Single-reference Coupled-cluster Methods Research Articles

First principles exploration of NiO and its ions NiO+ and NiO−

We present a high level ab initio study of NiO and its ions, NiO(+) and NiO(-). Employing variational multireference configuration interaction (MRCI) and single reference coupled-cluster methods combined with basis sets of quintuple quality, 54, 20, and 10 bound states of NiO, NiO(+), and NiO(-) have been studied. For all these states, complete potential energy curves have been constructed at the MRCI level of theory; in addition, for the ground states of the three species core subvalence (3s(2)3p(6)∕(Ni)) and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The agreement with experiment is in the case of NiO good, but certain discrepancies that need further investigation have arisen in the case of the anion whose ground state remains computationally a tantalizing matter. The cation is experimentally almost entirely unexplored, therefore, the study of many states shall prove valuable to further investigators. The ground state symmetry, bond distances, and binding energies of NiO and NiO(+) are (existing experimental values in parenthesis), X(3)Σ(-)(X(3)Σ(-)), r(e) = 1.606 (1.62712) Å, D(0) = 88.5 (89.2 ± 0.7) kcal/mol, and X(4)Σ(-)(?), r(e) = 1.60(?) Å, D(0) = 55 (62.4 ± 2.4) kcal/mol, respectively. The ground state of NiO(-) is (4)Σ(-) (but (2)Π experimentally) with D(0) = 85-87 (89.2 ± 0.7) kcal/mol.

Computational investigation of the photoinduced homolytic dissociation of water in the pyridine–water complex

The photochemistry of the hydrogen-bonded pyridine-water complex has been investigated with ab initio computational methods. Vertical excitation energies, excited-state reaction paths for proton transfer as well as structures and energies of conical intersections and reaction barriers have been determined with multi-configuration self-consistent-field and multi-reference perturbation methods, as well as with single-reference coupled-cluster and propagator methods. In the pyridine-water complex, the energies of two charge-separated excited states of (1)nπ* and (1)ππ* character are connected to the energies of the locally excited (1)nπ* and (1)ππ* states of the pyridine chromophore via a low energy barrier. The charge-separated excited states are strongly stabilized by the transfer of a proton from water to pyridine. The energies of the resulting biradical states intersect the potential-energy surface of the closed-shell ground state as a function of the proton-transfer coordinate. The resulting radical pair may dissociate to yield pyridinium and hydroxyl radicals. The photochemistry of the hypervalent pyridinium radical has been explored with the same computational methods. It has been found that a low-lying dissociative (2)πσ* excited state exists in pyridinium, which can lead to the photodetachment of the hydrogen atom. Overall, the H2O molecule can thus be dissociated into H˙ and OH˙ radicals by the absorption of two ultraviolet photons. The relevance of these results for solar water splitting and solar carbon dioxide reduction is discussed.

Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism

In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with exact full configuration interaction results for small systems (H(2)O, N(2), and Be(3)). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups.

Ab initiostudies of electron correlation effects in heavier closed-shell atoms: Structure of the all-electron correlation energies of Zn2+and Zn

To provide reliable reference results for various components of the electron correlation energies of Zn${}^{2+}$ and Zn, which play a similar role for $3d$-electron systems as Ne and Mg do for lighter atoms, we have performed extensive calculations of the all-electron correlation energy and of its various components with several state-of-the-art ab initio techniques. Two pairs of basis-set sequences that systematically converge to the complete basis set (CBS) limit have been employed in the calculations. One pair [cc-pV$n$Z and aug-cc-pV$n$Z (correlation consistent polarized valence $n$-zeta and augmented cc-pV$n$Z with $n=$ D, T, Q, 5, $6(\ensuremath{-}k)$)] is oriented towards the description of valence electron correlation. The second pair of sequences [cc-pCCV$n$Z and aug-cc-pCCV$n$Z (core core-valence $n$-zeta, with $n$ = D, T, Q, 5, $6(\ensuremath{-}k)$)] is developed for the description of all-electron correlation effects. The correlation energies have been determined with second-order M\o{}ller-Plesset perturbation theory (MP2) and several single-reference coupled-cluster (CC) methods. The present correlation energies represent accurate post-MP2 correlation energies for closed-shell atoms including 3$d$ electrons both at the all-electron and subshell levels and should be useful benchmark results for various transitions. We have also employed the present results for assessments of the focal-point approximation (FPA), broadly used in approximations of difference correlation effects for molecular interaction problems, in applications aiming at estimating correlation effects in heavier atoms. Our results indicate that for the systems considered, the magnitudes of the MP2 correlation energies overestimate the magnitudes of the CC values for all electrons correlated as well as of their various subsets. For the all-electron correlation energies of the Zn atom, our result confirms the finding of S. P. McCarthy and A. J. Thakkar [J. Chem. Phys. 134, 044102 (2011)] obtained by means of non--ab initio approaches for all heavy closed-shell atoms from Zn to Rn. We have shown that for both Zn${}^{2+}$ and Zn this overestimation is directly caused by the presence of the $3{d}^{10}$ electron configuration.

