Frequency-dependent hyperpolarizabilities of the Ne, Ar, and Kr atoms using the approximate coupled cluster triples model CC3

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities gamma of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities gamma(0) are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component gamma( parallel) agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component gamma( perpendicular) and the hyperpolarizability ratios gamma( parallel)gamma( perpendicular) has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed.     

Ab initio study of interaction-induced NMR shielding constants in mixed rare gas dimers

The interaction-induced contribution to the NMR shielding constants in homonuclear A2 and heteronuclear AB (A,B=He,Ne,Ar) dimers is obtained ab initio by employing a coupled cluster singles and doubles with perturbative treatment of triples wave function model and extended correlation-consistent basis sets. The second virial coefficients entering the expansion of the property with the density are then computed in a fully quantum mechanical approach, for temperatures ranging from the limit of dissociation of the dimer to well above standard conditions. The results can be used to describe the density and temperature dependence of the shielding constants in binary mixtures of helium, neon, and argon. The predicted effects should be observable for the interaction of 21Ne with other rare gases.     

Modeling 21Ne NMR parameters for carbon nanosystems

The potential of nuclear magnetic resonance (NMR) technique in probing the structure of porous systems including carbon nanostructures filled with inert gases is analysed theoretically using accurate calculations of neon (²¹Ne) nuclear magnetic shieldings. The CBS estimates of ²¹Ne NMR parameters were performed for single atom, its dimer and neon interacting with acetylene, ethylene and 1,3‐cyclopentadiene. Several levels of theory including restricted Hartree‐Fock (RHF), Møller‐Plesset perturbation theory to the second order (MP2), density functional theory (DFT) with van Voorhis and Scuseria's t‐dependent gradient‐corrected correlation functional (VSXC), coupled cluster with single and doubles excitations (CCSD), with single, doubles and triples included in a perturbative way (CCSD(T)) and single, doubles and tripes excitations (CCSDT) combined with polarization‐consistent aug‐pcS‐n series of basis sets were employed. The impact of neon confinement inside selected fullerene cages used as an NMR probe was studied at the RHF/pcS‐2 level of theory. A sensitivity of neon probe to the proximity of multiple CC bonds in C₂H₂, C₂H₄, C₅H₆ and inside C₂₈, C₃₀, C₃₂, C₃₄ and C₆₀ fullerenes was predicted from ²¹Ne NMR parameters' changes. Copyright © 2013 John Wiley & Sons, Ltd.     

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested for an extensive set of examples, and is shown to provide total energies that compare favorably with those obtained with the full singles, doubles, triples, and quadruples (CCSDTQ) method.     

Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems

We report the first implementation with correct scaling of the Mukherjee multireference coupled cluster method with singles, doubles, and approximate iterative triples (Mk-MRCCSDT-n, n=1a,1b,2,3) as well as full triples (Mk-MRCCSDT). These methods were applied to the classic H4, P4, BeH(2), and H8 model systems to assess the ability of the Mk-MRCCSDT-n schemes to accurately account for triple excitations. In all model systems the inclusion of triples via the various Mk-MRCCSDT-n approaches greatly reduces the nonparallelism error (NPE) and the mean nonparallelism derivative diagnostics for the potential energy curves, recovering between 59% and 73% of the full triples effect on average. The most complete triples approximation, Mk-MRCCSDT-3, exhibits the best average performance, reducing the mean NPE to below 0.6 mE(h), compared to 1.4 mE(h) for Mk-MRCCSD. Both linear and quadratic truncations of the Mk-MRCC triples coupling terms are viable simplifications producing no significant errors. If the off-diagonal parts of the occupied-occupied and virtual-virtual blocks of the Fock matrices are ignored, the storage of the triples amplitudes is no longer required for the Mk-MRCCSDT-n methods introduced here. This proves to be an effective approximation that gives results almost indistinguishable from those derived from full consideration of the Fock matrices.     

