Coupled Cluster Singles And Doubles Method Research Articles

Total and orbital density-based analyses of molecules revealing long-range interaction regions.

Total and orbital electron densities of molecules are explored for the effect of the long-range correction (LC) for density functional theory (DFT) exchange functionals by comparing to the effect of the ab initio coupled cluster singles and doubles (CCSD) method. Calculating the LC effect on the total electron densities shows that the LC stabilizes the electrons around the long-range interaction regions of kinetic energy density, which are assumed to be electrons other than free electrons and self-interacting electrons, while the CCSD method stabilizes the electrons in the long-range interaction regions in the vertical molecular planes. As a more precise test, the LC effect on orbital densities are compared to the CCSD effect on Dyson orbital densities. Surprisingly, these effects are similar for the unoccupied orbitals, indicating that the LC covers the effects required to reproduce the CCSD Dyson unoccupied orbitals. For exploring the discrepancies between these effects on the occupied orbitals, the photoionization cross sections are calculated as a direct test for the shapes of the HOMOs to investigate the differences between these effects on the occupied orbitals. Consequently, the LC clearly produces the canonical HOMOs close to the CCSD Dyson and experimental ones, except for the HOMO of benzene molecule that mixes with the HOMO 1 for the CCSD Dyson orbitals. This indicates that the orbital analyses using the photoionization cross sections are available as a direct test for the quality of DFT functionals.

Toward an efficient implementation of internally contracted coupled-cluster methods.

A new implementation of the internally contracted multireference coupled-cluster with singles and doubles (icMRCCSD) method is presented. The new code employs an efficient tensor contraction kernel and can also avoid full four-external integral transformations, which significantly extends the scope of the applicability of icMRCCSD. The new implementation is currently restricted to the simple case of two active electrons in two orbitals and also supports the computation of spin-adapted doublet and triplet coupled-cluster wavefunctions. This contribution describes the basic approach for the automated derivation of working equations and benchmarks the current code against efficient implementations of standard methods, such as single-reference coupled-cluster singles and doubles (CCSD) and internally contracted multireference configuration interaction (icMRCI). Run times for linearized variants of icMRCCSD are only twice as long as comparable CCSD runs and similar to those of the icMRCI implementation, while non-linear terms of more complete variants of icMRCCSD lead to an order of magnitude longer computation times. Nevertheless, the new code allows for computations at larger scales than it was possible previously, with less demands on memory and disk-space resources. This is exemplified by numerical structure optimizations and harmonic force field determinations of NC2H5 isomers and the singlet and triplet states of m-benzyne. In addition, the exchange coupling of a dinuclear copper complex is determined. This work also defines a new commutator approximation for icMRCCSD, which includes all terms that are also present in the single-reference CCSD method, thus yielding a consistent pair of single-reference and multireference coupled-cluster methods.

State-of-the-art computations of dipole moments using analytic gradients of high-level density-fitted coupled-cluster methods with focal-point approximations.

Using the analytic derivatives approach, dipole moments of high-level density-fitted coupled-cluster (CC) methods, such as coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], are presented. To obtain the high accuracy results, the computed dipole moments are extrapolated to the complete basis set (CBS) limits applying focal-point approximations. Dipole moments of the CC methods considered are compared with the experimental gas-phase values, as well as with the common DFT functionals, such as B3LYP, BP86, M06-2X, and BLYP. For all test sets considered, the CCSD(T) method provides substantial improvements over Hartree-Fock (HF), by 0.076-0.213 D, and its mean absolute errors are lower than 0.06 D. Furthermore, our results indicate that even though the performances of the common DFT functionals considered are significantly better than that of HF, their results are not comparable with the CC methods. Our results demonstrate that the CCSD(T)/CBS level of theory provides highly-accurate dipole moments, and its quality approaching the experimental results. © 2019 Wiley Periodicals, Inc.

Performance of Property-Optimized Basis Sets for Optical Rotation with Coupled Cluster Theory.