Electronic Structure and Bonding of Cobalt Monoxide, CoO, and Its Ions CoO+ and CoO–: An Ab Initio Study

We present a systematic and high-level ab initio study of CoO and its ions, CoO(+) and CoO(-). Employing variational multireference (MRCI) and single-reference coupled-cluster methods combined with basis sets of quintuple quality, we have calculated 50, 31, and 7 bound states for CoO, CoO(+), and CoO(-), respectively. For all these states, complete potential energy curves have been constructed at the MRCI level of theory, whereas for a few low-lying states core subvalence and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The ground states of CoO, CoO(+), and CoO(-) are X(4)Δ, X(5)Δ, and X(5)Δ, respectively, the latter established for the first time. The CoO is quite ionic with a Co to O Mulliken charge transfer of ~0.6 electrons and a dipole moment μ(X(4)Δ) = 4.5 ± 0.1 D. The overall agreement between theory and experiment is good, but there are also important deviations. Despite the seeming simplicity of these diatomic species, reliable results can only be obtained at a high level of theory.

A detailed test study of barrier heights for the HO2 + H2O + O3 reaction with various forms of multireference perturbation theory

We report an ab initio multireference perturbation theory investigation of the HO(2) + H(2)O + O(3) reaction, with particular emphasis on the barrier heights for two possible reaction mechanisms: oxygen abstraction and hydrogen abstraction, which are identified by two distinct saddle points. These saddle points and the corresponding pre-reactive complexes were optimized at the CASSCF(11,11) level while the single point energies were calculated with three different MRPT2 theories: MRMP, CASPT2, and SC-NEVPT2. Special attention has been drawn on the "intruder state" problem and the effect of its corrections on the relative energies. The results were then compared with single reference coupled-cluster methods and also with our recently obtained Kohn-Sham density functional theory (KS-DFT) calculations [L. P. Viegas and A. J. C. Varandas, Chem. Phys., (2011)]. It is found that the relative energies of the pre-reactive complexes have a very good agreement while the MRPT2 classical barrier heights are considerably higher than the KS-DFT ones, with the SC-NEVPT2 calculations having the highest energies between the MRPT2 methods. Possible explanations have been given to account for these differences.

Single reference coupled cluster calculations for weakly bound alkaline-earth metal dimers in the ground state: a useful perturbative scheme for an iterative triples correction

We apply here a new iterative triples correction for the single reference coupled-cluster method with singles and doubles scheme (termed as CCSDT-1a+d). All diagonal terms in have been included in the T 3 determining equation, in addition to . This minor change in the CCSDT-1a approximation (includes the primary effects of connected triples excitations iteratively) shows a dramatic change in the study of correlation of weakly bonded systems as discussed here. To achieve a general assessment of the potentiality of the CCSDT-1a + d calculations, the ground state potential energy surfaces (PESs) of alkaline-earth dimers, including Mg2, Ca2 and the challenging Be2 are considered. The systems considered here are treated as four-electron systems, keeping other electrons frozen in the correlation calculations. Generation of PESs for these dimers is very sensitive to the level of theory employed for the electron correlation. Basic spectroscopic constants including dissociation energy extracted from the calculated ground state PES are also reported. For all systems under study, the overall performance of CCSDT-1a+d is very competitive with that of the CCSD(T)/CCSDT method, and better than that of CCSDT-1a indicating that the former approach is more effective in handling dynamic correlation effects in comparison to the latter one in the presence of quasi-degeneracy to different extents. To calibrate our results we also report frozen-core FCI calculations.

Molecular ion LiHe +: ab initio study

High level ab initio calculations are performed on the molecular ion LiHe +. Potential energy curves for the low-lying singlet and triplet electronic states are calculated using the multi-reference configuration interaction and single-reference coupled cluster methods with large basis sets. The corresponding dipole moments and transition dipole moments functions are also determined. The basic spectroscopic properties and excitation energies of the electronic states are derived from rovibrational bound state calculations.

