A truncated version of reduced multireference coupled-cluster method with singles and doubles and noniterative triples: application to F2 and Ni(CO)n (n=1, 2, and 4)

A perturbatively truncated version of the reduced multireference coupled-cluster method with singles and doubles and noniterative triples RMR CCSD(T) is described. In the standard RMR CCSD method, the effect of all triples and quadruples that are singles or doubles relative to references spanning a chosen multireference (MR) model space is accounted for via the external corrections based on the MR CISD wave function. In the full version of RMR CCSD(T), the remaining triples are then handled via perturbative corrections as in the standard, single-reference (SR) CCSD(T) method. By using a perturbative threshold in the selection of MR CISD configuration space, we arrive at the truncated version of RMR CCSD(T), in which the dimension of the MR CISD problem is significantly reduced, thus leaving more triples to be treated perturbatively. This significantly reduces the computational cost. We illustrate this approach on the F2 molecule, in which case the computational cost of the truncated version of RMR CCSD(T) is only about 10%-20% higher than that of the standard CCSD(T), while still eliminating the failure of CCSD(T) in the bond breaking region of geometries. To demonstrate the capabilities of the method, we have also used it to examine the structure and binding energy of transition metal complexes Ni(CO)n with n=1, 2, and 4. In particular, Ni(CO)2 is shown to be bent rather than linear, as implied by some earlier studies. The RMR CCSD(T) binding energy differs from the SR CCSD(T) one by 1-2 kcal/mol, while the energy barrier separating the linear and bent structures of Ni(CO)2 is smaller than 1 kcal/mol.     

Binding in transition metal complexes: Reduced multireference coupled-cluster study of the MCH2+ (M=Sc to Cu) compounds

The recently developed reduced multireference coupled-cluster method with singles and doubles (RMR CCSD), which is perturbatively corrected for triples [RMR CCSD(T)], is employed to compute binding energies of nine transition metal ions with CH2. Unlike analogous compounds involving main-group elements, the MCH2+ (M=Sc to Cu) transition metal complexes often exhibit a non-negligible multireference character. The authors thus employ the RMR CCSD(T) method, which represents an extension of the standard single-reference (SR) CCSD(T) method and can account for multireference effects, while employing only small reference spaces. In this way the role of quasidegeneracy effects on the binding energies of these complexes can be assessed at a higher SD(T) level than is possible with the widely used ab initio methods, namely, with the standard SR CCSD(T) approach, and provide a new benchmark for these quantities. The difference between the RMR and the standard CCSD(T) methods becomes particularly evident when considering nonequilibrium geometries.     

Real or artifactual symmetry breaking in the BNB radical: a multireference coupled cluster viewpoint

The ground state of the linear BNB radical has been examined via the recently developed reduced multireference coupled cluster method with singles and doubles that is perturbatively corrected for triples [RMR CCSD(T)] using the correlation consistent basis sets (cc-pVXZ, X=D, T, and Q). Similar to earlier results that were based on the single reference CCSD(T) and BD(T) approaches, the RMR CCSD(T) method also predicts an asymmetric structure with two BN bonds of unequal length, even though the MR effects significantly reduce the barrier height. The computed frequencies for the symmetric and antisymmetric stretching modes agree reasonably well with the experimental data.     

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. II. Applications and performance

The partially linearized (pl), fully size-extensive multireference (MR) coupled-cluster (CC) method, fully accounting for singles (S) and doubles (D) and approximately for a subset of primary higher than doubles, referred to as plMR CCSD, as well as its plMR CCSD(T) version corrected for secondary triples, as described in Part I of this paper [X. Li and J. Paldus, J. Chem. Phys. 128, 144118 (2008)], are applied to the problem of bond breaking in the HF, F2, H2O, and N2 molecules, as well as to the H4 model, using basis sets of a DZ or a cc-pVDZ quality that enable a comparison with the full configuration interaction (FCI) exact energies for a given ab initio model. A comparison of the performance of the plMR CCSD/CCSD(T) approaches with those of the reduced MR (RMR) CCSD/CCSD(T) methods, as well as with the standard single reference (SR) CCSD and CCSD(T) methods, is made in each case. For the H4 model and N2 we also compare our results with the completely renormalized (CR) CC(2,3) method [P. Piecuch and M. W?och, J. Chem. Phys. 123, 224105 (2005)]. An important role of a proper choice of the model space for the MR-type methods is also addressed. The advantages and shortcomings of all these methods are pointed out and discussed, as well as their size-extensivity characteristics, in which case we distinguish supersystems involving noninteracting SR and MR subsystems from those involving only MR-type subsystems. Although the plMR-type approaches render fully size-extensive results, while the RMR CCSD may slightly violate this property, the latter method yields invariably superior results to the plMR CCSD ones and is more easy to apply in highly demanding cases, such as the triple-bond breaking in the nitrogen molecule.     

