Coupled-cluster Doubles Method Research Articles

Finite-size effects in periodic coupled cluster calculations

We provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as O(Nk−13). Here Nk is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as O(Nk−13). Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to O(Nk−1) with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.

A theoretical study of the intermolecular interactions of H2–CuF complex: Intermolecular vibrations, isotope effects, and rotational structure

In this paper, a theoretical study has been made on the intermolecular interactions of the H2–CuF complex, including binding energy, intermolecular vibrations, isotope effects, and rotational structure. Based on different bond lengths of H2 and CuF monomers, three intermolecular potential energy surfaces (PESs) were constructed at the level of single and double excitation coupled-cluster method with a non-iterative perturbation treatment of triple excitations [CCSD(T)] with aug-cc-pVTZ basis set supplemented with bond functions. A global minimum on the PESs show that H2–CuF complex belongs to C2ν point group with a T-shaped structure. The obtained binding energy ranges from 8890 to 10050 cm−1, which increases as the increment of H–H bond length, but opposite case has been determined as the increment of Cu–F bond length. The accuracy of PESs was examined by the available data of 101–000 transition. The predicted rotational transition frequency obtained from bound state calculations can reproduce the experimental observation very well, and the predicted error is 0.1% based on the PES1 constructed with rH2 and rCuF fixed at 0.838 and 1.7409 Å. By analyzing the wave function of the bound state, the intermolecular vibrational modes were assigned unambiguously. Isotope effects were also studied and the largest error is also 0.1% compared with the available 101–000 transition data. A set of spectroscopic parameters were obtained for six isotopologues to determine rotational structure of H2–CuF complex. Upon the complex formation, the obtained structure parameters show that H–H bond length is elongated by 0.081 Å, while Cu–F value is shortened by 0.008 Å from the respective average bond lengths of free monomer.

Multicomponent MP4 and the inclusion of triple excitations in multicomponent many-body methods.

This study implements the full multicomponent third-order (MP3) and fourth-order (MP4) many-body perturbation theory methods for the first time. Previous multicomponent studies have only implemented a subset of the full contributions, and the present implementation is the first multicomponent many-body method to include any connected triples contribution to the electron-proton correlation energy. The multicomponent MP3 method is shown to be comparable in accuracy to the multicomponent coupled-cluster doubles method for the calculation of proton affinities, while the multicomponent MP4 method is of similar accuracy as the multicomponent coupled-cluster singles and doubles method. From the results in this study, it is hypothesized that the relative accuracy of multicomponent methods is more similar to their single-component counterparts than previously assumed. It is demonstrated that for multicomponent MP4, the fourth-order triple-excitation contributions can be split into electron-electron and electron-proton contributions and the electron-electron contributions ignored with very little loss of accuracy of protonic properties.

Addressing the System-Size Dependence of the Local Approximation Error in Coupled-Cluster Calculations.

Over the last two decades, the local approximation has been successfully used to extend the range of applicability of the “gold standard” singles and doubles coupled-cluster method with perturbative triples CCSD(T) to systems with hundreds of atoms. The local approximation error grows in absolute value with the increasing system size, i.e., by increasing the number of electron pairs in the system. In this study, we demonstrate that the recently introduced two-point extrapolation scheme for approaching the complete pair natural orbital (PNOs) space limit in domain-based pair natural orbital CCSD(T) calculations drastically reduces the dependence of the error on the system size, thus opening up unprecedented opportunities for the calculation of benchmark quality relative energies for large systems.

Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation.