The effectiveness of the optical rotation prediction (ORP) basis set for computing specific rotations at the coupled cluster (CC) level has been evaluated for a test set of 14 chiral compounds. For this purpose, the ORP basis set has been developed for the second-row atoms present in the investigated systems (that is, for sulfur, phosphorus, and chlorine). The quality of the resulting set was preliminarily evaluated for seven molecules using time-dependent density-functional theory (TD-DFT). Rotations were calculated with the coupled cluster singles and doubles method (CCSD) as well as the second-order approximate coupled cluster singles and doubles method (CC2) with the correlation-consistent aug-cc-pVDZ and aug-cc-pVTZ basis sets and extrapolated to estimate the complete basis-set (CBS) limit for comparison with the ORP basis set. In the compounds examined here, the ORP calculations on molecules containing only first-row atoms compare favorably with results from the larger aug-cc-pVTZ basis set, in some cases lying closer to the estimated CBS limit, while results for molecules containing second-row atoms indicate that larger correlation-consistent basis sets are necessary to obtain reliable estimates of the CBS limit.

Systematic comparison of DFT and CCSD dipole moments, polarizabilities and hyperpolarizabilities

A comparative study of dipole moments, polarizabilities and hyperpolarizabilities of 16 different molecules is performed employing two completely different theoretical approaches namely, density functional theory (DFT) and coupled cluster singles and doubles (CCSD). Both methods include electron correlation. The CCSD method is more accurate but highly expensive. DFT with auxiliary density allows non-iterative solutions which is computational advantage and useful for large molecules. Dipole moments and polarizability calculations from DFT are in very good agreement with CCSD calculations. However, negative hyperpolarizability values from DFT differ significantly from their CCSD counterparts, whereas positive hyperpolarizabilities show reasonable agreement between these methodologies.

Implementation of the CCSD-PCM linear response function for frequency dependent properties in solution: Application to polarizability and specific rotation

This work reports the first implementation of the frequency dependent linear response (LR) function for the coupled cluster singles and doubles method (CCSD) combined with the polarizable continuum model of solvation for the calculation of frequency dependent properties in solution. In particular, values of static and dynamic polarizability as well as specific rotation are presented for various test molecules. Model calculations of polarizability show that a common approximation used in the definition of the LR function with solvation models recovers over 70% of the full response while maintaining a computational cost comparable to gas phase LR-CCSD. Calculations of specific rotation for three compounds for which gas phase methods predict the wrong sign of the rotation show that accounting for the electronic response of the solvent may be essential to assign the correct absolute configuration of chiral molecules.

Analytic energy gradients for the orbital-optimized third-order Møller–Plesset perturbation theory

Analytic energy gradients for the orbital-optimized third-order Møller-Plesset perturbation theory (OMP3) [U. Bozkaya, J. Chem. Phys. 135, 224103 (2011)] are presented. The OMP3 method is applied to problematic chemical systems with challenging electronic structures. The performance of the OMP3 method is compared with those of canonical second-order Møller-Plesset perturbation theory (MP2), third-order Møller-Plesset perturbation theory (MP3), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] for investigating equilibrium geometries, vibrational frequencies, and open-shell reaction energies. For bond lengths, the performance of OMP3 is in between those of MP3 and CCSD. For harmonic vibrational frequencies, the OMP3 method significantly eliminates the singularities arising from the abnormal response contributions observed for MP3 in case of symmetry-breaking problems, and provides noticeably improved vibrational frequencies for open-shell molecules. For open-shell reaction energies, OMP3 exhibits a better performance than MP3 and CCSD as in case of barrier heights and radical stabilization energies. As discussed in previous studies, the OMP3 method is several times faster than CCSD in energy computations. Further, in analytic gradient computations for the CCSD method one needs to solve λ-amplitude equations, however for OMP3 one does not since λ(ab)(ij(1))=t(ij)(ab(1)) and λ(ab)(ij(2))=t(ij)(ab(2)). Additionally, one needs to solve orbital Z-vector equations for CCSD, but for OMP3 orbital response contributions are zero owing to the stationary property of OMP3. Overall, for analytic gradient computations the OMP3 method is several times less expensive than CCSD (roughly ~4-6 times). Considering the balance of computational cost and accuracy we conclude that the OMP3 method emerges as a very useful tool for the study of electronically challenging chemical systems.