Investigation of a localised second-order Brueckner correlation method

Local second-order Brueckner correlation potentials have been derived from their non-local counterparts by starting from the assumption that the orbitals generated by these potentials are the same. The structure of the local correlation potentials and its components have been analysed for the neon atom and a range of small molecules, namely HF, HCl, H(2)O, CO and ethyne. The orbitals from the local Brueckner correlation potentials yield first-order electric molecular properties which are close to those inferred from second-order M?ller-Plesset theory and Brueckner coupled cluster doubles with perturbative triples.     

Self-assembled heterogeneous argon/neon core-shell clusters studied by photoelectron spectroscopy

Clusters formed by a coexpansion process of argon and neon have been studied using synchrotron radiation. Electrons from interatomic Coulombic decay as well as ultraviolet and x-ray photoelectron spectroscopy were used to determine the heterogeneous nature of the clusters and the cluster structure. Binary clusters of argon and neon produced by coexpansion are shown to exhibit a core-shell structure placing argon in the core and neon in the outer shells. Furthermore, the authors show that 2 ML of neon on the argon core is sufficient for neon valence band formation resembling the neon solid. For 1 ML of neon the authors observe a bandwidth narrowing to about half of the bulk value.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

Search of truncation of (N−1) electron basis containing full connected triple excitations in computing main and satellite ionization potentials via Fock‐space coupled cluster approach

A valence‐universal multireference coupled cluster (VUMRCC) theory, realized via the eigenvalue independent partitioning (EIP) route, has been implemented with full inclusion of triples excitations for computing and analyzing the entire main and several satellite peaks in the ionization potential spectra of several molecules. The EIP‐VUMRCC method, unlike the traditional VUMRCC theory, allows divergence‐free homing‐in to satellite roots which would otherwise have been plagued by intruders, and is thus numerically more robust to obtain more efficient and dependable computational schemes allowing more extensive use of the approach. The computed ionization potentials (IPs) as a result of truncation of the (N−1) electron basis manifold involving virtual functions such as 2h‐p and 3h‐2p by different energy thresholds varying from 5 to 15 a.u. with 1 a.u. intervals as well as thresholds such as 20, 25, and 30 a.u. have been carefully looked into. Cutoff at around 25 a.u. turns out to be an optimal threshold. Molecules such as C₂H₄ and C₂H₂ (X = D,T), and N₂ and CO (X = D,T,Q) with Dunning's cc‐pVXZ bases have been investigated to determine all main and 2h‐p shake‐up and 3h‐2p double shake‐up satellite IPs. We believe that the present work will pave the way to a wider application of the method by providing main and satellite IPs for some problematic N‐electron closed shell systems. © 2013 Wiley Periodicals, Inc.     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

Four-component Hartree-Fock calculations of magnetic-field induced circular birefringence--Faraday effect--in noble gases and dihalogens

The effects of relativity on the magnetic-field induced circular birefringence, or Faraday effect, in He, Ne, Ar, Xe, Rn, F2, Cl2, Br2, and I2 have been determined at the four-component Hartree-Fock level of theory. A measure of the birefringence is given by the Verdet constant, which is a third-order molecular property and thus relates to quadratic response functions. A fully analytical nonlinear polarization propagator approach is employed. The results are gauge invariant as a consequence of the spatial symmetries in the molecular systems. The calculations include electronic as well as vibrational contributions to the property. Comparison with experiment is made for He, Ne, Ar, Xe, and Cl2, and, apart from neon, the theoretical values of the Verdet constant are within 10% of the experimental ones. The inclusion of nonrelativistically spin-forbidden excitations in the propagator parametrization has significant effects on the dispersion in general, but such effects are in the general case largely explained by the use of a resonant-divergent propagator theory. In the present work we do, however, observe noticeable relativistic corrections to the Verdet constant in the off-resonant regions for systems with light elements (F2 and Cl2), and nonrelativistic results for the Verdet constant of Br2 are in error by 25% in the low-frequency region.     

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.     