Efficient implementations of the symmetric and asymmetric triple excitation corrections for the orbital-optimized coupled-cluster doubles (OCCD) method with the density-fitting approach, denoted by DF-OCCD(T) and DF-OCCD(T)Λ, are presented. The computational cost of the DF-OCCD(T) method is compared with that of the conventional OCCD(T). In the conventional OCCD(T) and OCCD(T)Λ methods, one needs to perform four-indexintegral transformations at each coupled-cluster doubles iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD(T) provides dramatically lower computational costs compared to OCCD(T), and there are more than 68-fold reductions in the computational time for the C5H12 molecule with the cc-pVTZ basis set. Our results show that the DF-OCCD(T) and DF-OCCD(T)Λ methods are very helpful for the study of single bond-breaking problems. Performances of the DF-OCCD(T) and DF-OCCD(T)Λ methods are noticeably better than that of the coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for the potential energy surfaces of the molecules considered. Specifically, the DF-OCCD(T)Λ method provides dramatic improvements upon CCSD(T), and there are 8-14-fold reductions in nonparallelity errors. Overall, we conclude that the DF-OCCD(T)Λ method is very promising for the study of challenging chemical systems, where the CCSD(T) fails.

Energy and analytic gradients for the orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation.

Efficient implementations of the orbital-optimized coupled-cluster doubles (or simply "optimized CCD," OCCD, for short) method and its analytic energy gradients with the density-fitting (DF) approach, denoted by DF-OCCD, are presented. In addition to the DF approach, the Cholesky-decomposed variant (CD-OCCD) is also implemented for energy computations. The computational cost of the DF-OCCD method (available in a plugin version of the DFOCC module of PSI4) is compared with that of the conventional OCCD (from the Q-CHEM package). The OCCD computations were performed with the Q-CHEM package in which OCCD are denoted by OD. In the conventional OCCD method, one needs to perform four-index integral transformations at each of the CCD iterations, which limits its applications to large chemical systems. Our results demonstrate that DF-OCCD provides dramatically lower computational costs compared to OCCD, and there are almost eightfold reductions in the computational time for the C6H14 molecule with the cc-pVTZ basis set. For open-shell geometries, interaction energies, and hydrogen transfer reactions, DF-OCCD provides significant improvements upon DF-CCD. Furthermore, the performance of the DF-OCCD method is substantially better for harmonic vibrational frequencies in the case of symmetry-breaking problems. Moreover, several factors make DF-OCCD more attractive compared to CCSD: (1) for DF-OCCD, there is no need for orbital relaxation contributions in analytic gradient computations; (2) active spaces can readily be incorporated into DF-OCCD; (3) DF-OCCD provides accurate vibrational frequencies when symmetry-breaking problems are observed; (4) in its response function, DF-OCCD avoids artificial poles; hence, excited-state molecular properties can be computed via linear response theory; and (5) symmetric and asymmetric triples corrections based on DF-OCCD [DF-OCCD(T)] have a significantly better performance in near degeneracy regions.

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach.

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

Calculation of dispersion interactions with the geminal-based ring Coupled Cluster Doubles method

The performance of the recently developed multi-reference extension of ring coupled cluster doubles is investigated for dispersion energy calculations, applied to the generalized valence bond wave function. The leading-order contribution to the dispersion energy is shown to have the correct asymptotic behaviour. Illustrative calculations on noble gas dimers are presented.

Highly Accurate Quartic Force Field and Rovibrational Spectroscopic Constants for the Azirinyl Cation (c-C2NH2+) and Its Isomers.

The azirinyl cation is an aromatic cyclic molecule that is isoelectronic with cyclopropenylidene, c-C3H2, and c-C3H3+. Cyclopropenylidene has been shown to be ubiquitous, existing in many different astrophysical environments. Given the similar chemistry between C and N, and the relative abundances between C and N in astrophysical environments, it is expected that there should be aromatic ringed molecules that incorporate N in the ring, but as yet, no such molecule has been identified. To address this issue, the present study uses high levels of electronic structure theory to compute a highly accurate quartic force field (QFF) for the azirinyl cation and its two lowest lying isomers, the cyanomethyl and isocyanomethyl cations. The theoretical approach uses the singles and doubles coupled-cluster method that includes a perturbative correction for connected triple excitations, CCSD(T), together with extrapolation to the one-particle basis set limit and corrections for scalar relativity and core-correlation. The QFF is then used in a second-order vibrational perturbation theory analysis (VPT2) to compute the fundamental vibrational frequencies and rovibrational spectroscopic constants for all three C2NH2+ isomers. The reliability of the VPT2 vibrational frequencies is tested by comparison to vibrational configuration interaction (VCI) calculations, and excellent agreement is found between the two approaches. Fundamental vibrational frequencies and rovibrational spectroscopic constants for all singly substituted 13C, 15N, and D isotopologues are also reported. It is expected that the highly accurate spectroscopic data reported herein will be useful in the identification of these cations in high-resolution experimental or astronomical observations.

