Coupled-cluster Approach Research Articles

Toward Accurate Ab Initio Ground-State Potential Energy and Electric Dipole Moment Functions of Carbon Monoxide.

Accurate potential energy and electric dipole moment functions of the CO molecule in its ground electronic state X1Σ+ have been obtained using the single-reference coupled-cluster approach, up to the CCSDTQP level of approximation, in conjunction with the augmented core-valence correlation-consistent basis sets, aug-cc-pCVnZ, up to octuple-zeta quality. The scalar relativistic, adiabatic, and nonadiabatic effects were discussed. The ab initio predicted functions were compared with their experimentally derived counterparts.

First Ab Initio Line Lists for Triatomic Sulfur-Containing Molecules: S2O and S3.

We present in this paper the first room temperature rovibrational line lists for the main isotopologues of disulfur monoxide (S2O) and thiozone (S3) variationally computed from newly developed ab initio potential energy and dipole moment surfaces (PESs and DMSs). S2O and S3 are supposed to be potential candidates for astronomical detection, especially in the Venusian atmosphere where sulfur chemistry plays a major role. Contrary to other stable sulfur-containing species like SO2 or H2S, there is much less experimental data for the short-lived reactive S2O and S3 molecules. Indeed, the infrared spectra of S2O and S3 are quite complicated to analyze without consistent theoretical predictions because they contain both high J (∼100) and a lot of hot band transitions, even at T = 296 K. In this work, we have constructed PESs based on the single-reference coupled cluster approach [CCSD(T)] and including corrections due to the scalar relativistic effects, DBOC, and highly excited Slater determinants. The structure of the excited electronic states of S3 was also discussed. The nuclear-motion Eckart-Watson Hamiltonian expressed in terms of normal-mode irreducible tensor operators was used to compute the energy levels. For line intensity calculation, ab initio DMSs were computed at the CCSD(T)/aug-cc-pV5Z level of the theory. Rotation-vibration patterns in the fundamental bands of S2O and S3 have been simulated taking into account the recent Fourier-transform spectra of S2O recorded at the SOLEIL synchrotron. The present work aims at providing line intensities of S2O and S3 that are missing in the literature as well as new spectroscopic support for atmospheric applications.

Calculation of Some Low-Lying Electronic Excitations of Barium Monofluoride Using the Equation of Motion (EOM)-CC3 Method with an Effective Core Potential Approach.

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.

Rovibrational Line Lists of Triplet and Singlet Methylene.

The methylene molecule (CH2) is a short-lived radical with lacking data on its spectral line intensities. Although the lifetime of CH2 is extremely short under Earth's conditions, it exists in a free form in interstellar media. CH2 is an important intermediate species in chemical reactions associated with the formation and destruction of complex hydrocarbons. We present the first rovibrational line lists of CH2 in its ground triplet and first excited singlet electronic state. To this end, our previously developed accurate ab initio potential energy surface (PES) was used for the ground electronic triplet state [Egorov et al. J. Comp. Chem. 2024. V. 45. (2). P. 83] while a new PES for the singlet state was constructed in this work using the single-reference coupled cluster approach [CCSD(T)] combined with the extrapolation to the complete basis set (CBS) limit based on the correlation-consistent orbital basis sets with the core-valence electron correlation effects [aug-cc-pCVXZ, X = T, Q, 5, and 6]. In addition, the contributions to the correlation energy from highly excited Slater determinants [CC(n), n = 3-5] were included as well as the scalar relativistic effects and DBOC. The most accurate description of the infrared band origins of singlet CH2 was thus achieved for the energy range where the impact of the nonadiabatic coupling due to the Renner-Teller effect can be neglected. To obtain the probabilities of the rovibrational transitions, new ab initio DMSs were constructed both for the triplet and singlet CH2 using the CCSD(T)/aug-cc-pCVQZ approach. Finally, the absorption spectra of triplet and singlet methylene were predicted from the variationally computed line lists.

Excited-state downfolding using ground-state formalisms

Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau reference determinants, paving the way for applications of quantum computing in excited-state chemistry. This study focuses on doubly excited states for which canonical equation-of-motion CC approaches struggle to describe unless one includes higher-than-double excitations. The downfolding technique results in state-specific effective Hamiltonians that, when diagonalized in their respective active spaces, provide ground- and excited-state total energies (and therefore excitation energies) comparable to high-level CC methods. The performance of this procedure is examined with doubly excited states of H2, Methylene, Formaldehyde, and Nitroxyl.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics.

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

New rotational rate coefficients computation of MgC3N(X2Σ+) by collision with He(1S)

ABSTRACT Determining physical conditions in interstellar environments requires reliable estimation of collisional data for molecules detected in space. In this work, we report a rate coefficients calculation of MgC3N(X2Σ+) induced by collision with He. This study is based on a new 2D potential energy surface (2D-PES), obtained from the explicitly correlated restricted open-shell coupled cluster approach with single, double, and perturbative triple excitation (rccsd(t)-f12) and the aug-cc-pVTZ basis sets. The MgC3N–He PES presents a global minimum with a well depth of −45.6 cm−1. Based on this interaction potential, we derived the excitation cross-sections using the close-coupling quantum time-independent formalism for total energies ≤500 cm−1 and N ≤ 40. These cross-sections were then integrated on a Maxwell–Boltzmann distribution of kinetic energies to obtain the collisional (de)-excitation rate coefficients for thermal temperature below 100 K. A non-LTE radiative transfer calculation was performed using the present collisional rates in order to estimate their impact on the abundance of MgC3N. These collisional data can help astronomers for the detection and an accurate determination of MgC3N abundance in the investigated interstellar clouds.

