Correlated calculations of indirect nuclear spin-spin coupling constants using second-order polarization propagator approximations: SOPPA and SOPPA(CCSD)

We present correlated calculations of the indirect nuclear spin-spin coupling constants of HD, HF, H₂O, CH₄, C₂H₂, BH, AlH, CO and N₂ at the level of the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes – SOPPA(CCSD). Attention is given to the effect of the so-called W ₄ term, which has not been included in previous SOPPA spin-spin coupling constant studies of these molecules. Large sets of Gaussian basis functions, optimized for the calculation of indirect nuclear spin-spin coupling constants, were used instead of the in general rather small basis sets used in previous studies. We find that for nearly all couplings the SOPPA(CCSD) method performs better than SOPPA. Received: 6 July 1998 / Accepted: 8 September 1998 / Published online: 23 November 1998     

Comparison of single and double excitation coupled cluster and configuration interaction theories: determination of structure and equilibrium propertie

Using our recently implemented closed-shell coupled cluster singles and doubles (CCSD) model, the equilibrium structure and vibrational harmonic frequency of N₂, CO, HF and OH⁻ have been determined. This set ofdiatomics was specially chosen so as to represent the range of bonding characteristics found in small molecules. The CCSD results are compared to analogous configuration interaction (CI) predictions and are found to be most similar to CISDQ or CISDTQ. That is, CI including all singles + doubles + quadruples (CISDQ) or CISDQ+all triple excitations (CISDTQ). The agreement of CCSD with CISDQ/CISDTQ is found to be much better for the singly bonded species with the agreement for neutral HF somewhat better than for anionic OH⁻. We arrive at two major conclusions. First, higher-order effects not present in the CCSD model are less negligible for multiply bonded species and, to a smaller degree, for anionic species as well. Secondly, even for the two types of molecules discussed above, the CCSD results are closer to the CISDQ/CISDTQ predictions than are CISD values. Since CCSD is less computationally time consuming than CISDQ/CISDTQ, we suggest that the CCSD model is one of the best methods available when highly accurate ab initio predictions for chemical species strongly dominated by a single-determinant wavefunction are desired.     

Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The vibrational frequencies of CaO2, ScO2, and TiO2: a comparison of theoretical methods

The vibrational frequencies of several states of␣CaO₂, ScO₂, and TiO₂ are computed using density functional theory (DFT), the Hartree-Fock approach, second-order M?ller-Plesset perturbation theory (MP2), and the complete-active-space self-consistent-field theory. Three different functionals are used in the DFT calculations, including two hybrid functionals. The coupled cluster singles and doubles approach including the effect of connected triples, determined using perturbation theory, is applied to selected states. The Becke-Perdew 86 functional appears to be the most cost-effective method of choice, although even this functional does not perform well for one state of CaO₂. The MP2 approach is significantly inferior to the DFT approaches. Received: 3 September 1997 / Accepted: 8 December 1997     

Boron as an Electron‐Pair Donor for B⋅⋅⋅Cl Halogen Bonds

MP2/aug′‐cc‐pVTZ calculations were performed to investigate boron as an electron‐pair donor in halogen‐bonded complexes (CO)₂(HB):ClX and (N₂)₂(HB):ClX, for X=F, Cl, OH, NC, CN, CCH, CH₃, and H. Equilibrium halogen‐bonded complexes with boron as the electron‐pair donor are found on all of the potential surfaces, except for (CO)₂(HB):ClCH₃ and (N₂)₂(HB):ClF. The majority of these complexes are stabilized by traditional halogen bonds, except for (CO)₂(HB):ClF, (CO)₂(HB):ClCl, (N₂)₂(HB):ClCl, and (N₂)₂(HB):ClOH, which are stabilized by chlorine‐shared halogen bonds. These complexes have increased binding energies and shorter B?Cl distances. Charge transfer stabilizes all complexes and occurs from the B lone pair to the σ* Cl?A orbital of ClX, in which A is the atom of X directly bonded to Cl. A second reduced charge‐transfer interaction occurs in (CO)₂(HB):ClX complexes from the Cl lone pair to the π* C≡O orbitals. Equation‐of‐motion coupled cluster singles and doubles (EOM‐CCSD) spin–spin coupling constants, ^1xJ(B‐Cl), across the halogen bonds are also indicative of the changing nature of this bond. ^1xJ(B‐Cl) values for both series of complexes are positive at long distances, increase as the distance decreases, and then decrease as the halogen bonds change from traditional to chlorine‐shared bonds, and begin to approach the values for the covalent bonds in the corresponding ions [(CO)₂(HB)?Cl]⁺ and [(N₂)₂(HB)?Cl]⁺. Changes in ¹¹B chemical shieldings upon complexation correlate with changes in the charges on B.     

