Coupled Cluster Models Research Articles

"Best" Iterative Coupled-Cluster Triples Model? More Evidence for 3CC.

To follow up on the unexpectedly good performance of several coupled-cluster models with approximate inclusion of 3-body clusters [Rishi, V.; Valeev, E. F. J. Chem. Phys. 2019, 151, 064102.] we performed a more complete assessment of the 3CC method [Feller, D. . J. Chem. Phys. 2008, 129, 204105.] for accurate computational thermochemistry in the standard HEAT framework. New spin-integrated implementation of the 3CC method applicable to closed- and open-shell systems utilizes a new automated toolchain for derivation, optimization, and evaluation of operator algebra in many-body electronic structure. We found that with a double-ζ basis set the 3CC correlation energies and their atomization energy contributions are almost always more accurate (with respect to the CCSDTQ reference) than the CCSDT model as well as the standard CCSD(T) model. The mean absolute errors in cc-pVDZ {3CC, CCSDT, and CCSD(T)} electronic (per valence electron) and atomization energies relative to the CCSDTQ reference for the HEAT data set [Tajti, A. . J. Chem. Phys. 2004, 121, 11599-11613.], were {24, 70, 122} μEh/e and {0.46, 2.00, 2.58} kJ/mol, respectively. The mean absolute errors in the complete-basis-set limit {3CC, CCSDT, and CCSD(T)} atomization energies relative to the HEAT model reference, were {0.52, 2.00, and 1.07} kJ/mol, The significant and systematic reduction of the error by the 3CC method and its lower cost than CCSDT suggests it as a viable candidate for post-CCSD(T) thermochemistry applications, as well as the preferred alternative to CCSDT in general.

Strong coupling electron-photon dynamics: A real-time investigation of energy redistribution in molecular polaritons

We analyze the real-time electron-photon dynamics in long- and short-range energy transfer using a real-time quantum electrodynamics coupled cluster model, which allows for spatial and temporal visualization of transport processes. We compute the time evolution of photonic and molecular observables, such as the dipole moment and the photon coordinate, following the excitation of the system induced by short laser pulses. Our simulations show that intermolecular interactions and light-matter strong coupling lead to modified electronic polarization compared to the undressed molecules. The developed method can simulate multiple high-intensity laser pulses while explicitly retaining electronic and electron-photon correlation and is thus suited for nonlinear optics and transient absorption spectroscopies of molecular polaritons. Published by the American Physical Society 2024

How Much Electron Donation Is There In Transition Metal Complexes? A Computational Study.

The "dative" covalent interactions between metals and ligands in coordination compounds, i.e., metal-to-ligand and ligand-to-metal donation, are manifestations of electron delocalization and subject to errors in approximate calculations. This work addresses the extent of dative bonding/donation in a series of closed-shell transition metal complexes. Several Kohn-Sham density functionals, representing different "rungs" of approximations, along with post-Hartree-Fock methods are assessed in comparison to CCSD(T). Two widely used nonhybrid and global hybrid density functionals (B3LYP, PBE0) tend to produce notably too strong donation. Global hybrids with elevated fractions of exact exchange (40 to 50%) and the range-separated exchange functional CAM-B3LYP tend to perform better for the description of the donation. The performance of a double-hybrid functional is found to be quite satisfactory, correcting errors seen in MP2 calculations. A fast approximate coupled-cluster model (DLPNO-CCSD) also gives a reasonable description of the donation, with a tendency to underestimate its extent.

Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models.

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.

Coupled cluster theory on modern heterogeneous supercomputers.

This study examines the computational challenges in elucidating intricate chemical systems, particularly through ab-initio methodologies. This work highlights the Divide-Expand-Consolidate (DEC) approach for coupled cluster (CC) theory-a linear-scaling, massively parallel framework-as a viable solution. Detailed scrutiny of the DEC framework reveals its extensive applicability for large chemical systems, yet it also acknowledges inherent limitations. To mitigate these constraints, the cluster perturbation theory is presented as an effective remedy. Attention is then directed towards the CPS (D-3) model, explicitly derived from a CC singles parent and a doubles auxiliary excitation space, for computing excitation energies. The reviewed new algorithms for the CPS (D-3) method efficiently capitalize on multiple nodes and graphical processing units, expediting heavy tensor contractions. As a result, CPS (D-3) emerges as a scalable, rapid, and precise solution for computing molecular properties in large molecular systems, marking it an efficient contender to conventional CC models.

