Showing papers on "Coupled cluster published in 2015"

Advances in molecular quantum chemistry contained in the Q-Chem 4 program package

Abstract: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Moller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr_2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.

Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory

Abstract: The domain based local pair natural orbital coupled cluster method with single-, double-, and perturbative triple excitations (DLPNO–CCSD(T)) is an efficient quantum chemical method that allows for coupled cluster calculations on molecules with hundreds of atoms. Because coupled-cluster theory is the method of choice if high-accuracy is needed, DLPNO–CCSD(T) is very promising for large-scale chemical application. However, the various approximations that have to be introduced in order to reach near linear scaling also introduce limited deviations from the canonical results. In the present work, we investigate how far the accuracy of the DLPNO–CCSD(T) method can be pushed for chemical applications. We also address the question at which additional computational cost improvements, relative to the previously established default scheme, come. To answer these questions, a series of benchmark sets covering a broad range of quantum chemical applications including reaction energies, hydrogen bonds, and other noncov...

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Abstract: Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei

Abstract: We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab inito method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell- model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory

Abstract: The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.

The theory of variational hybrid quantum-classical algorithms

Abstract: Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as "the quantum variational eigensolver" was developed with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through relaxation of exponential splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.

Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set.

Abstract: We perform benchmark calculations of the Bethe–Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe–Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average −0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe–Salpeter scheme based on self-consistent GW calculations comes close to the...

Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework

Abstract: We present a simple scheme to compute X-ray absorption spectra (e.g., near-edge absorption fine structure) and core ionisation energies within coupled cluster linear response theory. The approach exploits the so-called core-valence separation to effectively reduce the excitation space to processes involving at least one core orbital, and it can be easily implemented within any pre-existing coupled cluster code for low energy states. We further develop a perturbation correction that incorporates the effect of the excluded part of the excitation space. The correction is shown to be highly accurate. Test results are presented for a set of molecular systems for which well converged results in full space could be generated at the coupled cluster singles and doubles level of theory only, but the scheme is straightforwardly generalizable to all members of the coupled cluster hierarchy of approximations, including CC3.

Can Single-Reference Coupled Cluster Theory Describe Static Correlation?

Abstract: While restricted single-reference coupled cluster theory truncated to singles and doubles (CCSD) provides very accurate results for weakly correlated systems, it usually fails in the presence of static or strong correlation. This failure is generally attributed to the qualitative breakdown of the reference, and can accordingly be corrected by using a multideterminant reference, including higher-body cluster operators in the ansatz, or allowing symmetry breaking in the reference. None of these solutions are ideal; multireference coupled cluster is not black box, including higher-body cluster operators is computationally demanding, and allowing symmetry breaking leads to the loss of good quantum numbers. It has long been recognized that quasidegeneracies can instead be treated by modifying the coupled cluster ansatz. The recently introduced pair coupled cluster doubles (pCCD) approach is one such example which avoids catastrophic failures and accurately models strong correlations in a symmetry-adapted frame...

Correlation consistent basis sets for actinides. I. The Th and U atoms

Abstract: New correlation consistent basis sets based on both pseudopotential (PP) and all-electron Douglas-Kroll-Hess (DKH) Hamiltonians have been developed from double- to quadruple-zeta quality for the actinide atoms thorium and uranium. Sets for valence electron correlation (5f6s6p6d), cc − pV nZ − PP and cc − pV nZ − DK3, as well as outer-core correlation (valence + 5s5p5d), cc − pwCV nZ − PP and cc − pwCV nZ − DK3, are reported (n = D, T, Q). The -PP sets are constructed in conjunction with small-core, 60-electron PPs, while the -DK3 sets utilized the 3rd-order Douglas-Kroll-Hess scalar relativistic Hamiltonian. Both series of basis sets show systematic convergence towards the complete basis set limit, both at the Hartree-Fock and correlated levels of theory, making them amenable to standard basis set extrapolation techniques. To assess the utility of the new basis sets, extensive coupled cluster composite thermochemistry calculations of ThFn (n = 2 − 4), ThO2, and UFn (n = 4 − 6) have been carried out. After accurately accounting for valence and outer-core correlation, spin-orbit coupling, and even Lamb shift effects, the final 298 K atomization enthalpies of ThF4, ThF3, ThF2, and ThO2 are all within their experimental uncertainties. Bond dissociation energies of ThF4 and ThF3, as well as UF6 and UF5, were similarly accurate. The derived enthalpies of formation for these species also showed a very satisfactory agreement with experiment, demonstrating that the new basis sets allow for the use of accurate composite schemes just as in molecular systems composed only of lighter atoms. The differences between the PP and DK3 approaches were found to increase with the change in formal oxidation state on the actinide atom, approaching 5-6 kcal/mol for the atomization enthalpies of ThF4 and ThO2. The DKH3 atomization energy of ThO2 was calculated to be smaller than the DKH2 value by ∼1 kcal/mol.

