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     

The effect of basis set superposition error on the convergence of interaction energies

 For the intermolecular interaction energies of ion-water clusters [OH⁻(H₂O) _n (n=1,2), F⁻(H₂O), Cl⁻(H₂O), H₃O⁺(H₂O) _n (n=1,2), and NH₄ ⁺(H₂O) _n (n=1,2)] calculated with correlation-consistent basis sets at MP2, MP4, QCISD(T), and CCSD(T) levels, the basis set superposition error is nearly zero in the complete basis set (CBS) limit. That is, the counterpoise-uncorrected intermolecular interaction energies are nearly equal to the counterpoise-corrected intermolecular interaction energies in the CBS limit. When the basis set is smaller, the counterpoise-uncorrected intermolecular interaction energies are more reliable than the counterpoise-corrected intermolecular interaction energies. The counterpoise-uncorrected intermolecular interaction energies evaluated using the MP2/aug-cc-pVDZ level is reliable. Received: 14 March 2001 / Accepted: 25 April 2001 / Published online: 9 August 2001     

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     

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     

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     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

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     

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     

Endohedral chemical shifts in higher fullerenes with 72–86 carbon atoms

For all isolated pentagon isomers of the fullerenes C₆₀–C₈₆ with nonzero HOMO–LUMO gap and for one nonclassical C₇₂ isomer (C_{2 v} ), endohedral chemical shifts have been computed at the GIAO-SCF/3-21G level using B3LYP/6-31G* optimized structures. The experimental ³He NMR signals are reproduced reasonably well in cases where assignments are unambiguous (e.g. C₆₀, C₇₀ and C₇₆). On the basis of the calculated thermodynamic stability order and the comparison between the computed and experimental ³He chemical shifts, the assignments of the observed ³He NMR spectra are discussed for all higher fullerenes, and new assignments are proposed for one C₈₂ and one C₈₆ isomer (C₈₂:3 and C₈₆:17). The calculated helium chemical shifts also suggest the reassignment of the δ(³He) resonances of two C₇₈ isomers. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 2001     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 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     

Solid-Solute Phase Equilibria in Aqueous Solutions XIV [1]. Thermodynamic Analysisof the Solubility of Hellyerite in Water

Summary.  The solubility of hellyerite, NiCO₃ · 6H₂O, in water was studied at different temperatures. From the experimental data obtained, a preliminary set of the thermodynamic quantities Δ_f G ^⊖, Δ_f H ^⊖, and S ^⊖ for hellyerite was derived using the ChemSage optimizer routine. Received January 16, 2001. Accepted January 18, 2001     

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     

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     

Maxwell–Cartesian spherical harmonics in multipole potentials and atomic orbitals

 The nature of the Maxwell–Cartesian spherical harmonics S ⁽ⁿ⁾ _K and their relation to tesseral harmonics Y _nm is examined with the help of “tricorn arrays” that display the components of a totally symmetric Cartesian tensor of any rank in a systematic way. The arrays show the symmetries of the Maxwell–Cartesian harmonic tensors with respect to permutation of axes, the traceless properties of the tensors, the linearly independent subsets, the nonorthogonal subsets, and the subsets whose linear combinations produce the tesseral harmonics. The two families of harmonics are related by their connection with the gradients of 1/r, and explicit formulas for the transformation coefficients are derived. The rotational transformation of S ⁽ⁿ⁾ _K functions is described by a relatively simple Cartesian tensor method. The utility of the Maxwell–Cartesian harmonics in the theory of multipole potentials, where these functions originated in the work of Maxwell, is illustrated with some newer applications which employ a detracer exchange theorem and make use of the partial linear independence of the functions. The properties of atomic orbitals whose angular part is described by Maxwell–Cartesian harmonics are explored, including their angular momenta, adherence to an Uns?ld-type spherical symmetry relation, and potential for eliminating an angular momentum “contamination” problem in Cartesian Gaussian basis sets. Received: 9 July 2001 / Accepted: 7 September 2001 / Published online: 19 December 2001     

Structure and stability of gold-substituted diborane, boranes, and borohydride ions