Partially linearized, fully size-extensive, and reduced multireference coupled-cluster methods. I. Formalism and mutual relationship

We describe a fully size-extensive alternative of the reduced multireference (RMR) coupled-cluster (CC) method with singles (S) and doubles (D) that generates a subset of higher-than-pair cluster amplitudes, using linearized CC equations from the full CC chain, projected onto the corresponding higher-than-doubly excited configurations. This approach is referred to as partially linearized (pl) MR CCSD method and characterized by the acronym plMR CCSD. In contrast to a similar CCSDT-1 method [Y. S. Lee et al., J. Chem. Phys. 81, 5906 (1984)] this approach also considers higher than triples (currently up to hexuples), while focusing only on a small subset of such amplitudes, referred to as the primary ones. These amplitudes are selected using similar criteria as in RMR CCSD. An extension considering secondary triples via the standard (T)-type corrections, resulting in the plMR CCSD(T) method, is also considered. The relationship of RMR and plMR CCSD and CCSD(T) approaches is discussed, and their performance and characteristics are the subject of the subsequent Part II of this paper.     

Reduced multireference coupled cluster method with singles and doubles: Perturbative corrections for triples

The reduced multireference coupled-cluster method with singles and doubles (RMR CCSD) that employs multireference configuration interaction wave function as an external source for a small subset of approximate connected triples and quadruples, is perturbatively corrected for the remaining triples along the same lines as in the standard CCSD(T) method. The performance of the resulting RMR CCSD(T) method is tested on four molecular systems, namely, the HF and F(2) molecules, the NO radical, and the F(2) (+) cation, representing distinct types of molecular structure, using up to and including a cc-pVQZ basis set. The results are compared with those obtained with the standard CCSD(T), UCCSD(T), CCSD(2), and CR CCSD(T) methods, wherever applicable or available. An emphasis is made on the quality of the computed potentials in a broad range of internuclear separations and on the computed equilibrium spectroscopic properties, in particular, harmonic frequencies omega(e). It is shown that RMR CCSD(T) outperforms other triply corrected methods and is widely applicable.     

Multireference coupled-cluster study of the symmetry breaking in the C2B radical

The potential energy surfaces (PESs) for both the ground and the excited electronic states of the C(2)B radical are investigated using various multireference (MR) coupled-cluster (CC) approaches. In the ground state case we employ the reduced MR (RMR) CC approach with singles (S) and doubles (D), the RMR CCSD method, as well as its RMR CCSD(T) version corrected for secondary triples, relying on various model spaces and basis sets. The reliability of this approach is also tested against the benchmark full configuration interaction results obtained for a small Dunning-Hay (DH) basis set. The results imply a clear preference for a cyclic structure which, however, breaks the C(2v) symmetry. This symmetry breaking manifests itself strongly at the level of the independent particle model, as represented by the restricted open-shell Hartree-Fock approximation, but the tendency toward symmetry breaking diminishes with the increasing size of the basis set employed as well as with the enhanced account of the correlation effects. It is likely to disappear in the complete basis set limit. The general model space CCSD method is then used to compute vertical excitation energies for a number of excited states as well as the cuts of the PES as the boron atom moves around the C(2) fragment. These results also explain why no symmetry breaking is found when relying on a spin contaminated unrestricted Hartree-Fock reference, as in the UMP2 method.     

Full potential energy curve for N2 by the reduced multireference coupled-cluster method

Relying on a 56-dimensional reference space and using up to the correlation-consistent, polarized, valence-quadruple-zeta (cc-pVQZ) basis sets, the reduced multireference (RMR) coupled-cluster method with singles and doubles (CCSD), as well as its perturbatively corrected version for secondary triples [RMR CCSD(T)], is employed to generate the full potential energy curves for the nitrogen molecule. The resulting potentials are then compared to the recently published accurate analytic potential based on an extensive experimental data analysis [R. J. Le Roy et al., J. Chem. Phys. 125, 164310 (2006)], and the vibrational term values of these potentials are compared over the entire well. A comparison with single-reference CCSD and CCSD(T) results, as well as with earlier obtained eight-reference RMR CC results, is also made. Excellent performance of RMR CCSD, and its systematic improvement with the increasing dimension of the reference space employed, is demonstrated. For the first 19 vibrationally excited levels, which are based on experimentally observed bands, we find an absolute average deviation of 8 cm(-1) from the computed RMR CCSD/cc-pVQZ values. The perturbative correction for triples increases this deviation to 126 cm(-1), but only to 61 cm(-1) when extrapolated to the basis set limit. Both RMR CCSD and RMR CCSD(T) potentials perform well when compared to the experiment-based analytic potential in the entire range of internuclear separations.     