Massively parallel GPU enabled third-order cluster perturbation excitation energies for cost-effective large scale excitation energy calculations.

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model.

Dark Doubly Excited States with Modified Coupled Cluster Models: A Reliable Compromise between Cost and Accuracy?

To treat doubly excited states, the treatment of triple excitations is considered necessary in the framework of equation-of-motion coupled cluster (EOM-CC) methods. We investigate models without explicit triples and seek quantitative measure for the performance of EOM based on CC with singles and doubles (CCSD) or modified CCSD (Distinguishable Cluster Approximation) approaches for states with predominant double excitation character. We also test the efficacy of including triples in perturbative manner through EOM-CCSD(T) and in an iterative way through EOM-CCSDT-3 method. Extended similarity transformed EOM-CCSD(EXT-STEOM-CCSD) method is also tested and provides superior quality results at comparatively low cost. We use the QUEST2 benchmark set of double excitations proposed by Loos et al. [ J. Chem. Theory Comput.2019, 15, 1939] to investigate the performance of methods such as EOM-CCSD, EOM-DCSD, EXT-STEOM-CCSD, ΔCCSD, and ΔDCSD. We also test a tailored CC approach, ΔpairCCD-TCCSD.

Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian.

We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series (LCP) where the 2n + 1/2n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP (LCP) series, where the total cluster amplitudes and multipliers are determined through the same orders as in the LCP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the LCP series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models LCPS (D-4), LCPSD (T-4), and LCPSD(T-4) give energies of CC target state quality. For the LCPS (D-4) model, CC target state quality is obtained as the LCPS (D-4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the LCPS (D-4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the LCPSD (T-4) and LCPSD(T-4) models, CC target state quality was obtained, given that the LCPSD (T-4) and LCPSD(T-4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the LCPSD (T-4) and LCPSD(T-4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy.

Coupled-cluster calculation of neutron matter equation of state

Abstract We present a relation between the density and pressure of pure neutron matter derived from numerical calculations based on a truncated coupled cluster model using a simple bare nucleon-nucleon interaction in the Minnesota potential form. The obtained relationship exhibits well-known behaviour only at low densities ≲ 0.08 fm−3 and diverges from the supported by observations data equations of state at higher densities. Our results are compared with those derived from efective feld theory using realistic NN forces.

Choosing Bad versus Worse: Predictions of Two-Photon-Absorption Strengths Based on Popular Density Functional Approximations.

We present a benchmark study of density functional approximation (DFA) performances in predicting the two-photon-absorption strengths in π-conjugated molecules containing electron-donating/-accepting moieties. A set of 48 organic molecules is chosen for this purpose, for which the two-photon-absorption (2PA) parameters are evaluated using different DFAs, including BLYP, PBE, B3LYP, PBE0, CAM-B3LYP, LC-BLYP, and optimally tuned LC-BLYP. Minnesota functionals and ωB97X-D are also used, applying the two-state approximation, for a subset of molecules. The efficient resolution-of-identity implementation of the coupled-cluster CC2 model (RI-CC2) is used as a reference for the assessment of the DFAs. Two-state models within the framework of both DFAs and RI-CC2 are used to gain a deeper insight into the performance of different DFAs. Our results give a clear picture of the performance of the density functionals in describing the two-photon activity in dipolar π-conjugated systems. The results show that global hybrids are best suited to reproduce the absolute values of 2PA strengths of donor–acceptor molecules. The range-separated functionals CAM-B3LYP and optimally tuned LC-BLYP, however, show the highest linear correlations with the reference RI-CC2 results. Hence, we recommend the latter DFAs for structure–property studies across large series of dipolar compounds.