A comparison between state-specific and linear-response formalisms for the calculation of vertical electronic transition energy in solution with the CCSD-PCM method

The calculation of vertical electronic transition energies of molecular systems in solution with accurate quantum mechanical methods requires the use of approximate and yet reliable models to describe the effect of the solvent on the electronic structure of the solute. The polarizable continuum model (PCM) of solvation represents a computationally efficient way to describe this effect, especially when combined with coupled cluster (CC) methods. Two formalisms are available to compute transition energies within the PCM framework: State-Specific (SS) and Linear-Response (LR). The former provides a more complete account of the solute-solvent polarization in the excited states, while the latter is computationally very efficient (i.e., comparable to gas phase) and transition properties are well defined. In this work, I review the theory for the two formalisms within CC theory with a focus on their computational requirements, and present the first implementation of the LR-PCM formalism with the coupled cluster singles and doubles method (CCSD). Transition energies computed with LR- and SS-CCSD-PCM are presented, as well as a comparison between solvation models in the LR approach. The numerical results show that the two formalisms provide different absolute values of transition energy, but similar relative solvatochromic shifts (from nonpolar to polar solvents). The LR formalism may then be used to explore the solvent effect on multiple states and evaluate transition probabilities, while the SS formalism may be used to refine the description of specific states and for the exploration of excited state potential energy surfaces of solvated systems.

Carbon X-ray absorption spectra of fluoroethenes and acetone: A study at the coupled cluster, density functional, and static-exchange levels of theory

Near carbon K-edge X-ray absorption fine structure spectra of a series of fluorine-substituted ethenes and acetone have been studied using coupled cluster and density functional theory (DFT) polarization propagator methods, as well as the static-exchange (STEX) approach. With the complex polarization propagator (CPP) implemented in coupled cluster theory, relaxation effects following the excitation of core electrons are accounted for in terms of electron correlation, enabling a systematic convergence of these effects with respect to electron excitations in the cluster operator. Coupled cluster results have been used as benchmarks for the assessment of propagator methods in DFT as well as the state-specific static-exchange approach. Calculations on ethene and 1,1-difluoroethene illustrate the possibility of using nonrelativistic coupled cluster singles and doubles (CCSD) with additional effects of electron correlation and relativity added as scalar shifts in energetics. It has been demonstrated that CPP spectra obtained with coupled cluster singles and approximate doubles (CC2), CCSD, and DFT (with a Coulomb attenuated exchange-correlation functional) yield excellent predictions of chemical shifts for vinylfluoride, 1,1-difluoroethene, trifluoroethene, as well as good spectral features for acetone in the case of CCSD and DFT. Following this, CPP-DFT is considered to be a viable option for the calculation of X-ray absorption spectra of larger π-conjugated systems, and CC2 is deemed applicable for chemical shifts but not for studies of fine structure features. The CCSD method as well as the more approximate CC2 method are shown to yield spectral features relating to π∗-resonances in good agreement with experiment, not only for the aforementioned molecules but also for ethene, cis-1,2-difluoroethene, and tetrafluoroethene. The STEX approach is shown to underestimate π∗-peak separations due to spectral compressions, a characteristic which is inherent to this method.

Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method: Improving upon CCSD(T) and CCSD(T)Λ: Preliminary application

Symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OO-CCD or simply "OD" for short) method are investigated. The conventional symmetric and asymmetric perturbative triples corrections [(T) and (T)(Λ)] are implemented, the latter one for the first time. Additionally, two new triples corrections, denoted as OD(Λ) and OD(Λ)(T), are introduced. We applied the new methods to potential energy surfaces of the BH, HF, C(2), N(2), and CH(4) molecules, and compare the errors in total energies, with respect to full configuration interaction, with those from the standard coupled-cluster singles and doubles (CCSD), with perturbative triples [CCSD(T)], and asymmetric triples correction (CCSD(T)(Λ)) methods. The CCSD(T) method fails badly at stretched geometries, the corresponding nonparallelity error is 7-281 kcal mol(-1), although it gives reliable results near equilibrium geometries. The new symmetric triples correction, CCSD(Λ), noticeably improves upon CCSD(T) (by 4-14 kcal mol(-1)) for BH, HF, and CH(4); however, its performance is worse than CCSD(T) (by 1.6-4.2 kcal mol(-1)) for C(2) and N(2). The asymmetric triples corrections, CCSD(T)(Λ) and CCSD(Λ)(T), perform remarkably better than CCSD(T) (by 5-18 kcal mol(-1)) for the BH, HF, and CH(4) molecules, while for C(2) and N(2) their results are similar to those of CCSD(T). Although the performance of CCSD and OD is similar, the situation is significantly different in the case of triples corrections, especially at stretched geometries. The OD(T) method improves upon CCSD(T) by 1-279 kcal mol(-1). The new symmetric triples correction, OD(Λ), enhances the OD(T) results (by 0.01-2.0 kcal mol(-1)) for BH, HF, and CH(4); however, its performance is worse than OD(T) (by 1.9-2.3 kcal mol(-1)) for C(2) and N(2). The asymmetric triples corrections, OD(T)(Λ) and OD(Λ)(T), perform better than OD(T) (by 2.0-6.2 kcal mol(-1)). The latter method is slightly better for the BH, HF, and CH(4) molecules. However, for C(2) and N(2) the new results are similar to those of OD(T). For the BH, HF, and CH(4) molecules, OD(Λ)(T) provides the best potential energy curves among the considered methods, while for C(2) and N(2) the OD(T) method prevails. Hence, for single-bond breaking the OD(Λ)(T) method appears to be superior, whereas for multiple-bond breaking the OD(T) method is better.

The ‘tailored’ CCSD(T) description of the automerization of cyclobutadiene

An alternative route to extend the CCSD(T) approach to multireference problems is presented. The well-known defect of the CCSD(T) model in describing the non-dynamic electron correlation effects is remedied by ‘tailoring’ the underlying coupled-cluster singles and doubles (CCSD) approach and applying the perturbative triples correction to it. The TCCSD(T) approach suggested in the paper has the same computational demands as the CCSD(T) method, though being mostly free from its drawbacks pertinent to multireference (quasidegenerate) situations. To test the approach we calculate the potential energy surface for the automerization of cyclobutadiene where the transition state exhibits a strong multireference character.

NMR Spectroscopic Evidence for the Intermediacy of XeF3− in XeF2/F− Exchange, Attempted Syntheses and Thermochemistry of XeF3− Salts, and Theoretical Studies of the XeF3− Anion

The existence of the trifluoroxenate(II) anion, XeF(3)(-), had been postulated in a prior NMR study of the exchange between fluoride ion and XeF(2) in CH(3)CN solution. The enthalpy of activation for this exchange, ΔH(⧧), has now been determined by use of single selective inversion (19)F NMR spectroscopy to be 74.1 ± 5.0 kJ mol(-1) (0.18 M) and 56.9 ± 6.7 kJ mol(-1) (0.36 M) for equimolar amounts of [N(CH(3))(4)][F] and XeF(2) in CH(3)CN solvent. Although the XeF(3)(-) anion has been observed in the gas phase, attempts to prepare the Cs(+) and N(CH(3))(4)(+) salts of XeF(3)(-) have been unsuccessful, and are attributed to the low fluoride ion affinity of XeF(2) and fluoride ion solvation in CH(3)CN solution. The XeF(3)(-) anion would represent the first example of an AX(3)E(3) valence shell electron pair repulsion (VSEPR) arrangement of electron lone pair and bond pair domains. Fluorine-19 exchange between XeF(2) and the F(-) anion has also been probed computationally using coupled-cluster singles and doubles (CCSD) and density functional theory (DFT; PBE1PBE) methods. The energy-minimized geometry of the ground state shows that the F(-) anion is only weakly coordinated to XeF(2) (F(2)Xe---F(-); a distorted Y-shape possessing C(s) symmetry), while the XeF(3)(-) anion exists as a first-order transition state in the fluoride ion exchange mechanism, and is planar and Y-shaped (C(2v) symmetry). The molecular geometry and bonding of the XeF(3)(-) anion has been described and rationalized in terms of electron localization function (ELF) calculations, as well as the VSEPR model of molecular geometry. Quantum-chemical calculations, using the CCSD method and a continuum solvent model for CH(3)CN, accurately reproduced the transition-state enthalpy observed by (19)F NMR spectroscopy, and showed a negative but negligible enthalpy for the formation of the F(2)Xe---F(-) adduct in this medium.