Ground and excited state geometries via Mukherjee’s multireference coupled-cluster method

A comprehensive study of molecular equilibrium structures is conducted to benchmark the multireference coupled-cluster (CC) method suggested by Mukherjee and coworkers (Mk-MRCC). We determine equilibrium structures and adiabatic excitation energies by applying the Mk-MRCC method within the singles and doubles (SD) approximation to ground and excited states of various small and medium-sized molecules. The results are compared to those obtained using other multireference or single-reference CC methods. For most molecules with a multireference ground state, it is found that equilibrium structures and excitation energies computed at the Mk-MRCCSD, equation-of-motion CCSD, multireference averaged-quadratic CC, and CCSD(T) levels of theory qualitatively agree, while the single-reference CCSD method often leads to distinctly different results.

The electronic structure of Ti2 and Ti2+

The Ti(2) and Ti(2)(+) molecular systems have been studied through multireference variational and single reference coupled-cluster methods coupled with large basis sets. Potential energy curves have been constructed for 30 (Ti(2)) and 2 (Ti(2)(+)) states and the usual spectroscopic parameters have been extracted. The main feature of the potential curves is the existence of van der Waals minima (Ti(2)) around 7 bohr irrespective of the molecular symmetry, and 4s(2)-4s(1) interactions (Ti(2)(+)) around 6 bohr. Numerous avoided crossings lead to stronger covalent bonds emanating from 4s(1)-4s(1) atomic distributions. The X-state of the neutral species is formally a (3)Δ(g) state with the first excited state lying within 1 kcal/mol. The removal of the symmetry defining e(-) leads to the X(2)Σ(g)(+) state of Ti(2)(+).

Various formulations of the Fock-space coupled-cluster method: Advantages and disadvantages in their practical implementations

The single-reference coupled-cluster method is one of the most efficient approaches to the problem of describing electron correlation effects in situations when a single determinant gives reliable zeroth-order description of a system. Its multi-reference generalizations have not been, however, so successful mainly because of their effective Hamiltonian formulation. In this paper we present attempts that have been made to reformulate the Fock-space coupled-cluster method in order to obtain more efficient and dependable computational schemes allowing more extensive use of the approach. The first one is known as the eigenvalue independent partitioning version of the Fock-space coupled-cluster method. This approach has been an inspiration for other formulations of this type. The new formulations require to take a new look at the use of the connected diagram theorem since the theorem cannot be applied in such a straightforward manner as in the standard version. Another problem is posed by approximate schemes and noniterative corrections that are so popular within the single-reference coupled-cluster framework. These are not so easy to implement when the standard effective Hamiltonian formulation is abandoned. Fortunately, it looks that noniterative corrections can be relatively easily implemented. In the paper we discuss these issues trying to show advantages and disadvantages of different approaches.

Ab initio wavefunctions in bioinorganic chemistry: More than a succès d’estime?

Ab initio wavefunctions in bioinorganic chemistry: More than a succès d’estime?

Is HO3 minimum cis or trans? An analytic full-dimensional ab initio isomerization path

The minimum energy path for isomerization of HO(3) has been explored in detail using accurate high-level ab initio methods and techniques for extrapolation to the complete basis set limit. In agreement with other reports, the best estimates from both valence-only and all-electron single-reference methods here utilized predict the minimum of the cis-HO(3) isomer to be deeper than the trans-HO(3) one. They also show that the energy varies by less than 1 kcal mol(-1) or so over the full isomerization path. A similar result is found from valence-only multireference configuration interaction calculations with the size-extensive Davidson correction and a correlation consistent triple-zeta basis, which predict the energy difference between the two isomers to be of only Δ = -0.1 kcal mol(-1). However, single-point multireference calculations carried out at the optimum triple-zeta geometry with basis sets of the correlation consistent family but cardinal numbers up to X = 6 lead upon a dual-level extrapolation to the complete basis set limit of Δ = (0.12 ± 0.05) kcal mol(-1). In turn, extrapolations with the all-electron single-reference coupled-cluster method including the perturbative triples correction yield values of Δ = -0.19 and -0.03 kcal mol(-1) when done from triple-quadruple and quadruple-quintuple zeta pairs with two basis sets of increasing quality, namely cc-cpVXZ and aug-cc-pVXZ. Yet, if added a value of 0.25 kcal mol(-1) that accounts for the effect of triple and perturbative quadruple excitations with the VTZ basis set, one obtains a coupled cluster estimate of Δ = (0.14 ± 0.08) kcal mol(-1). It is then shown for the first time from systematic ab initio calculations that the trans-HO(3) isomer is more stable than the cis one, in agreement with the available experimental evidence. Inclusion of the best reported zero-point energy difference (0.382 kcal mol(-1)) from multireference configuration interaction calculations enhances further the relative stability to ΔE(ZPE) = (0.51 ± 0.08) kcal mol(-1). A scheme is also suggested to model the full-dimensional isomerization potential-energy surface using a quadratic expansion that is parametrically represented by a Fourier analysis in the torsion angle. The method illustrated at the raw and complete basis-set limit coupled-cluster levels can provide a valuable tool for a future analysis of the available (incomplete thus far) experimental rovibrational data.