Theoretical investigation of potential energy surface and bound states for the N2-OCS van der Waals complex.

In this work we report an ab initio intermolecular potential energy surface and theoretically spectroscopic studies for N2-OCS complex. A four-dimensional intermolecular potential energy surface (4D PES) is constructed at the level of single and double excitation coupled-cluster method with a non-iterative perturbation treatment of triple excitations [CCSD(T)] with aug-cc-pVTZ basis set supplemented with bond functions. A global minimum corresponding to a planar and nearly T-shaped structure, which has been observed experimentally, is located at R = 3.96 Å, θ1 = 8 or 172°, θ2 = 75°, φ = 180 or 0° with a well depth of 271.078 cm-1 on the potential energy surface. The local minimum corresponding to a linear geometry is also found at R = 5.06 Å, θ1 = 2 or 178°, θ2 = 179°, φ = 0 or 180° with a well depth of 224.743 cm-1. The bound state calculations have been performed for the complex by approximating the N2 and OCS molecules as the rigid rotors. The calculated structural parameters and rotational transition frequencies are in good agreement with the experimental observed values. Based on the ab initio PES, the tunneling splitting is calculated to be 0.052 cm-1 for the ground vibrational state, which can just reproduce 64% of experimental observation (0.082 cm-1). A refined method is used to calculate the tunneling splitting, and a much better result is obtained with the value of 0.094 cm-1.

Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. I. Excitation energies.

An ad hoc modification of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator is presented. Within this approach, all first-order Møller-Plesset correlation coefficients occurring in the second-order ADC secular matrix are replaced by amplitudes obtained from a coupled cluster doubles (CCD) calculation. This new hybrid method, denoted CCD-ADC(2), has been tested on a series of small diatomic and triatomic molecules and benchmarked with respect to Thiel's benchmark set of medium-sized organic molecules. For the latter, the calculation of 134 singlet and 71 triplet states has shown that CCD-ADC(2) exhibits a mean error and standard deviation of 0.15 ± 0.34 eV for singlet states and 0.0 ± 0.17 eV for triplet states with respect to the provided theoretical best estimates, whereas standard ADC(2) has a mean error and standard deviation of 0.22 ± 0.30 eV for singlet and 0.12 ± 0.16 eV for triplet states. The corresponding extended second-order schemes ADC(2)-x and CCD-ADC(2)-x revealed accuracies of -0.70 ± 0.32 eV and -0.76 ± 0.33 eV for singlet states and -0.55 ± 0.20 eV and -0.67 ± 0.22 eV for triplet states, respectively. Furthermore, the investigation of excited-state potential energy curves along the dissociation of the N2 molecule has shown that the higher reliability of the ground-state CCD method as compared to MP2 is also inherent to the excited states. While the curves obtained at the ADC(2) level break down at around 2 Å, the ones obtained at CCD-ADC(2) remain reasonable up to about 3.5 Å.

Theoretical studies of Ar–AgX (X = F, Cl, Br, I) complexes: Potential energy surfaces, intermolecualr vibrations and microwave spectra

