Coupled Cluster With Singles And Doubles Research Articles

Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters.

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

Ground- and Excited-State Dipole Moments and Oscillator Strengths of Full Configuration Interaction Quality

We report ground- and excited-state dipole moments and oscillator strengths (computed in different "gauges" or representations) of full configuration interaction (FCI) quality using the selected configuration interaction method known as Configuration Interaction using a Perturbative Selection made Iteratively (CIPSI). Thanks to a set encompassing 35 ground- and excited-state properties computed in 11 small molecules, the present near-FCI estimates allow us to assess the accuracy of high-order coupled-cluster (CC) calculations including up to quadruple excitations. In particular, we show that incrementing the excitation degree of the CC expansion (from CC with singles and doubles (CCSD) to CC with singles, doubles, and triples (CCSDT) or from CCSDT to CC with singles, doubles, triples, and quadruples (CCSDTQ)) reduces the average error with respect to the near-FCI reference values by approximately 1 order of magnitude.

Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking.

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) approach from a computational quantum chemistry perspective and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single-determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multireference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.

Electronic Structure, Stability, and Electrical Mobility of Cationic Silver Oxide Atomic Clusters.

Silver oxide cluster cations (AgnOm+) can readily be produced by a number of methods including atmospheric-pressure spark ablation of pure silver electrodes when trace amounts of oxygen are present in the carrier gas. Here we determine the equilibrium geometries of AgnOm+ clusters (n = 1-4; m = 1-5) using accurate coupled cluster with singles and doubles (CCSD) method, while the stabilization energies are calculated with additional perturbative triples correction (CCSD(T)). Although a number of stable states have been identified, our results show that the AgnOm+ clusters with m = 1 are more stable than those with m ≥ 2 due to the absence of the terminally attached O2 molecule, corroborating recent observations by mass spectrometry. Using the computed structures, we calculate the electrical mobilities of the AgnOm+ clusters and label the values on a respective experimentally determined spectrum in an attempt to better interpret the occurrence of the peaks and troughs in the measurements.

Bootstrap Embedding For Large Molecular Systems.

Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N3) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C36 Fullerene and an Iron Porphyrin Model Complex.

We present three distinct examples where phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant trial wave function with essential symmetry breaking. Essential symmetry breaking was first introduced by Lee and Head-Gordon [ Phys. Chem. Chem. Phys. 2019, 21, 4763-4778, 10.1039/C8CP07613H]. We utilized essential complex and time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the singlet-triplet gap of a known biradicaloid, C36. ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Brueckner orbitals obtained from regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C36. Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, κ-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and κ-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single-determinant trial wave function with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

Green's function coupled cluster simulation of the near-valence ionizations of DNA-fragments.

Accurate description of the ionization process in DNA is crucial to the understanding of the DNA damage under exposure to ionizing radiation and the exploration of the potential application of DNA strands in nanoelectronics. In this work, by employing our recently developed Green's function coupled-cluster library on supercomputing facilities, we have studied the spectral functions of several guanine-cytosine (G-C) base pair structures ([G-C]n, n = 1-3) for the first time in a relatively broad near-valence regime ([-25.0, -5.0] eV) in the coupled-cluster with singles and doubles level. Our focus is to give a preliminary many-body coupled-cluster understanding and guideline of the vertical ionization energy (VIE), spectral profile, and ionization feature changes of these systems as the system size expands in this near-valence regime. The results show that, as the system size expands, even though the lowest VIEs keep decreasing, the changes of spectral function profile and the relative peak positions get unexpectedly smaller. Further analysis of the ionized states associated with the most intensive peak in the spectral functions reveals non-negligible |2h, 1p⟩'s in the ionized wave functions of the considered G-C base pair systems. The leading |2h, 1p⟩'s associated with the main ionizations from the cytosine part of the G-C base pairs feature a transition from the intra-base-pair cytosine π → π* excitation to the inter-base-pair electron excitation as the size of G-C base pairs expands, which also indicates the minimum quantum region in the many-body calculations of DNA systems.