Electronic couplings for molecular charge transfer: benchmarking CDFT, FODFT and FODFTB against high-level ab initio calculations. II.

Abstract: A new database (HAB7-) of electronic coupling matrix elements (Hab) for electron transfer in seven medium-sized negatively charged π-conjugated organic dimers is introduced. Reference data are obtained with spin-component scaled approximate coupled cluster method (SCS-CC2) and large basis sets. Assessed DFT-based approaches include constrained density functional theory (CDFT), fragment-orbital DFT (FODFT), self-consistent charge density functional tight-binding (FODFTB) and the recently described analytic overlap method (AOM). This complements the previously reported HAB11 database where only cationic dimers were considered. The CDFT method in combination with a functional based on PBE and including 50% of exact exchange (HFX) was found to provide best estimates, with a mean relative unsigned error (MRUE) of 8.2%. CDFT couplings systematically increase with decreasing fraction of HFX as a consequence of increasing delocalisation of the SOMO orbital. The FODFT method is found to be very robust underestimating electronic couplings by 28%. The FODFTB and AOM methods, although orders of magnitude more efficient in terms of computational effort than the DFT approaches, perform well with reasonably small errors of 54% and 29%, respectively, translating in errors in the non-adiabatic electron transfer rate of a factor of 2.4 and 1.7, respectively. We discuss carefully various sources of errors and the scope and limitations of all assessed methods taking into account the results obtained for both HAB7- and HAB11 databases.

Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals?

Abstract: Coupled-cluster (CC) methods have been extensively used as the high-level approach in quantum electronic structure theory to predict various properties of molecules when experimental results are unavailable. It is often assumed that CC methods, if they include at least up to connected-triple-excitation quasiperturbative corrections to a full treatment of single and double excitations (in particular, CCSD(T)), and a very large basis set, are more accurate than Kohn-Sham (KS) density functional theory (DFT). In the present work, we tested and compared the performance of standard CC and KS methods on bond energy calculations of 20 3d transition metal-containing diatomic molecules against the most reliable experimental data available, as collected in a database called 3dMLBE20. It is found that, although the CCSD(T) and higher levels CC methods have mean unsigned deviations from experiment that are smaller than most exchange-correlation functionals for metal-ligand bond energies of transition metals, the improvement is less than one standard deviation of the mean unsigned deviation. Furthermore, on average, almost half of the 42 exchange-correlation functionals that we tested are closer to experiment than CCSD(T) with the same extended basis set for the same molecule. The results show that, when both relativistic and core-valence correlation effects are considered, even the very high-level (expensive) CC method with single, double, triple, and perturbative quadruple cluster operators, namely, CCSDT(2)Q, averaged over 20 bond energies, gives a mean unsigned deviation (MUD(20) = 4.7 kcal/mol when one correlates only valence, 3p, and 3s electrons of transition metals and only valence electrons of ligands, or 4.6 kcal/mol when one correlates all core electrons except for 1s shells of transition metals, S, and Cl); and that is similar to some good xc functionals (e.g., B97-1 (MUD(20) = 4.5 kcal/mol) and PW6B95 (MUD(20) = 4.9 kcal/mol)) when the same basis set is used. We found that, for both coupled cluster calculations and KS calculations, the T1 diagnostics correlate the errors better than either the M diagnostics or the B1 DFT-based diagnostics. The potential use of practical standard CC methods as a benchmark theory is further confounded by the finding that CC and DFT methods usually have different signs of the error. We conclude that the available experimental data do not provide a justification for using conventional single-reference CC theory calculations to validate or test xc functionals for systems involving 3d transition metals.