Coupled Cluster Calculations in Solution with the Polarizable Continuum Model of Solvation

Coupled cluster theory (CC) provides very accurate estimates of energies and molecular properties. Such calculations are often limited to gas-phase species due to the large computational cost of this level of theory; however, most of the chemical phenomena take place in solution. We propose an efficient implementation of the polarizable continuum model of solvation (PCM) with the coupled cluster singles and doubles method (CCSD) to take into account the solvent effects on the ground-state energy and geometry. Differently from atomistic representations, the PCM approach does not require conformational sampling of the solvent molecules and naturally describes mutual polarization effects between solute and solvent. Applications of the CCSD-PCM method to representative molecules are presented.

Improving upon the accuracy for doubly excited states within the coupled cluster singles and doubles theory

An alternative strategy of computations for double character excited states has been examined. The basic idea is to employ the reference function specific to the excited state of interest, as opposed to the traditionally used reference function, usually corresponding to the ground state, specific to the entire spectrum of a molecule. The procedure is used within the framework of the coupled cluster singles and doubles (CCSD) method. The conventional spin-conserving CC approach as well as its spin-flip (SF) extension has been analyzed. For the latter, two variants are considered, changing the S(z) value of the reference function by one [equation-of-motion (EOM)-SF] and two (EOM-2SF). The accuracy of the methods is benchmarked for the C(2) and C(4) molecules and referred to the full configuration interaction (FCI) or CC singles, doubles, and triples results. The vertical and adiabatic excitation energies, equilibrium geometries, and harmonic frequencies are studied. A significant improvement is demonstrated for the excitation energies of doubly excited states. Comparing these values with the FCI method, the errors of the conventional EOM CCSD method of about 1.7-2.2 eV are reduced to about 0.0-0.4 eV for the SF method. An improvement is also shown for the equilibrium geometries and harmonic frequencies.

Coupled-cluster methods with perturbative inclusion of explicitly correlated terms: a preliminary investigation

We propose to account for the large basis-set error of a conventional coupled-cluster energy and wave function by a simple perturbative correction. The perturbation expansion is constructed by Löwdin partitioning of the similarity-transformed Hamiltonian in a space that includes explicitly correlated basis functions. To test this idea, we investigate the second-order explicitly correlated correction to the coupled-cluster singles and doubles (CCSD) energy, denoted here as the CCSD(2)(R12) method. The proposed perturbation expansion presents a systematic and easy-to-interpret picture of the "interference" between the basis-set and correlation hierarchies in the many-body electronic-structure theory. The leading-order term in the energy correction is the amplitude-independent R12 correction from the standard second-order Møller-Plesset R12 method. The cluster amplitudes appear in the higher-order terms and their effect is to decrease the basis-set correction, in accordance with the usual experience. In addition to the use of the standard R12 technology which simplifies all matrix elements to at most two-electron integrals, we propose several optional approximations to select only the most important terms in the energy correction. For a limited test set, the valence CCSD energies computed with the approximate method, termed , are on average precise to (1.9, 1.4, 0.5 and 0.1%) when computed with Dunning's aug-cc-pVXZ basis sets [X = (D, T, Q, 5)] accompanied by a single Slater-type correlation factor. This precision is a roughly an order of magnitude improvement over the standard CCSD method, whose respective average basis-set errors are (28.2, 10.6, 4.4 and 2.1%). Performance of the method is almost identical to that of the more complex iterative counterpart, CCSD(R12). The proposed approach to explicitly correlated coupled-cluster methods is technically appealing since no modification of the coupled-cluster equations is necessary and the standard Møller-Plesset R12 machinery can be reused.