Theoretical studies of the potential energy surfaces (PESs) and bound state calculations were performed for Ar–AgX (X = F, Cl, Br, and I) complexes. A two-dimensional intermolecular PES was constructed at the level of single and double excitation coupled-cluster method with a non-iterative perturbation treatment of triple excitations [CCSD(T)] plus aug-cc-pVQZ basis set supplemented with bond functions for each complex. The global minimum was assigned as the collinear structure of Ar–Ag–X, while the local minimum was assigned as the anti-linear structure of Ar–X–Ag. Both Ar–Ag and Ar–X distances display us an increasing trend from Ar–AgF to Ar–AgI complexes. Based on the bound state results, the intermolecular vibrational modes of collinear and anti-linear isomers were studied in detail via the wavefunction analysis. Due to the very low well depth for the anti-linear structure, an obvious delocalization effect was observed for each complex, except for Ar–AgI. Furthermore, our calculated results suggest that the anti-linear isomer of Ar–AgBr and Ar–AgI could be observed in experiment. The rotational energy levels were also determined based on the ab initio PESs via the bound state calculations. The microwave spectrum for the collinear isomer of each complex was predicted with the maximal percentage error of 1.55% for the complex Ar–AgF. A simple method of coordinate translation was used to re-interpolate the PES for each isotopomer to determine the isotope effects for Ar–AgX complexes and the deduced results are in good agreement with those of experimental observation. The microwave spectrum can be much better reproduced with an equivalent percentage error of 0.07% cm−1 for each isotopomer based on a scaled PES. Finally, we checked the effects of the basis set superposition error (BSSE) correction and core correlation, and found that the BSSE correction has great influence on the intermolecular interactions for the Ar–AgX complexes.

The role of relativistic many-body theory in probing new physics beyond the standard model via the electric dipole moments of diamagnetic atoms

The observation of electric dipole moments (EDMs) in atomic systems due to parity and time-reversal violating (P,T-odd) interactions can probe new physics beyond the standard model and also provide insights into the matter-antimatter asymmetry in the Universe. The EDMs of open-shell atomic systems are sensitive to the electron EDM and the P,T-odd scalar-pseudoscalar (S-PS) semi-leptonic interaction, but the dominant contributions to the EDMs of diamagnetic atoms come from the hadronic and tensor-pseudotensor (T-PT) semi-leptonic interactions. Several diamagnetic atoms like 129Xe, 171Yb, 199Hg, 223Rn, and 225Ra are candidates for the experimental search for the possible existence of EDMs, and among these 199Hg has yielded the lowest limit till date. The T or CP violating coupling constants of the aforementioned interactions can be extracted by combining the EDM measurements from with atomic and nuclear calculations. In this work, we report the calculations of the EDMs of the above atoms by including both the electromagnetic and P,T-odd violating interactions simultaneously. These calculations are performed by employing relativistic many-body methods based on the random phase approximation (RPA) and the singles and doubles coupled-cluster (CCSD) method starting with the Dirac-Hartree-Fock (DHF) wave function in both cases. The differences in the results from both the methods shed light on the importance of the non-core-polarization electron correlation effects that are accounted for by the CCSD method. We also determine THE electric dipole polarizabilities of these atoms, which have computational similarities with EDMs and compare them with the available experimental and other theoretical results to assess the accuracy of our calculations.

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Orbital-optimized linearized coupled-cluster doubles with density-fitting and Cholesky decomposition approximations: an efficient implementation.

An efficient implementation of the orbital-optimized linearized coupled-cluster double method with the density-fitting (DF-OLCCD) and Cholesky decomposition (CD-OLCCD) approximations is presented. The DF-OLCCD and CD-OLCCD methods are applied to a set of alkanes to compare the computational cost with the conventional orbital-optimized linearized coupled-cluster doubles (OLCCD) [U. Bozkaya and C. D. Sherrill, J. Chem. Phys., 2013, 139, 054104]. Our results demonstrate that the DF-OLCCD method provides substantially lower computational costs than OLCCD, and there are more than 9-fold reductions in the computational time for the largest member of the alkane set (C8H18). For barrier heights of hydrogen transfer reaction energies, the DF-OLCCD method again exhibits a substantially better performance than DF-LCCD, providing a mean absolute error of 0.9 kcal mol(-1), which is 7 times lower than that of DF-LCCD (6.2 kcal mol(-1)), and compared to MP2 (9.6 kcal mol(-1)) there is a more than 10-fold reduction in errors. Furthermore, the MAE value of DF-OLCCD is also lower than that of CCSD (1.2 kcal mol(-1)). For open-shell noncovalent interactions, the performance of DF-OLCCD is significantly better than that of MP2, DF-LCCD, and CCSD. Overall, the present application results indicate that the DF-OLCCD and CD-OLCCD methods are very promising for challenging open-shell systems as well as closed-shell molecular systems.

