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     

Theoretical study of the potential-energy surface of C2NP

 The B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the singlet potential energy surface of C₂NP, in which seven stationary isomers and seventeen interconversion transition states are involved. At the final CCSD(T)/6-311G(2df)//B3LYP6-311G(d) level with zero-point vibrational energy correction the lowest-lying isomer is a linear NCCP followed by two linear CNCP isomers at 23.9  and CCNP at 65.8 kcal mol⁻¹, respectively. The three isomers are kinetically very stable towards both isomerization and dissociation, and CCNP is even more kinetically stable than CNCP – by 14.3 kcal mol⁻¹ despite its high energy. Further comparative calculations were performed at the QCISD and QCISD(T) levels with the 6-311G(d) and 6-311G(2d) basis sets to obtain more reliable structures and spectroscopy for the three isomers. The calculated bond lengths, rotational constant, and dipole moment for NCCP were in close agreement with the experimentally determined values. Finally, similarities and discrepancies between the potential energy surface of C₂NP and those of the analogous species C₂N₂ and C₂P₂ were compared. The results presented in this paper might be helpful for future identification of the two still unknown yet kinetically very stable isomers CNCP and CCNP, both in the laboratory and in interstellar space. Received: 3 January 2001 / Accepted: 6 June 2001 / Published online: 30 October 2001     

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     

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     

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     

A correlation-consistent basis set for Fe

 A series of correlation-consistent basis sets are developed for Fe. Our best computed ⁵F–⁵D separation in the Fe atom is in excellent agreement with experiment. Our best estimate for the FeCO D ₀ value is in good agreement with experiment. The ⁵Σ⁻–³Σ⁻ separation in FeCO has an error of 3.6 kcal/mol; while the origin of this error is not clear, it is probably not due to the basis set. Received: 5 March 2001 / Accepted: 2 May 2001 / Published online: 9 August 2001     

An ab initio Molecular Orbital Study of the Conformational Properties of all-(Z)-Cyclododeca-1,4,7,10-tetraene

Summary.  Ab initio HF/6-31G^* and MP2/6-31G^*//HF/6-31G^* methods were used to calculate the structure optimization and conformational interconversion pathways for all-(Z )-cyclododeca-1,4,7,10-tetraene. This compound adopts the symmetrical crown (C _4v) conformation. Ring inversion takes place via symmetrical intermediates, such as boat-chair (BC, C _s) and twist (C _2h) conformers and requires about 22.3 kJ · mol⁻¹. The calculated strain energies for BC and twist conformers are 5.9 and 13.5 kJ · mol⁻¹. The results of semiempirical AM1 calculations for structural parameters and relative energies of the important geometries of the title compound are in good agreement with the results of ab initio methods. Received July 9, 2001. Accepted September 26, 2001     

A theoretical study on the ionization of OCS with an analysis of vibrational structures of the photoelectron spectrum

 Ab initio calculations have been performed to study the molecular structures and vibrational levels of the four low-lying ionic states (1, 2²Π, and 1, 2²Σ⁺) of carbonyl sulfide. The global regions of the potential-energy surfaces have been obtained by multireference single and double excitation configuration interaction calculations. Vibrational calculations using explicit vibrational Hamiltonians have been used for vibrational analysis. The equilibrium molecular structures and a vibrational analysis of the four ionic states are presented. The theoretical ionization intensity curves including the vibrational structures of the ionic states are also presented and are compared with the photoelectron spectrum. Received: 20 January 2001 / Accepted: 22 August 2001 / Published online: 30 October 2001     

Theoretical investigation into structures and magnetic properties of smaller fullerenes and their heteroanalogues

The smaller fullerenes, C₂₀, C₂₄, C₂₈, C₃₂, C_36, C₄₀ and C₅₀, their hydrogenation products and selected B-, N- and P-doped analogues have been investigated systematically at the B3LYP/6-31G* density functional level of theory. The degree of spherical electron delocalization is evaluated by using the computed nucleus-independent chemical shifts ( NICS) at the cage center and the individual ring centers of interest. The calculated NMR chemical shifts and the NICS values at the cage center, which can be accessed by endohedral ³He chemical shifts, should provide a basis for further experimental characterization of these compounds. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 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     

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     

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     

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     

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     

Preparation,Thermal Behaviour,and Crystal Structure of MgAl<Subscript>2</Subscript>F<Subscript>8</Subscript>(H<Subscript>2</Subscript>O)<Subscript>2</Subscript>

Summary.  Single crystals of MgAl₂F₈(H₂O)₂ have been obtained under hydrothermal conditions (250°C, 14 d) from a starting mixture of AlF₃ and MgAlF₅(H₂O)₂ in a 5% (w/w) HF solution. The crystal structure has been determined and refined from single crystal data (Fmmm (#69), Z = 4, a = 7.2691(7), b = 7.0954(16), c = 12.452(2) ?, 281 structure factors, 27 parameters, R(F ² > 2σ (F ²)) = 0.0282, wR(F ² all) = 0.0885). The obtained crystals were systematically twinned according to (010/100/001) as twinning matrix, reflecting the pseudo-tetragonal metric. The crystal structure is composed of perowskite-type layers built of corner sharing AlF₆ octahedra with an overall composition of AlF₄ ⁻ which are connected via common fluorine atoms of [MgF_4/2(H₂O)_2/1] octahedra. Group-subgroup relations of MgAl₂F₈(H₂O)₂ to WO₃(H₂O)_0.33 and to other M(II)M(III)₂ F₈(H₂O)₂ structures are briefly discussed. Above 570°C, MgAl₂F₈(H₂O)₂ decomposes under elimination of water into α-AlF₃, β-AlF₃, and MgF₂. Received October 29, 2001. Accepted (revised) December 6, 2001     

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     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 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     

Sensitive determination of nitric oxide in some rat tissues using polymer monolith microextraction coupled to high-performance liquid chromatography with fluorescence detection

A simple, sensitive, selective, and low-cost method is proposed for rapidly determining nitric oxide (NO) in some rat tissues. Polymer monolith microextraction (PMME) using a poly(methacrylic acid–ethylene glycol dimethacrylate) (MAA-EGDMA) monolithic column was combined with derivatization of NO using 1,3,5,7-tetramethyl-8-(3′,4′-diaminophenyl)-difluoroboradiaza-s-indacene (TMDABODIPY), and this was used to analyze the derivatives of NO by high-performance liquid chromatography (HPLC) with fluorescence detection at λ _ex/λ _em = 498/507 nm. The baseline separation of TMDABODIPY and its NO derivative is performed under simple conditions in which a C₁₈ column is used and eluted with 50 mmol L⁻¹ ethanolamine and methanol. The conditions for the extraction of NO derivatives were optimized. The limit of detection of NO was 2 × 10⁻¹² mol L⁻¹ (S/N = 3). The linearity range of the method was 9 × 10⁻¹¹−4.5 × 10⁻⁸ mol L⁻¹. The interday and intraday relative standard deviations were less than 5%. The proposed method was successfully applied to the determination of NO levels in some rat tissue samples including heart, kidney, and liver with recoveries varying from 87.1 to 95.2%.     

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