Toward subchemical accuracy in computational thermochemistry: focal point analysis of the heat of formation of NCO and [H,N,C,O] isomers

In continuing pursuit of thermochemical accuracy to the level of 0.1 kcal mol(-1), the heats of formation of NCO, HNCO, HOCN, HCNO, and HONC have been rigorously determined using state-of-the-art ab initio electronic structure theory, including conventional coupled cluster methods [coupled cluster singles and doubles (CCSD), CCSD with perturbative triples (CCSD(T)), and full coupled cluster through triple excitations (CCSDT)] with large basis sets, conjoined in cases with explicitly correlated MP2-R12/A computations. Limits of valence and all-electron correlation energies were extrapolated via focal point analysis using correlation consistent basis sets of the form cc-pVXZ (X=2-6) and cc-pCVXZ (X=2-5), respectively. In order to reach subchemical accuracy targets, core correlation, spin-orbit coupling, special relativity, the diagonal Born-Oppenheimer correction, and anharmonicity in zero-point vibrational energies were accounted for. Various coupled cluster schemes for partially including connected quadruple excitations were also explored, although none of these approaches gave reliable improvements over CCSDT theory. Based on numerous, independent thermochemical paths, each designed to balance residual ab initio errors, our final proposals are DeltaH(f,0) ( composite function )(NCO)=+30.5, DeltaH(f,0) ( composite function )(HNCO)=-27.6, DeltaH(f,0) ( composite function )(HOCN)=-3.1, DeltaH(f,0) ( composite function )(HCNO)=+40.9, and DeltaH(f,0) ( composite function )(HONC)=+56.3 kcal mol(-1). The internal consistency and convergence behavior of the data suggests accuracies of +/-0.2 kcal mol(-1) in these predictions, except perhaps in the HCNO case. However, the possibility of somewhat larger systematic errors cannot be excluded, and the need for CCSDTQ [full coupled cluster through quadruple excitations] computations to eliminate remaining uncertainties is apparent.     

Matrix-isolation spectroscopy of Pb2

Fluorescence and Raman scattering were observed from Pb₂ isolated in neon and argon matrices. Two new excited states were observed by two-photon stepwise excitations, which involve low-lying electronic states of Pb₂. Most spectroscopic constants of the states observed could be given and complement previous results. Two resonance Raman progressions with ω_c = 112.5 and 123.1 cm⁻¹ and a single Raman signal at 80 cm⁻¹ were observed in argon matrices. The ω_c = 123.1 cm⁻¹ Raman signal which had recently been assigned to a larger Pb cluster was shown to arise from Raman scattering within the electronically excited A state of Pb₂ at 5500 cm⁻¹.     

In search of definitive signatures of the elusive NCCO radical

Previous experimental assignments of the fundamental vibrational frequencies of NCCO have been brought into question by subsequent unsuccessful attempts to observe IR signatures of this radical at these frequencies. Here we compute the fundamental vibrational frequencies by applying second-order vibrational perturbation theory to the complete quartic force field computed at the all-electron (AE) coupled cluster singles, doubles, and perturbative triples level [CCSD(T)] with the correlation-consistent, polarized core-valence quadruple-zeta (cc-pCVQZ) basis set, which has tight functions to correctly describe core correlation. The AE-CCSD(T)/cc-pCVQZ geometric parameters are r(e)(N-C)=1.1623 A, r(e)(C-C)=1.4370 A, r(e)(C-O)=1.1758 A, theta(e)(N-C-C)=168.55 degrees , and theta(e)(C-C-O)=132.22 degrees . Our CCSD(T)/cc-pCVQZ values of the characteristic stretching frequencies nu(1) and nu(2) are 2171 and 1898 cm(-1), respectively, in stark contrast to the experimentally derived values of 2093 and 1774 cm(-1). Finally, focal-point extrapolations using correlation-consistent basis sets cc-pVXZ (X=D,T,Q,5,6) and electron correlation treatments as extensive as full coupled cluster singles, doubles, and triples (CCSDT) with perturbative accounting of quadruple excitations [CCSDT(Q)] determine the vibrationless barrier to linearity of NCCO and the dissociation energy (D(0)) of NCCO-->NC+CO to be 8.4 and 26.5 kcal mol(-1), respectively. Using our precisely determined dissociation energy, we recommend a new 0 K enthalpy of formation for NCCO of 50.9+/-0.3 kcal mol(-1).     