Theoretical studies for the N2-N2O van der Waals complex: The potential energy surface, intermolecular vibrations, and rotational transition frequencies.

Theoretical studies of the potential energy surface (PES) and bound states are performed for the N2-N2O van der Waals (vdW) complex. A four-dimensional intermolecular PES is constructed at the level of single and double excitation coupled-cluster method with a non-iterative perturbation treatment of triple excitations [CCSD(T)] with aug-cc-pVTZ basis set supplemented with bond functions. Two equivalent T-shaped global minima are located, in which the O atom of N2O monomer is near the N2 monomer. The intermolecular fundamental vibrational states are assigned by inspecting the orientation of the nodal surface of the wavefunctions. The calculated frequency for intermolecular disrotation mode is 23.086 cm(-1), which is in good agreement with the available experimental data of 22.334 cm(-1). A negligible tunneling splitting with the value of 4.2 MHz is determined for the ground vibrational state and the tunneling splitting increases as the increment of the vibrational frequencies. Rotational levels and transition frequencies are calculated for both isotopomers (14)N2-N2O and (15)N2-N2O. The accuracy of the PES is validated by the good agreement between theoretical and experimental results for the transition frequencies and spectroscopic parameters.

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.

A theoretical study on CH2N2 isomers: structure and energetics

Five CH2N2 isomers, namely cyanamide, carbodiimide, diazomethane, isocyanamide and nitrilimine, have been investigated at a high level of accuracy. The singles and doubles coupled-cluster method including a perturbational correction for connected triple excitations, CCSD(T), in conjunction with correlation-consistent basis sets ranging in size from triple to quintuple zeta have been employed. Extrapolation to the complete basis set limit has been used with treatments of core-valence correlation effects in order to accurately predict structures, relative energies as well as N–H and C–H bond dissociation energies. The latter required to also investigate the HNNC radical with the same methodology used for CH2N2 isomers, while HCNN and HNCN data are available in the literature by the same authors (Puzzarini and Gambi in J Chem Phys 122:064316, 2005). For all the species studied, harmonic vibrational frequencies have also been evaluated at the CCSD(T) level in order to obtain zero-point corrections to total energies.

Accurate ab initio quartic force fields of cyclic and bent HC2N isomers

Highly correlated ab initio quartic force fields (QFFs) are used to calculate the equilibrium structures and predict the spectroscopic parameters of three HC(2)N isomers. Specifically, the ground state quasilinear triplet and the lowest cyclic and bent singlet isomers are included in the present study. Extensive treatment of correlation effects were included using the singles and doubles coupled-cluster method that includes a perturbational estimate of the effects of connected triple excitations, denoted as CCSD(T). Dunning's correlation-consistent basis sets cc-pVXZ, X = 3,4,5, were used, and a three-point formula for extrapolation to the one-particle basis set limit was used. Core-correlation and scalar relativistic corrections were also included to yield highly accurate QFFs. The QFFs were used together with second-order perturbation theory (PT) (with proper treatment of Fermi resonances) and variational methods to solve the nuclear Schrödinger equation. The quasilinear nature of the triplet isomer is problematic, and it is concluded that a QFF is not adequate to describe properly all of the fundamental vibrational frequencies and spectroscopic constants (though some constants not dependent on the bending motion are well reproduced by PT). On the other hand, this procedure (a QFF together with either PT or variational methods) leads to highly accurate fundamental vibrational frequencies and spectroscopic constants for the cyclic and bent singlet isomers of HC(2)N. All three isomers possess significant dipole moments, 3.05 D, 3.06 D, and 1.71 D, for the quasilinear triplet, the cyclic singlet, and the bent singlet isomers, respectively. It is concluded that the spectroscopic constants determined for the cyclic and bent singlet isomers are the most accurate available, and it is hoped that these will be useful in the interpretation of high-resolution astronomical observations or laboratory experiments.