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Notes: The mechanism for the gas-phase production of particulate ammonium halides is studied by density functional theory and ab initio calculations on the molecular clusters of ammonia–hydrogen halide, (NH3–HX)n, n=1, 2, 4; X=F, Cl, Br. The equilibrium structures of the clusters demonstrate an abrupt transition from hydrogen-bonding in the single unit of NH3–HX to the NH4+(centered ellipsis)X− ion-pair interactions in (NH3–HX)4 resulting from spontaneous proton transfer from hydrogen halide to ammonia. The onset of the ion-pair form is at n=2 for HCl and HBr and at n=4 for HF. The ion-pair structure is the stable form of the larger clusters to maximize favorable electrostatic interactions and to closely resemble the crystal structures of ammonium halides. The calculated vibrational frequencies of the clusters provide additional evidence in support of the transition from hydrogen-bonding to ion-pair interactions as cluster size increases. The study shows that it is possible to form particulate ammonium halides directly from pure NH3 and HX vapors in the homogeneous gas phase. © 2001 American Institute of Physics.

Notes: The hydrolysis reaction of sulfur trioxide to form sulfuric acid in small water clusters is investigated using density function theory and ab initio methods. The equilibrium geometries for the reactant clusters that contain SO3 and one to four water molecules, SO3⋅(H2O)n, n=1–4, as well as the corresponding transition state and product clusters, are calculated at the levels of B3LYP/6-31+G*, B3LYP/6-311++G**, and MP2/6-311++G**. The relative energies of the reactant, transition state, and product are determined for each of the four clusters. The energy barrier required to form H2SO4 from the reactant cluster is found to decrease sharply with the number of water molecules in the cluster. Most significantly, the SO3⋅(H2O)4 cluster is found to be unstable and to form the ion pair HSO4− and H3O+ with little or no energy barrier. This work reveals the possibility of more pathways for the formation of sulfuric acid than have been previously considered. © 2000 American Institute of Physics.

Notes: The intermolecular potential surfaces for ArHCN and ArHCCH are computed by Møller–Plesset perturbation theory at the fourth-order approximations (MP4) with a large basis set containing bond functions. Rovibrational energies and spectroscopic constants of the two systems are computed from the intermolecular potentials using the collocation method. The intermolecular potential for ArHCN at the MP4 level has a single minimum at the collinear Ar−H−C−N configuration (R=4.56 A(ring), θ=0°) with a minimum potential energy of Vm=−135.9 cm−1. The bending frequencies, rotational constants, and centrifugal distortion constants of ArHCN and ArDCN calculated using the MP4 potential are in good agreement with experiment. Rovibrational energies with J=0 through 6 arising from j=0 and j=1 levels of HCN are calculated and compared with the experimental transition frequencies. The intermolecular potential surface for ArHCCH has a symmetric double minimum near the T-shaped configuration. The minimum positions at the MP4 level are (R=4.05 A(ring), θ=60° and 120°) and the minimum potential energy is Vm=−110.9 cm−1. The rotational constants and bending frequency of ArHCCH arising from the MP4 potential are calculated and compared with experiment. The anisotropy of the MP4 potential is slightly underestimated. The effects of monomer bending vibration on the ArHCN and ArHCCH potentials are studied by additional calculations. The potential anisotropy of ArHCN decreases, whereas that of ArHCCH increases as the monomer vibration is taken into account. This might be partially responsible for the discrepancies between the theoretical predictions and experiment. © 1995 American Institute of Physics.