Pseudopotential ab initio calculations were performed for species of the type BH _n (AuPH₃) _m ^k , where n+m=3 or 4, and the charge k is −2,…,+1. Some derivatives of these and diaurated diboranes were also studied. The structural data agree well with the available experimental evidence. Factors affecting the stability of these systems, including the role of aurophilic attraction, are discussed. The singly charged anions and the diaurated diboranes are predicted to be the most stable members of these series. Received: 22 January 1999 / Accepted: 2 June 1999 / Published online: 4 October 1999     

Average inner product sums of electron linear momenta for atoms and ions

From the second moments of the electron-pair densities in momentum space, accurate Hartree–Fock values of the average inner product sum 〈∑ _i<j p _i ·p _j 〉 of electron linear momenta are evaluated for the 102 neutral atoms from He to Lr, the 53 singly charged cations from Li⁺ to Cs⁺, and the 43 stable anions from H⁻ to I⁻ in their experimental ground states. The present results are new for 38 species and improve the literature values for 68 species. Received: 18 July 2002 / Accepted: 4 September 2002 / Published online: 8 November 2002 Acknowledgement. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan. Correspondence to: H. Matsuyama e-mail: hisashi@mmm.muroran-it.ac.jp     

Exploring the quantum mechanical/molecular mechanical replica path method: a pathway optimization of the chorismate to prephenate Claisen rearrangement catalyzed by chorismate mutase

 A replica path method has been developed and extended for use in complex systems involving hybrid quantum/classical (quantum mechanical/molecular mechanical) coupled potentials. This method involves the definition of a reaction path via replication of a set of macromolecular atoms. An “important” subset of these replicated atoms is restrained with a penalty function based on weighted root-mean-square rotation/translation best-fit distances between adjacent (i±1) and next adjacent (i±2) pathway steps. An independent subset of the replicated atoms may be treated quantum mechanically using the computational engine Gamess-UK. This treatment can be performed in a highly parallel manner in which many dozens of processors can be efficiently employed. Computed forces may be projected onto a reference pathway and integrated to yield a potential of mean force (PMF). This PMF, which does not suffer from large errors associated with calculated potential-energy differences, is extremely advantageous. As an example, the QM/MM replica path method is applied to the study of the Claisen rearrangement of chorismate to prephenate which is catalyzed by the Bacillus subtilis isolated, chorismate mutase. Results of the QM/MM pathway minimizations yielded an activation enthalpy ΔH ^†† of 14.9 kcal/mol and a reaction enthalpy of −19.5 kcal/mol at the B3LYP/6-31G(d) level of theory. The resultant pathway was compared and contrasted with one obtained using a forced transition approach based on a reaction coordinate constrained repeated walk procedure (ΔH ^†† =20.1 kcal/mol, ΔH _rxn = −20.1 kcal/mol, RHF/4-31G). The optimized replica path results compare favorably to the experimental activation enthalpy of 12.7±0.4 kcal/mol. Received: 16 December 2001 / Accepted: 6 September 2002 / Published online: 8 April 2003 Contribution to the Proceedings of the Symposium on Combined QM/MM Methods at the 22nd National Meeting of the American Chemical Society, 2001. Correspondence to: H.L. Woodcock e-mail: hlwood@ccqc.uga.edu Acknowledgements. The authors thank Eric Billings, Xiongwu Wu, and Stephen Bogusz for helpful discussions and related work. The authors also show grateful appreciation to The National Institutes of Health and The National Science Foundation for support of the current research.     

Radial electron-pair densities in momentum space and shell structure of atoms

 The radial electron-pair intracule (relative motion) H(u) and extracule (center-of-mass motion) D(R) densities in position space were known to reveal four types of maxima which are related to the four inner electron shells, K, L, M, and N, of atoms. The corresponding radial electron-pair intracule Hˉ(v) and extracule Dˉ(P) densities in momentum space are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The densities Hˉ(v) and Dˉ(P) are found to have either one maximum or two maxima, and the numbers of maxima in Hˉ(v) and Dˉ(P) are the same for 98 atoms. For these atoms, the locations υ _max and P _max and the heights Hˉ _max and Dˉ _max of the corresponding maxima satisfy the approximate relations υ _max ≅ 2P _max and Hˉ _max ≅Dˉ _max /2. On the basis of their Z-dependence, the maxima in Hˉ(v) and Dˉ(P) of the 102 atoms are classified into five types. Shell-pair decompositions of the radial densities show that these maxima reflect five outer electron shells of atoms. Received: 24 January 2001 / Accepted: 12 March 2001 / Published online: 13 June 2001