Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

Infrared spectra of CO in absorption and evaluation of radial functions for potential energy and electric dipolar moment

From quantum-chemical calculations of rotational g factor and new experimental measurements of strengths of lines in infrared spectra of vibration–rotational bands v′–0 in absorption, with 1≤v′≤4, of ¹²C¹⁶O, and from analysis of 16,947 frequencies and wave numbers assigned to pure rotational and vibration–rotational transitions within electronic ground state X ¹Σ⁺, including new measurements of band 4–0 of ¹²C¹⁶O, we evaluate radial functions for potential energy and electric dipolar moment, the latter both in polynomial form and as a rational function that has qualitatively correct behaviour under limiting conditions. Received: 8 November 2001 / Accepted: 5 February 2002 / Published online: 14 August 2002     

Calculation of three-center electric and magnetic multipole moment integrals using translation formulas for Slater-type orbitals

 By the use of translation formulas for the expansion of Slater-type orbitals (STOs) in terms of STOs at a new origin, three-center electric and magnetic multipole moment integrals are expressed in terms of two-center multipole moment integrals for the evaluation of which closed analytical formulas are used. The convergence of the series is tested by calculating concrete cases. Computer results with an accuracy of 10⁻⁷ are obtained for 2^ν– pole electric and magnetic multipole moment integrals for 1≤ν≤5 and for arbitrary values of screening constants of atomic orbitals and internuclear distances. Received: 28 October 1999 / Accepted: 15 February 2000 / Published online: 5 June 2000     

An overlap criterion for selection of core orbitals

 An overlap criterion is defined that connects the identification of core orbitals in a molecular system, which can be problematic, to that in isolated atoms, which is well defined. This approach has been tested on a variety of troublesome systems that have been identified in the literature, including molecules containing third-row main-group elements, and is shown to remove errors of up to 100 kcal/mol arising from an inconsistent treatment of core orbitals at different locations on a potential-energy surface. For some systems and choices of core orbitals, errors as large as 19 kcal/mol can be introduced even when consistent sets of orbitals are frozen, and the new method is shown to identify these cases of substantial core–valence mixing. Finally, even when there is limited core–valence mixing, the frozen-core approximation can introduce errors of more than 5 kcal/mol, which is much larger than the presumed accuracy of models such as G2 and CBS-QB3. The source of these errors includes interatomic core–core and core–valence dispersion forces. Received: 31 August 2001 / Accepted: 11 October 2001 / Published online: 9 January 2002     

Expansion Formulae for Two-center Integer and Noninteger <Emphasis Type="Italic">n</Emphasis> STO Charge Densities and their Use in Evaluation of Multi-center Integrals

Using complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, α =1, 0, −1, −2, ...) introduced by the author, the series expansion formulae are derived for the two-center integer and noninteger n STO (ISTO and NISTO) charge densities in terms of integer n STOs at a third center. The expansion coefficients occurring in these relations are presented through the two-center overlap integrals between STOs with integer and noninteger principal quantum numbers. The general formulae obtained for the STO charge densities are utilized for the evaluation of two-center Coulomb and hybrid integrals of NISTOs appearing in the Hartee–Fock–Roothaan approximation. The final results are expressed in terms of both the overlap integrals and the one-center basic integrals over integer n STOs. It should be noted that the result for the multi-center multielectron integrals with two-center noninteger n STO charge densities presented in this paper were not appeared in our past publications.     

Solvent effects on the electronic absorption spectrum of formamide studied by a sequential Monte Carlo/quantum mechanical approach

Sequential Monte Carlo/quantum mechanical calculations are performed to study the solvent effects on the electronic absorption spectrum of formamide (FMA) in aqueous solution, varying from hydrogen bonds to the outer solvation shells. Full quantum-mechanical intermediate neglect of differential overlap/singly excited configuration interaction calculations are performed in the supermolecular structures generated by the Monte Carlo simulation. The largest calculation involves the ensemble average of 75 statistically uncorrelated quantum mechanical results obtained with the FMA solute surrounded by 150 water solvent molecules. We find that the n → π* transition suffers a blueshift of 1,600 cm⁻¹ upon solvation and the π → π* transition undergoes a redshift of 800 cm⁻¹. On average, 1.5 hydrogen bonds are formed between FMA and water and these contribute with about 20% and about 30% of the total solvation shifts of the n → π* and π → π* transitions, respectively. The autocorrelation function of the energy is used to sample configurations from the Monte Carlo simulation, and the solvation shifts are shown to be converged values. Received: 14 March 2002 / Accepted: 3 April 2002 / Published online: 24 June 2002     

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     

Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

Unified analytical treatment of one-electron two-center integrals with noninteger n Slater-type orbitals

A unified treatment of one-electron two-center integrals over noninteger n Slater-type orbitals is described. Using an appropriate prolate spheroidal coordinate system with the two atomic centers as foci, all the molecular integrals are expressed by a single analytical formula which can be readily and compactly programmed. The analysis of the numerical performance of the computational algorithm is also presented. Received: 1 April 1999 / Accepted: 2 July 1999 / Published online: 2 November 1999     