Deadwood in configuration spaces. II. Singles + doubles and singles + doubles + triples + quadruples spaces

The effect of truncating singles + doubles configuration interaction (CISD) and singles + doubles + triples + quadruples (CISDTQ) spaces on the energies of the systems Ne, H₂O, CO and C₂ is investigated through the use of a previously described, general, selected CI program. CI expansions generated by Hartree–Fock orbitals as well as by natural orbitals are examined and the latter typically exhibit faster convergence as regards the energy. For the CISD wavefunctions of Ne, H₂O, CO and C₂, chemical accuracy is reached by using, respectively, 34, 47, 53 and 55% of the full sets. For the triples + quadruples parts of the wavefunctions on the other hand, chemical accuracy is already reached by using only 1, 4, 6 and 9% of the respective full sets. Received: 14 August 2001 / Accepted: 6 December 2001 / Published online: 8 April 2002     

Extrapolation to the limit of a complete basis set for electronic structure calculations on the N2 molecule

Results obtained from nonrelativistic electronic structure calculations using finite Gaussian basis sets are extrapolated to the limit of a complete basis set, employing the results of explicitly correlated coupled-cluster calculations including singles and doubles substitutions (CCSD). For N₂, the basis-set limits for the electronic binding energy, equilibrium bond length and harmonic vibrational wave number are established for the CCSD model including a perturbative correction for triples substitutions and for the internally contracted multireference configuration interaction method. The resulting numbers are in good agreement with experimental values. Received: 2 December 1997 / Accepted: 3 February 1998 / Published online: 17 June 1998     

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.     

Longitudinal NLO properties of C2H2, HCCF,and C2F2: Electron correlation and vibration effects

Electron correlation and vibration effects on longitudinal nonlinear optical properties of acetylene (C₂H₂), fluoroacetylene (HCCF), and difluoroacetylene (C₂F₂) have been studied using various quantum chemistry methods, including the second‐order perturbation theory (MP2); coupled cluster approach with singles, doubles (CCSD), and noniterative triples (CCSD(T)); and density functional methods (B3LYP and B98). Evaluation of the static and dynamic vibration (nuclear relaxation) contributions was based on the finite field relaxation method. Particular attention has been devoted to the assessment of the electron correlation effects on the nuclear relaxation contributions to the molecular properties. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Hole-particle characterization of coupled-cluster singles and doubles and related models

The hole-particle analysis introduced in the paper [J. Chem. Phys. 124, 224109 (2006)] is fully described and extended for coupled-cluster models of practical importance. Based on operator renormalization of the conventional amplitudes t(ai) and t(ab,ij), we present a simplified method for estimating the hole-particle density matrices for coupled-cluster singles and doubles (CCSD). With this procedure we convert the first-order density matrix of the configuration interaction (CI) singles and doubles (CISD) model, which lacks size consistency, into an approximately size-consistent expression. This permits us to correctly estimate specific indices for CCSD, including the hole and particle occupation numbers for each atom, the total occupation of holes/particles, and the entropylike measure for effective unpaired geminals. Our calculations for simple diatomic and triatomic systems indicate reasonable agreement with the full CI values. For CCSD and CISD we derive special types of two-center indices, which are similar to the charge transfer analysis of excited states previously given within the CIS model. These new quantities, termed charge transfer correlation indices, reveal the concealed effects of atomic influence on electronic redistribution due to electron correlation.     

Coupled-cluster singles,doubles and perturbative triples with density fitting approximation for massively parallel heterogeneous platforms

A high-performance implementation of the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] is developed in the Massively Parallel Quantum Chemistry program. Novel features include: (1) reduced memory requirements via a density-fitting (DF) CCSD implementation utilizing distributed lazy evaluation for tensors with more than two unoccupied indices and (2) the ability to utilize efficiently many-core nodes (Intel Xeon Phi) and heterogeneous nodes with multiple NVIDIA GPUs on each node. All data that are greater than quadratic in the system size are distributed among processes. Excellent strong scaling is observed on distributed-memory computers equipped with conventional CPUs, Intel Xeon Phi processors, and heterogeneous nodes with multiple NVIDIA GPUs Canonical CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even larger computations possible on leadership-class computing resources.     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Ab initio study of the photochemistry of aminopyrimidine

Complete active space self‐consistent field (CASSCF), multi‐reference configuration interaction calculations (MR‐CISD), and equation of motion coupled‐cluster with singles and doubles (EOM‐CCSD) calculations are presented in order to elucidate the photodeactivation pathways of 6‐aminopyrimidine after vertical excitation to the S₁ ¹nπ* state. Vertical excitation energies are reported up to the S₇ state. Two S₁ excited state minima, both of ¹nπ* character, and three strongly puckered ¹ππ* minima on the crossing seam (MXS) between the S₀ and the S₁ potential energy surface were found. Nonadiabatic reaction paths are discussed by linearly interpolating between the two minima and all MXS, which explain and extend observations made in recent surface‐hopping dynamics CASSCF investigations [Barbatti and Lischka, J Phys Chem A 2007, 111, 2852]. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Temperature dependence of the 1J(11B19F) spin–spin coupling in BF3 molecule