Explicitly correlated Fock-space coupled-cluster singles and doubles method for (1,1), (0,2), and (2,0) sectors

A linearly approximated explicitly correlated coupled-cluster singles and doubles model for the Fock-space coupled-cluster method has been formulated and implemented. An extension of the Fock-space wave operators is introduced in order to treat the short-range correlation effects for excited and doubly electron-attached states. We show that an effective reduction in the number of active virtuals can also be obtained by improving how the short-range correlation is treated. Numerical results to gauge the performance for valence and Rydberg excitation energies, double ionization potentials, and double electron attachment energies of several molecules are obtained. Statistical measures of the errors in excitation energies show that the explicitly correlated results are within 0.1eV from the complete basis set limit already at the double-ζ level unless the excitation energies are too close to the ionization thresholds. Similar accuracy is seen for the double ionization potentials and double electron attachment energies.

How accurate are EOM-CC4 vertical excitation energies?

We report the first investigation of the performance of EOM-CC4-an approximate equation-of-motion coupled-cluster model, which includes iterative quadruple excitations-for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CC with singles, doubles, triples, quadruples, and pentuples and full configuration interaction reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ mol-1 accuracy (i.e., error below 0.01eV), in very close agreement with its more expensive CC with singles, doubles, triples, and quadruples parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CC with singles, doubles, and triples. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions with a dominant contribution from the double excitations.

Describing ground and excited state potential energy surfaces for molecular photoswitches using coupled cluster models.

In this article, we use two extensively studied systems, a retinal model system and azobenzene, to explore the use of coupled cluster models for describing ground and singlet excited state potential energy surfaces of photoswitchable systems. While not being suitable for describing nuclear dynamics of photoisomerization, coupled cluster models have useful attributes, such as the inclusion of dynamical correlation, their black box nature, and the systematic improvement offered by truncation level. Results for the studied systems show that when triple excitations (here through the CC3 model) are included, ground and excited state potential energy surfaces for isomerization paths may reliably be generated, also for states of doubly excited character. For ground state equilibrium cis- and trans-azobenzene, the molecular geometry and basis set is seen to significantly impact the vertical excitation energies for the two lowest excited states. Efficient implementations of coupled cluster models can therefore constitute valuable tools for investigating photoswitchable systems and can be used for preliminary black box studies to gather information before more complicated excited state dynamics approaches are pursued.

Multilevel CC2 and CCSD in Reduced Orbital Spaces: Electronic Excitations in Large Molecular Systems.

We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower-level coupled cluster model. To treat large systems, we combine MLCC2 and MLCCSD with a reduced-space approach in which the multilevel coupled cluster calculation is performed in a significantly truncated molecular orbital basis. The truncation scheme is based on the selection of an active region of the molecular system and the subsequent construction of localized Hartree–Fock orbitals. These orbitals are used in the multilevel coupled cluster calculation. The electron repulsion integrals are Cholesky decomposed using a screening protocol that guarantees accuracy in the truncated molecular orbital basis and reduces computational cost. The Cholesky factors are constructed directly in the truncated basis, ensuring low storage requirements. Systems for which Hartree–Fock is too expensive can be treated by using a multilevel Hartree–Fock reference. With the reduced-space approach, we can handle systems with more than a thousand atoms. This is demonstrated for paranitroaniline in aqueous solution.

Time-dependent coupled-cluster theory for ultrafast transient-absorption spectroscopy

We present a spin-adapted time-dependent coupled-cluster singles and doubles model for the molecular response to a sequence of ultrashort laser pulses. The implementation is used to calculate the electronic response to a valence-exciting pump pulse, and a subsequent core-exciting probe pulse. We assess the accuracy of the integration procedures used in solving the dynamic coupled-cluster equations, in order to find a compromise between computational cost and accuracy. The transient absorption spectrum of lithium fluoride is calculated for various delays of the probe pulse with respect to the pump pulse. We observe that the transient probe absorption oscillates with the pump-probe delay, an effect that is attributed to the interference of states in the pump-induced superposition.

Accelerated multimodel Newton-type algorithms for faster convergence of ground and excited state coupled cluster equations.

We introduce a multimodel approach to solve coupled cluster equations, employing a quasi-Newton algorithm for the ground state and an Olsen algorithm for the excited states. In these algorithms, both of which can be viewed as Newton algorithms, the Jacobian matrix of a lower level coupled cluster model is used in Newton equations associated with the target model. Improvements in convergence then imply savings for sufficiently large molecular systems, since the computational cost of macroiterations scales more steeply with system size than the cost of microiterations. The multimodel approach is suitable when there is a lower level Jacobian matrix that is much more accurate than the zeroth order approximation. Applying the approach to the CC3 equations, using the CCSD approximation of the Jacobian, we show that the time spent to determine the ground and valence excited states can be significantly reduced. We also find improved convergence for core excited states, indicating that similar savings will be obtained with an explicit implementation of the core-valence separated CCSD Jacobian transformation.