Pseudopotential study of lanthanum and lutetium dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart–Bonn variety and extended valence basis sets have been used for the investigation of the dimers La₂ and Lu₂. It was found that the ground states for La₂ and Lu₂ are most likely ¹∑ _g ⁺ (σ _g ²π _u ⁴) and ³∑ _g ⁻ (4f ¹⁴4f ¹⁴σ _g ²σ _u ²π_u ²), respectively. The molecular constants including error bars were derived from multireference configuration interaction as well as coupled-cluster calculations, taking into account corrections for atomic spin–orbit splitting as well as possible basis set superposition errors. The theoretical values for La₂ (R _e=2.70±0.03 ?, D _e=2.31±0.13 eV, ω_e=186±13 cm⁻¹) show good agreement with the experimental binding energy (D _e=2.52±0.22 eV), but the experimental vibrational constant in an Ar matrix (ω_e=236±0.8 cm⁻¹) is significantly higher. For Lu₂ the theoretical values (R _e=3.07±0.03 ?, D _e=1.40±0.12 eV, ω_e=123±1 cm⁻¹) are in overall excellent agreement with experimental data (D _e=1.43±0.34 eV, ω_e=122± 1 cm⁻¹). The electronic structures of La₂ and Lu₂ are compared to those other lanthanide dimers and trends in the series are discussed. Received: 25 March 2002 / Accepted: 2 June 2002 / Published online: 21 August 2002     

Structure and stability of hypervalent NLi n Na2 (n = 1–4) and related species at density functional theory level

A number of configurations of NLi _n Na₂ (n = 1–4) species were optimized using the B3LYP–density functional theory method; the 6-31G^* basis set was used in this calculation. In order to study all possible dissociation energies, some related species such as NLi₂Na, NLi _n (n = 1–4), Li _n (n = 1, 2) and Na _n (n = 1, 2) were also considered. Optimizations of these species were followed by fundamental frequency calculations at the same level. Global minima of these species were shown to adopt C _{2 v} (NLi₄Na₂, NLi₂Na₂), D _{3 h} (NLi₃Na₂) and C _s (NLiNa₂ and NLi₂Na) configurations. All possible dissociation energies were obtained. Received: 30 November 1998 / Accepted: 15 October 1999 / Published online: 14 March 2000     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

A new look at the reduced-gradient-following path

 The mathematical structure of the reduced-gradient-following (RGF) path introduced by Quapp et al. (1988 J. Comput. Chem. 19:1087) is reviewed and analyzed. We report two new algorithms to evaluate the RGF path. The RGF path is also compared mathematically and computationally with the gradient extremals path. An example of the evaluation of the RGF path is also reported. Received: 21 May 2001 / Accepted: 27 September 2001 / Published online: 9 January 2002     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001     

Convergence of multipole expanded intermolecular interaction energies for Gaussian-type-function and Slater-type-function basis sets

 It is shown that the multipole expansion of each order of the polarization series converges for large enough intermolecular distances when finite basis sets of Gaussian or Slater-type functions are used to approximate molecular response properties. Convergence of the multipole expansion for each order of the polarization series does not imply convergence of the polarization series itself. A corresponding convergence condition is extracted from the general perturbation theory in a finite-dimensional space and is applied to the H + H⁺ problem. Received: 29 September 1999 / Accepted: 22 May 2000 / Published online: 18 August 2000     

Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000     

A theoretical study of photoinduced electron transfer between tetracyanoethylene and arene

 Ab initio calculations have been performed to investigate the state transition in photoinduced electron transfer reactions between tetracyanoethylene and biphenyl as well as naphthalene. Face-to-face conformations of electron donor–acceptor (EDA) complexes were selected for this purpose. The geometries of the EDA complexes were determined by using the isolated optimized geometries of the donor and the acceptor to search for the maximum stabilization energy along the center-to-center distance. The correction of interaction energies for basis set superposition error was considered by using counterpoise methods. The ground and excited states of the EDA complexes were optimized with complete-active-space self-consistent-field calculations. The theoretical study of the ground state and excited states of the EDA complex in this work reveals that the S₁ and S₂ states of the EDA complexes are charge–transfer (CT) excited states, and CT absorption which corresponds to the S₀→S₁ and S₀→S₂ transitions arise from π−π^* excitation. On the basis of an Onsager model, CT absorption in dichloromethane was investigated by considering the solvent reorganization energy. Detailed discussions on the excited state and on the CT absorptions were made. Received: 30 April 2001 / Accepted: 18 October 2001 / Published online: 9 January 2002     

The search for stationary points on a quantum mechanical/molecular mechanical potential-energy surface

 We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden–Fletcher–Goldfarg–Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton–Raphson method. Some examples are presented and analyzed. Received: 16 July 2001 / Accepted: 9 October 2001 / Published online: 9 January 2002