Scalar Relativistic All-Electron and Pseudopotential Ab Initio Study of a Minimal Nitrogenase [Fe(SH)4H]- Model Employing Coupled-Cluster and Auxiliary-Field Quantum Monte Carlo Many-Body Methods.

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available to organisms. The detailed mechanism of this enzyme is currently not known, and computational studies are complicated by the fact that different density functional theory (DFT) methods give very different energetic results for calculations involving nitrogenase models. Recently, we designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S to mimic different possible protonation states of the nitrogenase active site. We showed that the energy difference between these two isomers (ΔE) is hard to estimate with quantum-mechanical methods. Based on nonrelativistic single-reference coupled-cluster (CC) calculations, we estimated that the ΔE is 101 kJ/mol. In this study, we demonstrate that scalar relativistic effects play an important role and significantly affect ΔE. Our best revised single-reference CC estimates for ΔE are 85-91 kJ/mol, including energy corrections to account for contributions beyond triples, core-valence correlation, and basis-set incompleteness error. Among coupled-cluster approaches with approximate triples, the canonical CCSD(T) exhibits the largest error for this problem. Complementary to CC, we also used phaseless auxiliary-field quantum Monte Carlo calculations (ph-AFQMC). We show that with a Hartree-Fock (HF) trial wave function, ph-AFQMC reproduces the CC results within 5 ± 1 kJ/mol. With multi-Slater-determinant (MSD) trials, the results are 82-84 ± 2 kJ/mol, indicating that multireference effects may be rather modest. Among the DFT methods tested, τ-HCTH, r2SCAN with 10-13% HF exchange with and without dispersion, and O3LYP/O3LYP-D4, and B3LYP*/B3LYP*-D4 generally perform the best. The r2SCAN12 (with 12% HF exchange) functional mimics both the best reference MSD ph-AFQMC and CC ΔE results within 2 kJ/mol.

Uncovering chemical homology of superheavy elements: a close look at astatine.

The fascination with superheavy elements (SHE) spans the nuclear physics, astrophysics, and theoretical chemistry communities. Extreme relativistic effects govern these elements' chemistry and challenge the traditional notion of the periodic law. The experimental quest for SHE critically depends on theoretical predictions of these elements' properties, especially chemical homology, which allows for successful prototypical experiments with more readily available lighter homologues of SHE. This work is a comprehensive quantum-chemical investigation into astatine (At) as a non-intuitive homologue of element 113, nihonium (Nh). Combining relativistic coupled-cluster and density functional theory approaches, we model the behaviour of At and AtOH in thermochromatographic experiments on a pristine gold surface. Insights into the electronic structure of AtOH and NhOH and accurate estimates of At-gold and AtOH-gold adsorption energies rationalise recent experimental findings and justify the use of At as a chemical homologue of Nh for the successful design of future experiments on Nh detection and chemical characterisation.

Collisional excitation of propargylimine by helium: new ab initio 3D-potential energy surfaces and scattering calculations.

We present quantum coupled-state calculations for the rotational excitation of interstellar propargylimine due to collisions with helium. The calculations are based on new high-accurate three-dimensional potential energy surfaces (3D-PESs) adapted for rigid-rotor scattering computations. The two PESs (Z/E-PGIM-He) were determined using the explicitly correlated coupled-cluster approach with single, double and perturbative triple excitation [CCSCD(T)-F12] and the standard aug-cc-pVTZ basis set. These PESs present many minima with a global minimum of -47.61 cm-1 for Z-PGIM-He and -54.16 cm-1 for E-PGIM-He. While the PESs for both complexes are qualitatively similar, that of E-PGIM-He is more anisotropic. The state-to-state collisional cross-section calculations are performed for all rotational levels J ≤ 12 with energies below Erot = 30 cm-1 and for total energies up to 500 cm-1. The corresponding collisional rate coefficients are derived for kinetic temperatures up to 120 K. A propensity rule is seen, for rotational excitation cross sections and de-excitation rate coefficients, that favors even ΔJ transitions but with different orders of magnitude. We expect that the retrieved results will contribute to improving atmospheric and astrophysics models.

Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study.

In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.