Coupled-cluster vibrational frequencies for open, ring and superoxide sulfur dioxide

The harmonic vibrational frequencies of the open, ring and superoxide isomers of sulfur dioxide are predicted with the coupled-cluster including all single and double excitations (CCSD) and coupled cluster singles and doubles with perturbative connected triples [CCSD(T)] methods. The reliability of the results is discussed and comparisons are made to the recent observations of the matrix-isolated SOO molecule reported by Chen, Lee and Lee. Received: 3 December 1996 / Accepted: 17 January 1997     

Hydration phenomena of sodium and potassium hydroxides by water molecules

The hydrated structures, dissociation energies, thermodynamic quantities, infrared spectra, and electronic properties of alkali-metal hydroxides (MOH, M = Na and K) hydrated by up to six water molecules [MOH(H(2)O)(n=1-6)], are investigated by using the density functional theory and M?ller-Plesset second-order perturbation theory. Further accurate analysis based on the coupled cluster theory with singles, doubles, and perturbative triples excitations is more consistent with the MP2 results. NaOH shows a peculiar trend in dissociation: it begins to form a partially dissociated structure for n = 3, and it dissociates for n = 4 and 6, whereas it is undissociated for n = 5. However, for n = 5, the dissociated structure is nearly isoenergetic to the undissociated structure. For KOH, it begins to show partial dissociation for n = 5, and complete dissociation for n = 6.     

The singlet electronic ground state isomers of dialuminum monoxide: AlOAl, AlAlO, and the transition state connecting them

The singlet electronic ground state isomers, X (1)Sigma(g) (+) (AlOAl D(infinityh)) and X (1)Sigma(+) (AlAlO C(infinitynu)), of dialuminum monoxide have been systematically investigated using ab initio electronic structure theory. The equilibrium structures and physical properties for the two molecules have been predicted employing self-consistent field (SCF) configuration interaction with single and double excitations (CISD), multireference CISD (MRCISD), coupled cluster with single and double excitations (CCSD), CCSD with perturbative triples [CCSD(T)], CCSD with iterative partial triple excitations (CCSDT-3 and CC3), and full triples (CCSDT) coupled cluster methods. Four correlation consistent polarized valence (cc-pVXZ) type basis sets were used. The AlAlO system is rather challenging theoretically. The two isomers are confirmed to have linear structures at all levels of theory. The symmetric isomer AlOAl is predicted to lie 81.9 kcal mol(-1) below the asymmetric isomer AlAlO at the cc-pV(Q+d)Z CCSD(T) level of theory. The predicted harmonic vibrational frequencies for the X (1)Sigma(g) (+) AlOAl molecule, omega(1)=517 cm(-1), omega(2)=95 cm(-1), and omega(3)=1014 cm(-1), are in good agreement with experimental values. The harmonic vibrational frequencies for the X (1)Sigma(+) AlAlO structure, omega(1)=1042 cm(-1), omega(2)=73 cm(-1), and omega(3)=253 cm(-1), presently have no experimental values with which to be compared. With the same methods the barrier heights for the isomerization AlOAl-->AlAlO and AlAlO-->AlOAl reactions were predicted to be 84.3 and 2.4 kcal mol(-1), respectively. The dissociation energies D(0) for AlOAl (X (1)Sigma(g) (+)) and AlAlO (X (1)Sigma(+))-->AlO (X (2)Sigma(+))+Al ((2)P) were determined to be 130.8 and 48.9 kcal mol(-1), respectively. Thus, both symmetric AlOAl (X (1)Sigma(g) (+)) and asymmetric AlAlO (X (1)Sigma(+)) isomers are expected to be thermodynamically stable with respect to the dissociation into AlO (X (2)Sigma(+)) + Al ((2)P) and kinetically stable for the isomerization reaction (AlAlO-->AlOAl) at sufficiently low temperatures.