The ¹J(¹¹B¹⁹F) spin–spin coupling of gaseous BF₃ was observed in ¹¹B NMR spectra as a function of density in a wide range of temperatures. Following the extrapolation of the measured values to the zero‐density limit, the coupling constant free from intermolecular effects ¹J₀(¹¹B¹⁹F) was obtained for each temperature. In contrast to previous investigations, the final results indicate a nonlinear dependence of ¹J₀(¹¹B¹⁹F) on temperature. In the corresponding ab initio calculations of spin–spin coupling constants performed at the coupled cluster singles and doubles (CCSD) level to obtain a reliable result for this coupling constant we had to take into account large vibrational corrections. Copyright © 2009 John Wiley & Sons, Ltd.     

Atomic level picture of stress relaxation in polymer melts

We have been developing a physical picture on the atomic level of stress relaxation in polymer melts by means of computer simulation of the process in model systems. In this article we treat a melt of freely jointed chains, each with N = 200 bonds and with excluded-volume interactions between all nonbonded atoms, that has been subjected to an initial constant-volume uniaxial extension. We consider both the stress relaxation history σ(t) based on atomic interactions, and the stress history σ_e(t; N_R) based on subdividing the chain into segments with N_R bonds each, with each segment regarded as an entropic spring. It is found that at early times σ(t) > σ_e(t; N_R) for all N_R, and that, for the remainder of the simulation, there is no value of N_R for which σ(t) = σ_e(t; N_R) for an extended period; by the end of the simulation σ(t) has fallen just below the value σ_e(t; 50). The decay of segment orientation, 〈P₂(t; N_R)〉, and of bond orientation 〈P₂(t; 1)〉, is computed during the simulation. It is found that the decay of the atom-based stress σ(t) is closely related to that of 〈P₂(t; 1)〉. This result may be understood through the concept of steric shielding. The change in local structure of the polymer melt during relaxation is also studied. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 143–154, 1998     

Highly Enantioselective Iron‐Catalyzed cis‐Dihydroxylation of Alkenes with Hydrogen Peroxide Oxidant via an FeIII‐OOH Reactive Intermediate

The development of environmentally benign catalysts for highly enantioselective asymmetric cis‐dihydroxylation (AD) of alkenes with broad substrate scope remains a challenge. By employing [Fe^II(L)(OTf)₂] (L=N,N′‐dimethyl‐N,N′‐bis(2‐methyl‐8‐quinolyl)‐cyclohexane‐1,2‐diamine) as a catalyst, cis‐diols in up to 99.8 % ee with 85 % isolated yield have been achieved in AD of alkenes with H₂O₂ as an oxidant and alkenes in a limiting amount. This “[Fe^II(L)(OTf)₂]+H₂O₂” method is applicable to both (E)‐alkenes and terminal alkenes (24 examples >80 % ee, up to 1 g scale). Mechanistic studies, including ¹⁸O‐labeling, UV/Vis, EPR, ESI‐MS analyses, and DFT calculations lend evidence for the involvement of chiral Fe^III‐OOH active species in enantioselective formation of the two C?O bonds.     

Substitution effects on the molecular structures and the longitudinal molecular polarizabilities of all‐trans polyacetylene oligomers of increasing size

AM1 calculations have been performed on all‐trans polyacetylene (PA) oligomers with an increasing number of unit cells to study the effect of donor or acceptor groups capped at opposite ends of PA chains, substituents included in the monomers, substituents' number and position in the monomers, on the molecular structures, and the static longitudinal polarizabilities (α_L) and second‐order hyperpolarizabilities (γ_L). Substitution of CH₃, Cl, or F group at opposite ends of an oligomer results in an increase of α_L and γ_L, but the substitution effects on Δα_L(N) and Δγ_L(N) are very small. The asymptotic limit values are unaffected by the substitution. F substituent included in the monomer of an oligomer enhances the Δα_L(N) and Δγ_L(N) values, especially at large N, but including monomers with CH₃ or Cl substituents substantially reduces the Δα_L(N) and Δγ_L(N) values. We alter the number of F substituents included in the monomers of oligomers and find that including two F substituents in the monomer leads to the larger enhancement of Δγ_L(N). The effect of F substituents' position in the monomers of oligomers on Δα_L and Δγ_L is obvious. The results may be helpful for the design of new materials for applications in nonlinear optics, particularly in the area of poled polymer films. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001