Three-body interaction-induced light scattering in krypton gas: a computer simulation of the spectral line shapes

The two-, three- and four-body effective collision induced scattering spectral line shapes are calculated for dense gaseous krypton using the pairwise additivity (PA) approximation and different polarizability models. These spectra and several interaction induced spectra calculated at various densities are compared with the experimental measurements of Barocchi et al. [1988, Europhys. Lett., 5, 607]. The potential effect on the spectrum is found to be weak. The results obtained with the Meinander et al. [1986, J. chem. Phys., 84, 3005] empirical polarizability model and molecular dynamics fit well the experimental two- and three-body spectral shapes. The irreducible contribution to the spectral shape is evaluated using the dipole induced dipole irreducible polarizability [buckingham, A. D., and Hands, I. D., 1991, Chem. Phys. Lett., 185, 544]. This contribution is found to be relatively weak for the anisotropic spectra in the frequency and density range studied, explaining the good agreement between the pairwise approximation calculations and the experimental data. The spectra radiated by the quasi-molecules Kr₂, Kr₃, and Kr₄ (the total spectrum within the PA approximation) are also simulated.     

Equation of state for systems of soft diatomic molecules

A new potential that is a modification of the BBL (Bratko, D.,Blum, L., and Luzar, A.,1985, J. chem. Phys., 83, 6367; Blum, L., Vericat, F., and Bratko, D., 1995, J. chem. Phys., 102, 1461) potential and of the one recently solved analytically by Blum and Vericat (BV) (1995, Molec. Phys., 86, 809; 1996, J. phys. Chem., 100, 1197) is studied by Monte Carlo simulation. The main feature of this potential is that it can be solved using only a small number of parameters (3 in the case treated by BV), and therefore produces a substantial simplification of earlier work. The new potential has an orientational octupole–octupole interaction term which is found necessary to reproduce the broad peak of the oxygen–oxygen structure function due to the tetrahedral position of the second nearest neighbour water molecule. This important feature was absent in the original BBL potential. This model agrees also with the experimental pair correlation functions for oxygen–hydrogen and hydrogen–hydrogen, and yields 42·6 kJ mol^-1 for the internal energy of water, also in agreement with experiment. The hard core central repulsion causes the sharpness of the first peaks in all three correlation functions. This is not necessary but convenient for an analytical solution.     

An approximate formula for the intermolecular Pauli repulsion between closed shell molecules

The exchange repulsion formula proposed by Murrell and co-workers (Proc. Roy. Soc. (Lond.) 1965, A284, 566; J. chem. Phys., 1967, 47, 4916) is considered in detail. Potentially important terms missing in the formalism of Murrell and co-workers are identified and evaluated for the water dimer using several basis sets. Insights into the contributing terms are obtained by using localized molecular orbitals. The results point towards a relatively simple expression for intermolecular exchange repulsion, based on the isolated wavefunctions of the two overlapping species.     

An accurate,global, ab initio potential energy surface for the H+ 3 molecule

A new global, ground-state, Born-Oppenheimer surface is presented for the H⁺ ₃ system. The energy switching approach has been used to combine different functional forms for three different regimes: a spectroscopic expansion at low energy, a Sorbie-Murrell function at high energy and known long-range terms combined with accurate diatomic potentials at large separations. At low energies we have used the ultra high accuracy ab initio data of Cencek et al. (1998, J. chem. Phys., 108, 2831). At intermediate energy we have calculated 134 new ab initio energies using a high accuracy, explicitly correlated procedure. The ab initio data of Schinke et al. (1980, J. chem. Phys., 72, 3909) has been used to constrain the high energy region. Two fits are presented which differ somewhat in their behaviour at energies over 45 000 cm^?1 above the H⁺ ₃ minimum. Below this energy, the fits reproduce each set of ab initio data close to their intrinsic accuracy. The ground state surface should provide a suitable starting point for renewed studies of the near-threshold photodissociation spectrum originally reported by Carrington et al. (1982, Molec. Phys., 45, 753).     

Phase Space Optimization of Quantum Representations: Non-Cartesian Coordinate Spaces

In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, whose eigenstates comprise the direct-product basis. In the present paper, this phase space optimized direct-product basis method is generalized to incorporate non-Cartesian coordinate spaces, composed of radii and angles, that arise in molecular applications. Analytical results are presented for certain standard systems, including rigid rotors, and three-body vibrators.     

On the gravitational effects of rotating masses: The Thirring-Lense papers

The purpose of this work is to provide a critical analysis of the classical papers of H. Thirring [Phys. Z.,19, 33 (1918);Phys. Z.,22, 29 (1921)] and J. Lense and H. Thirring [Phys. Z.,19, 156 (1918)] on rotating masses in the relativistic theory of gravitation and to render them accessible to a wider circle of scholars. An English translation of these papers is presented which follows the original German text as closely as possible. This is followed by a concise account of the significance of the results of these papers as well as the possibility of measuring the gravitational effects of rotating masses.     