Reactions of hydrogen atom with hydrogen peroxide

Rate coefficients are calculated using canonical variational transition state theory with multidimensional tunneling (CVT/SCT) for the reactions H + H2O2 --> H2O + OH (1a) and H + H2O2 --> HO2 + H2 (1b). Reaction barrier heights are determined using two theoretical approaches: (i) comparison of parametrized rate coefficient calculations employing CVT/SCT to experiment and (ii) high-level ab initio methods. The evaluated experimental data reveal considerable variations of the barrier height for the first reaction: although the zero-point-exclusive barrier for (1a) derived from the data by Klemm et al. (First Int. Chem. Kinet. Symposium 1975, 61) is 4.6 kcal/mol, other available measurements result in a higher barrier of 6.2 kcal/mol. The empirically derived zero-point-exclusive barrier for (1b) is 10.4 kcal/mol. The electronic structure of the system at transition state geometries in both reactions was found to have "multireference" character; therefore special care was taken when analyzing electronic structure calculations. Transition state geometries are optimized by multireference perturbation theory (MRMP2) with a variety of one-electron basis sets, and by a multireference coupled cluster (MR-AQCCSD) method. A variety of single-reference benchmark-level calculations have also been carried out; included among them are BMC-CCSD, G3SX(MP3), G3SX, G3, G2, MCG3, CBS-APNO, CBS-Q, CBS-QB3, and CCSD(T). Our data obtained at the MRMP2 level are the most complete; the barrier height for (1a) using MRMP2 at the infinite basis set limit is 4.8 kcal/mol. Results are also obtained with midlevel single-reference multicoefficient correlation methods, such as MC3BB, MC3MPW, MC-QCISD/3, and MC-QCISD-MPWB, and with a variety of hybrid density functional methods, which are compared with high-level theory. On the basis of the evaluated experimental values and the benchmark calculations, two possible recommended values are given for the rate coefficients.     

A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effects

The CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.     

Barrier heights of hydrogen‐transfer reactions with diffusion quantum monte carlo method

Hydrogen‐transfer reactions are an important class of reactions in many chemical and biological processes. Barrier heights of H‐transfer reactions are underestimated significantly by popular exchange–correlation functional with density functional theory (DFT), while coupled‐cluster (CC) method is quite expensive and can be applied only to rather small systems. Quantum Monte‐Carlo method can usually provide reliable results for large systems. Performance of fixed‐node diffusion quantum Monte‐Carlo method (FN‐DMC) on barrier heights of the 19 H‐transfer reactions in the HTBH38/08 database is investigated in this study with the trial wavefunctions of the single‐Slater–Jastrow form and orbitals from DFT using local density approximation. Our results show that barrier heights of these reactions can be calculated rather accurately using FN‐DMC and the mean absolute error is 1.0 kcal/mol in all‐electron calculations. Introduction of pseudopotentials (PP) in FN‐DMC calculations improves efficiency pronouncedly. According to our results, error of the employed PPs is smaller than that of the present CCSD(T) and FN‐DMC calculations. FN‐DMC using PPs can thus be applied to investigate H‐transfer reactions involving larger molecules reliably. In addition, bond dissociation energies of the involved molecules using FN‐DMC are in excellent agreement with reference values and they are even better than results of the employed CCSD(T) calculations using the aug‐cc‐pVQZ basis set. © 2017 Wiley Periodicals, Inc.     

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data

Reactions involving Criegee intermediates (CIs, R₁R₂COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R₁/R₂ = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol⁻¹. Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol⁻¹, respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol⁻¹, respectively. © 2019 Wiley Periodicals, Inc.     