Ab Initio Calculations on the Formation and Rearrangement of Spiropentane

The formation of spiropentane, by addition of singlet (1A1) methylene to methylenecyclopropane, and the unimolecular reactions of spiropentane have all been studied computationally. Benchmark calculations on two key biradicals were conducted by the multireference Mukherjee's coupled-cluster (MkCC) method. Various single-reference coupled-cluster methods and multireference second-order perturbation theory were then compared for accuracy against experimental data and the MkCC results. The object of the exercise was to get the best possible description of the potential energy surface for formation and reactions of spiropentane, as a prelude to molecular dynamics simulation of the reactions. The principal conclusions of the study were that none of the unimolecular reactions of spiropentane can be classified as pericyclic processes and that the observed stereoselectivities are probably of dynamical origin. A possible resolution of a disagreement between two studies on the dynamics of cyclopropanation reactions is also offered. Of the various approximate computational models evaluated in this study, the best fit came from a composite coupled-cluster approach in which the lower-energy result was selected from a restricted coupled-cluster and a broken-symmetry, unrestricted coupled-cluster calculation on each stationary point. However, such an approach is not strictly defensible, since coupled-cluster methods are not variational, and so further evaluation of its validity would be desirable.

Comparativeab initiostudies on the molecular structure and spectroscopic properties of FeF2: Single reference versus multireference methods

The electronic excitation energies, molecular geometry, quadratic force fields, and vibrational frequencies in the ground (5)Delta(g) and low-lying excited (5)Sigma(g) (+) and (5)Pi(g) electronic states of iron difluoride are studied at sophisticated levels of theory. Two families of basis sets, nonrelativistic and Douglas-Kroll-Hess relativistic, are used that range in quality from triple-zeta to quintuple-zeta. These are augmented by additional diffuse functions (on fluorine atoms) and tight functions (on all atoms) for the description of core-valence correlation and utilized to determine complete basis set molecular properties. The quality of electron correlation treatment using conventional single reference coupled cluster methods CCSD and CCSD(T) is compared to that attained at the multiconfigurational quasidegenerate second-order perturbation theory (CASSCF+MCQDPT2) and the electron attachment equation-of-motion coupled cluster (EOMEA-CCSD) levels. Spin-orbit coupling effects are studied by the SO-MCQDPT2 method using the full Breit-Pauli spin-orbit operator. Effects of spin contamination in the coupled cluster molecular calculations are carefully analyzed. Results of the single reference CCSD(T) and multireference calculations are found to be in a remarkable agreement. The calculations indicate that the EOMEA-CC approach provides a suitable tool for an accurate treatment of FeF(2) and other systems where delicate electron correlation effects have to be carefully dealt with. The inclusion of relativistic effects is shown to be necessary for an accurate description of the molecular geometry and excitation energies of FeF(2). The results of calculations are in good agreement with the experimental data available. The predicted FeF(2) molecular properties are compared to those of the related FeF(3).

A comparison of single-reference coupled-cluster and multi-reference configuration interaction methods for representative cuts of the [formula omitted] potential energy surface

Three cuts of the H 2 S ( 1 A ′ ) potential energy surface, which correspond to the dissociation of a single S–H bond [cut (i)], the simultaneous, C 2 v -symmetric, dissociation of both S–H bonds [cut (ii)], and the C 2 v -symmetric minimum energy dissociation pathway leading to H 2 ( X 1 Σ g + ) and S ( 3 p 4 1 D ) [cut (iii)], are examined with the conventional and completely renormalized (CR) coupled-cluster (CC) methods, and the multi-reference configuration interaction approach [MRCI(Q)]. The size extensive CR-CC method with singles, doubles, and non-iterative triples, termed CR-CC(2,3), provides the results of the MRCI(Q) quality for cuts (i) and (iii). To obtain a similar quality for cut (ii), the CR-CC(2,3) energy must be corrected for the effect of quadruply excited clusters.