Interactions of CO2 with various functional molecules

Abstract: The CO2 capturing and sequestration are of importance in environmental science. Understanding of the CO2-interactions with various functional molecules including multi-N-containing superbases and heteroaromatic ring systems is essential for designing novel materials to effectively capture the CO2 gas. These interactions are investigated using density functional theory (DFT) with dispersion correction and high level wave function theory (resolution-of-identity (RI) spin-component-scaling (scs) Moller-Plesset second-order perturbation theory (MP2) and coupled cluster with single, double and perturbative triple excitations (CCSD(T))). We found intriguing molecular systems of melamine, 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD), 7-azaindole and guanidine, which show much stronger CO2 interactions than the well-known functional systems such as amines. In particular, melamine could be exploited to design novel materials to capture the CO2 gas, since one CO2 molecule can be coordinated by four melamine molecules, which gives a binding energy (BE) of ∼85 kJ mol(-1), much larger than in other cases.

Selection of active spaces for multiconfigurational wavefunctions

Abstract: The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F2, ozone, and NO2), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr2). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed: finding the UHF solutions, discontinuities on potential energy surfaces, and inclusion of dynamical electron correlation and generalization to excited states.

Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-edge X-ray Absorption Spectroscopy.

Abstract: Single-reference techniques based on coupled-cluster (CC) theory, in the forms of linear response (LR) or equation of motion (EOM), are highly accurate and widely used approaches for modeling valence absorption spectra. Unfortunately, these equations with singles and doubles (LR-CCSD and EOM-CCSD) scale as O(N6), which may be prohibitively expensive for the study of high-energy excited states using a conventional eigensolver. In this paper, we present an energy-specific non-Hermitian eigensolver that is able to obtain high-energy excited states (e.g., XAS K-edge spectrum) at low computational cost. In addition, we also introduce an improved trial vector for iteratively solving the EOM-CCSD equation with a focus on high-energy eigenstates. The energy-specific EOM-CCSD approach and its low-scaling alternatives are applied to calculations of carbon, nitrogen, oxygen, and sulfur K-edge excitations. The results are compared to other implementations of CCSD for excited states, energy-specific linear response ti...

Spin-orbit couplings within the equation-of-motion coupled-cluster framework: Theory, implementation, and benchmark calculations

Abstract: We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.

Benchmark Calculations of Three-Body Intermolecular Interactions and the Performance of Low-Cost Electronic Structure Methods.

Abstract: Many-body noncovalent interactions are increasingly important in large and/or condensed-phase systems, but the current understanding of how well various models predict these interactions is limited. Here, benchmark complete-basis set coupled cluster singles, doubles, and perturbative triples (CCSD(T)) calculations have been performed to generate a new test set for three-body intermolecular interactions. This “3B-69” benchmark set includes three-body interaction energies for 69 total trimer structures, consisting of three structures from each of 23 different molecular crystals. By including structures that exhibit a variety of intermolecular interactions and packing arrangements, this set provides a stringent test for the ability of electronic structure methods to describe the correct physics involved in the interactions. Both MP2.5 (the average of second- and third-order Moller–Plesset perturbation theory) and spin-component-scaled CCSD for noncovalent interactions (SCS-MI-CCSD) perform well. MP2 handles ...

Control in the Rate-Determining Step Provides a Promising Strategy To Develop New Catalysts for CO2 Hydrogenation: A Local Pair Natural Orbital Coupled Cluster Theory Study.

Abstract: The development of efficient catalysts with base metals for CO2 hydrogenation has always been a major thrust of interest. A series of experimental and theoretical work has revealed that the catalytic cycle typically involves two key steps, namely, base-promoted heterolytic H2 splitting and hydride transfer to CO2, either of which can be the rate-determining step (RDS) of the entire reaction. To explore the determining factor for the nature of RDS, we present herein a comparative mechanistic investigation on CO2 hydrogenation mediated by [M(H)(η2-H2)(PP3Ph)]n+ (M = Fe(II), Ru(II), and Co(III); PP3Ph = tris(2-(diphenylphosphino)phenyl)phosphine) type complexes. In order to construct reliable free energy profiles, we used highly correlated wave function based ab initio methods of the coupled cluster type alongside the standard density functional theory. Our calculations demonstrate that the hydricity of the metal–hydride intermediate generated by H2 splitting dictates the nature of the RDS for the Fe(II) and...

Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states.

Abstract: We propose a multireference linearized coupled cluster theory using matrix product states (MPSs-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration interaction singles and doubles, for a wide variety of electronic Hamiltonians. These range from first-row dimers at equilibrium and stretched geometries to highly multireference systems such as the chromium dimer and lattice models such as periodic two-dimensional 1-band and 3-band Hubbard models. The MPS-LCC theory shows a speed up of several orders of magnitude over the usual Density Matrix Renormalization Group (DMRG) algorithm while delivering energies in excellent agreement with converged DMRG calculations. Also, in all the benchmark calculations presented here, MPS-LCC outperformed the commonly used multi-reference quantum chemistry methods in some cases giving energies in excess of an order of magnitude more accurate. As a size-extensive method that can treat large active spaces, MPS-LCC opens up the use of multireference quantum chemical techniques in strongly correlated ab initio Hamiltonians, including two- and three-dimensional solids.

Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide-Expand-Consolidate CCSD(T) Model.

Abstract: We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local Hartree–Fock (HF) orbitals such that its structural form aligns with our recently developed linear-scaling divide–expand–consolidate (DEC) coupled cluster family of local correlation methods. In a DEC-CCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DEC-CCSD(T) correlation energy, which formally scales linearly with the size of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energy-based input threshold. The theoretical developments are supported by proof of concept DEC-CCSD(T) calculations on ...

Communication: Improved pair approximations in local coupled-cluster methods

Abstract: In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Moller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger.

Ab initio Bogoliubov coupled cluster theory for open-shell nuclei

Abstract: Background: Ab initio many-body methods have been developed over the past 10 yr to address closed-shell nuclei up to mass $A\ensuremath{\approx}130$ on the basis of realistic two- and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei. Several routes to address open-shell nuclei are currently under investigation, including ideas that exploit spontaneous symmetry breaking.Purpose: Singly open-shell nuclei can be efficiently described via the sole breaking of U(1) gauge symmetry associated with particle-number conservation as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory.Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wave function of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCC code is implemented in $m$ scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU(2) symmetry associated with angular momentum conservation.Results: Proof-of-principle calculations in an ${N}_{\text{max}}=6$ spherical harmonic oscillator basis for $^{16,18}\mathrm{O}$ and $^{18}\mathrm{Ne}$ in the BCCD approximation are in good agreement with standard coupled cluster results with the same chiral two-nucleon interaction, while $^{20}\mathrm{O}$ and $^{20}\mathrm{Mg}$ display underbinding relative to experiment. The breaking of U(1) symmetry, monitored by computing the variance associated with the particle-number operator, is relatively constant for all five nuclei, in both the Hartree-Fock-Bogoliubov and BCCD approximations.Conclusions: The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e., potentially to reach several hundred additional midmass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground and excited states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Midterm extensions include the approximate treatment of triples corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U(1) and SU(2) symmetries.

Non-orthogonal spin-adaptation of coupled cluster methods: A new implementation of methods including quadruple excitations.

Abstract: The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is applied to coupled cluster methods with quadruple excitations (CCSDTQ). Calculations at this level of detail are of critical importance in describing the properties of molecular systems to an accuracy which can meet or exceed modern experimental techniques. Such calculations are of significant (and growing) importance in such fields as thermodynamics, kinetics, and atomic and molecular spectroscopies. With respect to the implementation of CCSDTQ and related methods, we show that there are significant advantages to non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to creating an efficient implementation. The resulting algorithm is implemented in the CFOUR program suite for CCSDT, CCSDTQ, and various approximate methods (CCSD(T), CC3, CCSDT-n, and CCSDT(Q)).

Coupled-cluster theory for atoms and molecules in strong magnetic fields.