Phosphorus mononitride: A difficult case for theory

AbstractPhosphorus nitride (PN) is the simplest molecule formed solely by phosphorus and nitrogen. It represents an interesting model for materials, where phosphorus is directly attached to nitrogen. Nevertheless, both theoretical and experimental studies often provide an incomplete picture on the structural, electronic, and spectral properties of PN. Theoretical predictions often suffer from insufficient level of theory, incomplete basis set, or from neglecting several effects, for example, zero‐point vibrational correction (ZPVC). Therefore, we performed an extensive benchmark study on structural, electronic, and spectral properties of PN at the Hartree‐Fock, density functional theory (DFT), or even the coupled‐cluster levels. We paid special attention to the basis set effect. We tested three variants of Dunning's aug‐cc‐pVXZ basis sets with the size from double‐ζ to sextuple‐ζ, as well as Jensen's aug‐pc‐n, aug‐pcJ‐n, and aug‐pcSseg‐n basis sets, where n = 1‐4. Obtained energetics, PN distance, dipole moment, vibrational frequencies, and nuclear magnetic resonance (NMR) parameters were extrapolated to the complete basis set limit (CBS) using three‐ or two‐parameter formulas. The 31P NMR shieldings estimated with the aug‐cc‐pVXZ and aug‐cc‐pV(X + d)Z basis sets strongly depend on the basis set size providing scattered convergence patterns toward CBS. The Hartree‐Fock self‐consistent field (HF‐SCF) NMR parameters evinced similar behavior as the coupled‐cluster data. The only smooth convergence was achieved using the aug‐cc‐pCVXZ basis sets that include core‐valence effects. The KT3 functional underestimated the phosphorus CBS shieldings by about 12 ppm compared to coupled cluster with singles and doubles (CCSD) (T). Nevertheless, KT3 unambiguously surpasses the HF‐SCF and CCSD levels that provide 31P shieldings that are lower by about 150 ppm and 24 ppm compared to CCSD(T). The convergence of nitrogen shieldings was regular for all basis set hierarchies and all theoretical methods. Relativistic and vibrational effects on selected properties were also discussed.

Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation.

This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] scheme, in which one-body substitutions are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid storage of large four-index intermediates, we propose a noninteracting virtual orbital (NIVO) approximation of the Baker-Campbell-Hausdorff series that neglects commutators terms with three and four virtual indices. The NIVO approximation reduces the computational prefactor of the MR-LDSRG(2), bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-ζ basis set. The predicted automerization energy is found to be similar to the value computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.

Fractional-occupation-number based divide-and-conquer coupled-cluster theory

We have extended the divide-and-conquer (DC) coupled-cluster with singles and doubles (CCSD) to a fractional occupation number (FON) formalism, denoted as FON-DC-CCSD, using the thermal Wick theorem. The motivation is to address the inconsistency in the treatment of orbital occupations between the DC-based Hartree–Fock and the DC-CCSD methods, which adopt the Fermi distribution function and the step function for orbital occupation, respectively. Numerical applications involving polyene chains and single-walled carbon nanotubes confirm that the proposed FON-DC-CCSD method reduces both energy errors and computational costs compared with the conventional DC-CCSD method.

On the calculations of the static electronic dipole (hyper)polarizability for the free and spatially confined H.

The quality of the static electronic dipole (hyper)polarizabilities (α and γ) calculated using the coupled cluster with singles and doubles (CCSD) method and various basis sets for the isolated hydrogen anion (H-) was verified against highly accurate results obtained within the variation-perturbation scheme with the optimized explicitly correlated Gaussian functions. Moreover, the influence of spatial confinement on α and γ of H- was analyzed. The effect of confinement (orbital compression) was modeled by the spherically symmetric harmonic oscillator potential. Our results demonstrate that in order to obtain the value of α with a relative error less than 10% and correct order of magnitude of γ for the unconfined H- at the CCSD level of theory, at least triply augmented correlation consistent basis set (t-aug-cc-pVXZ, X = D,T,Q,5,6) has to be used. Furthermore, it was found that the spatial confinement significantly affects α and γ of H-.

The Thermodynamic and Kinetic Properties of 2-Hydroxypyridine/2-Pyridone Tautomerization: A Theoretical and Computational Revisit.

The gas-phase thermal tautomerization reaction between 2-hydroxypyridine (2-HPY) and 2-pyridone (2-PY) was investigated by applying 6-311++G** and aug-cc-pvdz basis sets incorporated into some density functional theory (DFT) and coupled cluster with singles and doubles (CCSD) methods. The geometrical structures, dipole moments, HOMO-LUMO energy gaps, total hyperpolarizability, kinetics and thermodynamics functions were monitored against the effects of the corrections imposed on these functionals. The small experimental energy difference between the two tautomers of 3.23 kJ/mol; was a real test of the accuracy of the applied levels of theory. M062X and CCSD methods predicted the preference of 2-HPY over 2-PY by 5–9 kJ/mol; while B3LYP functional favoured 2-PY by 1–3 kJ/mol. The CAM-B3LYP and ωB97XD functionals yielded mixed results depending on the basis set used. The source of preference of 2-HPY is the minimal steric hindrance and electrostatic repulsion that subdued the huge hyperconjugation in 2-PY. A 1,3-proton shift intramolecular gas-phase tautomerization yielded a high average activation of 137.152 kJ/mol; while the intermolecular mixed dimer interconversion gave an average barrier height of 30.844 kJ/mol. These findings are boosted by a natural bond orbital (NBO) technique. The low total hyperpolarizabilities of both tautomers mark out their poor nonlinear optical (NLO) behaviour. The enhancement of the total hyperpolarizability of 2-HPY over that of 2-PY is interpreted by the bond length alternation.

