and simple molecules of heavy element compounds (I2 and TlF) are reported.