Theoretical study of the pyrolysis of methyltrichlorosilane in the gas phase. 2. Reaction paths and transition states

The kinetics for the previously proposed 114-reaction mechanism for the chemical vapor deposition (CVD) process that leads from methyltrichlorosilane (MTS) to silicon carbide (SiC) are examined. Among the 114 reactions, 41 are predicted to proceed with no intervening barrier. For the remaining 73 reactions, transition states and their corresponding barrier heights have been explored using second-order perturbation theory (MP2) with the aug-cc-pVDZ basis set. Final energies for the reaction barriers were obtained using both MP2 with the aug-cc-pVTZ basis set and coupled cluster theory (CCSD(T)) with the aug-cc-pVDZ basis set. CCSD(T)/aug-cc-pVTZ energies were estimated by assuming additivity of basis set and correlation effects. Partition functions for the computation of thermodynamic properties of the transition states were calculated with MP2/aug-cc-pVDZ. Forward and reverse Gibbs free energy barriers were obtained at 11 temperatures ranging from 0 to 2000 K. Important reaction pathways are illustrated at 0 and 1400 K.     

Can a single-reference approach provide a balanced description of ground and excited states? A comparison of the completely renormalized equation-of-motion coupled-cluster method with multireference quasidegenerate perturbation theory near a conical intersection and along a photodissociation coordinate in ammonia

We calculated the two lowest electronically adiabatic potential energy surfaces of ammonia in the region of the conical intersection and at a sequence of geometries along which one of the N-H bonds is broken. We employed both a multireference (MR) method and a single-reference (SR) method. The MR calculations are based on multiconfiguration quasidegenerate perturbation theory (MC-QDPT) with a 6-311+G(3df,3pd) basis set. The SR calculations, carried out with the same basis, employ the completely renormalized equation-of-motion coupled-cluster method with singles and doubles, and a noniterative treatment of triples, denoted CR-EOMCCSD(T). At 91 geometries used for comparison, including geometries near a conical intersection, the surfaces agree to 7% on average.     

1,2-Didehydro[10]annulenes: structures, aromaticity, and cyclizations

The conformational space of C(10)H(8) 1,2-didehydro[10]annulenes, along with their unimolecular conversion to isonaphthalenes (cyclic allenes), has been studied computationally using DFT (B3LYP), single-reference [CCSD(T)], and multireference (MCQDPT2) post-HF methods. The introduction of the linear alkynyl moiety releases enough angle strain to make a nearly planar "heart" aromatic form the preferred conformer by more than 6 kcal/mol [CCSD(T)] over a localized C(2) "twist" structure, as opposed to the closely related C(10)H(10) [10]annulene system. Computations also show that electrocyclic ring-opening of isonaphthalenes to the heart C(10)H(8) annulene takes place through a low barrier of 15 kcal/mol, and this should be considered the working mechanism for the reported isomerizations during dehydro Diels-Alder reactions of phenylacetylenes.     

Hybrid quantum mechanical and molecular mechanics study of the S(N)2 Reaction of CCl4 + OH- in aqueous solution: the potential of mean force, reaction energetics, and rate constants

The bimolecular nucleophilic substitution reaction of CCl(4) and OH(-) in aqueous solution was investigated on the basis of a combined quantum mechanical and molecular mechanics method. A multilayered representation approach is employed to achieve high accuracy results at the CCSD(T) level of theory. The potential of mean force calculations at the DFT level and CCSD(T) level of theory yield reaction barrier heights of 22.7 and 27.9 kcal/mol, respectively. Both the solvation effects and the solvent-induced polarization effect have significant contributions to the reaction energetics, for example, the solvation effect raises the saddle point by 10.6 kcal/mol. The calculated rate constant coefficient is 8.6 × 10(-28) cm(3) molecule(-1) s(-1) at the standard state condition, which is about 17 orders magnitude smaller than that in the gas phase. Among the four chloromethanes (CH(3)Cl, CH(2)Cl(2), CHCl(3), and CCl(4)), CCl(4) has the lowest free energy activation barrier for the reaction with OH(-) in aqueous solution, confirming the trend that substitution of Cl by H in chloromethanes diminishes the reactivity.     

