Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

A density functional theory test study on the N2··· He dimer

 In the present contribution we report a study of the weakly bound van der Waals N₂–He molecule in the framework of the supermolecule approach by means of the PWPW and mPW1PW exchange–correlation functionals, using density functional theory local-spin-optimized atom-centered basis sets complemented with bond functions optimized at the mPW1PW level of theory. Calculations show that the mPW1PW functional using bond functions gives a realistic representation of the interaction-energy potentials for this van der Waals dimer, comparable to reference M?ller–Plesset perturbation theory calculations. In contrast, the PWPW functional is unable to describe the bonding properties of this system and all values of the bonding properties obtained at different geometries with this functional are considered out-of-scale compared with the rest of the calculations presented in this study. Received: 30 October 2000 / Accepted: 3 January 2001 / Published online: 3 April 2001     

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η⁶-C₆H₆)₂, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η⁶-C₆H₆) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series. Received: 22 June 1998 / Accepted: 9 September 1998 / Published online: 17 December 1998     

The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

Multicenter bonding within the AIM theory

This study reports the incorporation of recently proposed formalism for the detection and localization of multicenter bonding in molecules, the so-called generalized population analysis, into the framework of the atoms in molecules (AIM) theory. The reliability of this new approach is tested by direct numerical comparison of the values of multicenter bond indices derived from both the original and the AIM-generalized forms of the population analysis. Received: 1 June 2000 / Accepted: 11 October 2000 / Published online: 23 January 2001     

Solid-State nuclear magnetic resonance: performance of point-charge distributions to model intermolecular effects in 19F chemical shifts

This contribution presents results from applying two different charge models to take into account intermolecular interactions to model the solid-state effects on the ¹⁹F NMR chemical-shift tensors. The density functional theory approach with the B3LYP gradient-corrected exchange correlation functional has been used because it includes electron correlation effects at a reasonable cost and is able to reproduce chemical shifts for a great variety of nuclei with reasonable accuracy. The results obtained with the charge models are compared with experimental data and with results obtained from employing the cluster model, which explicitly includes neighboring molecular fragments. The results show that the point-charge models offer similar accuracy to the cluster model with a lower cost. Received: 3 October 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Vibrational softening of diatomic molecules

An analysis of a model molecular oscillator is presented: a vibrating diatomic molecule carrying N ₀ electrons. The energy derivatives over the number of electron (N) and the deformation (Q), ∂ ⁿ /∂N ⁿ and ∂ ⁿ /∂Q ⁿ have been analyzed up to second order (n=2), including the appropriate mixed derivatives. The effect of coupling between distortion of the electron density induced by ΔN and the vibrational deformation of the molecule has been studied. Anharmonicity of the oscillator has been shown to be a possible result of that coupling; new relations between the parameters characterizing the anharmonicity of the oscillator and the energy derivatives at density functional theory level have been obtained. Ab initio calculations for a set of diatomic molecules have been performed, yielding values for all the derivatives discussed and demonstrating the effect of coupling with vibrations. Received: 1 June 2000 / Accepted: 20 October 2000 / Published online: 21 March 2001     

Domain-averaged Fermi holes – a new means of visualization of chemical bonds. Bonding in hypervalent molecules

The nature of bonding in several hypervalent molecules was analyzed at the ab initio SCF level using the recently proposed methodology based on the analysis of domain-averaged Fermi holes. The results of the analysis demonstrate that, for sufficiently flexible basis sets, the expansion of the valence shell does indeed take place for second row central atoms in PF₅, SF₄, and SF₆. On the other hand, no such expansion was observed for the first row N atom in NF₅. Received: 1 June 2000 / Accepted: 11 October 2000 / Published online: 23 January 2001     

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

Inexpensive and accurate predictions of optical excitations in transition-metal complexes: the TDDFT/PBE0 route

Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of three representative transition metal complexes. The computational model (PBE0) is obtained by combining the Perdew-Burke-Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange. Our results show that the TDDFT/PBE0 model represents a cheap and reliable tool for the computation of optical excitations for transition metal complexes. Received: 8 August 2000 / Accepted: 7 September 2000 / Published online: 23 November 2000     

Ab-initio study on low-lying states of the TiSi molecule

 The electronic structure of the TiSi molecule was examined using two types of multireference single and double excitation configuration interactions with highly extended basis sets, one including valence correlation and the other including valence and core–valence correlation. A multireference coupled-pair approximation (MRCPA) was further applied to the latter. The calculations suggest a ⁵Δ ground state, and the lowest excited state is ³Π and is only slightly (0.12 eV as estimated by MRCPA) above the ground state. The spectroscopic constants of the low-lying ¹Δ, ³Δ, ¹Π, ⁵Π, and ⁷Σ⁺ states as well as the ⁵Δ ground state and the ³Π excited states were evaluated, and we found that the molecule has only a weak σ bond and that six of the eight valence electrons essentially do not contribute to the bonding. The bonding nature of TiSi in these states is discussed in comparison with the TiC molecule. Received: 7 October 2000 / Accepted: 8 January 2001 / Published online: 3 May 2001     