On the electronic structure of small cyclic carbon clusters

We present the results of correlated calculations on a variety of small carbon rings. Equilibrium structures and vibrational frequencies are calculated and transition states connecting symmetry-equivalent minima are considered in detail. We show that neither single-reference coupled-cluster nor multiconfigurational self-consistent field methods (even after perturbational inclusion of dynamical correlation effects) give qualitatively correct potential surfaces in the vicinity of the minima, suggesting that there is little recourse for these systems other than a multireference coupled-cluster treatment. Density-functional theory using the B3LYP functional produces results broadly in agreement with single-reference coupled-cluster methods and is thus no more reliable, but considerably more economical.

Extrapolating to the one-electron basis-set limit in electronic structure calculations

A simple, yet reliable, scheme based on treating uniformly singlet-pair and triplet-pair interactions is suggested to extrapolate atomic and molecular electron correlation energies calculated at two basis-set levels of ab initio theory to the infinite one-electron basis-set limit. The novel dual-level method is first tested on extrapolating the full correlation in single-reference coupled-cluster singles and doubles energies for the closed-shell systems CH2((1)A1), H2O, HF, N2, CO, Ne, and F2 with correlation-consistent basis sets of the type cc-pVXZ (X=D,T,Q,5,6) reported by Klopper [Mol. Phys. 6, 481 (2001)] against his own benchmark calculations with large uncontracted basis sets obtained from explicit correlated singles and doubles coupled-cluster theory. Comparisons are also reported for the same data set but using both single-reference Moller-Plesset and coupled-cluster doubles methods. The results show a similar, often better, accordance with the target results than Klopper's extrapolations where singlet-pair and triplet-pair energies are extrapolated separately using the popular X(-3) and X(-5) dual-level laws, respectively. Applications to the extrapolation of the dynamical correlation in multireference configuration interaction calculations carried out anew for He, H2, HeH+, He2 ++, H3+(1 (1)A'), H3+(1 (3)A'), BH, CH, NH, OH, FH, B2, C2, N2, O2, F2, BO, CO, NO, BN, CN, SH, H2O, and NH3 with standard augmented correlation-consistent basis sets of the type aug-cc-pVXZ (X=D,T,Q,5,6) are also reported. Despite lacking accurate theoretical or experimental data for comparison in the case of most diatomic systems, the new method also shows in this case a good performance when judged from the results obtained with the traditional schemes which extrapolate using the two largest affordable basis sets. For the Hartree-Fock and complete-active space self-consistent field energies, a simple pragmatic extrapolation rule is examined whose results are shown to compare well with the ones obtained from the best reported schemes.

Application of renormalized coupled-cluster methods to potential function of water

The goal of this paper is to examine the performance of the conventional and renormalized single-reference coupled-cluster (CC) methods in calculations of the potential energy surface of the water molecule. A comparison with the results of the internally contracted multi-reference configuration interaction calculations including the quasi-degenerate Davidson correction (MRCI(Q)) and the spectroscopically accurate potential energy surface of water resulting from the use of the energy switching (ES) approach indicates that the relatively inexpensive completely renormalized (CR) CC methods with singles (S), doubles (D), and a non-iterative treatment of triples (T) or triples and quadruples (TQ), such as CR-CCSD(T), CR-CCSD(TQ), and the recently developed rigorously size extensive extension of CR-CCSD(T), termed CR-CC(2,3), provide substantial improvements in the results of conventional CCSD(T) and CCSD(TQ) calculations at larger internuclear separations. It is shown that the CR-CC(2,3) results corrected for the effect of quadruply excited clusters through the CR-CC(2,3)+Q approach can compete with the highly accurate MRCI(Q) data. The excellent agreement between the CR-CC(2,3)+Q and MRCI(Q) results suggests ways of improving the global potential energy surface of water resulting from the use of the ES approach in the regions of intermediate bond stretches and intermediate energies connecting the region of the global minimum with the asymptotic regions.

The EOM-CC studies of low-lying electronic states of [formula omitted], CCl 2 and [formula omitted

The equation-of-motion single-reference coupled-cluster (EOM-CC) method was combined with the aug-cc-pVTZ basis set to obtain the geometries and excitation energies of an extensive set of low-lying excited states of NO 2 - , CCl 2 and OF 2 + , which was previously studied by the multireference MRSDCI/DZ+P approach. The EOM-CC/aug-cc-pVTZ strategy yielded results close to the MRSDCI/DZ+P data and the experiment, which warrants its application for estimating unavailable experimental values.