Hybrid coupled cluster methods: combining active space coupled cluster methods with coupled cluster singles, doubles, and perturbative triples

Based on the coupled-cluster singles, doubles, and a hybrid treatment of triples (CCSD(T)-h) method developed by us [J. Shen, E. Xu, Z. Kou, and S. Li, J. Chem. Phys. 132, 114115 (2010); and ibid. 133, 234106 (2010); and ibid. 134, 044134 (2011)], we developed and implemented a new hybrid coupled cluster (CC) method, named CCSD(T)q-h, by combining CC singles and doubles, and active triples and quadruples (CCSDtq) with CCSD(T) to deal with the electronic structures of molecules with significant multireference character. These two hybrid CC methods can be solved with non-canonical and canonical MOs. With canonical MOs, the CCSD(T)-like equations in these two methods can be solved directly without iteration so that the storage of all triple excitation amplitudes can be avoided. A practical procedure to divide canonical MOs into active and inactive subsets is proposed. Numerical calculations demonstrated that CCSD(T)-h with canonical MOs can well reproduce the corresponding results obtained with non-canonical MOs. For three atom exchange reactions, we found that CCSD(T)-h can offer a significant improvement over the popular CCSD(T) method in describing the reaction barriers. For the bond-breaking processes in F(2) and H(2)O, our calculations demonstrated that CCSD(T)q-h is a good approximation to CCSDTQ over the entire bond dissociation processes.     

Potential energy curve for ring-opening reactions: comparison between broken-symmetry and multireference coupled cluster methods

The spin-unrestricted Hartree-Fock (UHF)-based coupled cluster singles and doubles (UHF-CCSD) and Mukherjee's state-specific multireference CCSD (MkCCSD) methods are applied to four ring-opening reactions. The spin-restricted Hartree-Fock (RHF)-based CCSD (RHF-CCSD) calculations are also performed for comparison. In the case of the UHF-CCSD method, an approximate spin-projection (AP) method is applied to the broken-symmetry (BS) singlet solution to remove the spin contamination effect. For potential energy curves (PECs) of all reactions presented in this study, the results of RHF-CCSD and UHF-CCSD are substantially different from those of MkCCSD, while the results after the AP method (AP-UCCSD) reproduce the MkCCSD results well. It strongly suggests that the spin contamination effect should be removed by the AP correction even at the UHF-CCSD level to predict reliable energetics of these reactions.     

Accurate thermochemistry from a parameterized coupled-cluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems

We have recently introduced a parameterized coupled-cluster singles and doubles model (pCCSD(α, β)) that consists of a bivariate parameterization of the CCSD equations and is inspired by the coupled electron pair approximations. In our previous work, it was demonstrated that the pCCSD(-1, 1) method is an improvement over CCSD for the calculation of geometries, harmonic frequencies, and potential energy surfaces for single bond-breaking. In this paper, we find suitable pCCSD parameters for applications in reaction thermochemistry and thermochemical kinetics. The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for large-scale thermochemical applications for sizeable molecular systems. It is demonstrated that the original pCCSD(-1, 1) method and several other pCCSD methods are a significant improvement upon the standard CCSD approach and that these methods often approach the accuracy of CCSD(T) for the calculation of reaction energies and barrier heights. We also show that a local version of the pCCSD methodology, implemented within the local pair natural orbital (LPNO) based CCSD code in ORCA, is sufficiently accurate for wide-scale chemical applications. The LPNO based methodology allows us for routine applications to intermediate sized (20-100 atoms) molecular systems and is a significantly more accurate alternative to MP2 and density functional theory for the prediction of reaction energies and barrier heights.     

Benchmark calculations on the electron detachment energies of MO3* and M2O6* (M = Cr, Mo, W)

Neutral and anionic molecules of the monomers and dimers of the group VIB transition metal oxides (MO3 and M2O6) were studied with density functional theory (DFT) and coupled cluster CCSD(T) theory. Franck-Condon simulations of the photoelectron spectra were carried out for the transition from the ground state of the anion to that of the neutral molecule. Molecular structures from the DFT and CCSD(T) methods are compared. Electron detachment energies reported in the literature were evaluated. The calculated adiabatic and vertical electron detachment energies (ADEs and VDEs) were compared with the experimental results. CCSD(T) gives results within 0.12 eV for the ADEs. CCSD(T) predicts VDEs that are in error by as much as 0.3 eV for M = Cr. DFT hybrid functionals were found to give poor results for the ADEs and VDEs for M = Cr due to the substantial amount of multireference character in the wavefunction, whereas the pure DFT functionals give superior results. For M = Mo and W, excellent agreement was found for both CCSD(T) and many DFT fucntionals. The BP86 functional yields the best overall results for the VDEs of all the metal oxide clusters considered. Heats of formation calculated at the CCSD(T) level extrapolated to the complete basis set limit are also in good agreement with available experimental data.