Ab initio investigation on predissociation of the A2Σ+ state of the SeH radical induced by spin-orbit coupling

High-level ab initio calculations are performed to investigate potential energy curves (PECs) of seven low-lying Λ-S states associated with the two lowest dissociation limits of the SeH radical by utilizing the internally contracted multireference configuration interaction (icMRCI) method in combination with the aug-cc-pwCV5Z Gaussian basis set. The scalar relativistic effect (SR), the electronic core-valence (CV) correction, and Davidson (+Q) modification are included in our calculations. The fourteen Ω states generated from the seven Λ-S states are yielded when the spin-orbit coupling (SOC) effect is taken into account by using the Breit-Pauli operator. On the ground of the obtained PECs, the spectroscopic constants of the bound Λ-S and Ω states are evaluated, which reproduce pretty well the available experimental and theoretical values. By virtue of SOC matrix elements between the bound A2Σ+ state and repulsive 4Σ–(I), 2Σ–(I), or 4∏(I) states crossing with the A2Σ+ state PEC, the spin-orbit perturbations in the A2Σ+ rovibrational manifold in the crossing region and the A-state predissociation mechanism are analyzed. It is clearly exhibited that the avoided crossing phenomena between electronic states possessing the same Ω quantum number provide obvious spectroscopic effects in the transition dipole moments (TMDs) and Franck-Condon factors (FCFs) of the A2Σ+-X2Π transition. The radiative lifetimes of the A2Σ+ vibrational sublevels are determined. In addition, we finalized our study of the SeH molecule by optimizing its equilibrium ground state geometry in terms of a restricted coupled cluster approach including singles and doubles with perturbative triples account (RCCSD(T) method) plus CV, SR, and SOC corrections with extrapolating to complete basis set (CBS) limit.

Accurate ab initio potential energy surface, rovibrational energy levels and resonance interactions of triplet ( 3 B1 ) methylene.

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2 , CHD, CD2 , and 13 CH2 ) in their ground triplet electronic state ( 3 B1 ) from variational calculation up to ~10,000 cm-1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large-amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm-1 ). To construct the ab initio PES, the Dunning's augmented correlation-consistent core-valence orbital basis sets were employed up to the sextuple-ζ quality [aug-cc-pCVXZ, X = T, Q, 5, and 6] combined with the single- and double-excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high-order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm-1 , without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A-reduced Hamiltonian, from the generating-function approach and from a variational calculation was given.

Excited-State-Specific Pseudoprojected Coupled-Cluster Theory.

We present an excited-state-specific coupled-cluster approach in which both the molecular orbitals and cluster amplitudes are optimized for an individual excited state. The theory is formulated via a pseudoprojection of the traditional coupled-cluster wavefunction that allows correlation effects to be introduced atop an excited-state mean field starting point. The approach shares much in common with ground-state CCSD, including size extensivity and an N6 cost scaling. Preliminary numerical tests show that, when augmented with N5 cost perturbative corrections for key terms, the method can improve over excited-state-specific second-order perturbation theory in valence, charge transfer, and Rydberg states.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art abinitio methods.

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Efficient Application of the Factorized form of the Unitary Coupled-Cluster Ansatz for the Variational Quantum Eigensolver Algorithm by Using Linear Combination of Unitaries

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select(U^) scheme uses O(n)Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n3, a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

Calculations of multipole transitions in Sn II for kilonova analysis

We use the method that combines linearized coupled-cluster and configuration interaction approaches for calculating energy levels and multipole transition probabilities in singly ionized tin ions. We show that our calculated energies agree very well with the experimental data. We present probabilities of magnetic dipole and electric quadrupole transitions and use them for the analysis of the AT2017gfo kilonova emission spectra. This study demonstrates the importance and utility of accurate atomic data for forbidden transitions in the examination of future kilonova events.Graphical abstract

Rotational (de-)excitation of protonated tricarbon monosulfide HC3S+ by collision with helium atoms

A new two-dimensional potential energy surface of the interaction between HC3S+ molecule and helium atom is mapped using an explicitly correlated coupled cluster approach with a single, double and perturbative triple excitation-F12a approach with an augmented-correlation-consistent polarized valence triple-zeta Gaussian basis set. The deepest potential well is identified at θ = 95∘ and R = 6.0 bohr with a depth of 100.67 cm−1. Cross-sections are determined for total energy up to 300 cm−1 using a coupled states method. Thermal rate coefficients are derived from the determined cross-sections for temperatures ranging between 3 K and 50 K. A clear predominance of = 2 processes is observed.

Optical telecommunications-band clock based on neutral titanium atoms

We propose an optical clock based on narrow, spin-forbidden M1 and E2 transitions in laser-cooled neutral titanium. These transitions exhibit much smaller black body radiation shifts than those in alkaline earth atoms, small quadratic Zeeman shifts, and have wavelengths in the S, C, and L-bands of fiber-optic telecommunication standards, allowing for integration with robust laser technology. We calculate lifetimes; transition matrix elements; dynamic scalar, vector, and tensor polarizabilities; and black body radiation shifts of the clock transitions using a high-precision relativistic hybrid method that combines a configuration interaction and coupled cluster approaches. We also calculate the line strengths and branching ratios of the transitions used for laser cooling. To identify magic trapping wavelengths, we have completed the largest-to-date direct dynamical polarizability calculations. Finally, we identify new challenges that arise in precision measurements due to magnetic dipole-dipole interactions and describe an approach to overcome them. Direct access to a telecommunications-band atomic frequency standard will aid the deployment of optical clock networks and clock comparisons over long distances.

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.