UV excitations of halons.

In the present study, we examined the UV excitations of a newly introduced molecular set, Halons-9, composed of nine gaseous halon molecules. The performance of the density functional-based multi-reference configuration interaction method (DFT/MRCI) and time-dependent density functional theory with CAM-B3LYP functional (TD-CAM-B3LYP) in the computation of singlet and triplet excited states of this set was evaluated against coupled-cluster with singles and doubles (CCSD). Excited states up to the corresponding ionization limits, including both localized and delocalized excitations, have been benchmarked. TD-CAM-B3LYP significantly underestimates excitation energies of the higher mixed valence-Rydberg and Rydberg states, with computed mean absolute deviations from the equation of motion (EOM)-CCSD results 1.06 and 0.76 eV, respectively. DFT/MRCI gives a significantly better description of higher excited states, albeit still poor, compared to the TD-CAM-B3LYP. The mean absolute deviations of mixed valence-Rydberg and Rydberg states from the reference EOM-CCSD values are 0.66 and 0.47 eV, respectively. The performance of DFT/MRCI for description of strongly correlated states with valence-Rydberg mixing is still not satisfactory enough. On the other hand, oscillator strengths of most of singlet states obtained with both methods are close to the EOM-CCSD values. The largest deviations, occurring in the case of several high-lying multiconfigurational states, are of an order of magnitude.

Improved description of the orbital relaxation effect by practical use of the self‐energy

The self‐energy shift in the orbital relaxation (OR) term of the polarization propagator complete through the second‐order is presented. In combination with the optimal damping parameter in the OR term, the modified propagator produces the excitation energy of the coupled‐cluster with singles and doubles (CCSD) accuracy. The self‐energy shift requires the floating‐point operation of , where N refers to the magnitude of the molecular size. Because the second‐order polarization propagator requires the floating‐point operation of , the additional computational effort to construct the self‐energy is negligibly small. Numerical results are shown for several molecules including glycine, 2,3,5,6‐tetrafluorobenzene, and naphthalene, and promising agreements with those of CCSD are confirmed within less than 0.2 eV. The basis set dependence is also tested for the water molecule using aug‐cc‐pV NZ (N = D–7), where this newly developed approach mimics the behavior of the CCSD values. The self‐energy shifting for the second‐order response matrix in combination with the use of a dumping parameter is efficiently implemented for calculations of medium‐sized molecular systems, including glycine and naphthalene. The developed approach provides CCSD‐like accuracy at a more affordable computational expense. © 2014 Wiley Periodicals, Inc.

Assessment of Density Functional Theory for Thermochemical Approaches Based on Bond Separation Reactions

The recently proposed ATOMIC protocol is a fully ab initio thermochemical protocol that rests upon the concept of bond separation reactions (BSRs) to correct for systematic errors of composite wave function approaches. It achieves high accuracy for atomization energies and derived heats of formation if basis set requirements for all contributing components are balanced carefully. The present work explores the potential of density functionals as possible replacements of composite wave function approaches in the ATOMIC protocol. Twenty density functionals are examined for their accuracy in thermochemical predictions based on calculated bond-separation energies and precomputed high-level data for the small parent molecules entering BSRs. The best density functionals outperform CCSD (coupled cluster with singles and doubles excitations), but none reaches the accuracy of well-balanced composite wave function approaches that consider quasiperturbational connected triples excitations at least with small basis sets. Some functionals show unexpected problems with bond separation reactions and are analyzed further with a model of empirically calibrated bond additivity corrections. Finally, the benefit of adding empirical dispersion terms to common density functionals is analyzed in the context of BSR-corrected thermochemistry.

QTAIM Study on the Degenerate Cope Rearrangements of 1,5-Hexadiene and Semibullvalene

Using the homotropylium cation (1) as an archetypal example of a homoaromatic molecule, we carried out a quantum theory of atoms-in-molecules (QTAIM) computational study--at DFT (density functional theory), CCSD (coupled cluster with singles and doubles), and CASSCF (complete active space self-consistent field) levels--on 1 and the degenerate Cope rearrangements of 1,5-hexadiene (2) and semibullvalene (3) including the evaluation of delocalization indexes and a visualization of atomic basins. This study yielded new insights into the factors determining the reaction barriers and the bonding of the ground and transitions states of 2 and 3. Contrary to conclusions reached in earlier studies, we found that the transition state for the degenerate rearrangement of 2 is not aromatic and that the driving force for the very facile Cope rearrangement of semibullvalene is caused by the stabilization of individual atoms as well as electronic delocalization, not by the release of strain in the three-membered ring.