The NMR indirect nuclear spin–spin coupling constants for some small rigid hydrocarbons: molecular equilibrium values and vibrational corrections

The indirect nuclear spin–spin coupling constants of allene and of two sterically strained hydrocarbons – cyclopropane and cyclopropene – calculated at different levels of electronic-structure theory are compared with each other and with experimental equilibrium constants, obtained from experiment by subtracting calculated vibrational contributions. It is found that, even in a relatively small basis set, the coupled-cluster singles-and-doubles (CCSD) method provides very good results, outperforming the other ab initio methods considered in this work – namely, the second-order polarization propagator approximation (SOPPA) and the multiconfigurational self-consistent field (MCSCF) approach. Calculations in the same basis set are also carried out at the hybrid level of density functional theory (DFT). Compared with the experimental equilibrium values the CCSD method gives the best results for the ab initio methods, while SOPPA consistently performs better than RASSCF. Hybrid DFT performs as well as SOPPA for the one-bond coupling constants, while, for the other constants, it provides results of similar quality as CCSD. The DFT approximation is also used to evaluate the indirect nuclear spin–spin coupling constants and their vibrational corrections for the larger cyclobutene and cyclobutane molecules.

Theoretical study of the potential stability of the peroxo nitrate radical

The existence of the peroxo nitrate radical (ONOO) has been discussed for some time and its formation has been used to explain aspects of the NO3 scavenging in the Earth’s atmosphere. In this study we report our thorough investigation of the stability of this species by means of highly correlated ab initio calculations. Single-reference coupled-cluster singles and doubles (CCSD) as well as multireference configuration interaction (MRCI) calculations were performed to optimize equilibrium structures and obtain harmonic force fields. The force fields were used to calculate the harmonic frequencies as well as isotopic shifts. The CCSD calculations result in shallow minima for both the |2A″〉 ground as well as the |2A′〉 excited state. However, the calculated isotopic shifts of the ground state show that the experimentally observed shift of 50 cm−1 cannot be due to ONOO. In contrast, no minima were found by the MRCI calculations. The analysis of the wave functions indicates that the potential wells obtained by CCSD are artifacts which are due to the single-reference nature of the CCSD method. Our conclusion is that ONOO is not a bound structure and cannot be observed experimentally. Our calculations also show that thermal decomposition of NO3 into NO and O2 is not possible under atmospheric conditions and thus this channel cannot be responsible for the unknown NO3 scavenging process discussed in the literature.

Electric field gradients of water: A systematic investigation of basis set, electron correlation, and rovibrational effects

Electric field gradients at the oxygen and hydrogen nuclei of water have been calculated using high level ab initio methods. Systematic studies of basis set truncation errors have been carried out at the Hartree–Fock and coupled cluster singles and doubles (CCSD) levels using extended correlation consistent basis sets with up to 398 basis functions. Correlation effects are investigated using a hierarchy of correlation methods extending up to the approximate inclusion of triples excitations by means of the CCSD(T) method. Rovibrational effects have been calculated combining accurate ab initio electric field gradient data and accurate experimental force fields. On the basis of the most accurate results for the electric field gradients, the nuclear quadrupole coupling constants for deuterium and oxygen-17 have been discussed including the temperature dependence. The final results are discussed in view of existing experimental data. Our best values for the nuclear quadrupole coupling constants are in excellent agreement (within 1%) of recent experimental results, while some earlier experimental values are shown to be less reliable.

A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2)

Recently, we introduced a new ansatz for developing perturbative corrections to methods based on coupled-cluster theory. In this article we apply this ansatz to the coupled-cluster singles and doubles (CCSD) method, generating the CCSD(2) method. We use the CCSD(2) method to study the double dissociation of water and to calculate spectroscopic constants of first row diatomic molecules. As long as Hartree–Fock is a reasonable approximation, CCSD(2) works very well.

Size-extensive calculations of static structure factors from the coupled cluster singles and doubles model

The x-ray incoherent scattering factor S(q), which is also called the static structure factor, is very sensitive to electron correlation. In this study a method for calculating S(q) based on coupled cluster singles and doubles (CCSD) approach is developed and the computed S(q) of H2O, CH3OH, CH3CN, C6H6, and C6H12 are compared with experimental results. It is shown that the CCSD method improves theoretical S(q) of large molecules significantly compared with those by configuration interaction singles and doubles (CISD) previously employed.