X-ray and UV Spectra of Glycine within Coupled Cluster Linear Response Theory.

The coupled cluster models CCSD and CC3 are used to investigate the (core) excited states and ionization energies of glycine in the gas phase. Excited states and ionization energies in the UV spectral range are calculated using a standard coupled cluster linear response, while core-level excited states and ionization potentials are calculated using the core-valence separation approximation. The temperature dependence from different conformers is also assessed.

Multilayer Divide-Expand-Consolidate Coupled-Cluster Method: Demonstrative Calculations of the Adsorption Energy of Carbon Dioxide in the Mg-MOF-74 Metal-Organic Framework.

The implementation and evaluation of a multilayer extension of the divide-expand-consolidate (DEC) scheme within the LSDalton program is presented. The DEC scheme is a linear-scaling, fragmentation-based local coupled-cluster (CC) method that provides a means of overcoming the scaling wall associated with canonical CC electronic structure calculations on large molecular systems. Taking advantage of the local nature of correlation effects, the correlation energy for the full molecule is calculated from a set of independent fragments using localized molecular orbitals. However, when only a small subsystem of a larger system is of interest, for example, adsorption sites or catalytically active sites, the majority of the computational time may be spent evaluating the correlation energy of fragments which have little effect on the properties in the area of interest (AOI). The multilayer DEC (ML-DEC) scheme addresses this by taking advantage of the independent nature of the fragments in order to evaluate the correlation energy of various regions of the system at different levels of theory. Regions far from the AOI are evaluated at lower (cheaper) levels of theory such as Hartree-Fock (HF) or Møller-Plesset second-order perturbation theory (MP2), while the area immediately surrounding the AOI is treated with a higher level CC model. Through the ML-DEC scheme, the computational cost of CC calculations on these types of systems can be significantly reduced while maintaining the accuracy of higher-level calculations. Results from HF/RI-MP2 and RI-MP2/CCSD ML-DEC calculations of the binding energy of a fatty acid dimer are presented. We find that the ML-DEC scheme is capable of reproducing DEC energy differences at a target level of theory, provided that the region treated at the target level of theory is chosen to be sufficiently large. Time-to-solution is found to be significantly reduced, particularly in the RI-MP2/CCSD calculations. Finally, the ML-DEC scheme is applied to the calculation of CO2 adsorption in a Mg-MOF-74 channel.

What Levels of Coupled Cluster Theory Are Appropriate for Transition Metal Systems? A Study Using Near-Exact Quantum Chemical Values for 3d Transition Metal Binary Compounds.

Transition metal compounds are traditionally considered to be challenging for standard quantum chemistry approximations like coupled cluster (CC) theory, which are usually employed to validate lower level methods like density functional theory (DFT). To explore this issue, we present a database of bond dissociation energies (BDEs) for 74 spin states of 69 diatomic species containing a 3d transition metal atom and a main group element, in the moderately sized def2-SVP basis. The presented BDEs appear to have an (estimated) 3σ error less than 1 kJ/mol relative to the exact solutions to the nonrelativistic Born-Oppenheimer Hamiltonian. These benchmark values were used to assess the performance of a wide range of standard single reference CC models, as the results should be beneficial for understanding the limitations of these models for transition metal systems. We find that interactions between metals and monovalent ligands like hydride and fluoride are well described by CCSDT. Similarly, CCSDTQ appears to be adequate for bonds between metals and nominally divalent ligands like oxide and sulfide. However, interactions with polyvalent ligands like nitride and carbide are more challenging, with even CCSDTQ(P)Λ yielding errors on the scale of a few kJ/mol. We also find that many perturbative and iterative approximations to higher order terms either yield disappointing results or actually worsen the performance relative to the baseline low level CC method, indicating that complexity does not always guarantee accuracy.

Spin-orbit splitted excited states using explicitly-correlated equation-of-motion coupled-cluster singles and doubles eigenvectors

An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple-ζ level.