Notes: We present accurate potential energy surfaces for Ar–HF, Ar–H2O, and Ar–NH3 from the supermolecular calculations using Møller–Plesset perturbation theory up to the complete fourth-order (MP4) and efficient basis sets containing bond functions. Preliminary calculations on Ar–HF are given to show the usefulness of bond functions and the stability of the results with respect to the change of the basis set. Detailed MP4 calculations on Ar–HF with a fixed HF bond length of r=〈r〉v=0 give a global potential minimum with a well depth of 200.0 cm−1 at the position R=3.470 A(ring), θ=0° (linear Ar–H–F), a secondary minimum with a well depth of 88.1 cm−1 at R=3.430 A(ring), θ=180° (linear Ar–F–H), and a potential barrier of 128.3 cm−1 that separats the two minima near R=3.555 A(ring), θ=90° (T shaped). Further calculations on the three main configurations of Ar–HF with varying HF bond length are performed to obtain vibrationally averaged well depths for v=0, 1, 2, and 3.Our primary wells are about 15 cm−1 higher than those of Hutson's H6(4,3,2) potential for v=0, 1, 2, and 3, and our minimum distances are about 0.05 A(ring) longer. Extensive MP2 calculations (R=3.1–5.0 A(ring)) and brief MP4 calculations (near the radial minimum) are performed for the intermolecular potentials of Ar–H2O and Ar–NH3 with the monomers held fixed at equilibrium geometry. For Ar–H2O, MP4 calculations give a single global minimum with a well depth of 130.2 cm−1 at R=3.603 A(ring), θ=75°, φ=0°, along with barriers of 22.6 and 26.6 cm−1 for in-plane rotation at θ=0° and 180° respectively, and a barrier of 52.6 cm−1 for out-of-plane rotation at θ=90°, φ=90°. All these are in good agreement with experiment, especially with Cohen and Saykally's AW2 potential. The dependence of the Ar–H2O potential on an OH bond length is calculated to study the effect from excitation of the bond stretching vibration and the result agrees well with the red shift observed. For Ar–NH3, MP4 calculations give a single global minimum with a well depth of 130.1 cm−1 at R=3.628 A(ring), θ=90°, φ=60°, along with barriers of 55.2 and 38.0 cm−1 for end-over-end rotation at θ=0° and 180°, respectively, and a barrier of 26.6 cm−1 for rotation about NH3 symmetry axis at θ=90°, φ=0°. All these are in good agreement with experiment and Schmuttenmaer et al. AA1 potential. The effects on potential from the change of the normal NH3 pyramidal geometry to the planar geometry are calculated and the results indicate that the Σ states with tunneling motion perpendicular to the radial coordinate remain virtually unchanged from free NH3 whereas the Π states with tunneling motion parallel to the radial coordinate have the tunneling motion nearly quenched. Comparisons of the potentials for the systems from Ar–HF, Ar–H2O, to Ar–NH3 are made to reveal the periodic trends of bonding and structure in the van der Waals complexes.

Notes: A perturbation correction term for the effect of attraction forces on the equation of state is calculated and combined with previous statistical-mechanical analytical equations of state proposed by Song and Mason and by Ihm, Song, and Mason. The major effect of the correction on the p–v isotherms occurs in the metastable and unstable regions (the "van der Waals loops''), with the result that the vapor pressures and orthobaric densities predicted from the Maxwell equal-area construction are greatly improved in accuracy. Comparison is made with experimental data for 13 selected nonpolar fluids (Ar, Kr, Xe, N2, O2, CO2, CH4, C2H6, C3H8, n-C4H10, i-C4H10, C2H4, and benzene) and one slightly polar fluid (toluene). Densities in the stable region of the p–v–T surface are accurate to about 1%–2% in the dense fluid region, and to better than 1% in the low-density gas region; the accuracy is slightly better than that achieved without the perturbation correction. Vapor pressures are predicted with an accuracy of about 2%, with orthobaric densities that are accurate to about 2% for the saturated vapor and to better than 1% for the saturated liquid. As usual for analytical equations of state, the critical region is described less accurately. In principle, the entire fluid equation of state and its vapor–liquid phase boundaries can be calculated from the intermolecular potential plus a few liquid densities. If the potential is not known, measurements of the second virial coefficient as a function of temperature can be used instead; in the absence of any such measurements, the calculation can use as input only the critical temperature, the critical pressure, and the Pitzer acentric factor, with only slight loss of accuracy. Comparison is also made with several widely used empirical equations of state. The present equation of state can be extended to include mixtures, but numerical computations on mixtures are postponed for future work.

Notes: Two forms for the HeCl2 potential are compared to the available experimental data. First, an atom–atom form that incorporates the recently measured anisotropic He–Cl potential is used. The anisotropy of this potential is slight, and its strengths and weaknesses are similar to previous potentials in which the He–Cl interaction was treated as isotropic. In particular, the fit to the scattering data is poor. Second, a fit to ab initio points calculated using Møller–Plesset perturbation theory to fourth order was performed. The resulting potential is much more anisotropic than any potential previously proposed and tested for HeCl2. This potential fits the rotationally resolved excitation spectra as well as do previous empirical potentials, and is consistent with certain features of the total differential scattering data with which previous potentials were not. Although the ab initio potential has a global minimum in the linear configuration, the probability distribution of the ground vibrational level still maximizes in the perpendicular configuration, accounting for the good fit to the rotationally resolved spectrum. We conclude that noble gas–halogen potentials are much more anisotropic than previously believed, and we suggest several experiments that could help to confirm this anisotropy. © 1995 American Institute of Physics.