Linear response coupled cluster singles and doubles approach with modified spectral resolution of the similarity transformed Hamiltonian

This paper discusses practical scheme for correcting the linear response coupled cluster with singles and doubles (CCSD) equations by shifting the poles corresponding to the equation-of-motion CCSD excitation energies by adding noniterative corrections due to triples. A simple criterion is derived for the excited states to be corrected in the spectral resolution of similarity transformed Hamiltonian on the CCSD level. Benchmark calculations were performed to compare the accuracies of static and dynamic polarizabilities obtained in this way with the CC3 and CCSDT counterparts.

Basis set convergence of post-CCSD contributions to molecular atomization energies

Basis set convergence of correlation effects on molecular atomization energies beyond the coupled cluster with singles and doubles (CCSD) approximation has been studied near the one-particle basis set limit. Quasiperturbative connected triple excitations, (T), converge more rapidly than L(-3) (where L is the highest angular momentum represented in the basis set), while higher-order connected triples, T3-(T), converge more slowly--empirically, proportional to L(-5/2). Quasiperturbative connected quadruple excitations, (Q), converge smoothly as proportional to L(-3) starting with the cc-pVTZ basis set, while the cc-pVDZ basis set causes overshooting of the contribution in highly polar systems. Higher-order connected quadruples display only weak, but somewhat erratic, basis set dependence. Connected quintuple excitations converge very rapidly with the basis set, to the point where even an unpolarized double-zeta basis set yields useful numbers. In cases where fully iterative coupled cluster up to connected quintuples (CCSDTQ5) calculations are not an option, CCSDTQ(5) (i.e., coupled cluster up to connected quadruples plus a quasiperturbative connected quintuples correction) cannot be relied upon in the presence of significant nondynamical correlation, whereas CCSDTQ(5)(Lambda) represents a viable alternative. Connected quadruples corrections to the core-valence contribution are thermochemically significant in some systems. We propose an additional variant of W4 theory [A. Karton et al., J. Chem. Phys. 125, 144108 (2006)], denoted W4.4 theory, which is shown to yield a rms deviation from experimental atomization energies (active thermochemical tables, ATcT) of only 0.05 kcal/mol for systems for which ATcT values are available. We conclude that "3sigma <or=1 kJ/mol" thermochemistry is feasible with current technology, but that the more ambitious goal of +/-10 cm(-1) accuracy is illusory, at least for atomization energies.

The ab initio model potential method with the spin-free relativistic scheme by eliminating small components Hamiltonian

A relativistic ab initio model potential (AIMP) for Pt, Au, and Hg atoms has been developed using a relativistic scheme by eliminating small components (RESC) in which the 5p, 5d, and 6s electrons are treated explicitly. The quality of new RESC–AIMP has been tested by calculating the spectroscopic properties of the hydrides of these elements using the Hartree–Fock and coupled cluster with singles and doubles (CCSD) methods. The agreement with reference all-electron RESC calculations is excellent. The RESC–AIMP method is applied successfully in the investigation of the spectroscopic constants of Au2 and Hg2 using the CCSD method with a perturbative estimate of the contributions of triples. The ground state of Pt2 is also determined by RESC–AIMP with the second-order complete active space perturbation method. The results show that scalar relativistic effects on the valence properties are well described by the RESC–AIMP method. The effect on the basis set superposition error on the spectroscopic constants is also examined.

Effect of spin contamination on the prediction of barrier heights by coupled-cluster theory: F+H2?HF+H reaction

The role of spin contamination and quasidegeneracy in the energetics of a simple hydrogen abstraction reaction is studied by applying recently developed coupled-cluster (CC) methods to an exactly solvable model for the F+H2→HF+H reaction [C. W. Bauschlicher and P. R. Taylor, J. Chem. Phys. 86, 858 (1987)]. To assess the role of spin contamination, the (spin)-unrestricted Hartree–Fock (UHF) CC with singles and doubles (CCSD) barrier height is compared with that obtained with a fully spin-adapted unitary group approach (UGA) based CCSD, while the quasidegeneracy effects are examined using the so-called reduced multireference (RMR) CCSD method. It is shown that the effect of spin contamination on the barrier height is more significant (0.7 kcal/mol) than that of the quasidegeneracy (0.2 kcal/mol), although the latter plays a more significant role for exothermicity. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 281–290, 2000