Rotational spectra and internal dynamics of Ne—H2S

Rotational spectra of 15 isotopomers of the Ne-H₂S van der Waals complex were measured in the frequency range 4–22 GHz using a pulsed molecular beam Fourier transform spectrometer. Two K = 0 progressions were observed for each of the symmetric isotopomers (with H₂S or D₂S). This doubling is attributed to an internal rotation motion of the H₂S subunit within the complex. These two states can be correlated with the 0₀₀ and 1₀₁ rotational states of free H₂S and D₂S. By contrast, symmetry constraints no longer apply to isotopomers with DHS. The excited internal rotor state is no longer metastable, and only one K = 0 progression could be observed. The rotational constants obtained were compared with those of Ar-H₂S and Ar—H₂O. The ground state rotational constant remained almost constant upon substitution of H with D, showing an unusual isotope effect, similarly to a previous observation in Ar-H₂S (GUTOWSKY, H. S., EMILSSON, T., and ARUNAN, E., 1997, J. chem. Phys., 106, 5309). This behaviour is in agreement with the ab initio study by OLIVEIRA, G. D., and DYKSTRA, C. E., 1999, J. chem. Phys., 110, 289. An approximate substitution analysis was carried out to deduce structural information from the ground state rotational constants. Nuclear quadrupole hyperfine structures were observed and resolved or partially resolved for isotopomers containing ³³S and D, respectively, and the corresponding nuclear quadrupole coupling constants were determined. These were used to derive information about the internal dynamics of the dimer. Different sensitivities of the quadrupole coupling constants of D and ³³S to the extent of out-of-plane motion were revealed.     

Assignment of a perturbation in the FT-ICLAS spectrum of 12C2H2 around 12 709.5 cm−1

The vibrational state perturbing the J = 17 and 18 rotational states of the zero-order v ₁ + 3v ₃ state of ¹²C₂H₂ is assigned to the state with vibrational energy predicted at G _ν = 12 685.1 cm^?1 using the cluster model (El Idrissi, M. I., Liévin, J., Campargue, A. and Herman, M., 1999, J. chem. Phys., 110, 2074). The assignment is discussed also in terms of the very special pressure shift behaviour demonstrated previously for absorption lines reaching these levels (Herregodts, F., Hepp, M., Hurtmans, D., Vander Auwera, J. and Herman, M., 1999, J. chem. Phys., 111, 7961). The experimental information arising from a set-up newly running at ULB, called FT-ICLAS brings decisive information in the assignment process. This set-up is described briefly.     

Vibrational-rotational energy transfer in H2-H2 collisions: III. Ortho-ortho collisions

A recently proposed[1999, J. chem. Phys., 111, 2401 and 1999, Chem. Phys. Lett., 312, 530] new semi-classical decoupling procedure for rotational projection states in ro-vibrationally inelastic atom-diatom and diatom-diatom collisions is applied to inelastic collisions in molecular hydrogen. The role of initial rotational excitation of both collision partners in the ro-vibrational transitions, attached to the vibrational (10 -> 00) transition in ortho-H₂, is analysed in detail. The computed vibrational self-relaxation rate constant for ortho-H₂ (as earlier for para-H₂, too) is in good quantitative agreement (within a factor of 2) with experimental data over the whole experimentally investigated temperature range, 50-3000 K. This also indicates that the more detailed (non-measured) rate constants for ro-vibrational state-to-state transitions in molecular hydrogen, calculated by our new model, are sufficiently accurate for astrophysical applications.     

Absolute line intensities in the ν1 + 3ν3 band of 12C2H2 by laser photoacoustic spectroscopy and Fourier transform spectroscopy

Line intensities and self-broadening coefficients in the ν₁ + 3ν₃ band of ¹²C₂H₂ near 0.8 μm at room temperature were measured by means of both laser photoacoustic and Fourier transform spectroscopy. An experimental protocol has been developed to obtain absolute intensities from the photoacoustic measurements. Namely, the spectrometer was calibrated using water vapour line intensities available in Hitran 1996 [L. S. Rothman et al. (1998) J. quant. Spectrosc. Radiat. Transfer, 60, 665–710]. These photoacoustic line intensities were found to be on average 5% higher than corresponding measurements performed using Fourier transform spectroscopy, the accuracy of the latter being estimated to better than 4%. The accuracy of the photoacoustic intensities is discussed. Previous results from the literature [F. Herregodts, D. Hurtmans, J. Vander Auwera, and M. Herman (1999) J. chem. Phys., 111, 7954—7960] are revised.     

Logarithmic interaction under periodic boundary conditions: closed form formulas for energy and forces

A method is given to obtain closed form formulas for the energy and forces for an aggregate of charges interacting via a logarithmic interaction under periodic boundary conditions. The work done here is a generalization of Glasser's results [J. Math. Phys., 15, 188 (1974)] and is obtained with a different and simpler method than that by Stremler [J. Math. Phys., 45, 3584 (2004)]. The simplicity of the formulas derived here makes them extremely convenient in a computer simulation.     