Notes: The potential energy surface for the He–CO van der Waals interaction is calculated by the supermolecular approach using fourth-order Møller–Plesset perturbation theory (MP4) with a large basis set containing bond functions. The rovibrational energies of He–CO are then calculated by the collocation method. Our ab initio surface has a single near T-shaped minimum (Rm=3.49 A(ring), θ=120°, Vm=−20.32 cm−1), in agreement with a recent experimental potential (R=3.394 A(ring), θ=121.3°, Vm=−22.91 cm−1), determined from high-resolution spectroscopic measurements, but significantly different from a previously published ab initio surface for this system. The calculated rovibrational energies are in good agreement with experiment. The explicit dependence of the intermolecular potential on the CO bond distance is also studied by MP4 calculations, and the results confirm the experimental observation that the intermolecular coordinates are approximately uncoupled from the CO bond distance.

Notes: An accurate potential energy surface of the He–H2 interaction is calculated with a large basis set at the complete fourth-order Møller–Plesset approximation. The basis set—a combination of a nucleus-centered set 6s4p2d and a bond function set 3s3p2d centered at the midpoint between He and the H2 center of mass—is designed to give the optimal description of both the intra- and intersystem correlation effects. The validity of the basis set is confirmed by extensive preliminary calculations on the linear (orientation angle θ=0°), bent (45°), and T-shaped (90°) structures at a fixed separation (R=6.5a0) with a series of large basis sets containing different polarization functions and/or bond functions. Bond functions are found more effective than polarization functions in recovering the intersystem correlation energy and they are particularly useful in removing the geometric bias of a basis to give an accurate description for the potential anisotropy and the relative energies of different structures. The effect of bond functions is insensitive to the displacement of bond functions and the geometric midpoint of the van der Waals bond is a satisfactory choice for the center of bond functions. The potential energy surface of He–H2 is calculated at 15 values of R from 2.0 to 15.0a0 along each of the three main configurations (θ=0°, 45°, and 90°) with the vibrationally averaged H2 bond length r=1.449a0. Additional calculations are given for r=1.28 and 1.618a0 to show the effect of H2 zero-point vibration. While our potential at the self-consistent field (SCF) level is essentially the same as the previous calculations, our potential at the correlated level is globally deeper in the attractive region and less repulsive in the shorter range. Our calculated well depth (47.19 μhartrees) corresponding to the global minimum at θ=0° and R=6.5a0, is very close to the estimated experimental value of 48 μhartrees. In the Legendre expansion, our potential compares very well with the empirical potential of Rodwell and Scoles, but differs considerably from the empirical potential of Tang and Toennies and the previous ab initio potentials.

Notes: The method of the bond function basis set combined with the counterpoise procedure is studied in detail by the complete fourth-order Møller–Plesset perturbation (MP4) theory, following from a recent communication report [J. Chem. Phys. 98, 2481 (1993)]. This method is applied to calculate molecular dissociation energies De as well as equilibrium bond distances re and harmonic frequencies ωe of a number of diatomic molecules (N2, O2, F2, Cl2, HF, HCl, and CO) and the results are compared with those from other methods, without either counterpoise procedure or bond functions or both. The usefulness of the method is shown by the results for all the molecules using a moderately polarized basis set (2p1d for H atom and 2d1f for heavy atoms) augmented with the universal bond functions 3s3p2d. The method has consistently recovered 98%–99% of the experimental values for De, compared to as low as 90% without bond functions. The effect of bond functions is less significant on the predictions of re and ωe, due primarily to the inadequacy of the MP4 theory, but our method is still shown to be favored over the other methods. The electric dipole moments of the polar molecules (HF, HCl, and CO) are also examined and it is found that the use of bond functions results in a significant improvement of the dipole values. Detailed discussions are given to explain the need for bond functions and the counterpoise procedure. The high linear independence with nucleus-centered basis functions is explained to be responsible for the efficiency of bond functions. The counterpoise procedure is logically justified from the conventional noncounterpoise procedure. Potential problems and limitations associated with the proposed method are also discussed.

Notes: The Kr2 interaction potential is studied by ab initio calculations using several large basis sets containing high polarization functions and/or bond functions. It is shown that the addition of bond functions results in a dramatic improvement for the convergence of the calculated interaction energies. At the frozen-core MP4 level, the large atomic basis set such as [9s7p4d3f2g] recovered less than 75% of the experimental well depth. In contrast, the bond function basis set such as [9s7p4d3f]-{3s3p2d1f} produced a well depth of 617 μhartrees, over 99% of the experimental well depth. The frozen-core MP4 calculation appears to overestimate the well depth by about 25 μhartrees as compared to the calculation at the CCSD(T) level. On the other hand, the inclusion of core electron correlation at the MP4 level may contribute 13 μhartrees to the well depth. Beyond the potential minimum, the use of bond functions consistently gives significant improvement in the calculated potential from the highly repulsive wall to the attractive tail region. Final remarks are made about the counterpoise method and the use of bond functions. © 1999 American Institute of Physics.