Nature and importance of three-body interactions in the (H2O)2HCl trimer

 The nature and importance of nonadditive three-body interactions in the (H₂O)₂HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H₂O)₂HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H₂O)₂HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Recombination of silicon ions by electron capture from atomic hydrogen and helium

 Ab initio potential-energy curves and coupling matrix elements of the Σ and Π molecular states involved in the collision of the Si²⁺, Si³⁺ and Si⁴⁺ multicharged ions on atomic hydrogen and helium have been determined by means of configuration interaction methods. The total and partial electron capture cross sections have been determined using a semiclassical or a quantal approach in the 0.002–0.1 au velocity range. A detailed comparison with very recent theoretical and experimental rate coefficient results is made. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Theoretical study of the reaction of CN with C2H2+

 A theoretical study of the reaction of CN with C₂H₂ ⁺ has been carried out at three levels of theory, namely G2, B3LYP and CCSD(T). The main conclusion is that this is a feasible process under interstellar conditions, but only linear species may be produced. The most favourable product is HCCCN⁺, followed by CCCNH⁺. Production of HCCNC⁺ is predicted to be slightly endothermic; therefore, the reaction of CN + C₂H₂ ⁺ may produce precursors of HC₃N and C₃N in space. Furthermore, the B3LYP level is found to perform rather well compared with G2 and even better than CCSD(T). Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 12 May 2000     

Modeling the H5+ potential-energy surface: a first attempt

 Ab initio molecular electronic structure calculations are performed for H₅ ⁺ at the QCISD(T) level of theory, using a correlation-consistent quadruple-zeta basis set. Structures, vibrational frequencies and thermochemical properties are evaluated for ten stationary points of the H₅ ⁺ hypersurface and are compared with previous calculations. The features of the H₃ ⁺…H₂ interaction at intermediate and large intermolecular distances are also investigated. Furthermore, an analytical functional form for the potential-energy surface of H₅ ⁺ is derived using a first-order diatomics-in-molecule perturbation theory approach. Its topology is found to be qualitatively correct for the short-range interaction region. Received: 15 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

 Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout. Received: 4 November 1999 / Accepted: 8 February 2000 / Published online: 12 May 2000     

Ab initio study of rate constants of the reaction: HCN + OH → CN + H2O

A method applying ab initio direct dynamics has been utilized in studying the hydrogen abstraction reaction HCN + OH → CN + H₂O. The geometries of the reactants, products, and the transition state have been optimized at the QCISD/6-311G(d, p) level. Single-point energies were further evaluated at the QCISD(T)/6-311+G(2df, 2p)//QCISD/6-311G(d, p) level. The barrier heights for the forward and reverse reactions were predicted to be 15.95 and 7.51 kcal mol⁻¹ at the QCISD(T)/6-311 + G(2df, 2p)//QCISD/6-311G(d, p) level, respectively. The reaction rate constants were calculated in the temperature range from 298 to 4,000 K using the canonical variational transition-state theory with a small-curvature tunneling correction. The results of the calculation show that the theoretical rate constants are in good agreement with experimental data over the measured temperature range of 400–2,600 K. Received: 18 August 2002 / Accepted: 30 August 2002 / Published online: 20 November 2002 Acknowledgements. Our thanks are due to D.G. Truhlar for providing the POLYRATE 8.2 program. This work was supported by the National Science Foundation of China. We also thank D.C. Fang and Y. M. Xie for their valuable help, and P.R. Yan for reading our paper. Correspondence to: Q. S. Li e-mail: qsli@mh.bit.edu.cn     

Molecular integrals by numerical quadrature. I. Radial integration

 This article presents a numerical quadrature intended primarily for evaluating integrals in quantum chemistry programs based on molecular orbital theory, in particular density functional methods. Typically, many integrals must be computed. They are divided up into different classes, on the basis of the required accuracy and spatial extent. Ideally, each batch should be integrated using the minimal set of integration points that at the same time guarantees the required precision. Currently used quadrature schemes are far from optimal in this sense, and we are now developing new algorithms. They are designed to be flexible, such that given the range of functions to be integrated, and the required precision, the integration is performed as economically as possible with error bounds within specification. A standard approach is to partition space into a set of regions, where each region is integrated using a spherically polar grid. This article presents a radial quadrature which allows error control, uniform error distribution and uniform error reduction with increased number of radial grid points. A relative error less than 10⁻¹⁴ for all s-type Gaussian integrands with an exponent range of 14 orders of magnitude is achieved with about 200 grid points. Higher angular l quantum numbers, lower precision or narrower exponent ranges require fewer points. The quadrature also allows controlled pruning of the angular grid in the vicinity of the nuclei. Received: 30 August 2000 / Accepted: 21 December 2000 / Published online: 3 April 2001