A refined potential energy surface and the rovibrational states for the electronic ground state of ozone

A potential energy surface for the electronic ground state of ozone has been optimized by using a variational procedure with the exact vibrational Hamiltonian in bond length-bond angle coordinates. In the optimization, the ab initio force field of Borowski, P., Andersson, K., Malmquist, P.-A., and Roos, B. O., 1992, J. chem. Phys., 97, 5568 is taken as the starting point, and the recent observed vibrational band origins up to 4900 cm^-1 reported by Floud, J.-M., Barbe, A., Camy-Peyret, C., and Plateaux, J. J., 1996, J. molec. Spectrosc., 177, 34 are involved. The root mean square error of this fit for the 39 observed vibrational energy levels is 0.83 cm^-1. In order to test the refined potential, the rovibrational energy levels up to J = 15 are calculated and compared with the observed values.     

New accurate binary hard sphere mixture radial distribution functions at contact and a new equation of state

New and very accurate formulae for additive binary hard sphere (HS) mixture radial distribution functions (RDFs) at contact are proposed in a simple analytical form. Using the virial theorem, the formulae also provide a new HS mixture equation of state (EOS). The new RDF formulae are the most accurate currently available. The new EOS is of comparable accuracy with that of Malijevsky, A., and Veverka, J. (1999, Phys. Chem. chem. Phys., 1, 4267), which is the most accurate HS mixture EOS currently available. However, the new EOS proposed here is of much simpler analytical form.     

A revised many-body potential energy function for the description of the H3O+(H2O)n clusters

A revised potential energy function that has been fitted to the latest set of Kebarle and coworkers [1982, J. Am. chem. Soc, 104, 1462] entropy and enthalpy measurements at T = 300 K is presented. The model assumes a rigid hydronium unit and accounts for all orders of many-body interactions explicitly. The difference with the older function that had been based on earlier measurements by Kebarle and co-workers [1972, J. Am. chem. Soc, 94, 7627; 1967, J. Am. chem. Soc, 89, 6393] is that more compact clusters are generated. We have studied the structural properties of water clusters in the size range 5–80 at T = 250 K within the framework of the (μPT) Grand Canonical ensemble. Clusters with sizes less than about 10 water molecules consist of a four-coordinated first shell, where the fourth water molecule is hydrogen bonded to the oxygen atom of the hydronium ion. The hydration number goes through a minimum value ～1.6, for a cluster size around 50, and it starts increasing again with further cluster growth, to ～2.5 for a cluster size of 250 water molecules, which is the largest cluster examined. On the other hand the water molecule coordination number shows a monotonic increase with cluster size. In small clusters, less than 10, water molecules prefer to be arranged in a chain-like fashion; at sizes around 50, tri-coordinated clathrate-like structures dominate whereas with further size increase the coordination number eventually levels off to the experimental bulk value, at 4.6.     

Franck—Condon factors for polyatomic molecules

The method of Sharp and Rosenstock for the calculation of Franck—Condon factors (J. chem. Phys. 41, 3453 (1964)) is revised. A few errors in the original contribution and in several subsequent papers are corrected. Explicit formulae for 141 FC factors including overtones up to the 11th order and hot bands are derived with the aid of a computer algebra system (Mathematica). As an example for an application of the newly derived FC factors, the fluorescence spectrum of acetylene is calculated within the Herzberg—Teller formalism.     

A quasiharmonic model calculation for non-markovian far-infrared spectra of HCl in Kr and Xe liquids

The far-infrared spectra (0–200 cm^?1) of dilute solutions of HCl in liquid Kr and Xe have been calculated by applying of a non-markovian spectral theory called PTOC (partial time ordering cumulants) and by using a quasiharmonic model for the liquid structure recently reported by us (A. Calvo Hernández et al., 1987, J. chem. Phys., 86, 4597) and successfully applied to HCl?Ar solution (Ibid., 86, 4607). The bath correlation functions which appear in the spectral theory involve a reduced set of parameters regarding both the HCl?Kr and HCl?Xe interactions and the liquid structure. From comparison between theoretical and experimental spectra it is possible to deduce quantitative values for the above parameters. The pronounced rotational fine structure of the experimental spectra for HCl in Kr and Xe liquids is quite well explained by the actual model.     

Phase coexistence and interface structure of a two-component Lennard-Jones fluid in porous media: application of Born—Green—Yvon equation

The Born-Green-Yvon equation with smoothed density approximation is used to calculate the liquid-liquid density profiles of a symmetric Lennard-Jones fluid in a hard sphere disordered matrix. The phase diagrams are evaluated for model systems characterized by different matrix densities and compared with the results of theoretical predictions and the Monte Carlo simulations of Gordon, P. A., and Glandt, E. D., 1996, J. chem. Phys., 105, 4257. It was found that increasing the matrix packing fraction reduces the magnitude of the miscibility gap and smooths the density profiles between two coexisting phases.