Abstract: An implementation of coupled-cluster (CC) theory to treat atoms and molecules in finite magnetic fields is presented. The main challenges for the implementation stem from the magnetic-field dependence in the Hamiltonian, or, more precisely, the appearance of the angular momentum operator, due to which the wave function becomes complex and which introduces a gauge-origin dependence. For this reason, an implementation of a complex CC code is required together with the use of gauge-including atomic orbitals to ensure gauge-origin independence. Results of coupled-cluster singles–doubles–perturbative-triples (CCSD(T)) calculations are presented for atoms and molecules with a focus on the dependence of correlation and binding energies on the magnetic field.

Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum

Abstract: We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.

Coupled-cluster reference values for the GW27 and GW100 test sets for the assessment of GW methods

Abstract: The vertical ionisation energies of the molecules of the GW27 (27 molecules) and GW100 (100 molecules) test sets are computed in a polarised triple-zeta-valence basis set in the framework of coupled-cluster theory with single, double, and non-iterative triple substitutions. The molecular geometries were kept fixed to those of the two test sets. To demonstrate the usefulness of the coupled-cluster reference values, they are compared with quasi-particle energies obtained in the G0W0 approximation for functionals commonly used in Kohn–Sham density-functional theory (DFT). Furthermore, an approximation is assessed, in which only exchange contributions are added to the DFT orbital energies.

Pair extended coupled cluster doubles

Abstract: The accurate and efficient description of strongly correlated systems remains an important challenge for computational methods. Doubly occupied configuration interaction (DOCI), in which all electrons are paired and no correlations which break these pairs are permitted, can in many cases provide an accurate account of strong correlations, albeit at combinatorial computational cost. Recently, there has been significant interest in a method we refer to as pair coupled cluster doubles (pCCD), a variant of coupled cluster doubles in which the electrons are paired. This is simply because pCCD provides energies nearly identical to those of DOCI, but at mean-field computational cost (disregarding the cost of the two-electron integral transformation). Here, we introduce the more complete pair extended coupled cluster doubles (pECCD) approach which, like pCCD, has mean-field cost and reproduces DOCI energetically. We show that unlike pCCD, pECCD also reproduces the DOCI wave function with high accuracy. Moreover, pECCD yields sensible albeit inexact results even for attractive interactions where pCCD breaks down.

A Local Pair Natural Orbital-Based Multireference Mukherjee's Coupled Cluster Method.

Abstract: This paper reports the development of a local variant of Mukherjee's state-specific multireference coupled cluster method based on the pair natural orbital approach (LPNO-MkCC). The current implementation is restricted to single and double excitations. The performance of the LPNO-MkCCSD method was tested on calculations of naphthyne isomers, tetramethyleneethane, and β-carotene molecules. The results show that 99.7-99.8% of correlation energy was recovered with respect to the MkCC method based on canonical orbitals. Moreover, the errors of relative energies between different isomers or along a potential energy curve (with respect to the canonical method) are below 0.4 kcal/mol, safely within the chemical accuracy. The computational efficiency of our implementation of LPNO-MkCCSD in the ORCA program allows calculation of the β-carotene molecule (96 atoms and 1984 basis functions) on a single CPU core.

Two-photon absorption cross sections within equation-of-motion coupled-cluster formalism using resolution-of-the-identity and Cholesky decomposition representations: Theory, implementation, and benchmarks.

Abstract: The equation-of-motion coupled-cluster (EOM-CC) methods provide a robust description of electronically excited states and their properties. Here, we present a formalism for two-photon absorption (2PA) cross sections for the equation-of-motion for excitation energies CC with single and double substitutions (EOM-CC for electronically excited states with single and double substitutions) wave functions. Rather than the response theory formulation, we employ the expectation-value approach which is commonly used within EOM-CC, configuration interaction, and algebraic diagrammatic construction frameworks. In addition to canonical implementation, we also exploit resolution-of-the-identity (RI) and Cholesky decomposition (CD) for the electron-repulsion integrals to reduce memory requirements and to increase parallel efficiency. The new methods are benchmarked against the CCSD and CC3 response theories for several small molecules. We found that the expectation-value 2PA cross sections are within 5% from the quadratic response CCSD values. The RI and CD approximations lead to small errors relative to the canonical implementation (less than 4%) while affording computational savings. RI/CD successfully address the well-known issue of large basis set requirements for 2PA cross sections calculations. The capabilities of the new code are illustrated by calculations of the 2PA cross sections for model chromophores of the photoactive yellow and green fluorescent proteins.